Displacement and strain estimation for evaluation of arterial wall stiffnessusing a familial hypercholesterolemia swine model of atherosclerosis

Wenqi GeDepartment of Medical Physics and Department of Electrical and Computer Engineering University ofWisconsin Madison Wisconsin 53705

Christian G Krueger Ashley Weichmann and Dhanansayan ShanmuganayagamReed Research Group Department of Animal Science University of Wisconsin Madison Wisconsin 53705

Tomy Varghesea)

Department of Medical Physics and Department of Electrical and Computer Engineering University ofWisconsin Madison Wisconsin 53705

(Received 28 January 2012 revised 27 April 2012 accepted for publication 9 May 2012published 2 July 2012)

Purpose To track variations in the deformation of the arterial wall noninvasively by estimating theaccumulated displacement and strain over a cardiac cycle may provide useful indicators of vascularhealthMethods In this paper we propose an approach to track a region of interest (ROI) locally andestimate arterial stiffness variation in a familial hypercholesterolemic swine model of spontaneousatherosclerosis that allows for systematic and reproducible study of progression of the disease mech-anismResults Strain and displacement indices may be derived from the variations of the accumulateddisplacement and accumulated strain (obtained from the gradient of the accumulated displacement)over a cardiac cycle to predict not only the likelihood of developing vascular diseases but also thesites where they may occur Currently an ROI thickness value of less than one mm within the arterialwall is necessary for the axial accumulated displacement and strain to obtain reproducible estimatesConclusions Accumulated axial displacement and strain estimation on the artery wall shown in thispaper indicate the repeatability of these measurements over several cardiac cycles and over five famil-ial hypercholesterolemic swine Our results also demonstrate the need for a small region of interestwithin the arterial walls for accurate and robust estimates of arterial function copy 2012 American As-sociation of Physicists in Medicine [httpdxdoiorg10111814722746]

Key words ultrasound elastography atherosclerosis arterial wall stiffness

I INTRODUCTION

The leading cause of death in the United States are cardiovas-cular diseases (CVD)1 In 2007 one out of every 29 deathsin the United States was attributed to cardiovascular disease2

Over 12 million Americans were estimated to have sufferedcoronary events and about 795 thousand suffered strokes2

Measurements of arterial stiffness are useful for identifyingthose with higher cardiovascular risk factors attributed to awide range of characteristics including age gender obe-sity hypertension and genetic factors3 In addition arterialstiffness can be used to detect various cardiovascular com-plications such as left ventricular hypertrophy and failureaneurysm formation and rupture and atherosclerosis whichcan lead to stroke myocardial infarction and renal failure4 5

Furthermore the younger population in the United Statesis increasingly at risk for CVD because of the increasedprevalence of childhood obesity metabolic syndrome dia-betes etc2 6 These increased risks warrant preventive and in-terventional measures be taken at earlier stages of disease pro-gression Early detection of CVD is therefore essential andnoninvasive methods for imaging and measuring arterial stiff-ness as described in this paper may provide new potentialdiagnostic information

Measurement of the pulse-wave velocity (PWV) is theprevalent method for noninvasively quantifying arterial stiff-ness and identifying cardiovascular risk factors3 7 8 TheMoens-Korteweg equation shows that the PWV is related tothe square root of vessel stiffness

PWV =radic

((E lowast h)(2rρ)) (1)

where E is the Youngrsquos modulus h is the vessel wall thick-ness r is the vessel radius and ρ is the blood density4 7

PWV is measured using the pulse transit time (PTT) calcu-lated from the foot-to-foot or wave front to wave front timedelay between two arterial sites divided over the separationdistance4 7 9 PWV can be meaningfully measured at mul-tiple locations in the body For example the brachial-anklePWV has been shown to be an indicator of atherosclerosis10

and the aortic PWV and carotid-femoral PWV (cfPWV) hasbeen shown to be predictive of cardiovascular events8 9 PWVhas numerous drawbacks First PWV measurements of up-per limb muscular arteries do not change significantly withage4 Since PWV measurements characterize a length of ves-sel they cannot be localized to any specific point11 Further-more effectiveness of PWV measurements can be affected bythe traveled medium such as muscular arteries which have

4483 Med Phys 39 (7) July 2012 copy 2012 Am Assoc Phys Med 44830094-2405201239(7)448310$3000

4484 Ge et al Displacement and strain estimation for arterial wall stiffness 4484

a different stiffness than elastic arteries10 Depending on thesite and methodology of the measurement finding the PWVcan also be inconvenient the pressure sensitive transducersused to measure carotid and femoral PWV requires trainingand could take more than 20 minutes10 Recent methods ofPWV measurement were shown to be viable for finding mea-surements in regions on the order of tens of millimeters12 13

Despite the increased ease of acquisition and precision in thelateral direction PWVrsquos largest weakness is that the measure-ment is confined to the temporal and lateral domains It cannotbe used to find varying stiffness among the layers of the arte-rial wall Strain estimation does not suffer from the aforemen-tioned issues and can be used to supplement existing methodsfor diagnosis and risk assessment

Measurement of the carotid intima-media thickness(CIMT) is another indicator of atherosclerosis and predictorof coronary artery diseases14 It has been shown to predictcardiovascular diseases independent of traditional risk factorssuch as coronary artery calcium (CAC) smoking hyperten-sion diabetes fibrinogen and LDL cholesterol15ndash17 CIMTis measured using high resolution ultrasound B mode imagesand can be used in conjunction with elastography based mea-surements of arterial stiffness

Elastography is a method of creating images that maptissue stiffness18 In classical external compression elas-tography strain tensors are estimated from local displace-ments caused by quasi-static uniaxial externally applieddeformations18ndash20 Local displacements are usually trackedand estimated using 2D cross-correlation based methods de-scribed in the current literature19 21ndash23 After correcting for theapplied stress and using the appropriate boundary conditionsthe displacementstrain images can be used to calculate theelastic modulus map18 The classical analogy of elastographyis palpation where manual pressure is applied by a medicalpractitioner to sense the position stiffness mobility and pul-sation of internal structures24 Strain is defined as the defor-mation per unit length in percentage of an object under stressand the normal strain is defined as

εzz = partuzpartz (2)

εyy = partuyparty (3)

where u is the displacement in the direction of the strain andz and y are the coordinates in the axial and lateral directions

Elastography has been utilized for vessel wall character-ization and assessment of atherosclerotic plaque utilizingthe internal deformation of the vessel generated by blood-flow25ndash28 Subsequent studies using acoustic radiation forceimpulse imaging (ARFI) have shown the ability to iden-tify the presence of and discriminate between hard and softplaques29ndash31

A study using hypercholesterolemic and normochole-strolemic swine also showed the effectiveness to materi-ally characterize atherosclerotic plaque32 Currently elastog-raphy is accepted as a safe noninvasive patient-friendlyand inexpensive method of imaging tissue stiffness and canhelp diagnose cancer identify atherosclerosis and monitorablation19 24 33 Elastography has the ability to locally charac-

terize the elastic properties of arterial wall along the dimen-sions of time and space with precision

Previously Shi et al25 utilized the accumulated axial strainvariation to compute the maximum accumulated axial strainand relative lateral shift as indices for the differentiation ofcalcified plaque from soft plaque in human subjects Varia-tions in the accumulated strain within a specified region ofinterest (ROI) in plaque tissue with dimensions of 64 pointsin the axial direction and 5 lines in the lateral direction wereutilized Strain estimates within the ROI were averaged andtheir values summed to produce their accumulated strain Theaccumulated strain used in this paper is generated by accumu-lating the displacement over time within the ROI The result-ing accumulated displacement is then summed point by pointover the cardiac cycle which is then utilized to obtain the ac-cumulated strain curve Effectively if local strain is definedby the expression εzz = partuzpartz the accumulated axial strainas defined in this paper is given by

αzz = partVzpartz (4)

Vz = 1

n

sumuz (5)

where Vz denotes the accumulated displacement over the car-diac cycle

In this paper we propose a method where the local straindistribution in an ROI in the arterial wall of a familial hy-percholesterolemic (FH) swine model is monitored over timeby acquiring and processing a time series of ultrasound ra-dio frequency (RF) echo-signal frames The FH swine is aunique validated animal model of spontaneous atherosclero-sis that allows for systematic and reproducible study of dis-ease mechanism and testing of emerging diagnostic and thera-peutic ultrasound technologies34ndash36 The FH swine is the onlylarge animal model that develops spontaneous atheroscle-rotic lesions when fed with a normal diet without addedcholesterol37ndash40 The FH swine with its genetic proximityto human41 and similarities in cardiovascular pathophysiol-ogy (atherogenesis coronary artery disease and ischemia)lipoprotein metabolism digestive physiology and dietaryadaptations makes it an excellent translational model for lon-gitudinal studies of vascular biology42ndash44

We utilize accumulated strain estimates calculated fromthe accumulated displacement over an ROI The ROI is oper-ator defined and the deformation of the region is tracked overmultiple cardiac cycles We address estimation of the axialand lateral displacement vectors and strain using backscat-tered ultrasound signals The maximum accumulated axialstrain and the maximum accumulated lateral displacementhave been utilized as indices to characterize plaque25 We pro-pose to utilize these indices for characterizing arterial stiffnessas also discussed next in this paper

II MATERIALS AND METHODS

The strain distribution within a vessel wall over a cardiaccycle may provide useful information indicative of age related

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4485 Ge et al Displacement and strain estimation for arterial wall stiffness 4485

FIG 1 Schematic diagram of the region of the femoral artery that was im-aged on the FH swine model of atherosclerosis

arterial stiffening and cardiovascular health An ROI is de-fined in the artery near and far walls that would exclusivelylie within the wall of the blood vessel Figure 1 provides aschematic diagram of the ultrasound scan performed alongwith identification of the ROI location using an FH swinemodel of atherosclerosis As the vessel expands and contractsover the cardiac cycle the ROI changes its shape and locationcorrespondingly This allows for the capture of a displace-mentstrain profile of the vessel wall over the cardiac cycleinstead of just a snapshot in time

At 6 weeks of age (2 weeks postweaning) the five femaleFH swine were placed on a cornndashsoybean mixed diet with 2added fat and fed twice daily The daily calorie intake waslimited to 80 of ad libitum intake (based on ad libitum in-take of age-matched FH swine) The diet was formulated tomeet nutrient requirements and was mixed weekly from feedcomponents (Arlington Feed Mill Arlington WI) At the timeof the ultrasound measurements the animals were 106 plusmn 05months old with a body weight of 836 plusmn 69 kg (246 plusmn 48body fat determined by dual energy x-ray absorptiometry) Amidline neck incision was made to access the internal carotidartery A catheter was placed in the artery for intra-arterialblood pressure (ABP) measurement via an attached pressuretransducer (PX600 Edwards Lifesciences Irvine CA) po-sitioned at the level of the heart and connected to an S5Datex-Ohmeda Anesthesia Monitoring System (GE Health-care Waukesha WI) ABP and heart rate measurements forthe 5 FH swine are shown in Table I

IIA Radio frequency data acquisition

Acquisition of the RF data was accomplished using theclinical Ultrasonix SonicTouch system (Ultrasonix MedicalCorporation Richmond BC) running Sonix RP 319 and us-ing an L14-538 transducer operating at 10 MHz center fre-quency The depth of the RF data acquired measured fromthe transducer to the vessel was 40 mm The sampling fre-

TABLE I Intra-arterial blood pressure (BP) and heart rate measurements forthe five FH swine

Animal no Systolic BP Diastolic BP Heart rate

1 75 38 1402 77 46 1533 79 40 1054 88 40 1105 82 46 94

quency for the acquired data was 40 MHz with a frame rateof 98 framess

Ultrasound scanning was performed on the FH swinemodel starting at six months of age This study was performedunder a protocol approved by the University of Wisconsin-Madison Animal Care and Use Committee (ACUC) The an-imals were sedated once per month with an injection of Tela-zol at 1ndash5 mgkg at the minimal dosage necessary for seda-tion prior to the use of a facemask The facemask then de-livered 15ndash5 isoflurane and 100 oxygen with a flowrate of 1ndash3 Lmin Heart monitor and oxygen saturation weremonitored via pulse oximetery After sedation the ultrasoundtransducers were held by hand to initiate scans that lasted forone or more cardiac cycles The field of view included thefemoral artery and the beginning of the bulb with a single fo-cus at the far wall of the vessel Atherosclerosis is a systemicdisease therefore plaque accumulation is expected to occurat multiple arterial locations The femoral artery was chosendue to the presence of a bifurcation site where atheroscleroticplaques tend to develop and is much easier to access using ul-trasound than the carotid artery in swine due to the differencein imaging depths

IIB Strain and displacement mapping

The 2D displacement tracking and strain estimation algo-rithm was implemented in MATLAB (The Mathworks Nat-ick RI) The code used to calculate the displacement was animplementation of the quality-guided displacement trackingalgorithm45 This multi-seed algorithm initially utilizes regu-larly spaced windows as initial seeds Cross correlation coeffi-cients between the tracked regions and the seeds were used todetermine the quality of each seed and the highest one wouldbe selected to be the initial estimation of displacement Thealgorithm then iterates to track the seedrsquos four neighbors andthe process repeats for the next windows to complete the en-tire scanned field A large window size allows for better track-ing of noisy data while a smaller window improves spatialresolution

RF data sets were upsampled by a factor of 5 using splineinterpolation to improve displacement tracking The dimen-sions of the 2D motion tracking kernel were 81 data pointsalong the beam direction and 15 data points along the lateraldirection for the upsampled data corresponding to 033 mmtimes 088 mm for the 2D tracking kernel dimensions respec-tively A 75 overlap was utilized to obtain consecutive dis-placement estimates Local strain estimates were obtainedusing a least squares fit to the displacement data using

Medical Physics Vol 39 No 7 July 2012

4486 Ge et al Displacement and strain estimation for arterial wall stiffness 4486

segments with a length of 066 mm for the axial strain esti-mates and 088 mm for the lateral strain estimates The frameskip amount which represents the number of frames that wereskipped to ensure a reasonably significant amount of deforma-tion between frames was set to 3 By increasing the amountof displacement between consecutively processed frames thesignal to quantization noise ratio and the subpixel displace-ment estimation errors were improved Before the displace-ment maps were used to calculate the local strain imagesthey were put through a 3 times 2 pixel median filter to removenoise spikes Displacements and strains estimated along the x(lateral) and y (axial) directions along with the strain distri-bution are stored for every frame-pair for further processingThe accumulated displacement was then computed from thestored displacement estimates Lastly the accumulated strainwas computed from the accumulated displacement estimatedover the cardiac cycle

IIC ROI creation and tracking

The positioning of the ROI on the artery wall was de-termined manually for the first frame and their coordinateswere adjusted using previously calculated displacements forthe following frames The ROI boundary was defined usingpoints marked along the vessel intima on the first frame ofthe RF data and extended from the beginning of the bifurca-tion toward the common femoral artery The lines that connectneighboring points were used to create the defining curvededge of the ROI and the ROI region is delineated accord-ing to the contours of this edge The opposite edge was cre-ated by translating the defining edge up or down by the in-tended thickness of the ROI resulting in an area that has uni-form thickness The resulting ROI was uniform in thicknessFor example on the near wall of an artery points should bemarked directly below and adjacent to the vessel wall and theROI would be defined to extend a set number of pixels abovethe defining edge to cover the wall and some of the surround-ing tissue the inverse holds true for the far wall This assureda uniform thickness for the initial ROI This method is validonly with the assumption that the ROI is intended for an objectthat is horizontally situated otherwise it would be necessaryto define the ROI width and height at different angles fromthe RF datarsquos cardinal directions An ROI maximum lengthcan optionally be defined and any region that extend abovethe set length would be cut off It is advantageous to use ROIsthat are larger than what is required so that data can be eas-ily derived as a subregion of the processed data Care shouldtherefore be made to mark the ROI with a starting point oneither the left or right side that is anatomically similar acrossdifferent data sets The ROI dimensions used for the swinedata were 10 mm in width and up to 3 mm in thickness ordepth the actual thickness used for processing was about onemm in thickness to correspond to and to lie within the actualthickness of the vessel walls

The data points that make up the defining edge of the nearwall and the far walls of the corresponding ROI were eachtracked over the cardiac cycle and the ROI was redrawn foreach subsequent frame based on this information The dis-

placement calculated from the RF data with coordinates inspace and time was added to the coordinates of the points ofthe ROIrsquos defining edge to form the ROI of the next frame intime The stored coordinates for the ROI edge were not inte-gers since subsample displacements were estimated Bilinearinterpolation was used to find the displacement values for thenext frame This reduces the rounding errors that can be sig-nificant in the lateral direction as discussed in the Appendix

Once the ROI was generated the strain displacement andany other relevant data points within the corresponding regioncan be stored First the ROI is made into a binary mask withones corresponding to pixels within the ROI and zeroes oth-erwise Then mask can then be applied to the strain and dis-placement images Since the initial ROI points were markedat the exact boundary between the vessel and the blood withinit to remove the contribution of the blood in the strain imageThe ROI follows the curvature of the vessel wall and is notdiscarded The ROI thickness is specified in the number ofdisplacementstrain pixels used to estimate the displacementand strain The two dimensions are therefore the location onthe vessel wall and the ROI thickness within the vessel wallThe strain and displacement maps can be saved directly as aresult of the mask and the accumulated strain and accumu-lated displacement maps can be found after accumulating thedisplacements

III RESULTS

Figure 2(a) presents the B-mode image of the femoralartery being scanned on the FH swine The location of thescan is relative to the femoral arteryrsquos bifurcation on the B-mode image The local displacement maps estimated alongthe axial (b) and lateral (c) directions are also shown alongthe corresponding axial (d) and lateral (e) strain distributionNoise artifacts in the lateral displacement and strain imagesare increased when compared to the axial displacement andstrain images respectively The locations of the ROI aroundthe near and far walls of the artery are illustrated in Fig 3(a)on the ultrasound B-mode image The ROIs are delineatedmanually on the B-mode image with the lumen of the arteryidentified in both the near and far walls of the artery TheROI over which local displacement and strain estimates areestimated and accumulated should ideally be marked individ-ually on ultrasound B-mode images rather than the derivedstrain image This can be done very accurately using imagesoftware such as MITK 3M3 program (Mint Medical GmbHHeidelberg Germany) to measure the B-mode vessel thick-ness Estimations are performed using the B-mode images bydetermining the edges of the vessel wall and using the ratioof the pixels making up the vessel thickness over the pixelheight of the image multiplied by the corresponding imagedepth The resulting vessel thickness obtained is on the or-der of 08ndash072 mm On the other hand the thickness of thefemoral artery obtained from a representative histopathologi-cal image in Fig 3(b) instead shows the vessel thickness tobe around 03ndash04 mm

The near wall of the artery is constrained by surroundingconnective tissue subcutaneous fat and the skin Since the

Medical Physics Vol 39 No 7 July 2012

4487 Ge et al Displacement and strain estimation for arterial wall stiffness 4487

FIG 2 Ultrasound B-mode image (a) the accumulated axial displacement (b) the accumulated lateral displacement (c) the corresponding accumulated axialstrain (d) and lateral strain images over a cardiac cycle (e)

transducer is placed next to the skin layer the near wall ofthe artery is not expected to deform significantly with bloodflow On the other hand the far wall of the artery is mainlyconstrained by connective tissue a vein that runs along withthe artery and is visible in the B-mode image and muscle tis-sue The far wall therefore usually deforms more than the nearwall of the artery in the geometry shown in Figs 2 and 3 Lo-cal displacements and strains within these ROIs are utilized inthe following plots to evaluate arterial stiffness variations

Figure 4 presents the variation of a single row of dis-placement and strain estimated along the inner boundaries ofthe ROI that are closest to the vessel wall lumen We trackthe displacement of these points that are drawn manuallyon the first B-mode images over all the RF data acquired overthe cardiac cycle Since this row of data points will movealong with the arterial wall and track the deformation intro-duced in a cardiac cycle we refer to the estimation presentedin Fig 4 as the localized displacement and strain since wetrack the same tissue structure over the entire cardiac cycleObserve the opposite directions of the periodic displacementvisualized on the near and far wall for the axial accumulateddisplacement (AAD) and the noisier variation for the axialaccumulated strain (AAS) A periodic trend in the AAS canhowever be visualized A phase lag between the AAD of thenear and far wall is also observed Although the lateral accu-mulated displacements (LAD) indicate the arterial deforma-tion along the lateral direction the lateral accumulated strains(LAS) do not present a trend and are extremely noisy esti-

mates The displacement and strain values of the near wall areusually lower in magnitude when compared to the far wallThis could be due to locationrsquos proximity to the transducerand the proximity of the scanned artery to the femoral vein

We now include additional displacement and strain esti-mates by increasing the thickness of the ROI to 1 mm withthe plots for the near and far wall shown in Fig 5 The AADand AAS curves are similar to those observed in Fig 4 whilethe LAD curve being slightly lower The LAS curves are stillnoisy and we will not discuss the variations associated withthis curve from this point forward due to the increased noiseartifacts observed

To clearly visualize the trend or variations in the mean ofthe AAS curves we replace the standard deviation with thestandard error in Fig 6 We present plots of the near and farwall for different ROI thicknesses in Fig 6 Note that forROI thickness of a single strain estimate (069 mm) in Fig6(a) 2 estimates (079 mm) 4 estimates (1 mm) and 10 es-timates (148 mm) in Figs 6(b)ndash6(d) respectively Note thatas the ROI thickness becomes larger it also incorporates esti-mates from surrounding overlying tissue which contrast fromthe strain in arterial tissue as seen in Fig 6(d) Appropriateselection of the dimensions of the ROIs and a fine resolu-tion are essential to properly characterize variations in arterialelasticity

Figures 7 and 8 present the changes in the accumulatedaxial and lateral displacements and strains around the peakand valley of the axial deformations over the cardiac cycle

Medical Physics Vol 39 No 7 July 2012

4488 Ge et al Displacement and strain estimation for arterial wall stiffness 4488

FIG 3 (a) Ultrasound B-mode image with the regions of interest on the nearwall and the far wall of the femoral artery and (b) representative photomicro-graph (5times objective) of a hematoxylin and eosin stained cross section of afemoral artery from an 8-month-old FH swine

at approximately 035 and 089 s into the cardiac cycle Esti-mated displacements are interpolated to provide similar pixeldensity as the underlying ultrasound radio frequency data foraccurate registration The strain is maximum on the interior ofthe vessel progressing to a zero point and ultimately to sur-rounding tissues with the opposite sign Larger ROI thicknessenables us to evaluate stiffness variations in tissues surround-

FIG 4 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 063 mm in thickness ora single row of strain estimates and 1 cm in length The error bars denote thestandard deviation for data points with the 1 mm ROI from the surface of theartery that are tracked over the cardiac cycle for both the near and far wall

FIG 5 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 1 mm in thickness and1 cm in length The error bars denote the standard deviation for data pointswith the 1 mm ROI from the surface of the artery that are tracked over thecardiac cycle for both the near and far walls

ing the vessel Note that accurate and robust estimates of ar-terial function are obtained for ROI thickness values less than1 mm for the axial accumulated displacement and strain andless than 05 mm for the lateral accumulated displacementsThe lateral accumulated strains are shown but the estimatesare rather noisy

Figure 9 shows the progression of strain away from thevessel walls The decaying shape of the far wall agrees withthe simulated strain of the mathematical vessel model putforth by Maurice et al27 and the phantom model by Korteet al46 made using a phantom with an inner lumen tube of 4mm diameter and outer vessel tube of 15 mm diameter withsoft gelatinous material filling in between The edge of thevessel wall exhibits a region of slower decay which is likelyto show a difference between the intima media and adventi-tia In addition the near wall clearly exhibits a different straincurve than the far wall The curve does not appear to be an

FIG 6 Plots of the accumulated axial strain for an ROI with a thickness ofone row (a) along with the corresponding curves for an ROI with a 079 mmthickness (b) 1 mm thickness (c) and 148 mm thickness (d) The error barsin this figure denote the standard error to clearly indicate the strain variationsin the near and far wall

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4485 Ge et al Displacement and strain estimation for arterial wall stiffness 4485

FIG 1 Schematic diagram of the region of the femoral artery that was im-aged on the FH swine model of atherosclerosis

arterial stiffening and cardiovascular health An ROI is de-fined in the artery near and far walls that would exclusivelylie within the wall of the blood vessel Figure 1 provides aschematic diagram of the ultrasound scan performed alongwith identification of the ROI location using an FH swinemodel of atherosclerosis As the vessel expands and contractsover the cardiac cycle the ROI changes its shape and locationcorrespondingly This allows for the capture of a displace-mentstrain profile of the vessel wall over the cardiac cycleinstead of just a snapshot in time

At 6 weeks of age (2 weeks postweaning) the five femaleFH swine were placed on a cornndashsoybean mixed diet with 2added fat and fed twice daily The daily calorie intake waslimited to 80 of ad libitum intake (based on ad libitum in-take of age-matched FH swine) The diet was formulated tomeet nutrient requirements and was mixed weekly from feedcomponents (Arlington Feed Mill Arlington WI) At the timeof the ultrasound measurements the animals were 106 plusmn 05months old with a body weight of 836 plusmn 69 kg (246 plusmn 48body fat determined by dual energy x-ray absorptiometry) Amidline neck incision was made to access the internal carotidartery A catheter was placed in the artery for intra-arterialblood pressure (ABP) measurement via an attached pressuretransducer (PX600 Edwards Lifesciences Irvine CA) po-sitioned at the level of the heart and connected to an S5Datex-Ohmeda Anesthesia Monitoring System (GE Health-care Waukesha WI) ABP and heart rate measurements forthe 5 FH swine are shown in Table I

IIA Radio frequency data acquisition

Acquisition of the RF data was accomplished using theclinical Ultrasonix SonicTouch system (Ultrasonix MedicalCorporation Richmond BC) running Sonix RP 319 and us-ing an L14-538 transducer operating at 10 MHz center fre-quency The depth of the RF data acquired measured fromthe transducer to the vessel was 40 mm The sampling fre-

TABLE I Intra-arterial blood pressure (BP) and heart rate measurements forthe five FH swine

Animal no Systolic BP Diastolic BP Heart rate

1 75 38 1402 77 46 1533 79 40 1054 88 40 1105 82 46 94

quency for the acquired data was 40 MHz with a frame rateof 98 framess

Ultrasound scanning was performed on the FH swinemodel starting at six months of age This study was performedunder a protocol approved by the University of Wisconsin-Madison Animal Care and Use Committee (ACUC) The an-imals were sedated once per month with an injection of Tela-zol at 1ndash5 mgkg at the minimal dosage necessary for seda-tion prior to the use of a facemask The facemask then de-livered 15ndash5 isoflurane and 100 oxygen with a flowrate of 1ndash3 Lmin Heart monitor and oxygen saturation weremonitored via pulse oximetery After sedation the ultrasoundtransducers were held by hand to initiate scans that lasted forone or more cardiac cycles The field of view included thefemoral artery and the beginning of the bulb with a single fo-cus at the far wall of the vessel Atherosclerosis is a systemicdisease therefore plaque accumulation is expected to occurat multiple arterial locations The femoral artery was chosendue to the presence of a bifurcation site where atheroscleroticplaques tend to develop and is much easier to access using ul-trasound than the carotid artery in swine due to the differencein imaging depths

IIB Strain and displacement mapping

The 2D displacement tracking and strain estimation algo-rithm was implemented in MATLAB (The Mathworks Nat-ick RI) The code used to calculate the displacement was animplementation of the quality-guided displacement trackingalgorithm45 This multi-seed algorithm initially utilizes regu-larly spaced windows as initial seeds Cross correlation coeffi-cients between the tracked regions and the seeds were used todetermine the quality of each seed and the highest one wouldbe selected to be the initial estimation of displacement Thealgorithm then iterates to track the seedrsquos four neighbors andthe process repeats for the next windows to complete the en-tire scanned field A large window size allows for better track-ing of noisy data while a smaller window improves spatialresolution

RF data sets were upsampled by a factor of 5 using splineinterpolation to improve displacement tracking The dimen-sions of the 2D motion tracking kernel were 81 data pointsalong the beam direction and 15 data points along the lateraldirection for the upsampled data corresponding to 033 mmtimes 088 mm for the 2D tracking kernel dimensions respec-tively A 75 overlap was utilized to obtain consecutive dis-placement estimates Local strain estimates were obtainedusing a least squares fit to the displacement data using

Medical Physics Vol 39 No 7 July 2012

4486 Ge et al Displacement and strain estimation for arterial wall stiffness 4486

segments with a length of 066 mm for the axial strain esti-mates and 088 mm for the lateral strain estimates The frameskip amount which represents the number of frames that wereskipped to ensure a reasonably significant amount of deforma-tion between frames was set to 3 By increasing the amountof displacement between consecutively processed frames thesignal to quantization noise ratio and the subpixel displace-ment estimation errors were improved Before the displace-ment maps were used to calculate the local strain imagesthey were put through a 3 times 2 pixel median filter to removenoise spikes Displacements and strains estimated along the x(lateral) and y (axial) directions along with the strain distri-bution are stored for every frame-pair for further processingThe accumulated displacement was then computed from thestored displacement estimates Lastly the accumulated strainwas computed from the accumulated displacement estimatedover the cardiac cycle

IIC ROI creation and tracking

The positioning of the ROI on the artery wall was de-termined manually for the first frame and their coordinateswere adjusted using previously calculated displacements forthe following frames The ROI boundary was defined usingpoints marked along the vessel intima on the first frame ofthe RF data and extended from the beginning of the bifurca-tion toward the common femoral artery The lines that connectneighboring points were used to create the defining curvededge of the ROI and the ROI region is delineated accord-ing to the contours of this edge The opposite edge was cre-ated by translating the defining edge up or down by the in-tended thickness of the ROI resulting in an area that has uni-form thickness The resulting ROI was uniform in thicknessFor example on the near wall of an artery points should bemarked directly below and adjacent to the vessel wall and theROI would be defined to extend a set number of pixels abovethe defining edge to cover the wall and some of the surround-ing tissue the inverse holds true for the far wall This assureda uniform thickness for the initial ROI This method is validonly with the assumption that the ROI is intended for an objectthat is horizontally situated otherwise it would be necessaryto define the ROI width and height at different angles fromthe RF datarsquos cardinal directions An ROI maximum lengthcan optionally be defined and any region that extend abovethe set length would be cut off It is advantageous to use ROIsthat are larger than what is required so that data can be eas-ily derived as a subregion of the processed data Care shouldtherefore be made to mark the ROI with a starting point oneither the left or right side that is anatomically similar acrossdifferent data sets The ROI dimensions used for the swinedata were 10 mm in width and up to 3 mm in thickness ordepth the actual thickness used for processing was about onemm in thickness to correspond to and to lie within the actualthickness of the vessel walls

The data points that make up the defining edge of the nearwall and the far walls of the corresponding ROI were eachtracked over the cardiac cycle and the ROI was redrawn foreach subsequent frame based on this information The dis-

placement calculated from the RF data with coordinates inspace and time was added to the coordinates of the points ofthe ROIrsquos defining edge to form the ROI of the next frame intime The stored coordinates for the ROI edge were not inte-gers since subsample displacements were estimated Bilinearinterpolation was used to find the displacement values for thenext frame This reduces the rounding errors that can be sig-nificant in the lateral direction as discussed in the Appendix

Once the ROI was generated the strain displacement andany other relevant data points within the corresponding regioncan be stored First the ROI is made into a binary mask withones corresponding to pixels within the ROI and zeroes oth-erwise Then mask can then be applied to the strain and dis-placement images Since the initial ROI points were markedat the exact boundary between the vessel and the blood withinit to remove the contribution of the blood in the strain imageThe ROI follows the curvature of the vessel wall and is notdiscarded The ROI thickness is specified in the number ofdisplacementstrain pixels used to estimate the displacementand strain The two dimensions are therefore the location onthe vessel wall and the ROI thickness within the vessel wallThe strain and displacement maps can be saved directly as aresult of the mask and the accumulated strain and accumu-lated displacement maps can be found after accumulating thedisplacements

III RESULTS

Figure 2(a) presents the B-mode image of the femoralartery being scanned on the FH swine The location of thescan is relative to the femoral arteryrsquos bifurcation on the B-mode image The local displacement maps estimated alongthe axial (b) and lateral (c) directions are also shown alongthe corresponding axial (d) and lateral (e) strain distributionNoise artifacts in the lateral displacement and strain imagesare increased when compared to the axial displacement andstrain images respectively The locations of the ROI aroundthe near and far walls of the artery are illustrated in Fig 3(a)on the ultrasound B-mode image The ROIs are delineatedmanually on the B-mode image with the lumen of the arteryidentified in both the near and far walls of the artery TheROI over which local displacement and strain estimates areestimated and accumulated should ideally be marked individ-ually on ultrasound B-mode images rather than the derivedstrain image This can be done very accurately using imagesoftware such as MITK 3M3 program (Mint Medical GmbHHeidelberg Germany) to measure the B-mode vessel thick-ness Estimations are performed using the B-mode images bydetermining the edges of the vessel wall and using the ratioof the pixels making up the vessel thickness over the pixelheight of the image multiplied by the corresponding imagedepth The resulting vessel thickness obtained is on the or-der of 08ndash072 mm On the other hand the thickness of thefemoral artery obtained from a representative histopathologi-cal image in Fig 3(b) instead shows the vessel thickness tobe around 03ndash04 mm

The near wall of the artery is constrained by surroundingconnective tissue subcutaneous fat and the skin Since the

Medical Physics Vol 39 No 7 July 2012

4487 Ge et al Displacement and strain estimation for arterial wall stiffness 4487

FIG 2 Ultrasound B-mode image (a) the accumulated axial displacement (b) the accumulated lateral displacement (c) the corresponding accumulated axialstrain (d) and lateral strain images over a cardiac cycle (e)

transducer is placed next to the skin layer the near wall ofthe artery is not expected to deform significantly with bloodflow On the other hand the far wall of the artery is mainlyconstrained by connective tissue a vein that runs along withthe artery and is visible in the B-mode image and muscle tis-sue The far wall therefore usually deforms more than the nearwall of the artery in the geometry shown in Figs 2 and 3 Lo-cal displacements and strains within these ROIs are utilized inthe following plots to evaluate arterial stiffness variations

Figure 4 presents the variation of a single row of dis-placement and strain estimated along the inner boundaries ofthe ROI that are closest to the vessel wall lumen We trackthe displacement of these points that are drawn manuallyon the first B-mode images over all the RF data acquired overthe cardiac cycle Since this row of data points will movealong with the arterial wall and track the deformation intro-duced in a cardiac cycle we refer to the estimation presentedin Fig 4 as the localized displacement and strain since wetrack the same tissue structure over the entire cardiac cycleObserve the opposite directions of the periodic displacementvisualized on the near and far wall for the axial accumulateddisplacement (AAD) and the noisier variation for the axialaccumulated strain (AAS) A periodic trend in the AAS canhowever be visualized A phase lag between the AAD of thenear and far wall is also observed Although the lateral accu-mulated displacements (LAD) indicate the arterial deforma-tion along the lateral direction the lateral accumulated strains(LAS) do not present a trend and are extremely noisy esti-

mates The displacement and strain values of the near wall areusually lower in magnitude when compared to the far wallThis could be due to locationrsquos proximity to the transducerand the proximity of the scanned artery to the femoral vein

We now include additional displacement and strain esti-mates by increasing the thickness of the ROI to 1 mm withthe plots for the near and far wall shown in Fig 5 The AADand AAS curves are similar to those observed in Fig 4 whilethe LAD curve being slightly lower The LAS curves are stillnoisy and we will not discuss the variations associated withthis curve from this point forward due to the increased noiseartifacts observed

To clearly visualize the trend or variations in the mean ofthe AAS curves we replace the standard deviation with thestandard error in Fig 6 We present plots of the near and farwall for different ROI thicknesses in Fig 6 Note that forROI thickness of a single strain estimate (069 mm) in Fig6(a) 2 estimates (079 mm) 4 estimates (1 mm) and 10 es-timates (148 mm) in Figs 6(b)ndash6(d) respectively Note thatas the ROI thickness becomes larger it also incorporates esti-mates from surrounding overlying tissue which contrast fromthe strain in arterial tissue as seen in Fig 6(d) Appropriateselection of the dimensions of the ROIs and a fine resolu-tion are essential to properly characterize variations in arterialelasticity

Figures 7 and 8 present the changes in the accumulatedaxial and lateral displacements and strains around the peakand valley of the axial deformations over the cardiac cycle

Medical Physics Vol 39 No 7 July 2012

4488 Ge et al Displacement and strain estimation for arterial wall stiffness 4488

FIG 3 (a) Ultrasound B-mode image with the regions of interest on the nearwall and the far wall of the femoral artery and (b) representative photomicro-graph (5times objective) of a hematoxylin and eosin stained cross section of afemoral artery from an 8-month-old FH swine

at approximately 035 and 089 s into the cardiac cycle Esti-mated displacements are interpolated to provide similar pixeldensity as the underlying ultrasound radio frequency data foraccurate registration The strain is maximum on the interior ofthe vessel progressing to a zero point and ultimately to sur-rounding tissues with the opposite sign Larger ROI thicknessenables us to evaluate stiffness variations in tissues surround-

FIG 4 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 063 mm in thickness ora single row of strain estimates and 1 cm in length The error bars denote thestandard deviation for data points with the 1 mm ROI from the surface of theartery that are tracked over the cardiac cycle for both the near and far wall

FIG 5 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 1 mm in thickness and1 cm in length The error bars denote the standard deviation for data pointswith the 1 mm ROI from the surface of the artery that are tracked over thecardiac cycle for both the near and far walls

ing the vessel Note that accurate and robust estimates of ar-terial function are obtained for ROI thickness values less than1 mm for the axial accumulated displacement and strain andless than 05 mm for the lateral accumulated displacementsThe lateral accumulated strains are shown but the estimatesare rather noisy

Figure 9 shows the progression of strain away from thevessel walls The decaying shape of the far wall agrees withthe simulated strain of the mathematical vessel model putforth by Maurice et al27 and the phantom model by Korteet al46 made using a phantom with an inner lumen tube of 4mm diameter and outer vessel tube of 15 mm diameter withsoft gelatinous material filling in between The edge of thevessel wall exhibits a region of slower decay which is likelyto show a difference between the intima media and adventi-tia In addition the near wall clearly exhibits a different straincurve than the far wall The curve does not appear to be an

FIG 6 Plots of the accumulated axial strain for an ROI with a thickness ofone row (a) along with the corresponding curves for an ROI with a 079 mmthickness (b) 1 mm thickness (c) and 148 mm thickness (d) The error barsin this figure denote the standard error to clearly indicate the strain variationsin the near and far wall

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4486 Ge et al Displacement and strain estimation for arterial wall stiffness 4486

segments with a length of 066 mm for the axial strain esti-mates and 088 mm for the lateral strain estimates The frameskip amount which represents the number of frames that wereskipped to ensure a reasonably significant amount of deforma-tion between frames was set to 3 By increasing the amountof displacement between consecutively processed frames thesignal to quantization noise ratio and the subpixel displace-ment estimation errors were improved Before the displace-ment maps were used to calculate the local strain imagesthey were put through a 3 times 2 pixel median filter to removenoise spikes Displacements and strains estimated along the x(lateral) and y (axial) directions along with the strain distri-bution are stored for every frame-pair for further processingThe accumulated displacement was then computed from thestored displacement estimates Lastly the accumulated strainwas computed from the accumulated displacement estimatedover the cardiac cycle

IIC ROI creation and tracking

The positioning of the ROI on the artery wall was de-termined manually for the first frame and their coordinateswere adjusted using previously calculated displacements forthe following frames The ROI boundary was defined usingpoints marked along the vessel intima on the first frame ofthe RF data and extended from the beginning of the bifurca-tion toward the common femoral artery The lines that connectneighboring points were used to create the defining curvededge of the ROI and the ROI region is delineated accord-ing to the contours of this edge The opposite edge was cre-ated by translating the defining edge up or down by the in-tended thickness of the ROI resulting in an area that has uni-form thickness The resulting ROI was uniform in thicknessFor example on the near wall of an artery points should bemarked directly below and adjacent to the vessel wall and theROI would be defined to extend a set number of pixels abovethe defining edge to cover the wall and some of the surround-ing tissue the inverse holds true for the far wall This assureda uniform thickness for the initial ROI This method is validonly with the assumption that the ROI is intended for an objectthat is horizontally situated otherwise it would be necessaryto define the ROI width and height at different angles fromthe RF datarsquos cardinal directions An ROI maximum lengthcan optionally be defined and any region that extend abovethe set length would be cut off It is advantageous to use ROIsthat are larger than what is required so that data can be eas-ily derived as a subregion of the processed data Care shouldtherefore be made to mark the ROI with a starting point oneither the left or right side that is anatomically similar acrossdifferent data sets The ROI dimensions used for the swinedata were 10 mm in width and up to 3 mm in thickness ordepth the actual thickness used for processing was about onemm in thickness to correspond to and to lie within the actualthickness of the vessel walls

The data points that make up the defining edge of the nearwall and the far walls of the corresponding ROI were eachtracked over the cardiac cycle and the ROI was redrawn foreach subsequent frame based on this information The dis-

placement calculated from the RF data with coordinates inspace and time was added to the coordinates of the points ofthe ROIrsquos defining edge to form the ROI of the next frame intime The stored coordinates for the ROI edge were not inte-gers since subsample displacements were estimated Bilinearinterpolation was used to find the displacement values for thenext frame This reduces the rounding errors that can be sig-nificant in the lateral direction as discussed in the Appendix

Once the ROI was generated the strain displacement andany other relevant data points within the corresponding regioncan be stored First the ROI is made into a binary mask withones corresponding to pixels within the ROI and zeroes oth-erwise Then mask can then be applied to the strain and dis-placement images Since the initial ROI points were markedat the exact boundary between the vessel and the blood withinit to remove the contribution of the blood in the strain imageThe ROI follows the curvature of the vessel wall and is notdiscarded The ROI thickness is specified in the number ofdisplacementstrain pixels used to estimate the displacementand strain The two dimensions are therefore the location onthe vessel wall and the ROI thickness within the vessel wallThe strain and displacement maps can be saved directly as aresult of the mask and the accumulated strain and accumu-lated displacement maps can be found after accumulating thedisplacements

III RESULTS

Figure 2(a) presents the B-mode image of the femoralartery being scanned on the FH swine The location of thescan is relative to the femoral arteryrsquos bifurcation on the B-mode image The local displacement maps estimated alongthe axial (b) and lateral (c) directions are also shown alongthe corresponding axial (d) and lateral (e) strain distributionNoise artifacts in the lateral displacement and strain imagesare increased when compared to the axial displacement andstrain images respectively The locations of the ROI aroundthe near and far walls of the artery are illustrated in Fig 3(a)on the ultrasound B-mode image The ROIs are delineatedmanually on the B-mode image with the lumen of the arteryidentified in both the near and far walls of the artery TheROI over which local displacement and strain estimates areestimated and accumulated should ideally be marked individ-ually on ultrasound B-mode images rather than the derivedstrain image This can be done very accurately using imagesoftware such as MITK 3M3 program (Mint Medical GmbHHeidelberg Germany) to measure the B-mode vessel thick-ness Estimations are performed using the B-mode images bydetermining the edges of the vessel wall and using the ratioof the pixels making up the vessel thickness over the pixelheight of the image multiplied by the corresponding imagedepth The resulting vessel thickness obtained is on the or-der of 08ndash072 mm On the other hand the thickness of thefemoral artery obtained from a representative histopathologi-cal image in Fig 3(b) instead shows the vessel thickness tobe around 03ndash04 mm

The near wall of the artery is constrained by surroundingconnective tissue subcutaneous fat and the skin Since the

Medical Physics Vol 39 No 7 July 2012

4487 Ge et al Displacement and strain estimation for arterial wall stiffness 4487

FIG 2 Ultrasound B-mode image (a) the accumulated axial displacement (b) the accumulated lateral displacement (c) the corresponding accumulated axialstrain (d) and lateral strain images over a cardiac cycle (e)

transducer is placed next to the skin layer the near wall ofthe artery is not expected to deform significantly with bloodflow On the other hand the far wall of the artery is mainlyconstrained by connective tissue a vein that runs along withthe artery and is visible in the B-mode image and muscle tis-sue The far wall therefore usually deforms more than the nearwall of the artery in the geometry shown in Figs 2 and 3 Lo-cal displacements and strains within these ROIs are utilized inthe following plots to evaluate arterial stiffness variations

Figure 4 presents the variation of a single row of dis-placement and strain estimated along the inner boundaries ofthe ROI that are closest to the vessel wall lumen We trackthe displacement of these points that are drawn manuallyon the first B-mode images over all the RF data acquired overthe cardiac cycle Since this row of data points will movealong with the arterial wall and track the deformation intro-duced in a cardiac cycle we refer to the estimation presentedin Fig 4 as the localized displacement and strain since wetrack the same tissue structure over the entire cardiac cycleObserve the opposite directions of the periodic displacementvisualized on the near and far wall for the axial accumulateddisplacement (AAD) and the noisier variation for the axialaccumulated strain (AAS) A periodic trend in the AAS canhowever be visualized A phase lag between the AAD of thenear and far wall is also observed Although the lateral accu-mulated displacements (LAD) indicate the arterial deforma-tion along the lateral direction the lateral accumulated strains(LAS) do not present a trend and are extremely noisy esti-

mates The displacement and strain values of the near wall areusually lower in magnitude when compared to the far wallThis could be due to locationrsquos proximity to the transducerand the proximity of the scanned artery to the femoral vein

We now include additional displacement and strain esti-mates by increasing the thickness of the ROI to 1 mm withthe plots for the near and far wall shown in Fig 5 The AADand AAS curves are similar to those observed in Fig 4 whilethe LAD curve being slightly lower The LAS curves are stillnoisy and we will not discuss the variations associated withthis curve from this point forward due to the increased noiseartifacts observed

To clearly visualize the trend or variations in the mean ofthe AAS curves we replace the standard deviation with thestandard error in Fig 6 We present plots of the near and farwall for different ROI thicknesses in Fig 6 Note that forROI thickness of a single strain estimate (069 mm) in Fig6(a) 2 estimates (079 mm) 4 estimates (1 mm) and 10 es-timates (148 mm) in Figs 6(b)ndash6(d) respectively Note thatas the ROI thickness becomes larger it also incorporates esti-mates from surrounding overlying tissue which contrast fromthe strain in arterial tissue as seen in Fig 6(d) Appropriateselection of the dimensions of the ROIs and a fine resolu-tion are essential to properly characterize variations in arterialelasticity

Figures 7 and 8 present the changes in the accumulatedaxial and lateral displacements and strains around the peakand valley of the axial deformations over the cardiac cycle

Medical Physics Vol 39 No 7 July 2012

4488 Ge et al Displacement and strain estimation for arterial wall stiffness 4488

FIG 3 (a) Ultrasound B-mode image with the regions of interest on the nearwall and the far wall of the femoral artery and (b) representative photomicro-graph (5times objective) of a hematoxylin and eosin stained cross section of afemoral artery from an 8-month-old FH swine

at approximately 035 and 089 s into the cardiac cycle Esti-mated displacements are interpolated to provide similar pixeldensity as the underlying ultrasound radio frequency data foraccurate registration The strain is maximum on the interior ofthe vessel progressing to a zero point and ultimately to sur-rounding tissues with the opposite sign Larger ROI thicknessenables us to evaluate stiffness variations in tissues surround-

FIG 4 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 063 mm in thickness ora single row of strain estimates and 1 cm in length The error bars denote thestandard deviation for data points with the 1 mm ROI from the surface of theartery that are tracked over the cardiac cycle for both the near and far wall

FIG 5 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 1 mm in thickness and1 cm in length The error bars denote the standard deviation for data pointswith the 1 mm ROI from the surface of the artery that are tracked over thecardiac cycle for both the near and far walls

ing the vessel Note that accurate and robust estimates of ar-terial function are obtained for ROI thickness values less than1 mm for the axial accumulated displacement and strain andless than 05 mm for the lateral accumulated displacementsThe lateral accumulated strains are shown but the estimatesare rather noisy

Figure 9 shows the progression of strain away from thevessel walls The decaying shape of the far wall agrees withthe simulated strain of the mathematical vessel model putforth by Maurice et al27 and the phantom model by Korteet al46 made using a phantom with an inner lumen tube of 4mm diameter and outer vessel tube of 15 mm diameter withsoft gelatinous material filling in between The edge of thevessel wall exhibits a region of slower decay which is likelyto show a difference between the intima media and adventi-tia In addition the near wall clearly exhibits a different straincurve than the far wall The curve does not appear to be an

FIG 6 Plots of the accumulated axial strain for an ROI with a thickness ofone row (a) along with the corresponding curves for an ROI with a 079 mmthickness (b) 1 mm thickness (c) and 148 mm thickness (d) The error barsin this figure denote the standard error to clearly indicate the strain variationsin the near and far wall

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4487 Ge et al Displacement and strain estimation for arterial wall stiffness 4487

FIG 2 Ultrasound B-mode image (a) the accumulated axial displacement (b) the accumulated lateral displacement (c) the corresponding accumulated axialstrain (d) and lateral strain images over a cardiac cycle (e)

transducer is placed next to the skin layer the near wall ofthe artery is not expected to deform significantly with bloodflow On the other hand the far wall of the artery is mainlyconstrained by connective tissue a vein that runs along withthe artery and is visible in the B-mode image and muscle tis-sue The far wall therefore usually deforms more than the nearwall of the artery in the geometry shown in Figs 2 and 3 Lo-cal displacements and strains within these ROIs are utilized inthe following plots to evaluate arterial stiffness variations

Figure 4 presents the variation of a single row of dis-placement and strain estimated along the inner boundaries ofthe ROI that are closest to the vessel wall lumen We trackthe displacement of these points that are drawn manuallyon the first B-mode images over all the RF data acquired overthe cardiac cycle Since this row of data points will movealong with the arterial wall and track the deformation intro-duced in a cardiac cycle we refer to the estimation presentedin Fig 4 as the localized displacement and strain since wetrack the same tissue structure over the entire cardiac cycleObserve the opposite directions of the periodic displacementvisualized on the near and far wall for the axial accumulateddisplacement (AAD) and the noisier variation for the axialaccumulated strain (AAS) A periodic trend in the AAS canhowever be visualized A phase lag between the AAD of thenear and far wall is also observed Although the lateral accu-mulated displacements (LAD) indicate the arterial deforma-tion along the lateral direction the lateral accumulated strains(LAS) do not present a trend and are extremely noisy esti-

mates The displacement and strain values of the near wall areusually lower in magnitude when compared to the far wallThis could be due to locationrsquos proximity to the transducerand the proximity of the scanned artery to the femoral vein

We now include additional displacement and strain esti-mates by increasing the thickness of the ROI to 1 mm withthe plots for the near and far wall shown in Fig 5 The AADand AAS curves are similar to those observed in Fig 4 whilethe LAD curve being slightly lower The LAS curves are stillnoisy and we will not discuss the variations associated withthis curve from this point forward due to the increased noiseartifacts observed

To clearly visualize the trend or variations in the mean ofthe AAS curves we replace the standard deviation with thestandard error in Fig 6 We present plots of the near and farwall for different ROI thicknesses in Fig 6 Note that forROI thickness of a single strain estimate (069 mm) in Fig6(a) 2 estimates (079 mm) 4 estimates (1 mm) and 10 es-timates (148 mm) in Figs 6(b)ndash6(d) respectively Note thatas the ROI thickness becomes larger it also incorporates esti-mates from surrounding overlying tissue which contrast fromthe strain in arterial tissue as seen in Fig 6(d) Appropriateselection of the dimensions of the ROIs and a fine resolu-tion are essential to properly characterize variations in arterialelasticity

Figures 7 and 8 present the changes in the accumulatedaxial and lateral displacements and strains around the peakand valley of the axial deformations over the cardiac cycle

Medical Physics Vol 39 No 7 July 2012

4488 Ge et al Displacement and strain estimation for arterial wall stiffness 4488

FIG 3 (a) Ultrasound B-mode image with the regions of interest on the nearwall and the far wall of the femoral artery and (b) representative photomicro-graph (5times objective) of a hematoxylin and eosin stained cross section of afemoral artery from an 8-month-old FH swine

at approximately 035 and 089 s into the cardiac cycle Esti-mated displacements are interpolated to provide similar pixeldensity as the underlying ultrasound radio frequency data foraccurate registration The strain is maximum on the interior ofthe vessel progressing to a zero point and ultimately to sur-rounding tissues with the opposite sign Larger ROI thicknessenables us to evaluate stiffness variations in tissues surround-

FIG 4 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 063 mm in thickness ora single row of strain estimates and 1 cm in length The error bars denote thestandard deviation for data points with the 1 mm ROI from the surface of theartery that are tracked over the cardiac cycle for both the near and far wall

FIG 5 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 1 mm in thickness and1 cm in length The error bars denote the standard deviation for data pointswith the 1 mm ROI from the surface of the artery that are tracked over thecardiac cycle for both the near and far walls

ing the vessel Note that accurate and robust estimates of ar-terial function are obtained for ROI thickness values less than1 mm for the axial accumulated displacement and strain andless than 05 mm for the lateral accumulated displacementsThe lateral accumulated strains are shown but the estimatesare rather noisy

Figure 9 shows the progression of strain away from thevessel walls The decaying shape of the far wall agrees withthe simulated strain of the mathematical vessel model putforth by Maurice et al27 and the phantom model by Korteet al46 made using a phantom with an inner lumen tube of 4mm diameter and outer vessel tube of 15 mm diameter withsoft gelatinous material filling in between The edge of thevessel wall exhibits a region of slower decay which is likelyto show a difference between the intima media and adventi-tia In addition the near wall clearly exhibits a different straincurve than the far wall The curve does not appear to be an

FIG 6 Plots of the accumulated axial strain for an ROI with a thickness ofone row (a) along with the corresponding curves for an ROI with a 079 mmthickness (b) 1 mm thickness (c) and 148 mm thickness (d) The error barsin this figure denote the standard error to clearly indicate the strain variationsin the near and far wall

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4488 Ge et al Displacement and strain estimation for arterial wall stiffness 4488

FIG 3 (a) Ultrasound B-mode image with the regions of interest on the nearwall and the far wall of the femoral artery and (b) representative photomicro-graph (5times objective) of a hematoxylin and eosin stained cross section of afemoral artery from an 8-month-old FH swine

at approximately 035 and 089 s into the cardiac cycle Esti-mated displacements are interpolated to provide similar pixeldensity as the underlying ultrasound radio frequency data foraccurate registration The strain is maximum on the interior ofthe vessel progressing to a zero point and ultimately to sur-rounding tissues with the opposite sign Larger ROI thicknessenables us to evaluate stiffness variations in tissues surround-

FIG 4 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 063 mm in thickness ora single row of strain estimates and 1 cm in length The error bars denote thestandard deviation for data points with the 1 mm ROI from the surface of theartery that are tracked over the cardiac cycle for both the near and far wall

FIG 5 Plots of the accumulated axial displacement (a) and strain (b) and theaccumulated lateral displacement (c) and strain (d) shown over two cardiaccycles and computed over a region of interest that is 1 mm in thickness and1 cm in length The error bars denote the standard deviation for data pointswith the 1 mm ROI from the surface of the artery that are tracked over thecardiac cycle for both the near and far walls

ing the vessel Note that accurate and robust estimates of ar-terial function are obtained for ROI thickness values less than1 mm for the axial accumulated displacement and strain andless than 05 mm for the lateral accumulated displacementsThe lateral accumulated strains are shown but the estimatesare rather noisy

Figure 9 shows the progression of strain away from thevessel walls The decaying shape of the far wall agrees withthe simulated strain of the mathematical vessel model putforth by Maurice et al27 and the phantom model by Korteet al46 made using a phantom with an inner lumen tube of 4mm diameter and outer vessel tube of 15 mm diameter withsoft gelatinous material filling in between The edge of thevessel wall exhibits a region of slower decay which is likelyto show a difference between the intima media and adventi-tia In addition the near wall clearly exhibits a different straincurve than the far wall The curve does not appear to be an

FIG 6 Plots of the accumulated axial strain for an ROI with a thickness ofone row (a) along with the corresponding curves for an ROI with a 079 mmthickness (b) 1 mm thickness (c) and 148 mm thickness (d) The error barsin this figure denote the standard error to clearly indicate the strain variationsin the near and far wall

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4489 Ge et al Displacement and strain estimation for arterial wall stiffness 4489

FIG 7 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the peak of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 035 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

artifact since the curve is consistent from one cardiac cycleto the next and transitions between the two waveforms shownin Figs 9(c) and 9(d) This illustrates that the vessel strainis not uniform in neither the radial nor the circumferentialdirections and could exhibit very different characteristics war-ranting further examinations The vessel wall thickness of ahealthy swine is between 03 mm and 05 mm and the in-tima media can progress to twice its thickness in less than ayear with plaque accumulation35 The human carotid artery isthicker on the order of 05ndash08 mm in healthy human malesubjects according to a 1996 study47 However stretching andthickening of the arterial wall occur during the cardiac cyclewhich may also increase the imaged thickness of the vascu-lar arterial wall The current displacement tracking and strainprocessing kernels are on the order of the vessel thicknesshowever the resolution is improved due to the overlappingkernels used for strain estimation

FIG 8 Plots of the accumulated axial displacement (a) and strain (b) andcorresponding lateral displacement (c) and strain (d) versus ROI thicknessValues are plotted at the valley of the cyclic curves shown in Figs 4ndash6 or at atime instant of approximately 089 s into the cardiac cycle The error bars inthis figure denote the standard error to clearly indicate mean variations in thenear and far wall

FIG 9 Plots showing the average axial strain of a single row of pixels versustheir distance from the far wall (a b) and the near wall (c d) at their peaksduring the cardiac cycle The values remain consistent from one cardiac cycleto the next The error bars in this figure denote the standard error to clearlyindicate mean variations in the near and far walls

Figure 10 shows the accumulated axial displacement andaccumulated axial strain curves for five FH swine The plotsare normalized in both time to two cardiac cycles and am-plitude to the systolic blood pressure of each model respec-tively The normalization is done frame by frame For eachframe of the far wall displacement the mean value is calcu-lated for an ROI of 06 mm depth and the peak to peak changeis computed The accumulated displacement for the near andfar walls are scaled by dividing by this value The scaled ac-cumulated displacement map is then used to calculate the ac-cumulated strain The amplitude of the plots contain strainand displacement contributions of tissue outside the vesselwall due to the thickness of the ROI but the curvature of thevessel wall is maintained The plots show the repeatability of

FIG 10 Plots showing accumulated axial displacement of the near and farwall (a b) and the accumulated axial strain of the near and far wall (c d)for five FH swine Plots are shown for ROI with 06 mm thickness Normal-ization was performed by dividing the amplitudes of the near and far walldisplacements by the systolic blood pressure The axes are both unit-less dueto the normalizations The error bars in this figure denote the standard errorto clearly indicate mean variations in the near and far walls

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4490 Ge et al Displacement and strain estimation for arterial wall stiffness 4490

FIG 11 Diagram showing the coordinate grid used for bilinear interpola-tion When a data point is located at a noninteger coordinate the data pointslocated at the four neighboring integer coordinates found via rounding areused for the estimation of the value at that location

our displacement tracking and strain estimation approach andalso the variability between the FH swine Table I provides theblood pressure and heart rate information that was used in thenormalization for each FH swine

IV DISCUSSION

In this paper we demonstrate the ability to accurately tracklocal displacements on either sides of the lumen of an arterywall The deformation of the artery wall within the cardiaccycle is expected to change with age with the stiffening ofthe arteries due to atherosclerosis The FH swine model usedin this paper can be used to track arterial stiffening for ani-mal with different diets and over age ranges The noninvasivearterial stiffening data obtained with strain imaging can becorrelated to histopathological assessments on the artery afterthe animal is sacrificed

Several features or indices can be derived from the vari-ation in the AAD AAS and LAD plots shown in this pa-per The more obvious features include the variations in themaximum and minimum mean and standard deviations of theAAD AAS and LAD estimates shown in Figs 7 and 8 overdifferent animals The phase difference or lag between theAAD AAS and LAD variations between the near and farwalls of the artery would be another feature that would pro-vide important information The slope of the increase of theAAD AAS and LAD curves during systole and the subse-quent decrease during diastole will also be tracked across asubgroup of these animals

The axial displacement and strain estimation on the arterywall shown in this paper indicate the repeatability of thesemeasurements over several cardiac cycles as illustrated inFigs 4ndash6 The larger dimensions or thickness of the ROI in-clude contributions from tissue surrounding the artery wallsuch as connective tissue subcutaneous fat or muscle tissue

The localized estimation of the displacement and strain in Fig4 with the ROI that tracks the movement of the lumen wouldprovide the most consistent results and larger ROIs shouldbe compared to the estimates to ensure that the ROI remainswithin the arterial wall Larger ROIs may reduce the statisti-cal fluctuation of the results since more independent estimatesare included in the computation of the mean and standard de-viation

V CONCLUSIONS

Currently the strain distribution is predominantly used tofind scalar values be it the maximum minimum or the meanstrain within a region By tracking arterial wall tissue as itdeforms over time strain can be seen as a multidimensionalmatrix not only in space but also in time By localizing strainonto an area of tissue ie the arterial wall it may be possibleto predict the likelihood of developing vascular diseases thenature and progression of the cardiovascular system and thesites where they may occur

Preliminary results demonstrated the feasibility of obtain-ing the required data Further improvements can be made tothe tracking accuracy especially in the lateral direction andimproved definition of the data in the axial direction whichcould potentially indicate individually the health of the mediaand adventitial layers The assumption of the ROIrsquos uniformthickness could be discarded for a mesh tracking approachthat allow for much higher precision in tissue tracking Thebiggest difficulty of tracking using ultrasound is the poor res-olution and sampling in the lateral direction Methods such asbeam steering and improved subpixel estimation may bringfurther improvements in this aspect The accumulated strainas defined in this paper will be explored for its potential fornoninvasive characterization of the vascular wall

ACKNOWLEDGMENTS

This research was supported in part by NIH Grant NosR21 EB010098-03 R01 CA112192-S103 and the Reed Re-search Group Multi-Donor Fund (UW-Madison)

APPENDIX SUB-SAMPLE DISPLACEMENTTRACKING

Bilinear interpolation was used in the process of incre-menting the ROI coordinates as described below and shownschematically in Fig 11 Let nonintegers xi and yi denote thecoordinates of a point in the ROI boundary with subscript in-dex i representing time let dy(xi yi) be the displacement es-timate located at (xi yi) and f and c correspond to the floorand ceil functions (round up and round down functions) re-spectively then

xi+1 = xi + dx(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dx(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dx(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A1)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4491 Ge et al Displacement and strain estimation for arterial wall stiffness 4491

yi+1 = yi + dy(f (xi) f (yi))(c(xi) minus xi)(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) f (yi))

(xi minus f (xi))(c(yi) minus yi)

(c(xi) minus f (xi))(c(yi) minus f (yi))

+ dy(f (xi) c(yi))(c(xi) minus xi)(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi))+ dy(c(xi) c(yi))

(xi minus f (xi))(yi minus f (yi))

(c(xi) minus f (xi))(c(yi) minus f (yi)) (A2)

a)Author to whom correspondence should be addressed Electronic mailtvarghesewiscedu Telephone (608) 265-8797 Fax (608) 262-2413

1K D Kochanek J Xu S L Murphy and A M Minintildeo ldquoNational VitalStatistics Reports Deaths Preliminary Data for 2009rdquo Statistics 59 5ndash38(2011)

2V L Roger A S Go D M Lloyd-Jones R J Adams J D BerryT M Brown M R Carnethon S Dai G de Simone E S Ford C S FoxH J Fullerton C Gillespie K J Greenlund S M Hailpern J A HeitP M Ho V J Howard B M Kissela S J Kittner D T LacklandJ H Lichtman L D Lisabeth D M Makuc G M Marcus A MarelliD B Matchar M M McDermott J B Meigs C S Moy D MozaffarianM E Mussolino G Nichol N P Paynter W D Rosamond P D SorlieR S Stafford T N Turan M B Turner N D Wong and J Wylie-RosettldquoHeart disease and stroke statisticsndash2011 update A report from the Amer-ican Heart Associationrdquo Circulation 123 e18ndashe209 (2011)

3V Kotsis S Stabouli I Karafillis S Papakatsika Z Rizos S MiyakisS Goulopoulou G Parati and P Nilsson ldquoArterial stiffness and 24hambulatory blood pressure monitoring in young healthy volunteers Theearly vascular ageing Aristotle University Thessaloniki Study (EVA-ARISStudy)rdquo Atherosclerosis 219(1) 194ndash199 (2011)

4M F OrsquoRourke J A Staessen C Vlachopoulos D Duprez andG E Plante ldquoClinical applications of arterial stiffness definitions and ref-erence valuesrdquo Am J Hypertens 15 426ndash444 (2002)

5N M van Popele D E Grobbee M L Bots R Asmar J TopouchianR S Reneman A P G Hoeks D A M van der Kuip A Hofman andJ C M Witteman ldquoAssociation between arterial stiffness and atheroscle-rosis The Rotterdam studyrdquo Stroke 32 454ndash460 (2001)

6D S Freedman Z Mei S R Srinivasan G S Berenson and W H DietzldquoCardiovascular risk factors and excess adiposity among overweight chil-dren and adolescents the Bogalusa Heart Studyrdquo J Pediatr 150 12ndash17e2(2007)

7J L Cavalcante J A C Lima A Redheuil and M H Al-Mallah ldquoAorticstiffness Current understanding and future directionsrdquo J Am Coll Car-diol 57 1511ndash1522 (2011)

8A Redheuil W-C Yu C O Wu E Mousseaux A de Cesare R YanN Kachenoura D Bluemke and J A C Lima ldquoReduced ascending aor-tic strain and distensibility earliest manifestations of vascular aging in hu-mansrdquo Hypertension 55 319ndash326 (2010)

9F U S Mattace-Raso T J M van der Cammen A Hofman N M vanPopele M L Bos M A D H Schalekamp R Asmar R S RenemanA P G Hoeks M M B Breteler and J C M Witteman ldquoArterial stiff-ness and risk of coronary heart disease and stroke the Rotterdam StudyrdquoCirculation 113 657ndash663 (2006)

10N Ito M Ohishi T Takagi M Terai A Shiota N Hayashi H Rakugiand T Ogihara ldquoClinical usefulness and limitations of brachial-ankle pulsewave velocity in the evaluation of cardiovascular complications in hyper-tensive patientsrdquo Hypertens Res 29 989ndash995 (2006)

11C Stefanadis C Stratos C Vlachopoulos S Marakas H BoudoulasI Kallikazaros E Tsiamis K Toutouzas L Sioros and P ToutouzasldquoPressure-diameter relation of the human aorta A new method of deter-mination by the application of a special ultrasonic dimension catheterrdquoCirculation 92 2210ndash2219 (1995)

12E Hermeling K D Reesink L M Kornmann R S Reneman andA P Hoeks ldquoThe dicrotic notch as alternative time-reference point to mea-sure local pulse wave velocity in the carotid artery by means of ultrasonog-raphyrdquo J Hypertens 27 2028ndash2035 (2009)

13J Luo R Li and E Konofagou ldquoPulse wave imaging of the human carotidartery an in vivo feasibility studyrdquo IEEE Trans Ultrason FerroelectrFreq Control 59 174ndash181 (2012)

14A Kablak-Ziembicka T Przewlocki W Tracz P Pieniazek P MusialekI Stopa J Zalewski and K Zmudka ldquoDiagnostic value of carotid intima-media thickness in indicating multi-level atherosclerosisrdquo Atherosclerosis193 395ndash400 (2007)

15L E Chambless G Heiss A R Folsom W Rosamond M SzkloA R Sharrett and L X Clegg ldquoAssociation of coronary heart diseaseincidence with carotid arterial wall thickness and major risk factors TheAtherosclerosis Risk in Communities (ARIC) Study 1987ndash1993rdquo Am JEpidemiol 146 483ndash494 (1997)

16A R Folsom R A Kronmal R C Detrano H Daniel O LearyD E Bild D A Bluemke M J Budoff K Liu S Shea M Szklo andR P Tracy ldquoNIH Public Accessrdquo Epidemiology 168 1333ndash1339 (2008)

17J H Stein C E Korcarz and W S Post ldquoUse of carotid ultrasound toidentify subclinical vascular disease and evaluate cardiovascular diseaserisk Summary and discussion of the American Society of Echocardiogra-phy Consensus Statementrdquo Prev Cardiol 12 34ndash38 (2009)

18J Ophir ldquoElastography A quantitative method for imaging the elasticityof biological tissuesrdquo Ultrason Imaging 13 111ndash134 (1991)

19T Varghese ldquoQuasi-static ultrasound elastographyrdquo Ultrasound Clin 4323ndash338 (2009)

20T Varghese J Ophir E Konofagou F Kallel and R Righetti ldquoTradeoffsin elastographic imagingrdquo Ultrason Imaging 23 216ndash248 (2001)

21P Chaturvedi M F Insana and T J Hall ldquo2D companding for noise re-duction in strain imagingrdquo IEEE Trans Ultrason Ferroelectr Freq Control45 179ndash191 (1998)

22J Jiang and T J Hall ldquoA parallelizable real-time motion tracking algo-rithm with applications to ultrasonic strain imagingrdquo Phys Med Biol 523773ndash3790 (2007)

23C Pellot-Barakat F Frouin M F Insana and A Herment ldquoUltrasoundelastography based on multiscale estimations of regularized displacementfieldsrdquo IEEE Trans Med Imaging 23 153ndash163 (2004)

24P N T Wells and H-D Liang ldquoMedical ultrasound Imaging of soft tissuestrain and elasticityrdquo J R Soc Interface 8 1521ndash1549 (2011)

25H Shi C Mitchell and M McCormick ldquoPreliminary in vivo atheroscle-rotic carotid plaque characterization using the accumulated axial strain andrelative lateral shift strain indicesrdquo Phys Med 53 6377ndash6394 (2008)

26H Shi and T Varghese ldquoTwo-dimensional multi-level strain estimation fordiscontinuous tissuerdquo Phys Med Biol 52 389ndash401 (2007)

27R L Maurice J Ohayon Y Freacutetigny M Bertrand G Soulez andG Cloutier ldquoNoninvasive vascular elastography Theoretical frameworkrdquoIEEE Trans Med Imaging 23 164ndash180 (2004)

28H Ribbers R G P Lopata S Holewijn G Pasterkamp J D Blanken-steijn and C L de Korte ldquoNoninvasive two-dimensional strain imagingof arteries Validation in phantoms and preliminary experience in carotidarteries in vivordquo Ultrasound Med Biol 33 530ndash540 (2007)

29D Dumont R H Behler T C Nichols E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sisrdquo Ultrasound Med Biol 32 1703ndash1711 (2006)

30W M Suh A H Seto R J P Margey I Cruz-Gonzalez and I-K JangldquoIntravascular detection of the vulnerable plaquerdquo Circulation 4 169ndash178(2011)

31G E Trahey M L Palmeri R C Bentley and K R Nightingale ldquoAcous-tic radiation force impulse imaging of the mechanical properties of arter-ies In vivo and ex vivo resultsrdquo Ultrasound Med Biol 30 1163ndash1171(2004)

32R H Behler T C Nichols H Zhu E P Merricks and C M GallippildquoARFI imaging for noninvasive material characterization of atherosclero-sis Part II Toward in vivo characterizationrdquo Ultrasound Med Biol 35278ndash295 (2009)

33P E Barbone and J C Bamber ldquoQuantitative elasticity imaging what canand cannot be inferred from strain imagesrdquo Phys Med Biol 47 2147ndash2164 (2002)

34J F Granada K Milewski H Zhao J J Stankus A Tellez M S AboodiG L Kaluza C G Krueger R Virmani L B Schwartz andA Nikanorov ldquoVascular response to zotarolimus-coated balloons in in-jured superficial femoral arteries of the familial hypercholesterolemicswinerdquo Circulation 4 447ndash455 (2011)

Medical Physics Vol 39 No 7 July 2012

4492 Ge et al Displacement and strain estimation for arterial wall stiffness 4492

35A F L Schinkel C G Krueger A Tellez J F Granada J D ReedA Hall W Zang C Owens G L Kaluza D Staub B Coll F J TenCate and S B Feinstein ldquoContrast-enhanced ultrasound for imaging vasavasorum comparison with histopathology in a swine model of atheroscle-rosisrdquo Eur J Echocardiogr 11 659ndash664 (2010)

36A Tellez C G Krueger P Seifert D Winsor-Hines C PiedrahitaY Cheng K Milewski M S Aboodi G Yi J C McGregor T CrenshawJ D Reed B Huibregtse G L Kaluza and J F Granada ldquoCoronary baremetal stent implantation in homozygous LDL receptor deficient swine in-duces a neointimal formation pattern similar to humansrdquo Atherosclerosis213 518ndash524 (2010)

37J Hasler-Rapacz H Ellegren A K Fridolfsson B Kirkpatrick S KirkL Andersson and J Rapacz ldquoIdentification of a mutation in the low den-sity lipoprotein receptor gene associated with recessive familial hyperc-holesterolemia in swinerdquo Am J Med Genet 76 379ndash386 (1998)

38J Hasler-Rapacz H J Kempen H M Princen B J KudchodkarA Lacko and J Rapacz ldquoEffects of simvastatin on plasma lipids andapolipoproteins in familial hypercholesterolemic swinerdquo ArteriosclerThromb Vasc Biol 16 137ndash143 (1996)

39J Hasler-Rapacz M F Prescott J Von Linden-Reed J M Rapacz Z Huand J Rapacz ldquoElevated concentrations of plasma lipids and apolipopro-teins B C-III and E are associated with the progression of coronary arterydisease in familial hypercholesterolemic swinerdquo Arterioscler ThrombVasc Biol 15 583ndash592 (1995)

40J O Hasler-Rapacz T C Nichols T R Griggs D A Bellinger and J Ra-pacz ldquoFamilial and diet-induced hypercholesterolemia in swine Lipid

ApoB and ApoA-I concentrations and distributions in plasma andlipoprotein subfractionsrdquo Arterioscler Thromb Vasc Biol 14 923ndash930(1994)

41R Wernersson M H Schierup F G Joslashrgensen J Gorodkin F PanitzH-H Staerfeldt O F Christensen T Mailund H Hornshoslashj A KleinJ Wang B Liu S Hu W Dong W Li G K S Wong J Yu J WangC Bendixen M Fredholm S Brunak H Yang and L Bolund ldquoPigs insequence space a 066X coverage pig genome survey based on shotgunsequencingrdquo BMC Genomics 6 70 (2005)

42A D Attie R J Aiello and W J Checovich The Spontaneously Hyper-cholesterolemic Pig as an Animal Model of Human Hypercholesterolemia1st ed (Iowa State College Ames 1992)

43M E Tumbleson Swine in Biomedical Research (Plenum New York1986) Vol 1

44W G Pond Nutrition and Cardiovascular System of Swine (CRC BocaRaton FL 1986) Vol 2

45L Chen G M Treece J E Lindop A H Gee and R W Prager ldquoAquality-guided displacement tracking algorithm for ultrasonic elasticityimagingrdquo Med Image Anal 13 286ndash96 (2009)

46C L de Korte E I Ceacutespedes A F van der Steen and C T Lanceacutee ldquoIn-travascular elasticity imaging using ultrasound Feasibility studies in phan-tomsrdquo Ultrasound Med 23 735ndash746 (1997)

47A Gnasso C Carallo C Irace V Spagnuolo G De Novara P L Mattioliand A Pujia ldquoAssociation between intima-media thickness and wall shearstress in common carotid arteries in healthy male subjectsrdquo Circulation94(12) 3257ndash3262 (1996)

Medical Physics Vol 39 No 7 July 2012