review bio medical imaging

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? PergamonComputerized Medical Imagmg and Graphics. Vol. 19, No. I. pp. 3-25, 1995Copyright 0 1995 Elsevier Science LtdPrinted in the USA. All rights reserved0895.61 I l/95 $9.50 + .oO

0895-6111(94)00043-3

BIOMEDICAL IMAGING MODALITIES: A TUTORIALRaj Acharya, Richard Wasserman, Jeffrey Stevens, and Carlos Hinojosa

Department of Electrical and Computer Engineering, Biomedical Imaging Group (BMIG), 201 Bell Hall,State University of New York at Buffalo, Buffalo, NY 14260, USA, E-mail: [email protected]

(Received 9 May 1994)Abstract-The introduction of advanced imaging technologies has improved significantly the quality ofmedical care available to patients. Non-invasive imaging modalities allow a physician to make increasinglyaccurate diagnoses and render precise and measured modes of treatment. Current uses of imaging technolog-ies include laboratory medicine, surgery, radiation therapy, nuclear medicine, and diagnostic radiology.This paper provides an overview of most of the popular imaging modalities currently in clinical use. It ishoped that a general understanding of the modality from which an image is derived will help researchersin the subsequent analysis of the image data.Key Weds: Tutorial, PET, MRI, CT, Medical imaging, DSA, Ultrasound, Squid

1 INTRODUCTIONThe Introduction of advanced imaging technologieshas improved significantly the quality of medical careavailable to patients. Noninvasive imaging modalitiesallow a physician to make increasingly accurate diag-noses and render precise and measured modes of treat-ment. Current uses of imaging technologies includelaboratory medicine, surgery, radiation therapy, nu-clear medicine, and diagnostic radiology. Commonmedical imaging methodologies may be dividedgrossly into two general groupings: (a) techniques thatseek to image internal anatomical structures and (b)methods that present mappings of physiological func-tion.

Rapid technological advances have made the ac-quisition of three and four-dimensional (4D) represen-tations of human and animal internal structures com-monplace. A multitude of imaging modalities areavailable currently.

X-Ray Computed Tomography (CT) is a popularmodality which is used routinely in clinical practice.CT generates a three-dimensional (3D) image set thatis representative of a patients anatomy. CT scannersproduce a set of two-dimensional (2D), axial crosssection images which may be stacked to form a 3Ddata :set. The mathematics of CT image reconstructionis also employed in many additional imaging modal-ities. The problem associated with CT reconstructionwas solved by Radon in 19 17. The availability of high

To whom correspondence should be addressed.

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speed computers and relatively inexpensive memoriesallow modem scanners to utilize sophisticated recon-struction algorithms. The majority of current X-RayCT scanners collect 3D images, at the rate of one 2Dslice at a time. Specialized scanners are also availablewhich collect an entire 3D volume within a very shorttime span.

Magnetic Resonance Imaging (MRI) is similar toCT imaging in that it generates 3D data sets correspond-ing to a patients anatomy. However, MRI differs funda-mentally from CT in the manner in which images areacquired. CT scanners employ x-ray radiation to gener-ate the data needed to reconstruct internal structures.Alternatively, MRI utilizes RF waves and magneticfields to obtain 3D images and is based on the principleof Nuclear Magnetic Resonance (NMR). MRI scannersutilize non-ionizing beams and provide unparalleled softtissue contrast in a noninvasive manner.

Emission CT techniques obtain 3D representa-tions of the location of injected pharmaceuticals. Theinjected pharmaceuticals are labelled with gamma rayemitting radionuclides. The emitted gamma rays aremeasured at sites external to a patient. Such measureddata may be utilized to reconstruct a 3D mapping ofinternal emission density. A 3D image is generated byreconstructing a measured set of 2D projection imagesacquired at various angles around the patient. EmissionTomography differs from MRI and CT in that it pro-vides physiological function information, such as per-fusion and metabolism, as opposed to strictly anatomi-cal information.

Another methodology which gathers functional


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4 Computerized Medical Imaging and Graphics January-Februaryll995, Volume 19, Number 1information is Biomagnetic Source Imaging. This tech-nology allows for the external measurement of the lowlevel magnetic fields generated by neuron activity. Bio-magnetic source imaging allows a clinician to gatherdata concerning brain function that has previouslyproved elusive (I).

Ultrasound based imaging techniques comprise aset of methodologies capable of acquiring both quanti-tative and qualitative diagnostic information. Many ul-trasound based methods are attractive due to their abil-ity to obtain real time imagery, employing compactand mobile equipment, at a significantly lower costthan is incurred with other medical imaging modalities.The real time nature of ultrasound makes it possible forphysicians to observe the motion of structures inside apatients body. This ability has resulted in the wide-spread use of ultrasound technology in the fields ofpediatrics and cardiology. Equipment which employsdoppler echo techniques can extract quantitative veloc-ity information such as the rate of blood flow in avessel of interest. Additionally, the introduction of ul-trasound signals into a patient, at the levels currentlyemployed, has been determined to be safe (2). Thelack of negative effects from exposure, portability ofequipment, relatively low cost and quantitative acquisi-tion modes distinguishes ultrasound techniques as animportant class of medical imaging technology.

This paper provides an overview of most of thepopular imaging modalities currently in clinical use.The foregoing discussion limits the use of advancedmathematical concepts, instead employing intuitive de-scriptions of each medical modality. It is hoped that ageneral understanding of the modality from which animage is derived will help researchers in the subse-quent analysis of the image data.

The sections to follow include discussions of X-Ray CT (section 2), MRI (section 3), Emission CT(section 4) Biomagnetic source imaging (section 5),Digital Subtraction Angiography (section 6), and ultra-sound imaging techniques (section 7).

2 X-RAY COMPUTED TOMOGRAPHYX-ray CT or Computed Axial Tomography (CAT)

is a medical imaging modality which is capable ofnoninvasively acquiring a 3D representation of a pa-tients internal anatomical structure. This 3D represen-tation may be visualized from an arbitrary viewpoint,providing vital information for anatomical mapping,tumor localization, stereotactic surgery planning andmany other diagnostic applications (3).

Physicians have long utilized x-ray based imagingsystems for non-invasive medical diagnostics. In the

case of the conventional radiograph, a patient is placedin front of an x-ray source which transmits radiationthrough the subjects body. Each x-ray incident on thepatient is attenuated by the tissues it passes throughalong its linear flight path. Differing tissue types in thebody exhibit differing densities with respect to x-rayradiation. Each tissue type may therefore be assigneda value ,LL(X, , Z) which denotes the tissue density atCartesian coordinate (x, y, z). The line integral of thesetissue densities,

s= sL(x,y, z)dl. (1)is proportional to the attenuation experienced by an x-ray passing along the given path. A 2D projection im-age or shadow of these x-rays is imaged by measur-ing the x-ray energy leaving the patients body in some2D region of interest. Conventional radiography is alimited diagnostic modality, in the sense that it pro-duces a 2D projection of a 3D object. Consequently,a large amount of information concerning internal ana-tomical structure is unavailable to the radiologist.

X-ray CT is a modality that is built upon the samephysical principles that form the basis of conventionalradiography. Differing tissue types possess differentlinear attenuation coefficients. This fact is utilized inconjunction with x-ray shadows from multiple view-points in order to reconstruct a representation of inter-nal anatomical structure.

The data resultant from a typical CT scan consistsof a series of 2D axial slices of a patient which maybe stacked to form a 3D representation (see Fig. 1 a,b).Each 2D slice is a matrix of voxel elements containingthe calculated tissue density at each point within theimaged region. Though CT scans typically acquireslice data along the axial plane, it is possible to obtainplanar views from other orientations. A mathematicalshuffling of the information contained in the array ofstacked slices allows a viewer to examine the patientfrom any viewpoint. However, such manipulation ofthe image viewpoint results in a degradation of imagequality and detail.In a common CT configuration, an x-ray sourceis located on one side of the patients body and anarray of x-ray detectors is located on the other side.The x-ray source and detectors are connected in a fixed,collinear arrangement forming a gantry, as illustratedin Fig. 2. The x-ray detectors consist of an array ofsensors that produce electrical data proportional to theamount of incident x-ray information. This informationis stored in the memory of a data acquisition computerunit until it is needed for analysis. The gantry may berotated around the patient about an origin centered in


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CT Slice n Y

X(a) Reconstructed CT Slice Data

3-D Representation made up (b) Individual CT Sliceof 2-D Slices. Voxel Matrix

Fig. 1. Data representation of reconstructed CT data.

the axial plane. Improvements in 4th generation CTdevices make use of differing geometrical configura-tions of sources and detectors, but employ similarphysical techniques of image generation.

The imaging problem in conventional radiographyis essentially a single step. A patient is placed betweena fixed x-ray source and a x-ray detector, the x-raysource is enabled, and the resultant x-ray projectionsare captured in some useful manner. Conversely, theCT imaging problem can be divided into two distinctparts, slice data acquisition and slice reconstruction.

The slice data acquisition sequence is initiated byactivating a thin x-ray beam that spreads out and entersthe patient along the edge of a desired image slice (seeFig. 3). As the x-ray energy passes through the pa-tients body it will penetrate differentially through vari-ous tissue types. The total attenuation along a rayspath is related to a line integral of tissue densities takenalong that path. As each ray exits the patient it strikesan element in the sensor array resulting in a measureof linear tissue density along the rays path. The set

X-Ray Soured

of readings taken from the sensor array is then storedin computer memory. A single array measurement setfor a fixed angular displacement of the gantry containsseverely limited information. Therefore the gantrymust be rotated around the patient, allowing for theacquisition of tissue line density measurements at mul-tiple angular orientations about the center of the axialplane. If the gantry is rotated a full 180 around thepatient and a sufficient number of density measure-ments are taken, then an appropriate algorithm willreconstruct a 2D view of the slice imaged.

A patient undergoing a CT scan is placed typicallyon a movable couch around which is located the rotat-ing gantry. The data for each CT slice is measured oneslice at a time employing the methodology describedabove. After acquisition of the information for a sliceis completed, the couch automatically moves the pa-tient into the correct position to image the next slice.This process is repeated until data has been collectedfor the entirety of the volume of interest.

At the completion of the data acquisition phase

X-Ray DetectorAnay

Fig. 2. CT Scanner gentry.


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6 Computerized Medical Imaging and Graphics January-February/l995 Volume 19, Number Iof image formation, the CT computer holds informa- sity (with respect to water) of the tissues located withintion on the line integrals of tissue densities along multi- an individual voxel. The voxel number is calculated forple paths. This information can be combined to recon- each pixel by the CT reconstruction algorithm. Priorstruct the internal tissue densities within each slice of to image display, the CT numbers are quantized tothe CT scan. The most commonly utilized reconstruc- correspond to allowable gray scale values for the dis-tion technique is thejiltered buck projection algorithm. play system in use.Filtered back projection is the process by whichthe one dimensional projections measured at multipleangles are reconstructed into the final slice matrix.Each slice is reconstructed individually and the re-sulting slices are stacked to form the final 3D CT repre-sentation. The scan and rotate data acquisition se-quence, which a CT machine employs for each slice,results in the data set (4).

2. I Dynumic spatial reconstructor (DSR)The Dynamic Spatial Reconstructor (DSR) is a

X-Ray CT scanner capable of providing dynamic syn-chronous volume 3D CT images, every l/60 s (5).The DSR has 14 source-detector pairs. Each sourcegenerates a cone beam which penetrates the subject tocreate a 2D image at the detector. The gantry rotates1S every l/60 s resulting in 14 new projections everyl/60 s. Reconstruction employing these 14 view, pro-jection data sets results in a 3D volume correspondingto the highest temporal resolution. Several such recon-structions, each corresponding to adjacent time inter-vals, can be combined to obtain a desired spatial reso-lution. Special reconstruction algorithms have beendesigned to exploit the temporal nature of the DSRscanner (6).

where n is an integer denoting a sensor element in thex-ray detector array and 19 is the angular position ofthe gantry.

The reconstruction is performed by first filteringthe one dimensional projections g(n, 0) appropriately.This filtering produces the data set

2(fl> f)) = R(n, H) 0 h(n), (3)where @ denotes convolution and h(n) is an appro-priate high pass filter.

The contents of the&n, 8) data set are then back-projected onto the slice data matrix. Back projectionis performed by the operation:

f(x. y) = s * (x cos 0 + y sin 8, 19)dB. (4)0wheref(x, y) is the reconstructed slice data set. Afterthis back-projection process is completed the slice ma-trix will contain voxel data corresponding to a slice ofthe patients body. A stacking of the reconstructed slicematrices results in a 3D CT volume representation.This 3D data set may then be manipulated to providevisualizations of the anatomical data from viewpointsother than the axial plane, provided that slices wereacquired without a significant gap between them.The product of the filtered back projection algo-rithm is an array of 2D matrices containing recon-structed voxel data points. In many imaging applica-tions image elements possess no depth, and are termedpixels or picture elements. In the case of CT each ofthe imaged slices has a certain thickness which mustbe taken into account. Therefore, each matrix elementin the reconstructed slice actually represents a tissuedensity within some volume element or voxel. Eachelement in the reconstructed slice matrix is assigned aCT number. This CT number is a measure of the den-

2.2 Cardiovascular computed tomogruphy (CVCT andCine CT)

CT imaging, as discussed in section 2, is a versa-tile modality with which to acquire 3D imagery of apatient. However, due to mechanical limitations, CTis best employed when the anatomical area to be im-aged has characteristically little motion. Consequently,the head region is an excellent candidate for CT im-aging studies. Non-static anatomical areas, such as thecardiac region, cannot be examined adequately usingtypical CT technology. The cardiovascular computedtomography scanner (CVCT) was developed to over-come the aforementioned difficulties that CT encoun-tered when imaging the dynamic cardiac region. Themore recent Cine CT or lmatron Cine CT scannershave offered advanced versions of the earlier CVCTunits.

CT scanners typically rely upon the mechanicalmotion of either the radiation source, detector, or both.Popular geometries for mechanical scanning include:translate-rotate, rotate-rotate, and rotate-stationary ge-ometries (7). The basic imaging processes inherent toCT image acquisition are discussed in section 2. Dueto physical constraints, the gantry can be rotatedaround the patient at a maximum rate of approximatelyonce every second. Due to the relatively slow motionof the gantry with respect to the dynamic system beingimaged, accurate visual data cannot be acquired. Inorder to image a non-static system, the CT apparatus


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CT Scan Employing A RotatingGantry and Adjustable Couch

Fig. 3. CT Scanner methodology

must be able to acquire imagery significantly fasterthan the systems rate of change. If image acquisitionis rapid enough, a single reconstructed image can beviewed as having occurred at a single instant of time.Consequently, a series of such high speed imageswould present a visual record of a systems motion.Due I:O the data acquisition techniques employed inCT, rapid image formation requires that the gantryrotate at high speeds. In the case of cardiac imagery,the acquisition time required, for each complete imageis of l.he order of milliseconds. Due to the mechanicalnature of the CT gantry such rotation speeds are notfeasible.

The rate of CT image acquisition can be increasedsignificantly by replacing the mechanical gantry sys-tem with an electrostatic scanning apparatus. As al-luded to previously, the angular sampling rate (4) mustbe increased in order to achieve clinically useful mo-tion imagery of the heart. Electrostatic scanning tech-niques are capable of generating angular sampling ratesat least an order of magnitude higher than those possi-ble via mechanical systems. The common televisionemploys a form of electronic scanning. An electronbeam is scanned over the television surface in orderto produce the desired picture. The beam is rapidlyswepl across the entire viewing area of the screen. Aslong as the beam is swept at a high enough rate, eachpixel on the televisions monitor appears to be illumi-nated simultaneously. Such a common example illus-trates the high speed capabilities of electrostatic scan-ning methods.

The cardiovascular computed tomography scan-

ner (CVCT), developed between 1978 and 1982 uti-lizes electronic scanning. It is capable of providingmultiple 1 cm. slices through the heart at scan rates of50 ms. The scanner consists of an electron beamsource, deflection coils, stationary target rings, detectorrings, and a data acquisition system (7). Electronbeams are generated at the head of the scanner. Thesebeams pass through deflection coils which direct themtowards one of four target rings. The target rings arelocated below the patient under the region of interest.

Each target ring corresponds to two adjacent slicesin the subject. The target rings redirect the incidentelectron beams upward through the patient. This radia-tion passes through the patient as in the case of CT.The radiation exiting the body is collected by detectorrings on the anterior side of the patient. The angularprojection information collected can be varied elec-tronically in such a system. Deflection coil characteris-tics may be altered electronically. Such changes inthe coils characteristics modify the angle at whichprojection data is obtained. This angular measurementposition may be varied rapidly, resulting in the collec-tion of data at a significantly higher rate than is possiblein mechanical systems. CVCT scanners employ thediscussed methodology to capture cardiac imagery ata high enough rate to allow for motion analysis of aheart under study.

3 MAGNETIC RESONANCE IMAGINGMagnetic resonance imaging represents a major

innovation in medical imaging technology. MR im-


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e-.......................................................................................................................................................................................................................................................................................................................................................... .s ................................................................................................ < ....................Fig. 4. Simplified view of nuclear magnetic resonance

aging can provide detailed images of the human bodywith unparalleled soft tissue contrast in a non-invasivemanner. The phenomenon of nuclear magnetic reso-nance (NMR) is relatively new to the field of diagnosticmedicine. The technique itself, has existed for over 45yr in the field of physical chemistry. NMR was firstdiscovered in 1946 by Bloch and Purcell, two research-ers working independently at Stanford and Harvard,respectively. Both were awarded the Nobel Prize in1952 for their work.3. I Mupetic resonance

Resonance, in the physical sense, is defined asthe absorption of energy from a source at a specificfrequency, often called the natural or resonant fre-quency. In the case of MRI or NMR the source isradiofrequency (RF) energy, and the object resonatingis the nuclei of atoms, while in an external magneticfield. Nuclei are promoted to a higher energy state viathe absorption of the RF energy. The higher energy orexcited state cannot be indefinitely maintained. Conse-quently the nuclei release energy in order to return totheir lower energy or ground state. RF energy is re-leased by the nuclei when the ground state is returnedto. This emitted RF energy can be referred to as theMR signal. The characteristics of the MR signal aredependent upon the specific molecular environment ofthe emitting nucleus. Diverse types of information canbe collected concerning a molecular environment fromthe MR signal. Figure 4 is a simplified version ofNMR. The bar below each side represents the energyin the system.3.2 Nuclei properties in external magnetic jields

MR imaging can not be applied to all nuclei. Nucleimust be either rotating, and therefore possessing angularmomentum (spin), or must possess an odd number ofprotons or neutrons. Only nuclei with these characteris-tics can be made to resonate. Since nuclei possess elec-tric charge, their spinning produces a magnetic moment,G, aligned on the axis of the spin. fi is a vector quantityindicating the strength and direction of the magnetic

field surrounding the nucleus. Hence, a spinning nucleiis a dipole (having two poles), and may be thought ofas a microscopic bar magnet (Fig. 5).

In the presence of an external static magnetic field,spins will align with the external field, similar to themanner in which a bar magnet would align in the samefield. Quantum physics dictates that a proton has onlytwo allowable quantum states as its spin quantum num-ber, I = l/2. These two states are the parallel (spinup) and antiparallel (spin down) states, pertaining tolow and high energy states respectively. Additionally,these states are slightly askew with respect to the exter-nal field direction (Fig. 6).

A nucleus containing a single proton is the princi-ple isotope of hydrogen. Hydrogen, H is the elementof preference in MRI since H has a high natural abun-dance, and has a high sensitivity to its MR signal.

Hydrogen is the most common element found inbiological tissue, concentrated in tissue water. 99% ofall hydrogen isotopes encountered are H (i.e. one pro-ton and no neutrons).

A nucleus sensitivity to its MR signal is ex-pressed in terms of its gyromagnetic ratio, y. The gyro-magnetic ratio represents a nucleus resonance fre-quency in a 1 Tesla external field. y is a nuclearconstant for every isotope. Sensitivity increases pro-portionally with signal frequency. Hydrogen has thelargest gyromagnetic ratio and therefore has the largestMR signal sensitivity.

When subjected to an external magnetic field,henceforth denoted by &, protons align with the fieldand simultaneously experience a torque due to B,,. Asa result, they precess about the & axis at a rate givenby the Larmor relationship.

,f;l,r,,,,>, Y&j. (5)where B(, is measured in Tesla (T) and y has unitsof MegaHertz per Tesla (MHz/T). For example, the

The terms spin and dipole will be used interchangeablythroughout the section, as both are identical for our discussion.

a Tesla is a unit of measurement for magnetic t&Ids.


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Biomedical imaging modalities l R. ACHARYA et al.

Fig. 5. Magnetic nuclei act like microscopic bar magnets.

resonance frequency of the hydrogen nucleus (y =42.58 MHz/T) with an external field strength of I Tesla(B, = 17) is 42.58 MHz. An illustration of precessionis presented in Fig. 7.

The effects of an external magnetic field, BO, upona single hydrogen nucleus have been discussed. Theseresults can be extended to a group of protons, analo-gous to a small volume of tissue.

Within any external magnetic field, there will al-ways be a small net excess of spins within a givenvolume aligned in the parallel (lower energy) state asopposed to the antiparallel (higher energy) state. Thisexcess parallel state population is represented by thenet magnetization vector, &l. k increases in direct pro-portion to external tield strength, B,). {See Fig. 8).

The net magnetization vector (M) is ultimatelyresponsible for the emitted MR signal. The need forpowerful magnets in MR imaging is apparent fromfigure 8. If k is maximized then so is the resultantMR signal. The subatomic MRI description is nolonger needed for the purposes of this paper. All thatneed be understood is that a net magnetization vectorexists. k, representing the aggregate magnetic state ofour tissue volume.

At this time, it is convenient to introduce a coordi-nate system for further discussions. The patient isplaced inside a gantry, which houses the hardware nec-

essary to create the magnetic fields required for MRimaging. The static magnetic field, &,, is taken to bein the z direction, from caudal to cranial. The xy plane,referring to axial or transverse slices through the pa-tient, is defined as x from left to right, and y posteriorto anterior.

M can be oriented in any direction, unlike ,G, whichhas only 2 orientations (parallel and antiparallel) (8).3.3 MR imaging process

Prior to imaging, fi is in its equilibrium position,aligned along the z axis of the gantry. There is nodetectable MR signal before the imaging sequence be-gins. The MR receiver coils are oriented such thatonly the component of fi in the transverse (xy) planeinduces a measurable signal. Components of & in thetransverse direction are referred to as transverse mag-netization, and the components along the z axis aslongitudinal magnetization. During the imaging pro-cess RF pulses modify k. This interaction, results inthe emission of RF energy which is then detected inthe receiver coils. As mentioned previously, this emit-ted RF energy is referred to as the MR signal.

Transverse magnetization is created by a RF field,denoted B,, applied in the transverse plane. If the RFfield is oscillating at the lurmor frequency k will mu-tate from its equilibrium alignment along the z axis.

Fig. 6. Nuclei alignment in external magnetic fields.


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Bo,.... t~,~,_,.,._..~~..............._..,&. ._. I., .__........:::.:::,::.:.:.:..lpig. 7. Nuclei precession in external magnetic fields.

There are two methods for visualizing this transition,stationary and rotating frames of reference (Fig. 9). Astationary frame of reference views the transitions fromoutside of the system. A complex spiralling motion isviewed due to spins mutated from their equilibriumposition while simultaneously precessing. In the caseof a rotating frame of reference the system observation

point is situated above the system and rotates at thela rmor frequency. Such a reference eliminates the pre-cessional component of the spins motion. Conse-quently, the rotation of the k vector from equilibriumcan be simply viewed. A rotating frame of referencewill be assumed throughout the rest of this discussion.The flip angle denotes the displacement overwhich k is rotated from equilibrium after the applica-tion of an RF signal. Figure 9 illustrates a 90 flipangle. Increasing the RF pulses power will cause aconsequent increase in the resultant flip angle. Flipangle can be determined by the relationship

0 = yB,r. (6)where t is the time duration of the RF pulse. Any flipangle is attainable.

Varied combinations of RF pulses and timing rela-tionships constitute a MR pulse sequence. Pulse se-quences can be employed to extract differing informa-

_.I.----- ...3.r >- ....xc. ..--. ._._.. ......... ..-


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Biomedical imaging modalities l R. ACHARYA et al. II

Fig. 9. Frames of reference in MR imaging. (a) Stationary frame. (b) Rotating frame.

tion from tissues. Section 3.4 discusses informationthat can be extracted from tissue via MRI techniques.

3.4 7issue characterizationThe impressive diagnostic potential of MRI de-

rives from its ability to provide a means of characteriz-ing both normal and pathological tissues. Hydrogen ispresent in nearly all tissues, therefore it can be assumedthat MRI data can be collected from nearly all tissues.Images of tissue hydrogen concentration, p[H], can beobtained by MRI techniques. However, variations inhydrogen concentration between tissues are quite smalltypically, yielding only moderate contrast images.Consequently, hydrogen concentration images are oflimited clinical interest.

The most clinically useful information lies almostentirely in the behavior of regional hydrogen, ratherthan its regional concentration. The molecular environ-ment influences the behavior of nuclei, which in turninfluences the characteristics of the MR signal. In thecase of MR imaging the hydrogen nuclei within a tissuevolume are observed, and characteristics about its mag-netic environment are inferred.

Several tissue-related factors influence the emittedMR signal. The most important of these are the relax-ation times. For brevity, only the relaxation time fac-tors will be discussed. The interested reader may referto (8, 9), for discussions of other MR signal influencingfactors.

Relaxation refers to the process by which the spinsrespond to the disrupting effects of both their environ-ment and external RF pulses. There are two types ofrelaxation, T, and T2 relaxation. MR signal strength ismore dependent on T2, hence this method first will bedescribed.

3.5 T2 relaxationThe MR signal decays within an exponential en-

velope with time constant T2. The MR signals decayis related to the loss of phase coherence between pre-cessing spins. This is most easily understood by meansof an example. (See figure 10).

Figure 10a presents a finite volume of tissue con-taining 4 nuclei at equilibrium. Three of the nucleisspins are in the parallel state and one is in the antiparal-lel state. All of the illustrated nuclei are precessing atrandom phase angles with respect to a point in thetransverse plane. Hence their transverse componentscancel and M,, = 0. The slight excess of spins in theparallel state creates a net magnetization componentin the z, direction, M,. Figure lob illustrates the nucleiof IOa after an RF pulse at the larmor frequency isapplied such that one of the nuclei absorbs energyresonantly, and is excited into the antiparallel state. Inaddition to promoting nuclei 3 to the antiparallel state,the RF pulse also creates phase coherence between thespins (9, 10). In this case, pi for i = 1, . . , 4 allproject onto the same spot in the transverse plane.Consequently, the vector sum of the transverse compo-nents produces a large net transverse magnetization,M,, f 0. Projections onto the z axis will thereforecancel, and A4? = 0. M,, is responsible for the resultantMR signal. Initially, M,, is large, and for the instantlyapplied pulse is equal to MZ at equilibrium. This repre-sents a RF pulse with a 90 flip angle. Figure 1Oc isequivalent to 1Ob except that arrows now correspond toindividual nuclei projections onto the transverse plane(i.e., fi.r ,,, for i = 1, . . , 4). Figure 1Od illustrateslocal magnetic field inhomogeneities creating differingeffective magnetic environments about each nuclei. Asa result, nuclei precess at slightly different rates, given


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Fig. IO. Tz relaxation: (a) System prior to pulse sequence. (b) After 90 RF pulse. (c) Transverse magnetization.(d) Dephasing proceeds to reduce transverse magnetization. (e) Spins are completely dephased, and transversemagnetization disappears.

by Eqn 4. As demonstrated by Eqn 4, nuclei in strongerfields precess faster, while those in weaker fields, moreslowly. As a result, the vector sum of transverse com-ponents is no longer a maximum. A smaller IV,,, willthen result in a weaker MR signal. As time progresses,the MR signal disappears due to dephasing processes.This is illustrated in Fig. IOe. After a sufficiently longtime, transverse components of the spins return to com-pletely random phases. Consequently, there is no de-tected signal.

Figure I 1 illustrates a typical MR signal knownas the free induction decay (FID). The decay envelopecorresponding to Tf effects is much sharper than thatof T,.

Two types of local field inhomogeneities arecaused by dephasing. Dephasing effects resulting frommicroscopic intrinsic field variations only are termed

T2. T, is a measure of how long it takes for M,,, todecrease, dependent upon intrinsic microscopic mag-netic inhomogeneities only. It is a characteristic param-eter of tissue. Dephasing due to both microscopic fieldvariations as well as external static field (B,) inhomo-

Fig. II. T2 and TT decay envelopes, FID shown within Tfenvelope.


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Biomedical imaging modalities l R. ACHARYA et d. 13

Fig. 12. T, relaxation: (a) System a equilibrium. (b) After RF 90 RF pulse. (c) Longitudinal component after ashort duration of time. (d, e, f) successively longer times.

geneities is referred to as T$ T$ is significantly shorterthan :f,, as static field inhomogeneities are many ordersof magnitude greater than microscopic field variations.Figure 11 illustrates the decay envelopes for both typesof decay. The FID is shown within the T$ envelopein figure 1 1. Information concerning T$# largely repre-sents characteristics of the scanners external static field.Methods exist to remove the effects of external fieldinhomogeneities (8- 10). The decay envelopes are expo-nential in nature, with 63% of the signal decaying afterone lZ interval and 84% after two T2 intervals, etc.3.6 T, relaxation

KF stimulation at the larmor frequency causesnuclei to resonantly absorb energy. In order for thesystem to return to equilibrium, energy must be re-leased, i.e., some spins must return to their parallelorientation. This energy is released into the molecularenvironment.

jr, is also an exponential time constant. It repre-sents the rate at which M, returns to its equilibriumvalue. This concept is most easily understood in termsof k (Fig. 12).

Figure 12a illustrates a system at rest (i.e., thelongitudinal component is at a maximum). Figure 12bpresents the system of 12a after being disturbed by a90 RF pulse. Immediately following the pulse, the netmagnetization in the z direction is zero [i.e., MZ = 0(see section 3.5)]. Figure 12c illustrates the longitudi-nal component, MZ, after a very short period of timerelative to T, . As time progresses, more energy is re-leased, and MS begins to grow toward the equilibriumvalue (12(d,e)). After a sufficient time interval, thesystem has returned to its initial state (illustrated inFig. 12f).

T2 and T, relaxation occur simultaneously, and arelargely independent. After a time interval of approxi-mately 5T2 the systems phase coherence has beencompletely lost. This dephasing occurs much more rap-idly than the release of energy to the surroundings(8, 11). Combining figures 10 and 12 illustrates therelaxation processes occurring simultaneously, withFig. 10 occurring between (b) and (c) in Fig. 12.

Through proper RF stimulation, in the form ofpulse sequences, it is possible to acquire informationregarding either of the two discussed tissue characteris-tics (8, 10). MR images created from sequences em-phasizing T, information are known as T, weightedimages. Images emphasizing T2 are analogously re-ferred to as T2 weighted. Within every pulse sequence,there is a specific time interval during which MR datais acquired. We shall refer to this time period as TE.Via proper selection of TE, it is possible to obtain goodcontrast between various tissue types whether normalor pathological. T, and T2 tissue contrast concepts areillustrated in Fig. 13.

It has been found that pathology often exhibitsT, and T2 values differing from surrounding healthytissue.3.7 Sputi$ localization in MR imaging

This section begins a discussion of methods withwhich to generate clinically useful image data by utiliz-ing the theoretical results of the past sections. Ideally,we would like to somehow divide tissue into tiny vol-ume elements, referred to as voxels. Voxels must havea finite volume in order to contain enough nuclei toproduce a measurable signal. Voxels need not be cubic,and are often elongated rectangles. The use of cubicvoxel will be assumed, without loss of generality.


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14 Computerized Medical Imaging and Graphicssignal

January-February/l995, Volume 19, Number Isignal

TISSUECONTRAST

TE TE wa) b)

Fig. 13. (a) TZ and (b) T, tissue contrast.

Spatial localization of these voxels is achievedthrough the use of magnetic field gradients. Magneticgradients are weak nonuniform magnetic fields, atmaximum a few percent as powerful as the static mag-netic field &. Gradients are superimposed over thestatic field to create a spatially varying magnetic fieldin the tissue (Fig. 14).

The effective magnetic field experienced by a pro-ton after superposition of a gradient is B0 + G,x. Ateach location along the direction of the gradient, thereis a unique magnetic field. Therefore, by Eqn 4, therewill also be a unique larmor frequency for each posi-tion along the direction of the gradient, given by

.fL?!,,, = y&, + r(G, .x1. (7)where the term on the right is the larmor frequencyadjustment due to the presence of the magnetic gradi-ent. The gradient technique results in spatial locationbeing encoded into the frequency of the MR signal.

There are several methods for spatially localizingthe MR signal. The methods to be reviewed fall into

+ Gx

B, + Gx

Fig. 14. Magnetic field gradients add to the static externalfiled, resulting in a spatially varying magnetic field.

either 2D (planar) strategies, or 3D (volume) strategies.The planar strategies will be considered first, as the3D strategies are simple extensions of 2D techniques.

3.8 Plunar data collectionWhen planar techniques are employed, the first

step is to select a plane through the tissue under investi-gation (Fig. 15). A plane is selected by applying agradient in the z direction to a volume of tissue ina uniform magnetic field, BO. Each location along zexperiences a unique magnetic field, and consequentlya unique larmor frequency (Eqn 6). Each point alongz defines a x-y plane in our coordinate system. Allnuclei in this plane experience the same magnetic fieldand will resonate at the same frequency. If a 90 RFpulse is applied, corresponding to the larmor frequencyat z,~, the entire plane z = Z, will acquire a non-zerotransverse magnetization, Mxy (Fig. 10). Any MR sig-nal subsequently received will be from protons in theselected plane only. This process is known as plane orslice section.

All protons in the selected plane z = z,, will pre-cess at ,fLZ,nn,,r y& + Y(G_~-z,,). The slice selectiongradient is then removed. Protons return to precessingat the rate given by equation 4. The only volumes(planes have a finite width) with non-zero transversecomponent are those in the plane z = z,,.

3.8.1 Polar data collection. Polar data collectionis the simplest of collection strategies, and provides theclosest analogy to transmission tomography. A slice isfirst selected via gradient techniques as described insection 3.8. At signal measurement time, TE, additionalgradients are applied in both the x and y directions, G,and G,. This subjects all protons at an angle (b = arctanG,/G, to the same magnetic field, i.e., there is a gradientalong the C#J 7r/2 direction. The simultaneous applica-


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Biomedical imaging modalities l R. ACHARYA et l.

Bo + G, :::.::::::.:.:;.:..:...:.:,:......:.:.:.:.:.:.::.:::.:.::::::::::~,.: ,.,.

Fig. 15. Slice selection utilizing a z gradient,

tion of GX and G, divides the selected plane into lines(Fig. 16).The information received from the slice is com-posed of several frequencies. Each frequency repre-sents the combined signals of protons along a linethrough the plane. The information may be arrangedsuch that data is acquired on equally spaced intervalsalong, the direction 4 + 7r/2. This method results in aprojection of the tissue in the selected plane beingmeasured. Projections are collected for 0 5 4 < 7r,allowing the use of computed tomography reconstruc-tion algorithms, such as convolution/filtered back pro-jection for image reconstruction.

3.8.2 2-D Four ier transform collection, 2DFT .The polar collection strategy consists of slice selection,followed by simultaneous application of G, and G, toreduce dimensionality from a plane to a line. Conse-quently, backprojection is required to reorganize infor-mation into an image. Two Dimensional Fourier Trans-form imaging allows the further segmentation of a lineinto pixels (image pixels represent physical voxels). It

Y 9 plane z = zp. . .>.:::::::::.:.:.:.:.:::::::::.,. .T ,.:>:,.,I::i:j:j:::;:..:.:.:.:.~.:~~,.,,i::,:::::j:j:i:I:i:j:::::::.::.:::::,::~:::.:i:i:I:!I:::~

t- ~~~~~~~---,: .::::(::,:::,::,:::::,:~:~~:~:,::;,'..::j:j::::'::::.::.::.:::::.j.>:.,.>..,.~.:.. .v.:...:.:.......~::.:.:::::::::j:jj:I:I:~:~:~:.../v.:.:.: . .. ,:..:............,.....,:.:....................~........'.:::::::::.:.:::,::)


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16 Computerized Medical Imaging and Graphics January-February/l995. Volume 19. Number I

Ine widthf(q) f(x2) f(Xj) . . . . . . . . . f(xM)

Fig. 17. Locations in space have a unique pair of frequency and phase values.

Imaging Time = TR* N* NEX. (8)where TR = time to repetition; the time it takes forthe plane to return to equilibrium such that it may beexcited again. N is equal to the number of phase encod-ing steps for 2DFT imaging, and the number of angularviews for polar collection. NEX is equal to the numberof excitations; the number of times the entire imagingprocess will be repeated (used for signal averaging toimprove signal to noise ratio). For TR = 1.5 s, N =120, and NEX = 2, the time required to collect thedata necessary to image one plane is 384 s. For 20slices, each 1 O mm. thick, the scan would require over2 h. It is easy to see how imaging time could begin tobe a practical problem. Fortunately, there exists fastimaging techniques as well as multislice methods tominimize the scan time and optimize patientthroughput (8, 13).

3.9 3DFT and spherical imaging3DFT Imaging is a simple extension of 2DFT

imaging. The only difference is that there is no sliceselection. Information for an entire volume is obtainedby phase encoding in 2 directions (z and y). and fre-quency encoding in the x direction.

Spherical imaging involves simultaneous applica-tion of G,, G,., and G,. These gradients are adjustedsuch that samples are obtained in full azimuthal andpolar increments.

3.10 Recent advances in magnetic resonance imagingRecent advances in high speed imaging allow

cross sectional images to be obtained in extremelyshort periods of time. This opens a new horizon forthe use of MRI. The clinical potential of observingmotion in both normal and pathological tissue is devas-tating.

Let us assume that it is possible to generate MRimages rapidly enough to observe motion in a singleplane. For many processes, this is currently possible. Itis often desirable to study the motion of tissue betweenconsecutive time frames. Image processing techniquescould be employed to identify tissue contours, and themotion of these contours tracked. However, even ifthe contours could be properly found, and the corre-spondence problem solved, any motion seen wouldsimply be that of the inner and outer surfaces of thetissue. Nothing would be known about the motion oftissue between the surfaces. Identifiable and trackablelandmarks are needed within the tissue, just as thecontours are for the outside of the tissue. Several pre-imaging pulse sequences have been suggested to createsuch landmarks. These pulse sequences are appliedprior to the imaging sequence, and alter the magneticproperties of tissue in such a way as to create land-marks. Since magnetization is a property of tissue,when the tissue moves, the magnetization moves withit. Three of these sequences are described below. Thesemethods are collectively referred to as tagged MRI.


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Biomedical imaging modalities l R. ACHARYA et al. 17

Fig. IX. Tagging profile created by selectivity excitingplanes.

3.10. I Selective tugging. Selective tagging, intro-duced by Zerhouni, et al. (14), involves perturbing themagnetization of protons in specified lines, such thatthese regions exhibit no MR signal. Dark bands areconsequently produced in the image. Typically theselines are oriented in a polar fashion (Fig. 18). Selectivetagging is useful for observing motion most easily seenin polar coordinates, such as the twisting motion ofthe heart.

3.10.2 Spatial modulation of magnetization. Spa-tial modulation of magnetization (SPAMM), intro-duced by Axel and Dougherty (l5), makes use of manyprinciples common to 2DFT imaging. This methodcreates a series of evenly spaced stripes in any direc-tion. For two orthogonal directions, a grid-like patternis produced (Fig. 19).

The intersection of grid lines creates trackablemarkers in the tissue. Motion parameters may then be

Fig. 19 Tagging profile created by spatial modulation ofmagnetization.

estimated based upon motion of these non-invasivemarkers.

3.10.3 Striped tagging. Striped tagging (STAG),introduced by Bolster, McVeigh, and Zerhouni (16),is a hybrid of the above two techniques. A series ofevenly spaced beads are produced along any line. Themotion of these beads may then be followed (Fig. 20).

The choice of tagging sequence employed islargely application dependent. Tagging in Fig. 18 andFig. 20 were introduced artificially for illustration pur-poses. Actual tags are not as distinct as shown here.

3. I I Summary Magnetic Resonance Imaging of-fers an abundance of diagnostic information. An inher-ent physical advantage MRI has over CT, PET,SPECT, and other imaging modalities is that imagesmay be collected physically from any plane throughthe volume. The other modalities are limited totransaxial or close to transaxial images. There is awealth of literature regarding MRI principles, imaging,and pre-imaging techniques (8- 11, 17).

4 EMISSION-COMPUTED TOMOGRAPHYEmission-computed tomography (ECT) has been

widely employed in biomedical research and clinicalmedicine during the last two decades. ECT differs fun-damentally from many other medical imaging modal-ities in that it produces a mapping of physiologicalfunctions as opposed to imaging anatomical structure.In the case of transmission mode modalities such asX-ray CT discussed in section 2 a source of radiationis external to the patient and is perfectly localized be-fore the process of reconstruction. The basic purposein transmission tomography is the mapping of the ab-sorption coefficient distribution. Internal structuralviews can then be reconstructed utilizing the absorp-tion distribution.

Fig. 20. Profile created by striped tagging.


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1X Computerized Medical Imaging and Graphics January-February/1995 Volume 19. Number IIn the case of positron emission tomography

(PET) and single photon emission (SPECT) (whichconstitute the two different modalities of ECT), theradiation source utilized is a radioisotope compoundthat has been introduced into a patients body. Theradioactive compound is metabolically distributed intovarious organs and tissues and no a priori informationconcerning the radiations location is known. The maingoal of ECT is the determination of the isotope com-pound distribution within a patients body. Measure-ments are taken of radiation leaving the patients bodyusing a specially designed detector system. The detec-tor readings are employed as input to a reconstructionalgorithm to produce the internal isotope compounddistribution.4. I Single-photon emission computed tomogruphy

SPECT imaging techniques employ radioisotopeswhich decay emitting a single gamma photon. Thisrepresents the fundamental difference between PETand SPECT. PET systems employ isotopes in whicha couple of photons are produced in each individualannihilation. There are a rich variety of isotopes thatdecay, emitting a single-photon and which conse-quently can be utilized in SPECT. Some of the mostcommonly employed isotopes are Tc-99m, I- 125 andI- 13 1. These isotopes present the advantages of beingproduced at relatively low cost and of having long halflives. The long half lives of these isotopes permits theirproduction in a laboratory external to the hospital.

When the nucleus of a radioisotope disintegrates,a gamma photon is emitted with a random directionwhich is uniformly distributed in the sphere sur-rounding the nucleus. If the photon is unimpeded bya collision with electrons or other particle within thebody, its trajectory will be a straight line or ray.

In order for a photon detector external to the pa-tient to discriminate the direction that a ray is incidentfrom, a physical collimation is required. Typically,lead collimator plates are placed prior to the the detec-tors crystal in such a manner that the photons incidentfrom all but a single direction are blocked by the plates.This guarantees that only photons incident from thedesired direction will strike the photon detector.

When a gamma photon collides with matter in apatients body, photoelectric absorption and Comptonscattering effects occur. These two type of interactionscan be summarized as:l photoelectric absorption: The photon hits an atom

and its energy is essentially transferred to the atomor to an electron. The particular gamma photon in-volved in this collision will consequently not bedetected by the detector system.

l Compton stuttering: The photon strikes one of theelectrons surrounding an atom and the gamma rayis deflected from its original path. The photon con-tinues in a new direction with reduced energy. Thisparticular photon may be detected by the camera,however information on its original path will be lost.

Most modem detector systems consist of stacked,circular detector arrays. These detector arrays are oftenreferred to as x-ray cameras. Each detector crystal pro-duces an electrical pulse when it is struck by a gammaphoton. The electrical pulses are counted by supporthardware and provide a measure of the number ofphotons incident on each detector in the array duringthe interval of measurement. The sensor arrays areconstructed so that the photon detection process takesplace in one plane or slice at a time. Therefore, onlythe gamma rays that lie in this plane will have a chanceto be registered or detected.

Considering the collimation process, interactioneffects, and measurements being limited to a singleslice, one can note that only a small percentage ofthe original number of the emitted photons will beregistered by the detector apparatus. A typical percent-age is 5% or less. The number of emitted photons cannot be increased limitlessly since this would representan increase in the gamma ray energy that the patientis exposed to. It seems that these constraints are im-plicit in single photon emission tomography and efti-cient reconstruction algorithm design must take opti-mal advantage of the measurement counts of thedetector arrays.

In order to avoid further information loss, the reg-istration efficiency of the detector crystals must beclose to 100%. The most commonly employed detectorfor SPECT applications is a thallium-activated sodiumiodide single crystal due to the relatively high atomicweight of iodine and consequently good gamma-rayabsorption properties. Crystal thickness selection musttake into account the trade off between spatial rcsolu-tion and sensitivity; thick crystals absorb more gammarays but exhibit poor resolution while thin crystals havegood resolution and poor sensitivity. Typically, thecrystal thickness lies between 0.375 to 0.5 inches.When a gamma-ray photon enters the crystal a fastelectron is formed due to either photoelectric effectsor Compton scattering with the crystals iodide ions.When this electron decelerates due to interactions withthe crystal, a scintillation is produced. This radiationof visible light is sensed by a photomultiplier tube andis converted to an electrical pulse.

Scattering and attenuation of gamma photonswithin a patients body produce inaccuracies in the


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Biomedical imaging modalities l R. ACHARYA et al. 19estimation of radioisotope distribution. After a Comp-ton interaction with an electron, gamma photons losea portion their original energy and proceed along analtered trajectory. If such an altered photon is detectedby the camera, the apparent position of the photonsoriginal emission point will be the location of theCompton interaction. This incorrect determination ofthe photons point of initial production results in aninaccurate estimation of the radioisotope distribution.If attenuation effects were ignored the resultant under-estimation of the radioactivity concentration wouldmake most clinical analysis impossible. A large num-ber of the scattered photons can be eliminated fromthe registered photons by employing the fact that radio-isotopes generally emits one or two groups of photonsof well-defined energy. Therefore the electronics ofthe detector system can be designed in such a way thatonly the photons inside an energy acceptance windowbe registered. However this window can not be infini-tesimally small in practice and we still have a good dealof the scattering problem. One simple approximation toimprobe the distribution estimation is to assume thatthe transaxial contour of the patient is an ellipse andconsists of a single tissue type with an uniform attenua-tion. A more accurate method is to employ additionalattenuation measurements using an external gammasource. A simplified attenuation map of the transaxialsection can be used as additional information in theattenuation-correction reconstruction algorithm.

The resolution of an image refers to the degreeof discrimination that is possible between two small,closely placed objects. When an image reconstructionof a single point of radioisotope concentration is per-formed, a bell-shape plot is obtained that approximatesa Gaussian curve. Typically, the spatial resolution isdefined as the width of this curve at half its maximumheight (full width at half maximum, or FWHM). Atypical transaxial resolution in SPECT ranges from 10to 20 mm which is significantly poorer than the fineresolution achieved in transmission tomography (l-2mm). Resolution in the axial direction specifies theslice thickness and is determined by the collimationproperties of the detectors; typically the axial resolu-tion ranges from 10 to 20 mm.4.2 Positron emission tomography

The distinguishing physical feature of the radionu-elides used in positron emission tomography (PET) isthat they decay via the emission of positrons. Whenthis emission occurs inside a patients body, the posi-tron travels a short distance, approximately 1 mm, be-fore its motion is slowed enough to find a nearby elec-tron and interact with it. A positron is the anti-particle

of an electron and is almost identical to it, except thatpositrons possess a positive charge. When a positronand an electron interact, their masses are convertedinto two photons traveling in opposite directions alonga nearly collinear path. This physical process occursfor every matter-antimatter particle pair interaction andit is known as a pair annihilation. Each of the annihila-tion photons possesses a high energy (5 11 keV). Thisenergy is equal to one half of the energy correspondingto the particles mass.

Annihilation radiation produces high-energy pho-ton rays with opposite collinear trajectories. This per-mits a unique opportunity to detect the direction oftravel of these photons without the use of a physicalcollimator. This is performed by placing two positronsensitive detectors on opposite sides of the patient. Thesimplest PET scanner consists of a circular array ofgamma detectors equipped electronics that can deter-mine instances of gamma rays being simultaneouslyincident at two detectors. When two photons strike thetwo members of an opposing pair of detectors in thesensor ring, the system records a coincident event.A coincident registration usually implies that the anni-hilation occurred somewhere along the line defined bythe 2 detectors. These coincidence registrations consti-tute the raw data upon which the reconstruction ofa tomographic slice is based. The PET camera haselectronic circuits that can distinguish coincidencesfrom every possible pair of detectors. The set of detec-tor bins aligned on a particular angle define a set ofprojection lines of the object or a view.

In order to achieve good spatial resolution thedistance between the projection lines should be rathersmall. The distance should be no greater than the dis-tance between the closest two points of concentrationwe wish to distinguish in the reconstructed image. Thiscan be accomplished through the design of cameraswith small detectors and placing such cameras withthe tightest possible packing arrangement. Howeverthe detectors can not practically be made arbitrarilysmall and a large number of detectors substantiallyincreases the cameras cost. In practice a typicaltransaxial resolution in PET is approximately 4-6 mmFWHM.

In order to increase spatial resolution many PETscanners have a system of wobbling motion. Thiswobbling consists of a small circular motion (1 cm orless) of the ring detector in such a manner that thedetectors cover the missing gaps. Of course, this addi-tional information must be treated in the reconstructionalgorithm employed for such a scanner.

The attenuation and scattering of gamma photonswithin the body make PET a difficult imaging task. In


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20 Computerized Medical Imaging and Graphics January_February/l995, Volume 19, Number Isome typical chest PET scans, for example, approxi-mately 15% of the annihilation photon pairs headedto a particular bin detector are registered; the rest ofthe photons are attenuated. If no correction approachis implemented, attenuation of photons would lead toan underestimation of the radioisotope concentration.Fortunately attenuation correction techniques can beapplied. One approach consists of introducing an atten-uation correction factor in the estimation of the radio-nuclide concentration. This correction factor is the ra-tio of the measurement of a detector bin when apositron-emitting source point is placed on one side ofthe PET scan area and a measurement taken with andwithout a patient in the PET scanner. A complete atten-uation correction is then possible, disposing of the cor-rection factor for all detector pairs.

The problem of scattering is more difficult to treat.If a deflected photon continues travelling in the planeof the ring detector after the scattering, this photon maystill hit a detector and generate a false coincidence. Aenergy window approach similar to that employed forSPECT can be implemented for PET scanning. How-ever, this represents only a partial solution due to thefinite accuracy in energy measurement by the scintilla-tion crystals employed in PET. New approaches toscatter correction are currently undergoing active re-search.

Another factor which complicates PET is the pres-ence of accidental coincidences. The detection sys-tem registers a coincidence event when both detectorsof a bin are triggered within some resolving time r,which is typically measured in nsec. Usually these pho-tons are produced by the same annihilation event.However it is possible that the system can be trickedby photons produced in unrelated annihilations. Therate of accidental coincidences per second N is givenby

N = 2 X T X s, X &. (9)where S, and Sz are the counting rates of each of thedetectors. The problem of accidental coincidence rap-idly increases with the radionuclide concentration. Therate of counts measured by the detectors are propor-tional to the concentration value. The influence of acci-dental coincidence can be reduced by subtracting thecomputed number of random coincidences using theequation above.4.3 PET reconstruction algorithms

Estimation of the positron-emitter compound dis-tribution f (x, y, 2, t) is realized through computationalalgorithms. These algorithms are provided the numberof counts M, associated with the projection lines L,. If

the period At in which the data was collected is shortenough and if we proceed to reconstruct one transaxialslice at the time, the problem reduces to the determina-tion of the 2D functionf (x, v). The basic problem canbe stated as follows:

Estimate the function ,f (x, y) from the system ofequations

where L, is the i-th line of the I projection lines (detec-tor bin lines in the PET case); c, = M,IV, depends onthe attenuation line integral V, which can be eithercalculated from a hypothetical attenuation coefficientor from an experimental measurement.

Reconstruction algorithms can be divided into;back-projection methods, Fourier methods and itera-tive methods. The first two methods (transform meth-ods) are the most commonly employed due to relativeease of implementation and low computational cost.The images obtained by transform methods are goodenough for a great variety of applications. On the otherhand, iterative methods provide greater flexibility inthe introduction of attenuation correction informationto the algorithm and statistical treatment of the data.

A simple reconstruction scheme is the back pro-jection process. This method consists of reconstructingeach transaxial slice image by a method similar tothat described in section 2 for CT machines. The filteremployed in this filtered back projection is typically amultiplicative combination in Fourier space of a rampand another filter, such as the Hamming, Butterworthor Shepp-Logan filter (18).

Iterative reconstruction methods include; the alge-braic reconstruction technique (ART), the simultane-ous iterative reconstruction technique (SIRT) and theleast-squared iterative technique. The first two methodsinvolve the alteration of the estimate of the transaxialimage around a circle by adding or subtracting fromeach point to what is called for. The least-squared itera-tive technique is based on the minimization of thesquared error which is defined as the square of thedifference between the measured and calculated pro-jection. The minimization process is performed by cal-culating the partial derivatives of the squared errorwith respect to variables of interest and setting thisderivative equal to zero ( 19).

Shepp and Vardi have presented a reconstructionmethodology based on statistical methods (20). Theirmethod is based on the expectation maximization ofthe emission distribution. Shepp and Vardi take in ac-count the Poisson statistics of radioactive decay. Con-vergency to a global maximum is guaranteed by the


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Biomedical imaging modalities l R. ACHARYA et ul. 21

Shepp-Vardi algorithm. However, approaching thismaximum value can be exceedingly slow in somecases.

5 BIOMAGNETIC SOURCE IMAGINGWITH SQUIDS

Blomagnetic source imaging is a relatively newmedical imaging modality which produces representa-tions ot the minute magnetic fields created by neuronalactivit) within the body (I). As in the case of ECT,images produced via Biomagnetic Source Imaging pro-vide mappings of functional rather than anatomicalinformation. An important goal of this technology isthe ability to localize neuron activity in response tospecifically applied sensory stimuli (21).

Biomagnetic source imaging is made possible bya solid state sensor known as a Superconducting Quan-tum Interference Device (SQUID). SQUID sensors canbe employed to measure the magnetic fields producedin the hrain by neural currents. Given a set of externalmagnetic measurements, it is desirable to generate avisual mapping of the current densities, in three dimen-sions, that gave rise to the external magnetic field (21).It is hoped that SQUID technology and Biomagneticsource Imaging will be of significant assistance to re-searchers investigating epilepsy, Alzheimers disease,Parkinsons disease, and schizophrenia (1).6 DIGITAL SUBTRACTION ANGIOGRAPHY

A common problem with the radiograph discussedin section 2 is the poor contrast between anatomicalstructures. This low contrast resolution limits the utilityof such radiographs severely. However through the useof digital acquisition systems it is possible to greatlyincrease the utility of 2D projection radiographs forcertain, specific applications. Digital Subtraction Angi-ography (DSA) is a modality that exploits the digitalacquisition of radiographs to produce high contrast im-ages of blood vessels.

A common problem with radiograph technologyis the fact that many internal tissues are superimposedon each other. The projection nature of the radiographyields a final image in which it is difficult to delineateindividual structures. Wherein a specific structure isanalyzed it would be advantageous to acquire a radio-graph which displayed only that structure without anysubsequent loss of resolution. This result could beachieved in a digital image if the values of all pixelswithout information on that structure were set to zeroand all pixels corresponding to the structure of interestwere allowed to maintain their natural values. Whilesuch a result could be obtained using image processing

techniques, such as segmentation, the resulting lossin resolution would degrade severely an already poorcontrast image. However if two images were taken ofa subject, in which the contrast of the anatomical struc-ture of interest changed significantly from one imageto the next, excellent results could be achieved. Thesubtraction of two digital images results in a differenceimage. This difference image retains only the informa-tion that has changed from one image to the other.The digital subtraction of radiographs is the conceptunderlying DSA (22). This concept is illustrated witha ID signal in Fig. 2 1.

The basis for a DSA device consists of x-ray sys-tem very similar to that used for a conventional radio-graph. The main difference occurs in the techniqueused to acquire the radiograph. Conventional radiogra-phy utilizes typically a film, which after processingwill contain an image proportional to the amount ofx-ray energy leaving the patients body. Subtractionangiography has been practiced employing film tech-nology (23). However such techniques possess disad-vantages, such as the long time interval that takes placebetween subsequent radiographs. Patient movementduring the entire radiograph acquisition sequence cre-ates significant problems for the subtraction processsince the methodology is premised on registration be-tween the subtracted images.

In the case of DSA, the film acquisition apparatusis replaced by a system that can rapidly acquire a highresolution image of x-ray radiation incident on it. Afterproper patient positioning, an initial radiograph istaken of a patient. This initial radiograph is called com-monly the musk image and contains the base informa-tion that will be subtracted from the second image.The mask radiograph is acquired and stored in a com-puter. A contrast medium is then injected into the pa-tient. This contrast medium is designed to elicit a sig-nificant change in the contrast of blood in the vesselsof interest. A second radiograph is then taken of thepatient with the contrast agent in place. This secondimage is again acquired and stored in a computersmemory. This image is referred to as the l i v e imagein that it contains vessel information that was not pres-ent in the mask image. The digital results of theseradiographs can now be subtracted and their differenceamplified. After subtraction, all information that wasin both the mask and live images has been eliminated.The resulting image is now a high contrast image of thepatients blood vessels in a region of interest. Clinicalapplications of DSA differ in some ways from thesimplistic description above. However such techniquesutilized for the improvement of image quality do notaffect the underlying methodology described herein.


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22 Computerized Medical Imaging and Graphics January-February/l995, Volume 19. Number I

mesh image ::

live image J---y n]r

differenceimage

: : :

Fig. 21. Illustration of DSA signal subtraction concept.

In the past, prior to the use of digital technology,the above discussed two image subtraction angiographencompassed the limits of technology. However, DSAallows for a variety of subtraction techniques includingmask or temporal mode subtraction, time differencesubtraction and energy subtraction (23). All of the sub-traction techniques employ the basic methodology dis-cussed previously. Specific DSA subtraction methodsdiffer in the techniques used to select the mask andlive images.

The mask or temporal mode subtraction techniqueseeks to provide a physician with a temporal view of acontrast media through the patients vessels of interest.When digital acquisition techniques are employed, ra-diographs can be collected typically as a sequence ofimages occurring at a fixed time interval (at) apart.This method can be utilized to acquire a series of maskradiographs prior to the introduction of the contrastmedia. One of these mask images is selected as thegeneral mask image u,~(x, y). After the contrast agentis introduced, a series of live digital radiographs u,(x,y) will be acquired, where i denotes the number of theradiograph in the acquisition sequence. In the subtrac-tion of u,(x, y) from U&Y,y) for all values of i, theprogress of the contrast media may be viewed tempo-rally. This methodology is limited mainly by patientmotion though some correction can be employed viacomputer based registration techniques.A technique referred to as time interval differencesubtraction (TID) has been utilized to reduce effectscaused by patient motion during the imaging process.When employing TID, a subtraction is performed con-tinuously between subsequent live images by: u, -u,_, While this method reduces significantly the effectsassociated with patient motion, it produces images ofvery poor contrast quality. This poor quality is associ-ated with the closeness of the mask and live imagesin time. This temporal proximity results in the fullcontrast that could be generated by the contrast agent

not being realized. Due to the summarized drawbacksthe TID technique is not utilized extensively in clinicalsettings.

Another method that seeks to address the artifactsthat can be caused by patient motion and misregistra-tion are energy subtraction methods. Energy subtrac-tion approaches may be subdivided into two sub-classes, K-edge subtraction and photoelectric/comptondecomposition.

K-edge subtraction techniques are based upon thex-ray energy absorption properties of the iodine con-trast agent that is employed typically in DSA applica-tions. Such contrast agents exhibit excellent energyabsorption above the binding energy in the K shell,and little absorption below this K shell (23). If a radio-graph is taken of the patient utilizing x-rays of anenergy below this k line then the contrast agent willnot be visible. This image can then be employed asthe mask agent for DSA. The patient is then imagedutilizing x-rays above the Kl i ne of iodine. This secondimage will include a high contrast image of the iodinewhich can then be employed as the live image. Digitalsubtraction can now be performed. Problems associ-ated with this technique involve difficulties in produc-ing proper intensity levels of such monochromatic x-ray photon beams.

A method known as photoelectric/compton de-composition operates on a principle similar to that ofK-edge subtraction. The iodine contrast agent em-ployed commonly for DSA responds differentially todifferent x-ray photon energy ranges. This knowledgeis employed to acquire a mask image and a live imagevia the utilization of carefully chosen differential en-ergy levels for the x-ray source. Photoelectric/comptondecomposition virtually eliminates effects based on pa-tient motion (23) since the mask and live image aregenerated only milliseconds apart. The photoelectricdecomposition technique requires x-ray generators thatcan switch rapidly between the required kVp levels.


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Biomedical imaging modalities l R. ACHARYA et al. 23

The major practical difference between the twoenergy subtraction based techniques discussed is therequirements they place on the employed x-ray genera-tor. K-edge subtraction requires difficult to produce,monochromatic x-ray beams while the photoelectricsubtraction approach employs beams of differing ener-gies. While the decomposition approach utilizes easierto produce x-ray beams, it has the disadvantage of areduction in output signal to noise ratio for low kVpx-rays. This drawback is due to the significant attenua-tion of the low energy beams by thicker structures inthe patient.

7 ULTRASOUND IMAGINGUI trasound based imaging techniques comprise a

set of methodologies capable of acquiring both quanti-tative and qualitative diagnostic information. Many ul-trasound based methods are attractive due to their abil-ity to obtain real time imagery employing compact andmobile equipment at a significantly lower cost than isincurred with other medical imaging modalities. Thereal time nature of ultrasound makes it possible forphysicians to observe the motion of structures insidea patients body. This ability has resulted in the wide-spread use of ultrasound technology in the fields ofpediatrics and cardiology. Equipment which employsdoppler echo techniques can extract quantitative veloc-ity information such as the rate of blood flow in avessel of interest. Additionally, the introduction of ul-trasound signals into a patient at the levels currentlyemployed has been determined to be very safe (2). Thelack of negative exposure effects, portability, relativelylow cost and quantitative acquisition modes makes ul-trasound techniques an important class of medical im-aging methods.

Ultrasound is classified as sound waves pos-sessing a high temporal frequency. Typical medicalinstruments for diagnostic ultrasound employ wave-forms that oscillate in the range of I-1OMHz. (2). Suchwaves can be produced using a single ultrasound trans-ducer or an array of transducers. Ultrasound transduc-ers are capable of producing ultrasound signals whenthey are excited electrically. Inversely, these transduc-ers produce an electric signal when excited by incidentultrasound rays. Consequently, the same set of ultra-sound transducers are typically used for both ultra-sound transmission and detection in medical applica-tions.

The sound waves transmitted by the ultrasoundtransducers are introduced into the patients body inthe area of diagnostic interest. As the waves passthrough the body they travel through differing tissue

types with correspondingly differing acoustic proper-ties. At the boundary between two tissues types a par-tial reflection of the ultrasound signal will take place.Some portion of the sound waves will be reflected backtowards the source transmitter while the remaining por-tion of the incident ultrasound will continue propagat-ing onwards. This process is not idealized in livingtissue and results in complex scattering interactionsthat are out of the scope of this paper. Reflected wave-forms are measured with respect to their time of origi-nal transmission by employing the source transducerapparatus as mentioned above. It should be intuitivelyclear that only waveforms reflected along the incidentpath will be detectable by the original transducer.

It has been previously mentioned that ultrasoundsource/detector configurations can consist of a singletransducer or an array of transducers. Array transduc-ers arrangements are often employed in modem medi-cal ultrasound units. These array configurations pro-vide a larger receptor aperture and subsequentlyimproved image reconstruction.

In order to understand the manner in which ultra-sound machines acquire images it is best to first investi-gate a simple, idealized scenario. One such case mightbe a task that entails imaging a 1D scene consistingof a single, ideal reflector using a single transmitterlocated at the origin. If an ultrasound pulse is transmit-ted at time I, and a return pulse is detected at time t2then the distance to the target from the transmitter maybe calculated as

t2 - IIx=- c (11)where c is the speed of sound in the instant medium.Extending this approach to medical applications, onecan view the body as a series of point sources locatedat the junctions of tissues with differing characteristicacoustic impedances. Ultrasound units designed to im-age internal structures for applications such as echo-graphic and in pediatric settings are designed to mea-sure the time of reception of ultrasound signals withrespect to their time of transmission in real time. Thisresults in the real time measurement of the distancefrom the transducer to internal anatomical surfaces,resulting in real time imagery of these structures.

Information from returned echoes or reflectionswith respect to time can be presented to the physicianin several ways (2). Two commonly employed tech-niques are time amplified and brightness mode dis-plays. Time amplified or A mode displays present theamplitudes of the returned ultrasound signals with re-spect to their time of return as a series of ID spikesof varying height. Brightness or B mode displays pres-


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24 Computerized Medical Imaging and Graphics JanuaryFebruary/l995. Volume 19,Number Ient the same data on a single line. The brightness ofeach point on this line indicates the signal amplitudedetected at that time or depth. If an array of detectorsare employed with the proper mechanisms then it ispossible to generate a series of B mode scan lines. Thecombination of these scan lines results in a 2D fanlike view. This 2D view can be generated in real timeallowing for the detection and viewing of moving inter-nal structures such as a beating heart. Another modeof image presentation commonly referred to is timemotion or M mode. M mode employs a display of Bmode lines with respect to a time axis acquired bymoving the source/transmitter wand across the area ofinterest (24).

Quantitative information can be extracted fromecho reflections through an understanding and utiliza-tion of the Doppler effect. In short, when a signal withfrequency .fo and propagating at speed u, is reflectedfrom a target moving at a speed u, then the frequencyof the echoed signal received at the ultrasound detectoris shifted by a factor described by the Doppler princi-ple. The frequency of the transmitted wave is shiftedby a factor of

f d _ 2v,fuv, (12)where fd is the approximate, detected doppler fre-quency shift and fr = fd + ,fo, where fr is the actualfrequency received at the detector.

An area in which Doppler techniques are com-monly employed is Doppler Echocurdiogruphy. Dopp-ler Echocardiography allows the measurement of thevelocity and direction of blood flow at a fixed distancefrom the ultrasound transducer within a patients body.The Doppler shifted frequencies to be measured areproduced by the reflection of injected ultrasound wavesfrom flowing red blood cells in the vessels of interest.When utilizing the method of pulsed Doppler echocar-diography, short bursts of ultrasound are introducedinto the patient. Pulsed echo techniques keep the targetdistance fixed and retrieve velocity measurements fortargets located at that distance. Since the desired dis-tance of measurement is fixed, the expected echo timeis also fixed. Echoes not received in a neighborhoodof this expected echo time are not processed by theimaging instrumentation. This technique is often re-ferred to as range gating (2). An alternative Dopplertechnique is continuous wave Doppler. When thismethod is employed, ultrasound is continuously in-jected into the patient. Such an approach is advanta-geous in that it allows for very accurate, high velocitymeasurements. Unfortunately, when continuous Dopp-ler is employed the depth at which the velocity is being

measured cannot be determined due to the fact that norange gating takes place. For either of the Dopplerprinciple based techniques, the echoed signals fre-quency components are measured so as to determinethe Doppler frequency shift using the fast fourier trans-form (FFT).

8 CONCLUSIONAdvancing technology is increasing steadily the

radiologists ability to learn accurate and precise infor-mation about a patient in a non-invasive manner. Cur-rent medical imaging modalities are capable of acquir-ing data on internal anatomical structures, as well asmappings of physiological function. Advanced soft-ware reconstruction algorithms and analytic techniquesseek to maximize the information derived from currentmedical modalities while driving the development ofeven more advanced technologies.

An overview has been provided of some of themore popular medical imaging modalities currently inclinical use. It is hoped that a general understandingof the modality from which an image is derived willhelp researchers in the subsequent analysis of the im-age data.

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About the Author-RAJ ACHARYA obtained his Ph.D from theUniverslry of Minnesota/Mayo Graduate School of Medicine in 1984

and is currently an Associate Professor of Electrical and ComputerEngineering at SUNY-Buffalo. He worked with the Dynamic SpatialReconstructor project at the Mayo Clinic from 19XI - 1985 and wasa research scientist at GE-CGR in Paris, France during 1984 to 1986.He is presently the Director of SUNY Buffalos Biomedical ImagingGroup (BMIG). He is a member of the editorial board of the Journalof Computerized Medical Imaging and Graphics as well as Cochairof the 1994 IEEE Workshop in Biomedical Image Analysis. He hasalso served as the General Chair of the SPIE Conference on Biomedi-cal Image Processing in both 1992 and 1993, and is currently theGeneral Chair of the 1994 SPIE International Conference on Physiol-ogy and Function from Multidimensional Images.About the Author-RICHARD WASSERMAN is currently workingtowards his doctorate in electrical engineering at the University ofBuffalo. His research interests include the application of data fusiontechniques to multimodality imaging as well as applications in thefield of radiation therapy treatment planning.About the Author-J EFFRw STEVENS was born in Buffalo, NewYork on January 25, 1970. He received h

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