Accuracy of finite element model-based multi-organ deformable image registrationK. K. Brock, M. B. Sharpe, L. A. Dawson, S. M. Kim, and D. A. Jaffray Citation: Medical Physics 32, 1647 (2005); doi: 10.1118/1.1915012 View online: http://dx.doi.org/10.1118/1.1915012 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/32/6?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Position tracking of moving liver lesion based on real-time registration between 2D ultrasound and 3Dpreoperative images Med. Phys. 42, 335 (2015); 10.1118/1.4903945 Four-dimensional dose evaluation using deformable image registration in radiotherapy for liver cancer Med. Phys. 40, 011706 (2013); 10.1118/1.4769427 Accuracy and sensitivity of finite element model-based deformable registration of the prostate Med. Phys. 35, 4019 (2008); 10.1118/1.2965263 Technical note: A novel boundary condition using contact elements for finite element based deformable imageregistration Med. Phys. 31, 2412 (2004); 10.1118/1.1774131 Evaluation of three-dimensional finite element-based deformable registration of pre- and intraoperative prostateimaging Med. Phys. 28, 2551 (2001); 10.1118/1.1414009

Accuracy of finite element model-based multi-organ deformable imageregistration

K. K. Brock,a! M. B. Sharpe, L. A. Dawson, S. M. Kim, and D. A. JaffrayRadiation Medicine Program, Princess Margaret Hospital, University Health Network,610 University Avenue, Toronto, Ontario, Canada M5G 2M9

sReceived 31 August 2004; revised 21 March 2005; accepted for publication 24 March 2005;published 20 May 2005d

As more pretreatment imaging becomes integrated into the treatment planning process and fullthree-dimensional image-guidance becomes part of the treatment delivery the need for a deformableimage registration technique becomes more apparent. A novel finite element model-based multi-organ deformable image registration method,MORFEUS, has been developed. The basis of thismethod is twofold: first, individual organ deformation can be accurately modeled by deforming thesurface of the organ at one instance into the surface of the organ at another instance and assigningthe material properties that allow the internal structures to be accurately deformed into the second-ary position and second, multi-organ deformable alignment can be achieved by explicitly definingthe deformation of a subset of organs and assigning surface interfaces between organs. The feasi-bility and accuracy of the method was tested on MR thoracic and abdominal images of healthyvolunteers at inhale and exhale. For the thoracic cases, the lungs and external surface were explic-itly deformed and the breasts were implicitly deformed based on its relation to the lung and externalsurface. For the abdominal cases, the liver, spleen, and external surface were explicitly deformedand the stomach and kidneys were implicitly deformed. The average accuracysaverage absoluteerrord of the lung and liver deformation, determined by tracking visible bifurcations, was 0.19ss.d.:0.09d, 0.28 ss.d.: 0.12d and 0.17ss.d.:0.07d cm, in the LR, AP, and IS directions, respectively. Theaverage accuracy of implicitly deformed organs was 0.11ss.d.: 0.11d, 0.13 ss.d.: 0.12d, and0.08 ss.d.:0.09d cm, in the LR, AP, and IS directions, respectively. The average vector magnitude ofthe accuracy was 0.44ss.d.:0.20d cm for the lung and liver deformation and 0.24ss.d.:0.18d cmfor the implicitly deformed organs. The two main processes, explicit deformation of the selectedorgans and finite element analysis calculations, require less than 120 and 495 s, respectively. Thisplatform can facilitate the integration of deformable image registration into online image guidanceprocedures, dose calculations, and tissue response monitoring as well as performing multi-modalityimage registration for purposes of treatment planning. ©2005 American Association of Physicistsin Medicine. fDOI: 10.1118/1.1915012g

I. INTRODUCTION

As more pretreatment imagingsi.e., PET,1–4 MRS,5–8 4DCT,9–12 and MR13–17d becomes integrated into the treatmentplanning process and full three-dimensionals3Dd image-guidance si.e., kV and MV cone-beam,18–23

tomotherapy,24–26 and conventional CTd,27–29 becomes partof the treatment delivery the need for a deformable imageregistration technique becomes more apparent. In addition tobeing accurate and efficient, the image registration techniquemust include deformable alignment, allow various regions ofinterest to behave differently, and maintain the geometricintegrity of regions of interest that are presented differentlyon different imaging modalities.

Image intensity-based deformable image registration hasbeen shown to be very effective for single organ imageregistration.30–36 However, including multiple organs in theregistration becomes challenging, as the interface betweenorgans can be difficult to model using splines, fluid-flow, andoptical flow. Boundary conditions are inherent in the biome-chanical modeling used in finite element analysissFEAd,which allows multiple organs to be registered simulta-neously.

An extensive amount of research has investigated the ben-efit of finite element modelingsFEMd in surgical simulation,especially for modeling brain deformation,37–40 however,only limited investigations into its potential in radiotherapyhave been reported and has primarily focused on single or-gan deformable registration.41–45

A novel method has been developed to perform deform-able, multi-organ image registration using FEM. The basis ofthis method is twofold: first, individual organ deformationcan be accurately modeled by deforming the surface of theorgan at one instance into the surface of the organ at anotherinstance and assigning the material properties that allow theinternal structures to be accurately deformed into the second-ary position and second, multi-organ deformable alignmentcan be achieved by explicitly defining the deformation of asubset or limited number of organs and assigning surfaceinterfaces between organs.

Naturally occurring surrogatessor landmarksd for bound-ary registration across multiple imaging modalities are essen-tial for the proposed registration method. For some organs,such as the liver and lung, the boundary representation of theorgan is consistent between different imaging modalities al-

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though the internal image intensity representation may vary.Comparing the boundary representation and assigning cor-rect material properties can allow explicit deformation ofthese organs. Other organs, such as the prostate, have incon-sistent boundary definition between imaging modalities, i.e.,the visible boundary of the prostate is inconsistent betweenMR, CT, and cone-beam CT. This subset of organs must beimplicitly deformed by explicitly deforming neighboring or-gans and assigning appropriate material properties and sur-face interfaces. In the case of the prostate, the bladder andrectal boundary representation is consistent between imagingmodalities and can serve as the explicitly deformed organs.In addition, as biological imaging advances the position ofthe biological target volume can also be inferred from theanatomical surrogates in a similar manner.46

II. METHODS AND MATERIALS

A FEM-based multi-organ deformable image registrationplatform, MORFEUS, was developed to facilitate deformableregistration of multi-modality images for tissue responsetracking, image-guided radiotherapy, and improved dose cal-culations. This was achieved by integrating a FEM pre-processorsHYPERMESHversion 6.0, Altair Engineering, Troy,MI d, FEA sABAQUS version 6.4, ABAQUS Inc, Pawtucket,RId, and radiation therapy treatment planning systemsPINNACLE

3 version 6.2b, Philips Radiation Oncology Sys-tems, Milpitas, CAd, as shown in Fig. 1. The FEM pre-processor,HYPERMESH, is used to construct the FEM, assignmaterial properties, surface interfaces, and boundary condi-tions, and determine the boundary conditions usingHYPER-

MORPH, an application available in the software program.The FEA software package,ABAQUS, generates differentialequations that describe the model constructed in the prepro-cessor and then solves these equations simultaneously. Thetreatment planning systemsTPSd performs rigid body, bonyregistration of the multiple data sets, allows contouring ofthe selected regions of interestsROIsd, and provides amethod of exporting the ROIs. It is important to note that,although specific commercial products were used for this de-velopment and analysis, the general concept of FEM-baseddeformable image registration can be employed using anycommercial or research FEM, FEA, and TPS software. Theprocess developed is illustrated in Fig. 2, and will be de-scribed in the following.

FIG. 1. Integration of FEM/FEA into RTTP.

FIG. 2. MORFEUS process.

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A. Data collection

Five healthy female volunteers participated in researchethics boardsREBd approved MR scanning study to imagetheir thorax and abdominal regions at a normal inhalationand exhalation breath hold. The average age of the volun-teers was 33 yearssrange: 25–49d. The volunteerssreferredto as V1–V5d were scanned in the supine position, on a flattable without immobilization and with their arms over theirhead. A 3D inhalation and exhalation MR scan of the thorax,including the whole lungs and breasts, was acquired for eachvolunteer. The thoracic study was followed immediately byinhalation and exhalation scans of the abdominal region, in-cluding liver, spleen, stomach, and kidneys. The volunteer’sposition was adjusted between the thorax and abdominalscans to optimize position in the scanner. An axial Fast-SpinGradient RecoverysFSPGRd imaging sequencesTE/TR1.6/325 ms, 1 NEX, FOV 34–44 cmd was used for all scanscombined with Array Spatial Sensitivity Encoding Tech-niquessASSET™d to decrease imaging time and allow forcomplete coverage of organs of interest in one comfortablebreath hold on a GE 1.5 T MR unitsExcite, 4 channel, GEMedical Systems, Milwaukee, WId. The sequence was cho-sen to optimize enhancement of vessel bifurcations in theliver and bronchial bifurcations in the lung. These structuresserve as anatomical landmarks to estimate the accuracy ofthe FEM-based deformable alignment. The scanning timeranged from 22 to 36 s for a complete 25632563N vol-ume, whereN is the number of slices necessary to cover theentire volume of interest. Slice thickness ranged from4 to 5 mm with no gap, depending on patient breath holdcomfort andN ranged from 50 to 58 for the abdomen scansand 54 to 59 for the thoracic scans. An ASSET calibrationsFast GRE calibration, TE/TR 1.4/3.6 ms, FOV 48, slicethickness 9 mm, 30 slices, 0:06 s imaging timed image wasobtained at breath hold position prior to image acquisition.

Following the imaging session, the images were trans-ferred into the treatment planning system, where the organswere segmented to generate anatomical ROIs, as shown instep 1 of Fig. 2. Segmentation of the ROIs produces a seriesof discrete transverse “contours,” which are represented by alist of vertices and associated which each of the transverseimages slices. The ROIs for the thorax data sets includedright and left lungs, right and left breasts, spinal cord, andexternal surface. The ROIs for the abdominal scan includedliver, spleen, stomach, right and left kidneys, and externalsurface. In addition all data sets had an “internal” ROI cre-ated which comprised the volume of the patient delineatedby the external surface, but excluding a 0.5 cm isotropic ex-pansion of the spinal cord. The purpose of the internal ROIwill become apparent in Sec. II C. The ROIs representingeach organ were converted from contours to a volumetricbinary mask, and then exported from the TPS as a file.

B. Conversion of ROIs to triangular surface mesh

The binary mask files were imported into a mathematicaldevelopment environment used commonly for image analy-sissInteractive Data Language, IDL, Research Systems Inc.d.

To manage the size of the mesh generated, the data files werefirst reduced in size from 25632563N sN=slice numberd to643643N. The resampled binary files were then convertedinto a triangular surface mesh using an algorithm describedby Klemp et al.47 which is similar to the marching cubesalgorithm.48 Both algorithms search the data on a voxel-by-voxel basis, creating a triangle representation based on theintersection of the 3D contour surface with each voxel, dif-fering only in search algorithm implementation. The normalto the surface is also computed to define the “inside” and“outside” of the surface. The surface mesh, with an exampletriangular element, is shown in step 2 of Fig. 2. The meshwas smoothed using a Laplacian smoothing described in Eq.s1d, whereXin is the vertexi for iterationn, l is the smooth-ing factor, andM is the number of vertices that share a com-mon edge withXin. Laplacian smoothing adjusts the verticesin the mesh to smooth the shape, improving the appearanceand shape, without significantly changing its topology,

Xisn+1d = Xin +l

Moj=0

M

sXjn − Xind. s1d

The mesh was smoothed with 10 iterations at a smoothingfactor of 10 and further smoothed in Geomagic DecimatorsRaindrop Geomagic, Raleigh, NCd using the “relax” sLa-placian smoothingd function, for 50 iterations. An example ofthe process is illustrated in Fig. 3.

In three casessV3, V4, and V5d, the inferior extent of thelung became extremely narrow and extended further into theabdominal cavity. Reduction to 643643N did not maintainthis detail. For these three cases, the lung and breast datawere only reduced to 1283128. A higher resolution wasused to ensure proper modeling of the inferior extent of thelung. To maintain a reasonable mesh size, the mesh wassmoothed and the number of elements describing the surfacewas reduced, using the decimate function, inDECIMATOR™.The decimate function reduces the number of elements de-

FIG. 3. Smoothing process for abdominal organs:sad original mesh with nodata reduction and no smoothing,sbd reduced to 64364 data,scd resultsfrom sbd smoothed using a Laplacian smoothing with 10 iterations at afactor of 10, sdd results from scd smoothed in geomagic decimators50iterationsd.

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scribing the surface while maintaining as much of the origi-nal surface information as possible. Combining mesh deci-mation and Laplacian smoothing allows significant reductionin the number of elements while maintaining accurate meshtopology. The decimatesdecd and smoothingsusing the relax,Laplacian smoothing functiond schema utilized for the lungwas R=50, dec=75,R=50, dec=75,R=50. For the breast,the decimate and smoothing schema wasR=50 and dec=75. An example of the process is shown in Fig. 4.

C. Finite element model construction

The triangular surface meshes representing the segmentedorgans for a given image set were imported into the FEMpreprocessor. A 3D four-node tetrahedral FEM was createdfrom all organ ROI triangular surface meshes. An example ofa liver tetrahedral mesh is shown in step 3 of Fig. 2, with aninset showing an example of a tetrahedral element. The inte-rior FEM is created from the interior surface mesh, excludingall internal organ FEMs. This completed the multi-organ sys-tem. Nodes on the surface of each organ FEM were definedto be common to both the organ FEM and the interior FEMresulting in a “tied” connection. The average median lengthof an element side was 0.49 cm and the average elementvolume was 0.03 cm3.

The spinal cord was allowed to move independently inthese investigations and did not contribute to the registration.The cord is a strong structure for use in aligning bonyanatomy even under conditions of spinal column flexure. Thespine was not needed in this alignment because both imageswere obtained at the same imaging session and thereforethere was no difference in position of bony anatomy. It willbe very useful to include the spine in multi-modality imagingor images obtained from the same modality but on differentdays when bony setup varies.

As indicated in step 4 of Fig. 2, material properties andsurface interfaces were assigned to each organ. A linear elas-tic material model was used to describe the FEM. Materialproperties were assigned to each element in the multi-organFEM with these properties varying between organs, but ho-mogeneous in each organ. Material properties were taken

from the literature49–53 and then manually optimized by ad-justing the parameters on the first three volunteerssV1–V3duntil the accuracy was 0.3 cm or better for implicitly de-formed organs. These parameters were then validated by en-suring similar accuracy for the remaining two volunteerssV4and V5d. Each subject was assigned the same organ-specificmaterial properties. The parameters for each organ are shownin Table I. The Young’s Modulus for the stomachs500 kPadis much larger than typical published values for soft tissues1–100 kPad. This value was employed to accommodate thecontents of the stomach as they were included in the FEMand no food or beverage intake instructions were given to thevolunteers prior to imaging.

Finite element modeling has the ability to describe biome-chanical materials using simple and complex models. A sim-plistic model, the linear elastic material model, was usedhere as a starting point because parameters for complex mod-els are difficult to obtain for human tissues and significantlyincrease computational time. In the future, as more accuratemethods of obtaining material properties are further devel-oped, such as MR elastography, more complex models canbe directly integrated into theMORFEUSsystem by changingthe parameters in the model.54,55

D. Individual organ deformation

When performing image alignment, one representationmust be selected as the “base model” that will be deformedinto all other representations. The base model provides therelationship between all images. The ideal base model de-scribes the boundary representation of all regions of interestwith geometric accuracy. The element structure of the basemodel will also serve as the “storage” system for the patientfor dose tracking, tumor classification, and tissue response.

Explicit organ deformation was performed on selected or-gans in the model to achieve the multi-organ deformablealignment. Organ selection was based on the ability to accu-rately contour and easily visualize on all images. For theabdominal data sets, the liver, spleen, and external were ex-plicitly deformed. For the thoracic data sets, the lungs andexternal were explicitly deformed. The exhale data set wasthe base model for the abdominal data sets, and deformable

FIG. 4. Smoothing process for lungs:sad original mesh with no data reduc-tion and no smoothing,sbd reduced to 1283128 data,scd reduced to 1283128 smootheds50 iterationsd, decimated to 75%, smootheds50 iterationsd,decimated to 75% and sootheds50 iterationsd.

TABLE I. Linear elastic material parameters for each organ modeled. Pois-son’s ratio,n, the ratio of transverse contraction strain to longitudinal exten-sion strain in the direction of stretching force, describes the compressibilityof the material. Young’s modulus,E, the ratio of stress to strain on theloading plane along the loading direction, describes the stiffness of the ma-terial.

Poisson’s ratiosnd Young’s modulussEd skPad

Interior 0.400 1.5sabdomend 6.0 sthoraxdLung 0.450 5.0Breast 0.450 19Liver 0.450 7.8

Spleen 0.499 50Stomach 0.499 500Kidney 0.499 24

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registration was performed to align it to the secondarymodel, the inhale data set. For the thoracic data sets, theinhale data set was the base model, and deformable registra-tion is performed to align it to the secondary model, theexhale data set. The exhale data set was used as the basemodel for the abdominal scans to simulate the current treat-ment planning process for liver cancer at our institution,which performs treatment planning on the patient in the ex-hale breath hold position, which has been shown to be morereproducible.56 Research has shown a reduction in cardiacand lung doses when treating breast cancer patients at inspi-ration breath hold, therefore, the inhale data set was used asthe base model for the thoracic scans.57,58

The explicit organ deformation from one instance of ge-ometry to anothersi.e., from exhale to inhaled was performedusing HYPERMORPH, a surface-based projection algorithmavailable inHYPERMESH, shown in step 5 of Fig. 2. For or-gans undergoing substantial motion, i.e., a change in centerof gravity sCOGd of greater than 0.5 cm, which can be de-scribed as rigid-body motion, a COG alignment was per-formed as an initial step. This was performed when deter-mining the deformable alignment of the liver and spleen. ACOG registration was performed in the anterior–posterior,AP, and left–right, LR, directions only for the lung. No COGregistration was performed for the external surface, as theback of the patient remained against the table during inhaleand exhale breath holds.

For one casesV2 abdomend substantial rotation was notedin the coronal plane. Initial results using only a COG regis-tration resulted in a poor surface alignment. A 7° in-planerotation about the COG was applied in addition to the COGregistration leading to a successful surface alignment. Morepatient data will be necessary to determine if this is a com-mon problem, which may require a systematic solution, pos-sibly a more complex rigid body initial registration.59–61

The HYPERMORPHalignment procedure is outlined in Fig.5. Both FEM surface mesh representations of the organ areimported intoHYPERMESHfFig. 5sadg. The FEM of the organin the secondary model is converted to a surface and a COGregistration is performed, if required, as defined above, Fig.5sbd. The elements on the surface of the FEM of the organ inthe base model are automatically grouped into a series ofdomains based on the curvature of the FEM. The relationshipbetween the curvature of the FEM and the domains can beadjusted in the software—this results in more or less do-mains being created. The default parameters were used inthis study and it will be the subject of further research toinvestigate the effect of these parameters. A “handle” is thenautomatically created which guides the nodes in each do-main, coronal and sagittal view of FEM with handles, blackdots, shown in Fig. 5scd. The domains, on the base model,are mapped to the surface, from the secondary model. Thehandles drive the deformable alignment and an orthogonalnode projection completes the alignment of the base-modelFEM to the surface of the secondary model, results shown inFig. 5sdd. It is important to emphasize that this is a node tosurface alignment, not a node-to-node alignment between thecorresponding FEM of the organs in the base and secondary

model. The node to surface alignment eliminates thestime-consumingd need to identify corresponding points on tworepresentations of a region of interest. This vector projectionfor each node, i.e., the difference between each node positionon the base model and after theHYPERMORPHalignment, isthen assigned as a boundary condition on the multi-organbase model. TheHYPERMORPH process takes an average of45–120 s on a Pentium 4 2.4 GHz processor, depending onthe number of nodes and complexity of the FEM.

E. Finite element analysis

Once theHYPERMORPHalignment is performed on the se-lected organs and the results are applied as boundary condi-tions sconstraints, displayed in step 6 of Fig. 2d, finite ele-ment analysis sFEAd is performed to determine thedisplacements of all nodes not explicitly constrained withloads defined from theHYPERMORPHprocess, and the result-ing stress and strain on the elements.

The FEA was performed as a static direct single step. Theanalysis was performed on a Quad Xeon MP 2.0 GHz DellP6600 with 4 Gbytes of RAM. The average wall clock timefor the FEA analysis was 332 s for the abdominal cases and

FIG. 5. HYPERMORPH deformable registration: liver example:sad inhalespinkd and exhalesblued liver, sbd after COG registration,scd surface definedfor inhale liverspinkd, sdd liver prior to deformable alignment, with handlessyellowd, sed after deformable alignment, andsfd exhale liver in inhaleposition.

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495 s for the thoracic cases. The average total CPU time was1064 s for the abdominal cases and 1623 s for the thoraciccases.

The results of the FEA can be viewed as a set of displace-ment vectors, contoured color washes of the FEM of dis-placementssshown in step 7 of Fig. 2d, stress, or strain, as ananimation of the deformation results, or by applying the re-sults and comparing to the actual FEM of the secondary dataset. Raw numerical data can also be exported for quantitativeanalysis.

F. Accuracy and residual error calculation

The accuracy of the explicit organ deformation was deter-mined by calculating the difference between the actual dis-placement of the vessel and bronchial bifurcations identifiedon both inhale and exhale data setssACTd to the displace-ment predicted by the FEAsPREDd. An average of 8.6 vesselbifurcationssrange: 7–10d were selected in each liver and 10bronchial bifurcationssrange: 6–14d were selected in eachlung. The bifurcations were selected to best encompass all ofthe organ volume, however the lung bifurcations were biasedto the hilum area where bifurcations were larger and moreeasily seen on the MR image. The accuracy is reported asboth the average and standard deviation of the signed differ-ence sPRED-ACTd, indicating any bias in the registration,and the average and standard deviation of the unsigned dif-ferencesuPRED-ACTud, indicating the expected distance toagreement between the deformable registration and the dis-placement predicted by the bifurcations.

The precision of selecting the same bifurcation locationon each MR scan was limited by the slice thickness,4–5 mm, and the resolution of the image, an average in-plane pixel size of 0.14 by 0.14 cm, reduced slightly fromthe use of ASSET. For three liver scans and three lung scans,six randomly selected bifurcations were used to test repro-ducibility of bifurcation localization. Assessments were per-formed once a week, for four weeks. The reproducibility ofbifurcation selection was determined by displaying the origi-nal identifying mark on the base image and having the cor-responding bifurcation on the secondary image dataset rese-lected in a random order.

The accuracy of the deformable alignment of organs notexplicitly deformed was determined by applying the resultsof the FEA and then performing volumetricHYPERMORPH

deformable alignment between the predicted secondary posi-tion and the actual secondary position to determine the re-sidual error. The volumetricHYPERMORPHprocess is an ex-

pansion of theHYPERMORPHprocess described in Sec. II Dand is performed on a volumetric tetrahedral mesh.

III. RESULTS

A. Reproducibility of bifurcation selection

The precision of the bifurcation identification, determinedby repeat bifurcation selection, was less than 0.1 cm in eachdirection sTable IId. The maximum standard deviation for abifurcation was 0.47, 0.20, and 0.25 cm in the LR, AP, andIS direction, respectively.

B. Accuracy of individual organ deformableregistration

HYPERMORPH organ deformation was successfullyperformed on the liver, spleen, lungs, and body organ meshesof all five volunteers. The average liver motion over allcases from exhale to inhale, based on FEM node displace-ments, and range of individual node displacements, was0.09 cm srange: −1.42 to 1.25 cmd, 0.75 cm srange:−0.65 to 2.23 cmd, and −1.20 cmsrange: −3.15 to 0.78 cmd,in the LR, AP, and IS direction, respectively. Positivedisplacement values indicate motion in the right, anterior,superior direction. The average lung motion from inhale toexhale, based on the FEM node displacements, was−0.11 cm srange: −2.11 to 1.81 cmd, −0.78 cm srange:−2.11 to 0.89 cmd, and 0.59 cmsrange: −1.11 to 5.30 cmd,in the LR, AP, and IS direction, respectively.

The accuracy of the liver and lung deformable registrationis summarized in Table III. The accuracy of the deformableregistration of the liver, as measured by the average standarddeviation of the differencesPRED-ACTd is less than 0.20 cmin each direction, on the same order of the in-plane pixel sizeof the image, 0.14 cm. The average error is 0.10 cm or lessin each direction, indicating no apparent systematic error inregistration. The average absolute differencesuPRED-ACTudis 0.12 cm ss.d. 0.07 cmd, 0.17 cm ss.d. 0.14 cmd, and0.14 cmss.d. 0.10 cmd, in the LR, AP, and IS direction, re-spectively.

The accuracy of the deformable registration of the lung,as measured by the average standard deviation of the differ-encesPRED-ACTd, is 0.26 cm or less in each direction, alsoon the same order of the in-plane pixel size of the image,0.14 cm. The average error is 0.17 cm or less in the LR andIS direction, however, the average error is slightly larger,0.24 and 0.40 cm in the AP direction for the right and leftlung, respectively, indicating a potential systematic AP error.

TABLE II. Precision of bifurcation identification for the lung and liverscmd. LR=left–right, AP=anterior–posterior, IS=inferior–superior.

Average

Liver Lung

LR AP IS LR AP IS

Average 0.05 0.05 0.06 0.01 0.09 0.06 0.01Standard deviation 0.06 0.02 0.04 0.05 0.10 0.04 0.06

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The average absolute differencesuPRED-ACTud is 0.23 cmss.d. 0.14 cmd, 0.36 cm ss.d. 0.17 cmd, and 0.19 ss.d.0.14 cmd, in the LR, AP, and IS direction, respectively.

C. Accuracy of multi-organ deformable registration

Multi-organ deformable registration was successfully per-formed for all five thoracic and abdominal cases. Figure 6illustrates the initial differences between the exhale and in-hale position for thoracic and abdominal regions of one case,V4. Figure 6sad illustrates the differences through a transpar-ency overlay of the abdominal regionsleftd and thoracic re-gion srightd. Figure 6sbd shows the difference in organ posi-tion between inhale and exhale, for the abdominal regionsleftd and thoracic regionsrightd. Organs to be registered areshown in multiple colorssexhale liver, spleen kidneys, andstomach for the abdominal region; inhale breast and lungsfor the thoracic regiond, inhale abdominal organs are shownin blue and exhale thoracic organs are shown in orange. Theresults of the FEA are shown as a color wash on the organmeshes in Fig. 6scd. The average displacement and rangeover all volunteers, of the left and right kidneys, stomach,spleen, and right and left breasts are shown in Table IV.

The accuracy of the secondary-organ deformable registra-tion, shown in Table V, reflects the displacement of all nodesrepresenting the organ volume mesh between the predictedsecondary position and actual secondary position. This erroralso includes the error in manual organ contouring, from

which the organ mesh is created. The average error is lessthan 0.10 cm in each direction for all organs, standard devia-tion of 0.21 cm or less in each direction. The average abso-lute differencesuPRED-ACTud of implicitly deformed organswas 0.11 ss.d.: 0.11d, 0.13 ss.d.: 0.12d, and 0.08ss.d.:0.09d cm, in the LR, AP, and IS directions, respectively.Figure 7 illustrates the excellent agreement between the FEApredicted positionsinhale for abdominal, exhale for thoracicdand the actual position. The residual error for one case, ab-dominal V4, is highlighted in Fig. 8, which shows a colorwash of the residual error as well as a plot of the vectorresidual error as a function on IS position, with correspon-dence to the color wash for the larger residual error regionsfor the stomach, Fig. 8sad, right kidney, Fig. 8sbd, and leftkidney, Fig. 8scd. The small clusters of residual error sup-ports the rationale that these discrepancies are largely due tolocal contouring errors.

IV. DISCUSSION

A novel finite element model-based multi-organ imageregistration technique,MORFEUS, has been described and itsaccuracy assessed. In addition to being fast and accurate, thisbiomechanical based method allows the registration of or-gans based on their biomechanical properties and their posi-tion with respect to other organs, which are explicitly regis-tered.MORFEUS has been developed through a combinationof commercially available software programs; however, thefundamental aspects of the processscontour-based guidedsurface projection of a limited number of regions of interestto determine explicit deformation and the correct assignmentof material properties and surface interfaces to determine im-plicit deformationd can be applied using other commerciallyavailable or in-house developed programs. Several param-eters associated withMORFEUS have been described in thismanuscript, with initial values reported. These parameters,which allow potentially great flexibility in the model, alsorequire understanding and investigation. Research into thesensitivity and optimal values of these parameters is the sub-ject of current and future work.

Surface matching algorithms for deformable registrationhave been previously described for single organ deformableregistration, most using an internal energy function. Ferrantet al.describe a method for registering 3D intraoperative MRimages of the brain using a deformable surface matchingalgorithm, based on iteratively image-derived forces and anenergy minimization, which tracks the cortical surface andlateral ventricles.62 The algorithm reduced surface-basedlandmark discrepancies from 1.0 cm to less than 0.1 cm andsubsurface landmarks from 0.6 to 0.3 cm or less. Lianget al.describe a method for single-organ image registration usingFEM, organ boundary point correspondences, and a surfaceenergy minimization.44 The algorithm was tested on simu-lated deformation of the rectum. The error in registration wasreduced from 0.9 cmsmaximumd based on initial boundarypoint correspondence to 0.16 cm after optimization. Zhanget al. have reported on initial investigations using a deform-

TABLE III. Accuracy of deformable image registration for organs directlyundergoingHYPERMORPHalignment, for each volunteer and the average overall five, sPRED-ACTd. sR=Right, L=Left, LR=left–right, AP=anterior–posterior, IS=inferior–superiord scmd.

Organ

Averagess.d.d

LR AP IS

Liver −0.05s0.27d −0.10s0.24d −0.03s0.15dV1 R Lung −0.11s0.22d 0.30s0.15d 0.05s0.42d

L Lung 0.13s0.21d 0.55s0.18d −0.11s0.18d

Liver 0.01s0.10d −0.17s0.27d −0.07s0.19dV2 R Lung 0.32s0.14d 0.28s0.32d −0.03s0.31d

L Lung 0.31s0.22d 0.39s0.33d −0.17s0.28d

Liver −0.04s0.15d −0.09s0.17d 0.05s0.21dV3 R Lung 0.10s0.34d 0.27s0.09d 0.00s0.08d

L Lung 0.27s0.29d 0.47s0.19d 0.00s0.19d

Liver 0.04s0.10d −0.10s0.21d 0.07s0.14dV4 R Lung 0.07s0.22d 0.24s0.21d −0.18s0.14d

L Lung 0.12s0.20d 0.30s0.39d −0.17s0.16d

Liver 0.04s0.08d −0.04s0.10d 0.11s0.17dV5 R Lung 0.08s0.12d 0.10s0.20d −0.03s0.17d

L Lung 0.05s0.18d 0.28s0.19d 0.10s0.25d

Liver 0.00(0.14) −0.10(0.20) 0.02(0.17)Average R Lung 0.09(0.21) 0.24(0.19) −0.04(0.22)

L Lung 0.17(0.22) 0.40(0.26) −0.07(0.21)Overall 0.09(0.19) 0.18(0.22) −0.03(0.20)

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able lung model based on negative surface pressure, howeverquantitative results have not yet been reported.63

The accuracy of the direct organ deformable registrationis dependent, to some extent, on the accuracy and consis-tency of the contouring and on material properties. Auto-contouring was performed on the lung and external surface,all other organs were manually contoured in a clinically rea-sonable amount of time. Contouring was performed by aphysicistsKKB d and checked for accuracy and edited if re-quired by a physiciansLAD d. Attention was paid in assessingthe auto-contours of the lung to ensure that the inclusion ofbronchi was consistent between inhale and exhale images.

There is a small, yet potentially significant, systematicerror in the AP direction of the lung accuracy, maximum of0.47 cm for one volunteer. We are currently investigating thisdiscrepancy, by creating a predicted, deformed MR image tocompare to the actual MR image. Ongoing work will alsoassess deformable registration of the lung, using patient CTscans, where bronchial bifurcations should be easier to visu-alize, allowing more bifurcations to be localized for a morecomplete analysis of the accuracy of the deformable registra-tion of the lung.

The material properties for the liver and lung were deter-mined after a patient population optimization. The optimal

FIG. 6. sad FEM transparency overlayprior to registration,sbd comparison ofFEM between exhale and inhalesex-hale abdominal organs in color, inhalein light blue; inhale thoracic organs incolor, exhale in oranged, scd displace-ment contours of FEA resultsscmd.

TABLE IV. Average sranged of organ motionsLR=left–right, AP=anterior–posterior, IS=inferior–superiordscmd.

LR AP IS

Left kidney −0.19s−1.11 to 0.65d 0.59 s−1.11 to 1.33d −1.00 s−2.01 to 0.02dRight kidney −0.15s−0.77 to 0.08d 0.48 s−0.77 to 1.39d −1.08 s−1.75 to −0.34d

Stomach −0.17s−1.19 to 0.42d 0.73 s−1.03 to 1.64d −0.94 s−2.07 to 1.03dSpleen −0.59s−1.76 to 1.00d 0.71 s−1.46 to 1.74d −1.56 s−3.15 to −0.45d

Right breast −0.19s−0.41 to 0.02d −0.82 s−1.17 to −0.27d −0.18 s−0.41 to 0.16dLeft breast 0.19s−0.17 to 0.47d −0.84 s−1.36 to −0.29d −0.18 s−0.40 to 0.34d

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value of Poisson’s ratio,n, across all five subjects, was 0.45for the liver. Individual optimal values ranged from 0.36 to0.49, however, the difference in the average bifurcation errorcomputed with the population optimal value and the patientspecific optimal value was less than 0.008 cm in all cases,indicating a relatively small fluctuation with changingn. Anoptimal n value was difficult to determine for the lung.Trends varied between subjects as well as between LR, AP,and IS directions. The variation in the vector magnitude errorof the FEA’s prediction of the bifurcation displacement was0.11 cm or less between the range ofn=0.35 to 0.48, for allsubjects. The optimal value was determined from the error inthe IS direction only for four of the five subjects, as onevolunteer sV5d had an optimaln smaller than 0.35. Thetrends in the IS direction showed a distinct minimum for allfour patients. The optimal value ofn was 0.45 for the lungacross all five subjects. This difference in optimaln between

different directions of motion could explain the small sys-tematic error in the AP direction. It is the goal of future workto investigate the potential benefit of anisotropic linear elas-tic material properties and hyperelastic material propertiesusing multi-step, incremental fixed boundary conditions.

For organs explicitly deformed using the surface projec-tion method, Young’s modulus was irrelevant because aboundary constraint was applied to every node on the surfaceof the organ. A full optimization on all organ parameters wasnot performed because of the coupled parameters, Young’smodulus and Poisson’s ratio for each organ and dependenceof the three separate organs in the thoracic case and fiveorgans in the abdominal case.

In the present study, the accuracy of secondary organ reg-istration is determined by comparing the predicted contourposition with the actual contour position, since reliable inter-nal landmarks are not present. Efforts are ongoing to developa method of generating a predicted image, from the FEAresults, to compare to the actual image to allow for quantifi-cation of the error that is independent of the accuracy of thecontours.

There are many potential applications for this registrationmethod. In the pretreatment setting, multi-modality imagescan be registered to the planning CT using FEM-based de-formable image registration. Organs that can be easily visu-

TABLE V. Accuracy, average, and standard deviation, of secondary organs,not directly deformed usingHYPERMORPH sPRED-ACTd. sLR=left–right,AP=anterior–posterior, IS=inferior–superiord scmd.

Organ

Averagesstandard deviationd

LR AP IS

V1 R Breast 0.04s0.16d 0.00s0.16d −0.01s0.07dL Breast −0.03s0.15d 0.00s0.14d −0.01s0.07dR Kidney −0.01s0.10d −0.01s0.15d 0.01s0.10dL Kidney −0.03s0.24d −0.10s0.20d −0.02s0.15dStomach 0.02s0.14d −0.02s0.17d 0.01s0.13d

V2 R Breast 0.01s0.10d 0.05s0.15d −0.04s0.10dL Breast −0.01s0.14d 0.04s0.16d −0.03s0.12dR Kidney 0.16s0.23d −0.05s0.27d −0.01s0.20dL Kidney 0.18s0.23d −0.27s0.25d −0.12s0.16dStomach 0.09s0.26d −0.15s0.32d 0.01s0.23d

V3 R Breast 0.19s0.22d 0.03s0.21d −0.11s0.16dL Breast 0.04s0.13d 0.03s0.13d −0.07s0.10dR Kidney −0.01s0.10d 0.04s0.10d −0.03s0.08dL Kidney 0.00s0.16d −0.04s0.17d −0.02s0.10dStomach 0.09s0.19d −0.06s0.19d −0.11s0.23d

V4 R Breast −0.02s0.08d −0.02s0.10d −0.01s0.08dL Breast 0.00s0.12d −0.03s0.14d −0.07s0.16dR Kidney 0.00s0.14d 0.12s0.12d 0.07s0.11dL Kidney −0.01s0.09d 0.05s0.10d 0.06s0.09dStomach 0.04s0.10d 0.01s0.10d −0.02s0.12d

V5 R Breast 0.02s0.07d 0.06s0.10d 0.01s0.05dL Breast −0.01s0.12d 0.09s0.13d −0.10s0.15dR Kidney 0.06s0.12d 0.09s0.10d 0.01s0.10dL Kidney −0.07s0.08d 0.04s0.10d −0.02s0.08dStomach 0.04s0.17d 0.01s0.21d −0.07s0.13d

Average R Breast 0.05(0.13) 0.02(0.14) −0.03(0.09)L Breast 0.00(0.13) 0.03(0.14) −0.06(0.12)R Kidney 0.04(0.13) 0.04(0.15) 0.01(0.12)L Kidney 0.02(0.16) −0.06(0.16) −0.02(0.12)Stomach 0.06(0.17) −0.04(0.21) −0.04(0.17)Overall 0.03(0.14) 0.00(0.16) −0.03(0.12)

FIG. 7. Organ comparison with FEA results applied. Predicted position inblue sinhale abdominal organs, exhale thoracic organsd and actual positionin red.

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alized on each image data set can be contoured and used toguide the deformation of other regions of interest, whichmay not be as easily visible on one imaging modality. Thiscan be especially useful for registering MR to CT, where thetumor may have different image characteristics on each mo-dality and image deformation may compromise geometricaccuracy. The proposed FEM-based deformable image regis-tration will allow the tumor to be registered according to thematerial properties and the deformation of the organ withwhich it resides. This will allow a direct comparison of thetumor region on MR to CT, whereas with image-intensitybased registrations, the change in intensity of the tumor willdrive the tumor on one imaging modality to match that onthe other imaging modality, losing the ability to quantify thedifferences in the tumor across imaging modalities. In addi-tion to registering anatomical data, functional informationcan also be incorporated into the treatment planning processby registering functional images, such as MR spectroscopy.

In addition to registering and comparing pretreatment im-ages from different modalities to compare tumor extent,post-treatment follow-up images can also be registered todetermine tumor response and changes in normal tissue. AsFEM-based deformable image registration is biomechanical-based, it has the potential to model both normal tissue hy-pertrophy and tumor shrinkage for an accurate assessment ofdisease status and change in normal tissues.

Another application is the on-line treatment setting using,for example, cone-beam CT or MV CT. Registering the sur-rounding organs, visible on the CBCT or MVCT, to the plan-ning imaging data set which may include multiple imagingmodalitiesse.g., PET, MRSd, allows localization of a tumoror another functional volume of interestse.g., hypoxic vol-umed for at the time of treatment, based on prior knowledgeof the interaction between the tumor and surrounding organs.The combination of image-guidance registration and the abil-ity to track response of tissues to radiation has the potentialto provide image-guidance and adaptive treatment to tumors,which may respond quickly to radiation and therefore changeduring the course of treatment.64–66

For each registration setting and anatomical location onemust determine the appropriate regions of interest to explic-itly deform. For multiple scans during the same imaging ses-sion, such as variations in breath hold or monitoring of blad-der and rectal filling, setup error does not exist and thereforebony registration is not important. The majority of imageregistration includes setup error resulting from subtlechanges in patient position. For these cases, bones should beincluded in the registration process, as discussed in Sec. II C.The accuracy of registration will increase as the number oforgans explicitly deformed increases, however, this will alsoincrease the amount of time required. For example, for atumor located in the center of the liver, acceptable deform-able registration of the planning CT to the daily cone-beamCT may only require that the liver be accurately registered.However, if the tumor is in the inferior region and there issignificant risk to the kidney and stomach, explicitly deform-ing the liver and spleen is necessary.

FIG. 8. Vector magnitude of the residual error after deformable registrationof the sad stomach,sbd right kidney, andscd left kidney. Frequency plotindicating residual error as a function of IS positionscmd.

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The results of the FEA can be illustrated as vector plots,indicating the motion and deformation of a selected ROI.This is a natural assessment of a patient-specific internal tar-get volumesITV d margin, allowing for anisotropic margins,which will allow for sparing of normal tissue. These vectorscan also be overlaid on the dose distribution to provide in-formation on the movement of sensitive structures into thehigh dose region.

Dose calculations and optimizations can also be improvedby including respiration or other physiological motion byincorporating the motion and deformation into the dosecalculation.42,45 Intermediate positions can be generated bylinear interpolation of the FEA results. Figure 9 shows theprogression of the thoracic organs over five steps from inhaleto exhale position.

V. CONCLUSIONS

In summary, a platform to perform multi-organ deform-able image registration using finite element modeling has

been developed. Its feasibility and accuracy has been shownthrough deformable image registration of MR images at dif-ferent respiratory states for both the thorax and the abdomi-nal regions. Future research will expand this platform to per-form deformable registration in other anatomical sites, suchas the pelvis and integrated into online image guidance pro-cedures, dose calculations that include deformation, and tu-mor and normal tissue follow-up.

ACKNOWLEDGMENTS

This work was supported in-part by a research grant fromVarian Medical Systems. The authors would also like tothank Anna Kirilova for her assistance with the MR imaging.

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FIG. 9. Linear progression from initialposition to completion of deformableregistration from inhale to exhale. Ex-hale organssredd, inhale organssblued,inhale externalslight grayd, exhale ex-ternal snot shownd.

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