Medical Image Analysis 22 (2015) 22–34

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Medical Image Analysis

journal homepage: www.elsevier .com/locate /media

Patient-specific biomechanical model as whole-body CT imageregistration tool

http://dx.doi.org/10.1016/j.media.2014.12.0081361-8415/� 2015 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Intelligent Systems for Medicine Laboratory, School ofMechanical and Chemical Engineering, The University of Western Australia,Crawley, Perth, WA 6009, Australia.

E-mail address: adam.wittek@uwa.edu.au (A. Wittek).

Mao Li a, Karol Miller a,b, Grand Roman Joldes a, Barry Doyle c,d, Revanth Reddy Garlapati a, Ron Kikinis e,f,g,Adam Wittek a,⇑a Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, Perth, Australiab Institute of Mechanics and Advanced Materials, Cardiff School of Engineering, Cardiff University, Cardiff, Wales, UKc Vascular Engineering, Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, Perth, Australiad Centre for Cardiovascular Science, The University of Edinburgh, Edinburgh, UKe Surgical Planning Laboratory, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USAf Fraunhofer MEVIS, Bremen, Germanyg Professor für Medical Image Computing, MZH, University of Bremen, Bremen, Germany

a r t i c l e i n f o

Article history:Received 10 December 2013Received in revised form 8 August 2014Accepted 13 December 2014Available online 30 January 2015

Keywords:Whole-body image registrationPatient-specific biomechanical modelNon-linear finite element analysisFuzzy-C MeansHausdorff distance

a b s t r a c t

Whole-body computed tomography (CT) image registration is important for cancer diagnosis, therapyplanning and treatment. Such registration requires accounting for large differences between sourceand target images caused by deformations of soft organs/tissues and articulated motion of skeletal struc-tures. The registration algorithms relying solely on image processing methods exhibit deficiencies inaccounting for such deformations and motion. We propose to predict the deformations and movementsof body organs/tissues and skeletal structures for whole-body CT image registration using patient-speci-fic non-linear biomechanical modelling. Unlike the conventional biomechanical modelling, our approachfor building the biomechanical models does not require time-consuming segmentation of CT scans todivide the whole body into non-overlapping constituents with different material properties. Instead, aFuzzy C-Means (FCM) algorithm is used for tissue classification to assign the constitutive properties auto-matically at integration points of the computation grid. We use only very simple segmentation of thespine when determining vertebrae displacements to define loading for biomechanical models. Wedemonstrate the feasibility and accuracy of our approach on CT images of seven patients suffering fromcancer and aortic disease. The results confirm that accurate whole-body CT image registration can beachieved using a patient-specific non-linear biomechanical model constructed without time-consumingsegmentation of the whole-body images.

� 2015 Elsevier B.V. All rights reserved.

1. Introduction

Reliable and accurate radiographic image registration thataligns the source and target images is critical for application ofmedical imaging in cancer diagnosis, therapy planning and treat-ment (Black et al., 1997; D’Amico et al., 2000; Jenkinson andSmith, 2001; Spicer et al., 2004; Van Sint Jan et al., 2006;Warfield et al., 2005; Zaidi, 2007). A large number of medicalimage registration algorithms solely relying on image processingmethods have been successfully developed over the years (Caoand Ruan, 2007; Jenkinson and Smith, 2001; Sotiras et al., 2013;

Wells et al., 1996). Many of them have been demonstrated to beeffective for selected organs, such as the brain, breast, prostateand lungs (Goerres et al., 2002; Mattes et al., 2003; Oguro et al.,2011; Rueckert et al., 1999; Warfield et al., 2005). However, ithas been also recognised that large differences between the sourceand target images caused by complex rigid-body motion ofarticulated bones, skeletal segments and body organs and largedeformations of soft tissues associated with whole-body CT/MRIregistration are very challenging for such algorithms (Baikeret al., 2007; Li et al., 2008; Martin-Fernandez et al., 2005; Witteket al., 2007). Despite some successful attempts to improve robust-ness of registration algorithms (Toews and Wells, 2013) and regis-tration accuracy for selected body segments for limited range ofrigid body motion and soft organs/tissues deformation (Mahfouzet al., 2003; Stromqvist et al., 2009), the whole-body CT image reg-istration still remains a largely unsolved problem (Li et al., 2008).

Source Target Source Target

Case I Case II

Case III Case IV

Case V Case VI

Case VII

Fig. 1. Sagittal sections of seven CT image datasets analysed in this study. For Case I, no information about the pathology type is available. Cases II–V are patients sufferingfrom cancer. Cases VI and VII are patients suffering from aortic disease.

M. Li et al. / Medical Image Analysis 22 (2015) 22–34 23

Therefore, patient-specific biomechanical modelling methodsthat account for the mechanical behaviour of organs/tissues wererecommended by many researchers for registration problemsinvolving large differences (deformations) between the sourceand target images (Al-Mayah et al., 2010; Hopp et al., 2013;Warfield et al., 2002; Wittek et al., 2007). Unlike image-basedmatching, registration algorithms using biomechanical models donot require selection of specific type of source-to-target imagetransformation and optimisation of the transformation parameters

to maximise a selected similarity measure between the trans-formed and target images. Instead, they rely on principles ofmechanics to compute deformations that transform source imageto target image. This ensures plausibility and robustness of the pre-dicted deformations. In particular, patient-specific biomechanicalmodelling has been successfully used in numerous studies on com-puting the brain deformations for neuroimage registration(Garlapati et al., 2014; Hu et al., 2007; Ji et al., 2009; Mostayedet al., 2013; Wittek et al., 2010; Xu and Nowinski, 2001).

Table 1Resolution (in mm) of seven CT image datasets analysed in this study.

Source image (mm) Target image (mm)

Case I 0.98 � 0.98 � 5.0 0.98 � 0.98 � 5.0Case II 1.00 � 1.00 � 5.0 1.00 � 1.00 � 5.0Case III 0.84 � 0.84 � 2.5 0.80 � 0.80 � 2.5Case IV 0.90 � 0.90 � 2.5 0.98 � 0.98 � 2.5Case V 1.05 � 1.05 � 2.5 1.06 � 1.06 � 2.5Case VI 1.00 � 1.00 � 2.5 1.00 � 1.00 � 2.5Case VII 0.86 � 0.86 � 3.0 0.76 � 0.76 � 3.0

24 M. Li et al. / Medical Image Analysis 22 (2015) 22–34

Challenges to overcome when applying biomechanical mod-elling for medical image registration include quick and reliable gen-eration of patient-specific computational models, automaticsegmentation of radiographic images and efficient solution of themodels (Miller, 2011; Miller et al., 2010; Mostayed et al., 2013). Tofacilitate rapid generation of patient-specific biomechanical modelsfor whole-body CT image registration, we abandon time-consumingimage segmentation that divides the problem domain into non-overlapping constituents with different material properties. Instead,we apply tissue classification based on the Fuzzy C-Means (FCM)algorithm to assign the constitutive properties automatically atintegration points of the computation grid (Bezdek et al., 1984;Zhang et al., 2013). This, allows us to generate the patient-specificbiomechanical model automatically and rapidly.

In principle, any verified method of non-linear computationalmechanics accounting for both geometric and material nonlin-earity can be used to solve biomechanical models for computingsoft organ/tissue deformations for image registration. Non-linearfinite element analysis with either implicit (Allard et al., 2007;Taylor et al., 2008) or explicit (Hu et al., 2007; Joldes et al.,2009b; Miller et al., 2007; Wittek et al., 2007) integration in timedomain remains the most commonly used approach. In our previ-ous research, we have developed and verified a suite of efficientalgorithms for computing soft tissue deformations in the contextof neuroimage registration (Joldes et al., 2009b; Miller et al.,2007, 2011). In this study, we adapt and apply these algorithmsin registration of whole-body CT images.

To demonstrate feasibility and accuracy of whole-body CTimage registration using the proposed non-linear biomechanicalmodel, we analysed sets of whole-body/torso CT images of sevenpatients. Deformation within the patient’s body to align a sourceimage to target image is predicted using a patient-specific modelthat relies on Total Lagrangian Explicit Dynamics TLED non-linearfinite element algorithm (Joldes et al., 2009b; Miller et al., 2007,2011). Accuracy of the registration is quantitatively assessed usingthe Hausdorff distance metric to measure the spatial distancebetween the corresponding Canny edges in the registered (i.e.deformed using the deformations computed by means of biome-chanical model) and target images (Fedorov et al., 2008;Garlapati et al., 2013, 2014; Huttenlocher et al., 1993).

This paper is organised as follows: the proposed patient-specificnon-linear finite element model and the TLED algorithm are pre-sented in Section 2; the computational results, including accuracyevaluation, are given in Section 3 which is followed by the discus-sion and conclusions in Section 4.

2. Methods

2.1. CT image datasets used in the study

As CT carries health hazard due to large radiation doses, thereare very strict clinical guidelines limiting the number of situationswhere acquiring whole-body CT should be considered(Environmental Protection Authority, 2013; American College of

Radiology, 2011a, 2011b). Therefore, we created a challengingtest-bed for our registration method not through registration of alarge number of image datasets, but by applying them to imagedatasets for different diseases/pathologies: cancer (Cases II–V inFig. 1) and aortic diseases (Cases VI and VII in Fig. 1). Each of theanalysed datasets consists of two sets of images of a given patientacquired at different times. We treated one of them as mov-ing/source image and another as a target image (Fig. 1 shows sagit-tal sections for each dataset).

Case I is from the publicly available Slicer Registration Library

(Case #20: Intra-subject whole-body/torso PET–CT (http://www.na-mic.org/Wiki/index.php/Projects:RegistrationLibrary:

RegLib_C20b). The Slicer Registration Library contains no informa-tion about a pathology type for Case I. The CT image datasets ofcancer patients (Cases II, III, IV and V) were obtained the NationalBiomedical Image Archive (http://public.cancerimagingarchive.net/ncia/login.jsf)—freely available to browse, download and usefor commercial, scientific and educational purpose under the Crea-tive Commons Attribution 3.0 Unported Licence.

Case VI is from the University Hospital Limerick, Ireland, and CTscan data was acquired for surgical planning and treatment ofabdominal aortic aneurysm. Case VII was acquired at the FremantleHospital, Australia, with scans taken as part of type B aortic dissec-tion diagnosis and treatment. Local ethics approval was obtainedfrom both institutions. All imaging datasets were anonymous andnot acquired specifically for this study.

The CT datasets used in this study were acquired in differentresolutions (Table 1). Before conducting the analysis, we resampledthem to a common resolution of 1 mm � 1 mm � 2.5 mm. Resam-pling was conducted using linear interpolation—we applied the‘‘Resample Scalar Volume’’ procedure in 3D SLICER open sourcesoftware package for medical image computing (Fedorov et al.,2012).

2.2. Patient-specific non-linear biomechanical model

Biomechanics-based medical image registration requires incor-poration of patient-specific data in the biomechanical model. How-ever, how to generate biomechanical model quickly and reliablyremains unsolved (Miller et al., 2011). A set of methods employedin this study can be regarded as one possible solution to thisproblem.

2.2.1. Element type, geometry and mesh generation for patient-specificbiomechanical model2.2.1.1. Element type selection. In practice, in computational biome-chanics tetrahedral elements are often used for spatial discretisa-tion of the problem domain due to availability of automaticmesh generators for complex geometries of the body organs(Irving et al., 2006; Wittek et al., 2007). However, a 4-noded tetra-hedral element has an intrinsic drawback of volumetric locking forincompressible or nearly incompressible materials such as soft tis-sues (Hughes, 2000). Therefore, we used under-integrated (withone Gauss point) 8-noded hexahedral elements that do not exhibitlocking (Flanagan and Belytschko, 1981; Irving et al., 2006). Practi-cal aspects of application of hexahedral elements in biomechanicalmodels include preventing of instabilities due to zero energy(hourglass) modes and ensuring the element quality (Yang andKing, 2011). For hourglass control, we used the method proposedby Joldes et al. (2008). The efficiency and effectiveness of thismethod has been verified through application in the studies oncomputation of brain deformation for neuroimage registration(Joldes et al., 2009b; Wittek et al., 2010). Although no commonlyaccepted specific guidelines regarding the required quality ofhexahedral meshes in biomechanics are available, several authors

Case I Case II Case III

Case IV Case V Case VI

Case VII

Fig. 2. Patient-specific hexahedral meshes built in this study. We used Fuzzy C-Means (FCM) algorithm for tissue classification to assign the constitutive propertiesautomatically at integration points, there was no need to distinguish internal organs when constructing the meshes.

M. Li et al. / Medical Image Analysis 22 (2015) 22–34 25

have formulated their experience-based recommendations (Itoet al., 2009; Mostayed et al., 2013; Shepherd and Johnson, 2009;Yang and King, 2011). Following Ito et al. (2009), Shepherd andJohnson (2009) and Yang and King (2011), we used element Jaco-bian and warpage to assess mesh quality. We regarded hexahedralelements with Jacobian below 0.2 as unacceptable poor quality andelements with Jacobian between 0.2 and 0.3 – as questionable

quality. In all models used in this study, the element Jacobianwas above 0.35 and maximum warpage was 25.

2.2.1.2. Patient-specific geometry. The 3D patient-specific torso geo-metry was created from the CTs using the 3D SLICER (http://www.slicer.org/), an open-source software for visualisation, registration,segmentation and quantification of medical data developed by

Table 2Numbers of hexahedral elements and nodes for seven analysed cases.

Number of nodes Number of elements

Case I 55,944 51,479Case II 88,265 82,301Case III 54,190 49,950Case IV 137,344 128,989Case V 78,573 72,897Case VI 86,016 92,625Case VII 50,889 49,478

Fig. 3. Tissue classification for a torso CT transverse section. A certain number oforgans/tissues (i.e. bones and fat) can be recognised by distinctive image intensity.Some organs/tissues have similar image intensity (i.e. kidneys, liver, small/largeintestines and muscles).

26 M. Li et al. / Medical Image Analysis 22 (2015) 22–34

Artificial Intelligence Laboratory of Massachusetts Institute ofTechnology and Surgical Planning Laboratory at Brigham andWomen’s Hospital and Harvard Medical School. Geometry creationinvolved application of automated level tracing algorithm availablein 3D SLICER to distinguish the patient’s body from the rest of theimage and creation of the 3D discrete representation (surface mod-el) of the patient’s body. Internal organs, muscles, fat and other tis-sues were not segmented.

2.2.1.3. Patient-specific mesh generation. 3D surface model of thepatient’s body was used as the boundary for volumetric discretisa-tion (meshing) using hexahedral elements. Hexahedral mesh wascreated using IA-FEMesh (a freely available software toolkit forhexahedral mesh generation developed at the University of Iowa)(Grosland et al., 2009) (http://www.ccad.uiowa.edu/MIMX/projects/IA-FEMesh) and HyperMesh™ (a high-performance com-mercial finite element mesh generator by Altair, Ltd. of Troy, MI,USA). The maximum element size was designated a value of5 mm (the maximum voxel in the analysed CTs). However, dueto differences in body dimension between the patients, the gener-ated meshes appreciably vary in size (as measured by the numberof nodes and elements) as indicated in Fig. 2 and Table 2.

As we used Fuzzy C-Means (FCM) algorithm for tissue classifica-tion to assign the constitutive properties automatically at integra-tion points, there was no need to distinguish internal organs whenconstructing the meshes (Fig. 2).

2.2.2. Load and boundary conditionsAs suggested in our previous studies (Miller and Lu, 2013;

Miller et al., 2011, 2010), for problems where loading is prescribedas forced motion of boundaries, the unknown deformation fieldwithin the domain depends very weakly on the mechanical prop-erties of the continuum. In studies involving application of biome-chanical models in image registration, the displacements to defineforced motion of the boundaries are typically determined by com-paring position of corresponding points in the source and targetimages (Wittek et al., 2010). Body surface (skin) appears to beone possible source of information to determine such displace-ments. However, there are only very few features (landmarks) onthe skin that can be reliably distinguished in CT images. Therefore,we used the spine (vertebrae) when determining the displace-ments (between the source and target images) to prescribe forcedmotion of the boundaries—in CT images vertebrae are easy to dis-tinguish from the surrounding soft tissues and their shape does notchange between the images.

For a given vertebra, spatial distance between the source andtarget position was calculated using rigid registration (a built-inalgorithm from 3D SLICER) (Fedorov et al., 2012):

D ¼xf

yf

zf

0B@

1CA�

xm

ym

zm

0B@

1CA ¼ ðR� IÞ �

xm

ym

zm

0B@

1CAþ T ð1Þ

where D is the distance vector between two corresponding points inthe source and target images: Pm(xm, ym, zm) in the source (moving)

image and Pf(xf, yf, zf) in the target (fixed) image. R is the rotationtransformation, T is the translation transformation and I is a diago-nal (identity) matrix.

For the seven CT image sets analysed in this study, the magni-tude of the distance vector between the vertebrae in source andtarget images ranged from 19 mm to 21 mm.

When conducting the registration, the body surface (skin) wasallowed to move freely without any contact conditions and con-straints. Our method, however, allows for adding correspondencebetween easily distinguishable surface points as constraints ifdesirable.

2.2.3. Material propertiesAs stated in Section 2.2.2, our previous studies (Miller and Lu,

2013; Miller et al., 2011) suggest that for problems where loadingis prescribed as forced motion of boundaries, results of computa-tion of (unknown) deformation field within the domain dependvery weakly on the mechanical properties of the continuum. How-ever, given large tissue deformations between the source and tar-get images and overwhelming experimental evidence that softtissues behave like hyperelastic/hyperviscoelastic continua(Bilston et al., 2001; Estes and McElhaney, 1970; Farshad et al.,1999; Fung, 1993; Jin et al., 2013; Miller, 2000; Miller andChinzei, 1997, 2002; Pamidi and Advani, 1978; Prange andMargulies, 2002; Snedeker et al., 2005; Snedeker, 2005), a constitu-tive model compatible with finite deformation solution proceduresis needed. Therefore, following Miller et al. (2011) we used theNeo-Hookean hyperelastic model—the simplest constitutive modelthat satisfies this requirement:

t0S ¼ lJ�2=3 I3 �

13

It0C�1

� �þ kðJ � 1ÞJt

0C�1 ð2Þ

where t0S is the second Piola–Kirchhoff stress, l is the shear modu-

lus, k is the bulk modulus, J is the determinant of the deformationgradient, I is the first invariant of the deviatoric Right Cauchy Greendeformation tensor C (the first strain invariant), and I3 is the iden-tity matrix.

Despite recent progress in magnetic resonance (MR) and ultra-sound elastography (Kwah et al., 2012), there is no reliable non-in-vasive method to determine constitutive properties of human softtissues in vivo (Miller and Lu, 2013). Therefore, we adapted amethod for tissue classification and material properties assign-ment based on the Fuzzy C-Means (FCM) algorithm. This methodhas been successfully used in our previous study for computation

M. Li et al. / Medical Image Analysis 22 (2015) 22–34 27

of the brain deformations due to craniotomy-induced brain shift(Zhang et al., 2013). The study by Zhang et al. (2013) indicated lessthan 1 mm differences between the organ deformations predictedusing the model relying on tissue classification based on the FCMalgorithm and model with detailed representation of anatomicalstructures determined through tedious segmentation. A key stepin implementation of the FCM algorithm for whole-body tissueclassification is to determine the relationship between types/class-es of tissues depicted in the image and image intensity. For a givennumber of intensity cluster centres, the FCM algorithm divides theimage intensity into different groups by computing the member-ship functions that link the intensity at each pixel with all the spe-cified cluster centres (Bezdek et al., 1984; Zhang et al., 2013):

JFCM ¼XN

i¼1

XC

j¼1

uqijdðxi; hjÞ ð3Þ

where N is data samples (i.e. pixels in CT images), C is the number ofcluster centres (tissue types/classes), q is the weighting factorreferred to in the literature (Balafar et al., 2010) as the fuzzinessdegree of clustering, uij is the fuzzy membership function thatexpresses the probability of one data sample xi (pixel) belongingto a specified cluster centre hj (tissue class), and d is the spatial dis-tance between data sample xi and cluster centre hj. We used thefuzziness degree of clustering q of 2 which is a value commonlyapplied for soft tissue classification (Hall et al., 1992; Pham andPrince, 1999).

Following Pohle and Toennies (2001) and Balafar et al. (2010),we calculated the membership functions uij at each cluster centrehj using the following formula

uij ¼1

PCk¼1

dðxi ;hjÞdðxi ;hkÞ

� � 2q�1

ð4Þ

where

hj ¼PN

i¼1uqijxiPN

i¼1uqij

ð5Þ

and d(xi, hj) is the Euclidean distance d2(xi, hj) = ||xi � hj||2 betweenthe data point xi and cluster centre hj.

FCM algorithm minimises the objective function JFCM (see Eq.(3)) by updating of the membership function uij and centres ofclusters hj. For the image datasets analysed in this study, the mini-mum was achieved within 100 iterations.

The only parameter that has to be selected by the analyst in Eqs.(3)–(5) is the number of cluster centres C. Detailed explanation ofhow this parameter was selected for the image datasets analysedin this study is given in Section 3.1.

2.3. Numerical solution

We used Total Lagrangian Explicit Dynamics (TLED) algorithmproposed by Miller et al. (2007) with dynamic relaxation toimprove rate of convergence to the steady state solution (Joldes

Table 3Cluster centres obtained using the FCM algorithm for seven analysed CT image datasets.

(8 Classes) Class 1 Class 2 Class 3 Clas

Case I �842 �715 �215 �9Case II �779 �522 �323 �9Case III �826 �537 �326 �9Case IV �711 �519 �303 �10Case V �650 �481 �247 �8Case VI �825 �656 �388 �10Case VII �704 �530 �319 �9

et al., 2009a). This algorithm refers all variables to the original con-figuration, i.e. the second Piola–Kirchhoff stress and Green–La-grange strain are used. The advantage is that all the derivativeswith respect to spatial coordinates can be pre-computed. Anotherimportant feature of the TLED algorithm is that it utilises centraldifference method to discretise the temporal derivatives so thatthe discretised equations are integrated in stepping forward man-ner without any iteration. Detailed description of the TLED-basedsuite of finite element procedures used in this study is given inJoldes et al. (2009a,b) and Miller et al. (2007). These proceduresrely on explicit integration in time domain and can be easily paral-lelised to harness computational power of Graphics ProcessingUnits (GPUs) as shown in Joldes et al. (2010).

2.4. Evaluation of the registration accuracy

2.4.1. Qualitative evaluationFollowing Garlapati et al. (2014) and Mostayed et al. (2013), we

qualitatively compared the contours/edges automatically detectedusing Canny edge filter (Canny, 1986; Li et al., 2014; Mostayedet al., 2013) in the registered (i.e. source image warped using thedeformations predicted by means of a biomechanical model) andtarget images.

2.4.2. Quantitative evaluationFollowing our previous studies, edge-based Hausdorff distance

(HD) metric (on consistent edges detected using Canny filter) isused here to objectively measure the spatial misalignmentbetween the registered (warped using the deformations predictedby means of a biomechanical model) and target images (Canny,1986; Garlapati et al., 2013, 2014; Mostayed et al., 2013):

HðX;YÞ ¼maxðhðX;YÞ; hðY ;XÞÞ ð6Þ

and

hðX;YÞ ¼maxx2X

miny2Y

h0ðx; yÞ

h0ðx; yÞ ¼maxðh00ðx; yÞ; h00ðy; xÞÞh00ðx; yÞ ¼max

x02xminy02ykx0 � y0k

ð7Þ

where X = {x1,x2, . . . ,xm} and Y = {y1,y2, . . . ,yn} are the consistent (i.e.depicting the same anatomical features) Canny edges in thedeformed (registered) and target image respectively.x ¼ fx01; x02; . . . x0pg and y ¼ fy01; y02; . . . y0lg are the point sets that con-tain the consistent points from two consistent edges. Operator kkrepresents the calculation of direct distance between two pointsas used in the point-based HD metric (Huttenlocher et al., 1993).

From Eq. (7) we construct percentile edge-based Hausdorff dis-tance (Garlapati et al., 2013; Mostayed et al., 2013):

HpðX;YÞ ¼ Pth½arg minkx� yk2� ð8Þ

Following Garlapati et al. (2014) and Mostayed et al. (2013), we donot report here a single Hausdorff distance value (Eq. (6)), but useEq. (8) to report Hausdorff distance values for different percentiles.

s 4 Class 5 Class 6 Class 7 Class 8

8 �31 29 240 6417 �29 28 245 5900 �32 43 274 6614 �45 57 253 6659 �38 16 238 5273 �20 52 219 4535 �15 61 231 446

Table 4Shear modulus (�103 Pa) at cluster centres for seven analysed CT image datasets.

Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8

Shearmodulus(kPa)

0.53 0.53 0.53 1.07 3.57 4.02 Rigid Rigid(Alcaraz et al.,2003)

(Alcaraz et al.,2003)

(Alcaraz et al.,2003)

(Samani et al.,2007)

(Bensamoun et al., 2011;Collinsworth et al., 2002;Gennisson et al., 2010)

(Watters et al.,1985)

Fig. 4. (a) Material properties (shear modulus) assignment for body tissues using FCM algorithm for Case I. Shear modulus magnitude is represented by colour scale. (b) Thecorresponding CT slice. Note that the points belonging to the same tissue class have similar image intensity and concentrate around the class centre. This can be seen in (a) asa spatial clustering of pixels of the same colour. Only in the boundary areas between different tissue classes, some variation of the pixel colour (shear modulus) occurs. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

28 M. Li et al. / Medical Image Analysis 22 (2015) 22–34

(A) (B) (A) (B)

IIesaCIesaC

(A) (B) (A) (B)

VIesaCIIIesaC

(A) (B) (A) (B)

Case V Case VI

)B()A(

Case VII

Fig. 5. Qualitative evaluation of the registration accuracy for seven CT image datasets analysed in this study (transverse slices). For each case, (A) comparison of the edges inthe source and target image; and (B)—indicates comparison of the edges in the registered (i.e. warped using the deformation computed by biomechanical models developedin this study) and target image. Edges in the source image are indicated by red colour; edges in target image—by green colour; and the edges in the registered image—by pinkcolour. Good overlap (with some local misalignment) between the edges in registered and target images is evident. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

M. Li et al. / Medical Image Analysis 22 (2015) 22–34 29

A plot of the Hausdorff distance values for different percentiles (seeSection 3.2.1) immediately reveals the percentage of edges thathave acceptable misalignment errors. Following Mostayed et al.(2013), two-times the voxel size of the original CT image wasregarded here as an acceptable error.

3. Results

3.1. Selection of cluster centres for tissue classification

With exception of our preliminary analysis of a single CT scanset (Li et al., 2014), there have been no attempts to apply FCM tis-sue classification for biomechanical models for whole-body CT reg-istration. Therefore, there are no guidelines regarding the numberof tissue types (intensity cluster centres) (Fig. 3) that need to bedistinguished to achieve desired registration accuracy. Below, weexplain, how we determined the number of tissue types (cluster

centres) for the Fuzzy C-Means FCM algorithm for seven CT data-sets used in this study.

One may expect that bones, muscles, fat, lungs, kidneys, heart,blood vessels and other abdominal organs (including liver, stom-ach/intestines) need to be distinguished in biomechanical modelsfor computing the deformation for whole body CT registration.Bones and fat can be easily identified as they have distinctiveimage intensity (Fig. 3). On the other hand, the intensity of mus-cles, liver and kidneys is similar. Consequently, the FCM algorithm(solely based on image intensity) would classify them as belongingto the same tissue category. There is, however, no drawback as ourprevious studies on neuroimage registration (Miller and Lu, 2013;Miller et al., 2011; Wittek et al., 2009) suggest that if the loading isprescribed via forced motion of the boundary, the results of com-putation of deformation field within the domain depend veryweakly on the mechanical properties of the analysed continuum.

In the CT scans we analysed in this study, the intensity range forlungs and bones was large, from �1100 to �200 and from 250 to

(A) (B) (A) (B)

Case I Case II

(A) (B) (A) (B)

Case III Case IV

(A) (B) (A) (B)

Case V Case VI

(A) (B)

Case VII

Fig. 6. Qualitative evaluation of the registration accuracy for seven CT image datasets analysed in this study (frontal slices). For each case, (A) comparison of the edges in thesource and target image; and (B)—indicates comparison of the edges in the registered (i.e. warped using the deformation computed by biomechanical models developed inthis study) and target image. Edges in the source image are indicated by red colour; edges in target image—by green colour; and the edges in the registered image—by pinkcolour. Good overlap (with some local misalignment) between the edges in registered and target images is evident. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

30 M. Li et al. / Medical Image Analysis 22 (2015) 22–34

(a)

(b)

(c)

0 20 40 60 80 1002

4

6

8

10

12

14

16

18

20

Percentiles

HD

Met

ric (

mm

)

Case ICase II

0 20 40 60 80 1000

5

10

15

20

Percentiles

HD

Met

ric (

mm

)

Case IIICase IVCase VCase VI

0 20 40 60 80 1002

4

6

8

10

12

Percentiles

HD

Met

ric (

mm

)

Case VII

Fig. 7. Quantitative evaluation of the registration accuracy for seven whole-body CTimage datasets analysed in this study: edge-based Hausdorff Distance (HD) betweenthe registered (i.e. source images warped using the deformation computed by meansof non-linear biomechanical models created in this study) and target images againstthe percentile of edges for transverse slices. The horizontal line is two times voxel sizeregistration accuracy threshold. Plots for Cases I and II, Cases III–V and Case VII areshown separately due to the differences in image resolution (Cases I and II—sagittalresolution of 5 mm; Cases III–V—sagittal resolution of 2.5 mm; Case VII—sagittalresolution of 3.0 mm). (a) Cases I and II; (b) Cases III–VI; (c) Case VII.

M. Li et al. / Medical Image Analysis 22 (2015) 22–34 31

1100 respectively. Thus, we defined three intensity cluster centresfor lungs and two intensity cluster centres for bones. Therefore,when assigning the material properties at the integration pointusing the FCM algorithm, we distinguished eight tissue classes:(1) Classes 1, 2 and 3 for lungs and other gas-filled spaces (suchas abdominal cavity); (2) Class 4 for fat; (3) Class 5 for muscles, liv-er and kidneys; (4) Class 6 for stomach and intestines; and (5)Classes 7 and 8 for bones. This resulted in the FCM algorithm witheight intensity cluster centres as indicated in Table 3. The numberof tissue classes was kept constant in this study, but the clustercentres have different values for different cases, i.e. the same num-ber of intensity clusters and the different position of the clustercentres were used for all CTs in this study. Table 3 shows the posi-tion of cluster centres calculated using FCM algorithm for sevenanalysed cases.

Table 4 shows the material property (shear modulus) calculated(Alcaraz et al., 2003; Bensamoun et al., 2011; Collinsworth et al.,2002; Gennisson et al., 2010; Samani et al., 2007; Watters et al.,1985) at class centres defined in Table 3 for all seven analysed cas-es, and an example of applying the FCM algorithm to assign thematerial properties (shear modulus) at the integration points ofthe biomechanical model is shown in Fig. 4a. Comparison of thisfigure with the corresponding CT slice (Fig. 4b) indicates that, withexception of very few outliers, the shear modulus assigned by theFCM algorithm is consistent with a tissue type depicted in theimage at location of the integration points.

3.2. Results of evaluation of the registration accuracy

3.2.1. Qualitative evaluationAs shown in Fig. 5 (column A) and Fig. 6 (column A), for all sev-

en whole-body/torso CT image datasets analysed in this study,large differences in the edge features between the source and tar-get CTs were present. On the other hand, for the registered (i.e. thesource images warped using the deformations predicted by biome-chanical models) and target images good overlap (with some localmisalignment) of edge features was observed (Fig. 5—column Band Fig. 6—column B). The overlap tended to be better in the pos-terior than anterior and lateral image parts. One possible explana-tion for this tendency can be that the biomechanical models forcomputing the tissue deformations were loaded by prescribingthe vertebrae motion as described in Section 2.2.2.

3.2.2. Quantitative evaluationAnalysis of Hausdorff Distance (HD) percentile values indicates

that for Case I and Case II, the average HD (as presented in Suh et al.(2012)) between the edges in the registered and target images wasless than the original (i.e. before resampling) CT image voxel size of5 mm (Table 1). For none of the analysed cases, the average HD wasgreater than two times the voxel size (10 mm for Cases I and II,5 mm for Cases III–VI and 6 mm for Case VII)—a value selected hereas the allowable misalignment threshold (see Section 2.4.2). Usingthis threshold, it can be concluded from Fig. 7 and Table 5 that 95%of edges were successfully registered for Cases I and II, 85%—forCases III–VI and 90% for Case VII. For Cases I and II the resolutionin sagittal plane was 5 mm, 2.5 mm for Cases III–VI and 3 mm forCase VII.

For all seven analysed CT image datasets, the percentile edge-based HD curves tend to rise steeply around 95th percentile(Fig. 7). Therefore, it can be suggested that most edge pairs thatlie between 96th and 100th percentile are possible outliers as theydo not have any correspondence (i.e. edges in the source/registeredand target images do not correspond to each other).

No differences in the registration accuracy were observedbetween the datasets obtained from patients suffering from cancer(Cases II–V) and aortic disease (Cases VI and VII), (Table 5). This

Table 595, 85, 75 and 60-percentile, average HD metric and voxel size in inferior–superior direction (mm) for the registration accuracy of whole-body CT image of seven cases.

95-percentile HDmetric

85-percentile HDmetric

75-percentile HDmetric

60-percentile HDmetric

Average HDmetric

Voxel size in inferior–superiordirection

Case I 8.86 6.33 5.83 5.03 4.93 5.0Case II 9.21 7.07 6.32 5.17 5.20 5.0Case III 6.70 5.00 4.47 3.64 3.77 2.5Case IV 7.10 4.86 4.12 3.61 3.90 2.5Case V 6.39 5.00 4.14 3.60 3.71 2.5Case VI 8.00 5.00 4.47 3.72 3.64 2.5Case VII 7.61 5.21 4.30 3.60 3.88 3.0

32 M. Li et al. / Medical Image Analysis 22 (2015) 22–34

confirms feasibility and accuracy of our approach for patients suf-fering from different diseases.

4. Discussion and conclusions

In this study, a comprehensive patient-specific non-linear finiteelement model is proposed for computing the deformations withinthe patient’s body for registration of whole-body CT images. Theproposed approach accounts for rigid body motion of bones/skele-tal segments, large deformations, and non-linear constitutive prop-erties of soft tissues. The most commonly used approach forgenerating patient-specific finite element models involves imagesegmentation to divide the human body into non-overlapping con-stituents with different material properties—a very tedious andtime consuming process. Therefore, we replaced segmentationwith the Fuzzy C-Means algorithm to quickly and automaticallyclassify the tissues and assign the mechanical properties directlyat the integration points based on this classification (see Sec-tion 2.2.3). Therefore, we eliminated the need for body organ/tis-sue segmentation when constructing biomechanical models forregistration of whole-body radiographic images. Selection of‘fuzzy’ method rather than traditionally used ‘‘exact’’ (i.e. relyingon image segmentation) approach to assign the mechanical prop-erties is supported by the fact that when loading is prescribedthrough forced motion of the boundary (vertebrae motion in thisstudy), the computed deformations are only very weakly sensitiveto the mechanical properties of the modelled continuum providingthat appropriate algorithms of non-linear computational mechan-ics are used (Miller, 2005; Miller and Lu, 2013; Wittek et al., 2009).

The feasibility and accuracy of the proposed approach forwhole-body CT image registration were verified for CT datasetsof seven patients suffering from cancer and aortic disease obtainedfrom publicly available image databases (http://www.na-mic.org/Wiki/index.php/Projects:RegistrationLibrary:RegLib_C20b andhttps://public.cancerimagingarchive.net/ncia/login.jsf) and twohospitals (the University Hospital Limerick, Ireland and the Fre-mantle Hospital, Australia). Hausdorff Distance HD metric betweenthe corresponding features (Canny edges) in the registered (i.e.source image warped using the deformations predicted by meansof a biomechanical model) and target images was used as a quan-titative measure of the registration accuracy. The results indicatethat for all analysed cases, 85–95% of edge pairs were registeredwith an error within two times the voxel size which is a criterionof successful registration used in the literature (Mostayed et al.,2013). However, some local misalignments are clearly visible inFigs. 5 and 6. One possible source of these misalignments can bethat we used very sparse information (vertebrae displacementsbetween the source and target images) to define the model loading.Although one may argue that providing more information to drivecomputation of the organ and tissue deformations may improvethe registration accuracy, the overall results are very promising.It should be noted that to define forced motion of the boundary

we relied on simple segmentation of the spine to determine verte-brae displacements between the source and target images.

The present study can be regarded as a pioneering effort tosolve challenging problem of whole-body CT image registrationby applying a biomechanical model using non-linear finite elementprocedures to compute the deformations to warp a source image tothe patient’s target geometry. For all the analysed image sets, theaverage Hausdorff distance between the pairs edges in registeredand target images was within two times the voxel size, which com-pares well with the studies on non-rigid registration of whole-bodyCTs relying solely on image-processing algorithms. For instance,Suh et al. (2012) reported the maximum-likelihood HD (M-HD)of an order of 4 image voxels in their study for rat whole-bodyCT non-rigid registration using a weighted demons algorithm.Similarly, Toews and Wells (2013) observed errors of an order of6 image voxel when applying their feature-based alignment(FBA) method for inter-subject registration of human whole-bodyCT images.

Acknowledgments

The first author is a recipient of the SIRF scholarship andacknowledges the financial support of the University of WesternAustralia. The financial support of National Health and MedicalResearch Council (Grant No. APP1006031) and Australian ResearchCouncil (Discovery Grant DP120100402) is gratefully acknowl-edged. This investigation was also supported in part by NIH grantsP41EB015902, P41EB015898 and U24CA180918. In addition, theauthors also gratefully acknowledge the financial support ofNational Centre for Image Guided Therapy (NIH U41RR019703)and the National Alliance for Medical Image Computing (NA-MIC), funded by the National Institutes of Health through the NIBIBNIH HHS Roadmap for Medical Research Program, Grant U54EB005149. We would also like to thank Paul Norman (at TheUniversity of Western Australia and Fremantle Hospital), EamonKavanagh and Pierce Grace (at the University Hospital Limerick)for providing some of the CT datasets used in the study. NHMRCProject Grant (1063986) and NHMRC Career Development Fellow-ship (Grant No. 1083572) are also gratefully acknowledged.

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