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A robust protocol for the creation of patient-specific finite element models of the musculoskeletal system from medical imaging data

A robust protocol for the creation of patient-specific finite element models of the musculoskeletal system from medical imaging data
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  This article was downloaded by: [BUTC Univ Technologie De Compiegne], [Alain Rassineux]On: 19 March 2014, At: 01:56Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK Computer Methods in Biomechanics and BiomedicalEngineering: Imaging & Visualization Publication details, including instructions for authors and subscription information: A robust protocol for the creation of patient-specificfinite element models of the musculoskeletal systemfrom medical imaging data Tien Tuan Dao a , Alain Rassineux b , Fabrice Charleux c  & Marie-Christine Ho Ba Tho aa  UTC CNRS UMR 7338, Biomécanique et Bioingénierie (BMBI), Université de Technologie deCompiègne (UTC), BP 20529, 60205, Compiègne Cedex, France b  UTC CNRS UMR 7337 Roberval, Université de Technologie de Compiègne (UTC), BP 20529,60205, Compiègne Cedex, France c  ACRIM-Polyclinique St Côme, BP 70409, 60204, Compiègne Cedex, FrancePublished online: 13 Mar 2014. To cite this article:  Tien Tuan Dao, Alain Rassineux, Fabrice Charleux & Marie-Christine Ho Ba Tho (2014): A robustprotocol for the creation of patient-specific finite element models of the musculoskeletal system from medicalimaging data, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, DOI:10.1080/21681163.2014.896226 To link to this article: PLEASE SCROLL DOWN FOR ARTICLETaylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. 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Terms & Conditions of access and use can be found at  A robust protocol for the creation of patient-specific finite element models of the musculoskeletalsystem from medical imaging data Tien Tuan Dao a *, Alain Rassineux b1 , Fabrice Charleux c2 and Marie-Christine Ho Ba Tho a3 a UTC CNRS UMR 7338, Biome´ canique et Bioinge´ nierie (BMBI), Universite´  de Technologie de Compie`gne (UTC), BP 20529, 60205Compie`gne Cedex, France;  b UTC CNRS UMR 7337 Roberval, Universite´  de Technologie de Compie`gne (UTC), BP 20529, 60205Compie`gne Cedex, France;  c  ACRIM-Polyclinique St Coˆ me, BP 70409, 60204 Compie`gne Cedex, France (  Received 18 September 2013; accepted 17 February 2014 ) A robust, accurate and flexible computational protocol to create personalised finite element models of musculoskeletalsystems from medical images is presented. A contour-based geometrical reconstruction well suited to the complex andintrinsic character of living biological tissues and structures is used. The 3D surface model is decomposed into a number of stripes considered as quasi-developable domains which can be, therefore, meshed in a 2D parametric space. Once allboundary domains have been meshed, nodes are projected on a Hermite bicubic patch model derived from the segmentationpoints. A specific procedure to handle branching structures is proposed. In a final step, a tetrahedron mesh is generated andthe mechanical properties could be assigned. Case studies using magnetic resonance imaging and computed tomographydata are carried out and demonstrated. Results of the protocol are presented and discussed. Keywords:  robust computational protocol; patient-specific finite element model; 3D mesh generation; medical imaging 1. Introduction A living system such as the human musculoskeletal systemis a complex biological system. The understanding of itsbehaviour allows the use of appropriate treatmentprescription in the case of musculoskeletal disorders(Mayer 2005; Koch 2012). Experimental science (Botstein and Fink  1988) has been widely applied to obtain thequalitative and quantitative information inside thebiological tissues such as morphological or mechanicalproperties (Ho Ba Tho 2003; Debernard et al. 2011). However, experimental research cannot provide intrinsicinformation inside the biological tissue such as tissuestress under internal or external loading conditions in anon-invasive manner. Multi-physical finite elementanalysis is commonly used to provide such useful data,which can be used as an objective criterion for a betterunderstanding of living tissue behaviour as well as toperform appropriate clinical decision-making recommen-dations (diagnosis, treatment prescription, or evaluation of treatment outcomes) (Chabanas et al. 2003; Yosibash et al.2007; Ovaere et al. 2009; Erdemir et al. 2012; Completo et al. 2013). For such clinical purposes, finite elementmodels must integrate all required individualised infor-mation of the subject under investigation. At the presenttime, patient-specific modelling (PSM) has become acustomised approach to develop such a model for thebenefit of patients. Subject- or patient-specific finiteelement analysis has become a customised tool forassisting the clinicians in their decision-making process(Chabanas et al. 2003; Gibson et al. 2003; Trabelsi et al. 2011;Ruessetal.2012),especiallyinthecaseofprosthetic or orthotic device prescription (Portnoy et al. 2007, 2009; Lacroix and Patin˜o 2011). Therefore, a patient-specificmethodology must be easy-to-use and have a limitednumber of manual inputs and an acceptable computationalcost. Moreover, the development of a computationalprotocol, which includes all the necessary steps to createsuchamodel,requiresanumberoftheoreticalandtechnicalskills as varied as image processing, geometric modelling,computational mechanics and indeed biomechanics.A number of the tools required to build a completeprocedure can be found in image processing, computer-aided design (CAD) or finite element method (FEM)commercial codes. However, the variety of skills requiredtocreatearelevantprotocoldedicatedtopersonalisedfiniteelementmodels makes the integration ofthese componentsdifficult. Therefore, in this study, we propose a robustprotocol for such useful integration.Among the required steps necessary to obtain an FEMmodel of biological tissues, meshing is a major componentof the methodology and remains a current challenge for thedevelopment of accurate musculoskeletal finite elementmodels as the accuracy and the convergence of the finiteelement analysis results depend strongly on the used mesh.This topic is emphasised in this study. When dealing withcomplex shape models in an FEM context with automaticmesh generation and especially when the element sizemay vary, tetrahedral elements are mostly used. A volume q 2014 Taylor & Francis *Corresponding author. Email: Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization , 2014    D  o  w  n   l  o  a   d  e   d   b  y   [   B   U   T   C   U  n   i  v   T  e  c   h  n  o   l  o  g   i  e   D  e   C  o  m  p   i  e  g  n  e   ] ,   [   A   l  a   i  n   R  a  s  s   i  n  e  u  x   ]  a   t   0   1  :   5   6   1   9   M  a  r  c   h   2   0   1   4  model described by its boundaries and a surface geometry,denoted as BREP (boundary representation) model in anyCAD system, must be first created and then meshed. Thesurface model must be indeed accurate, continuous (atleast C  0 and C  1 ) in order to perform good-quality meshingand re-meshing if requested. This work therefore focuseson these techniques, which provide a surface triangulationfrom image data. Magnetic resonance imaging (MRI) or computedtomography (CT) have been commonly used to acquiresubject-specific anatomical images of the biological tissuesand to compute their individualised mechanical properties(HoBa Tho2003;Daoetal.2011).Advancedsegmentation and reconstruction methods from commercial image-processing tools (Simpleware, Amira, Mimics) have beenwidely applied on anatomical slide-by-slide images toextract surface-based structures of interest. Most of thesetools can export a surface geometry into a stereolithography(STL)surfacemeshfile.STLrepresentationprovidesagoodapproximationofthesurfacemodelintotrianglesbutinmostcases, a poor mesh for finite element analysis purpose.However, most of the CAD software create STLtriangulations with minimal number of elements whileproviding an accurate representation of the curvatures. Thisdrawback can be avoided by controlling the outputparameters of the STL triangulation or by developingtechniques that enhance the triangulation. A number of authors have proposed hints to use these meshes for finiteelement analysis (Tyndyka et al. 2007; Magne and Tan2008). In most cases, defects in the surface representationmust be corrected in order to obtain an accurate topologicaldescription of the geometry (Szilvasi-Nagy and Matyasi2003) which can be meshed thereafter. Moreover, specificre-meshing approaches based on local optimisation of procedures or on the building of a local geometrical modelwere used to locate newly created nodes (Rassineux et al.2000;Hassanetal.2007).Thus,thecommongoalistoobtain a “better-shaped quality” mesh while being adapted to therequirements of the analysis. The technique proved to beefficient but highly dependent on the quality of the initialmesh. Among techniques providing a triangulation, march-ing cubes techniques (Newman and Yi 2006) proved to be flexible but can only provide regular meshes. Besides,contour-based segmentation of biological tissues demon-strated its flexibility for generating 3D geometries andrelated meshed models of the biological tissues andstructures (Ho Ba Tho 1993; Sangeux et al. 2006). In this study, this contour-based segmentation was applied toprovide flexible models for robust and accurate meshgeneration process. In fact, the objective was to propose acomputational protocol to create subject- or patient-specificfinite element models derived from medical imagingtechniques. The overall procedure is detailed thereafter. 2. Materials and methods  2.1. Computational protocol  The objective of this work was to propose a computationalprotocol, and the following required steps are presentedthereafter: data acquisition using CT or MRI techniques,2D segmentation using a threshold-based method, a 3Dreconstruction procedure based on bicubic Hermitepatches, a specific geometric model for branchedstructures, a meshing procedure based on the creation of a parametric space suitable for contour-based geometries,tet-mesh generation, mechanical property assignment andfinite element analysis to provide objective data forclinical decision-making. The flow diagram of ourcomputational protocol is illustrated in Figure 1. Note Figure 1. Flow diagram of our computational protocol: bold box illustrate focused components of this study. T.T. Dao  et al. 2    D  o  w  n   l  o  a   d  e   d   b  y   [   B   U   T   C   U  n   i  v   T  e  c   h  n  o   l  o  g   i  e   D  e   C  o  m  p   i  e  g  n  e   ] ,   [   A   l  a   i  n   R  a  s  s   i  n  e  u  x   ]  a   t   0   1  :   5   6   1   9   M  a  r  c   h   2   0   1   4  that in this study, we focus only on the segmentation, 3Dreconstruction and mesh generation components.  2.2. Segmentation and 3D reconstruction The segmentation of 2D images was performed using ourSIP software (Ho Ba Tho 1993). The process is semi-automatic as the position of the points is controlled by theexpert. All contours are described by the same number of ordered points. First, a threshold-based method wasapplied to separate the tissue or structure of interest fromits surrounding tissues. Then, edge detection algorithmwas applied to develop contours (e.g. inner and outer) of tissue of interest for each 2D image. For this purpose,interpolation method using Hermite parametric cubiccurve was used (Ho Ba Tho 2003). The parametric cubicequation under geometric constraint of two end points( P 0  & P 1 ) is as follows: P ð u Þ ¼  P 0 ð 1 2 3 u 2 þ  2 u 3 Þ þ P 1 ð 3 u 2 2 2 u 3 Þþ P 0 0 ð u 2 2 u 2 þ u 3 Þ þ P 0 1 ð 2 u 2 þ u 3 Þ ;  ð 1 Þ where P 0 0  & P 0 1  are the tangent vectors at the two end points P 0  & P 1 , respectively. C  1 continuity of two adjacent curves is ensured byusing the same tangent vector at the ending point of thefirst curve and the first ones of the second curve (Ho BaTho 2003). The number of slices and their altitude aredetermined by the user. Initially, we suppose that at each altitude only onecontour is created. A specific procedure to handle (i.e.create and mesh) bifurcations in which a contour must bepaired to two contours is described later.The surface of the model can be seen as a multi-sectionsurface. A structured quadrangular skeleton mesh can beobtained by connecting all corresponding points of the iso-altitude contours while respecting the given order in thelist. The result is shown in Figure 2. In most cases, this mesh cannot be used for FEM analysis. Element distortionmay be the result of a stiff variation of perimeter betweenconsecutive contours. Similarly, in areas where the shapeof the cross-section of the object does not vary, a reducednumber of slices are created and elements can beelongated. This mesh was used to define a continuousgeometrical model, which will carry the final finiteelement mesh.The creation of a bicubic patch is presented here.At each point, a quadrangle, two tangent vectors ineach direction (one along an iso-altitude contour), can bederived from the initial mesh as shown in Figure 3. Atpoint  O , tangent vectors  O 0 u  and  O 0 v  were computed byaveraging the directions given by segments  AO ,  OB  and CO ,  OD  at the coincident point. We considered the patch defined by the four points  P 0 , P 1 ,  P 2  and  P 3 , as shown in Figure 4. The dotted linesrepresent the initial background mesh used for theinterpolation. Two curves  C  1 ( u ) and  C  2 ( u ) can be defined,respectively, from points  P 0 ,  P 1  and  P 2 ,  P 3 , as follows: Figure 3. Geometrical model.Figure 4. Mesh-based Hermite bicubic rectangular patch.Figure 2. Quadrangular skeleton mesh. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization  3    D  o  w  n   l  o  a   d  e   d   b  y   [   B   U   T   C   U  n   i  v   T  e  c   h  n  o   l  o  g   i  e   D  e   C  o  m  p   i  e  g  n  e   ] ,   [   A   l  a   i  n   R  a  s  s   i  n  e  u  x   ]  a   t   0   1  :   5   6   1   9   M  a  r  c   h   2   0   1   4  C  1 ð u Þ ¼  P 0 ð 1 2 3 u 2 þ  2 u 3 Þ þ P 1 ð 3 u 2 2 2 u 3 Þþ P 0 0 ; u ð u 2 2 u 2 þ u 3 Þ þ P 0 1 ; u ð 2 u 2 þ u 3 Þ ;  ð 2 Þ C  2 ð u Þ ¼  P 2 ð 1 2 3 u 2 þ  2 u 3 Þ þ P 2 ð 3 u 2 2 2 u 3 Þþ P 0 2 ; u ð u 2 2 u 2 þ u 3 Þ þ P 0 3 ; u ð 2 u 2 þ u 3 Þ :  ð 3 Þ Tangent vectors  T  1 ( u ) and  T  2 ( u ) at points  C  1 ( u ) and C  2 ( u ) were derived from a linear interpolation of vectors P 0 0 ; v  and  P 0 1 ; v  and  P 0 2 ; v  and  P 0 3 ; v , respectively. T  1 ð u Þ ¼ ð 1 2 u Þ £ P 0 ; v  þ u £ P 1 ; v ;  ð 4 Þ T  2 ð u Þ ¼ ð 1 2 u Þ £ P 2 ; v  þ u £ P 3 ; v :  ð 5 Þ The curve  K  u ( v ) defining the cubic Hermite patch canbe thereafter determined. Ku ð v Þ ¼  C  1 ð u Þð 1 2 3 v 2 þ  2 v 3 Þ þ T  1 ð u Þð 3 v 2 2 2 v 3 Þ þ T  2 ð u Þð v 2 2 v 2 þ v 3 Þ þ C  2 ð u Þ ð 2 v 2 þ v 3 Þ :  ð 6 Þ At this step, each of these patches could be meshedindividually in order to get a finite element mesh. Thegeneration of patch-dependent surface mesh respects thepatch boundaries to avoid the creation of small edgeswhich may not be useful for the analysis. In order to get ridof the boundary constraints, we propose to apply betweentwo contours a patch-independent meshing techniquebased on quasi-developable surface.  2.3. Mesh generation Theinitialskeletonquadrangularmeshwastransformedintotriangles. The surface was made of a number of stripesbetweencontours.Eachstripeisnowcomposedoftriangles.An intuitive way to re-mesh an existing input mesh (i.e.replace a triangulation by another one) is to segment theinitialsurfacemeshintosub-domains,whichcanbeunfoldedwith little stretch onto a plane and meshed by any 2D meshgenerator. Parameterisations introduce distortion in themetric properties of the surface (distances, angles or areas).When unfolding a surface onto a plane, stretching occurs if the surface contains spherical or hyperbolic regions. Whenthesurfacecanbedeveloped,thetransformationbetweenthe3D triangulated surface and the planar triangulation is anisometry, which preserves the distance between any twopoints of the surface. If we consider domains composed of the sets of elements contained between two consecutivecontours,thesestripescanbeconsideredasdevelopable,andweproposeatechniquetore-meshthemwiththeuseofa2Dadaptive planar mesh generator. Using a 2D mesh generatorinthespaceparameterprovidestheoreticalconvergenceandrobustness through Delaunay criterion together with highperformance. 2.3.1. Unfolding the mesh When unfolding the mesh on the plane, a choice must bemade to preserve distances, angles, areas or even acompromise of these features. We chose to use a projectionbasedonthedistances.TheprocessisshowninFigure5.3Dfaces are displayed in Figure 5(a) and their projection inFigure 5(b). During the projection, as shown for node C  , theheight of the triangle  ABC  was preserved. The process stopswhen all triangles have been unfolded. 2.3.2. Re-meshing process The initial mesh of a stripe is shown in Figure 6(a). Theresult of the unfolding process is displayed in Figure 6(b).Domain boundary curves were thereafter discretised withrespect to the prescribed density. A re-meshing wasperformed in the unfolded plane (Figure 6(c)). A mappingbetween the 2D plane and the 3D space was done. Figure 6(d) represents the set of 3D elements which has beenunfolded. New points have been created in the parametricspace (Figure 6(c)). If we consider a point from the newplanarmeshinFigure6(c),thispointbelongstoatriangleof the initial coarse mesh (Figure 6(b)), and the barycentriccoordinates of this point inside the triangle can bedetermined. All nodes of this triangle were located on thefrontier of the domain and, therefore, the 3D location of these nodes was also known. The 3D coordinates of thisnewly created point can be determined with the samebarycentric coordinates.At this step, 3D nodes were located on the surface of the initial skeleton mesh. In order to position the nodeswith respect to the curvature, these nodes were projectedon the Hermite bicubic model presented in Section 2.2. 2.3.3. Branched structures As the object was defined slice-by-slices by an automatedprocess, one contour may be connected to two facingcontours when a bifurcation occurs. A procedure to createa mesh of the bifurcation with minor user interventionis proposed. Figure 5. Unfolding process: distances are preserved. T.T. Dao  et al. 4    D  o  w  n   l  o  a   d  e   d   b  y   [   B   U   T   C   U  n   i  v   T  e  c   h  n  o   l  o  g   i  e   D  e   C  o  m  p   i  e  g  n  e   ] ,   [   A   l  a   i  n   R  a  s  s   i  n  e  u  x   ]  a   t   0   1  :   5   6   1   9   M  a  r  c   h   2   0   1   4
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