Modelling the Hip and Ankle Joints in OpenFOAM

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17th January 2017

5th United Kingdom & Éire OpenFOAM® User Meeting

Philip CardiffAlojz Ivanković Rob FlavinLaxmi Muralidharan

Karen FitzGeraldkaren.fitzgerald@ucdconnect.ie

Biomechanics with OpenFOAM

Geometry Creation

Computed Tomography (CT) image sets.

Segmentation - 3D Slicer (open source).

Castellated 3-D Geometry

Smoothing & Cleaning Operations

bone is extracted by selecting pixels in the range 400–1585Hounsfield Units (HU), while the cancellous bone is extractedselecting pixels in the range 200–400 HU [48]. Subsequently, theexterior bone surfaces are clearly discernible, and with minimumuser effort, manual separation of the femur, pelvis and sacrum isperformed. However, the cortical-cancellous bone interface canbe much more difficult to distinguish necessitating time consum-ing manual segmentation. During the difficult task of distinguish-ing the cortical-cancellous bone interface, the MRI image set canbe combined with the CT images, using a fast rigid registrationprocedure [47], limiting the subjectively of the segmentation.

Once the bone pixels of interest have been selected, an enclos-ing triangulated surface is constructed using a marching cubesprocedure [47], producing a castellated surface mesh of the bone,3

illustrated in Fig. 1(a).To remove unwanted noise, the castellated surface meshes are

smoothed to ten iterations using a volume conserving Laplaciansmoothing algorithm (Fig. 1(b)) [49], as implemented in the open-source software Meshlab [50].

Decimation, the process of combining small faces together, isconducted using a quadric based edge collapse decimation proce-dure, making the surface files more manageable for subsequentmeshing procedures. A decimation factor of 0.2 is employedreducing the number of faces by a factor of 5, with negligibleeffect to the bone features. This has been verified using open-source software Metro [51] by examining the geometric deviationbetween the original surface mesh and the decimated mesh. Themean geometric deviation is 0.0059 mm and the maximum is0.1441 mm, which is considered acceptable.

Finally, cleaning operations are performed on the surface meshwhere close vertices are merged, short edges are removed, smallholes are filled, and isolated faces and vertices are eliminated[52]. The final surfaces (Fig. 2) are exported in stereolithography(STL) format, a facet-based surface composed of triangles, suita-ble for input to most volumetric meshing software.

2.2 Volume Meshing. Although, hexahedral meshes havebeen found to be more accurate than tetrahedral meshes [53,54],generation of fully hexahedral hip joint meshes is far from a trivialprocess. Consequently, tetrahedral meshes are often employed, asis the case in the current study.

The femur, pelvis, and cortical-cancellous STL surfaces areimported into ANSYS ICEM CFD [55], and partitioned intopatches of interest, distal femur, femur head, acetabulum, iliosac-ral joint, and pubic symphysis joint, for application of boundaryconditions. The cortical and cancellous bone volumes are meshedusing the patch independent Delaunay tetrahedral approach, andincrementally smoothed to improve the quality. Triangular prismsare grown from the boundary surface and cortical-cancellousinterface, which is favorable for accurate boundary stresses, and

the entire volume mesh is incrementally smoothed. The volumemeshes are exported via the ANSYS Fluent “.msh” format andconverted to the OpenFOAM format using the OpenFOAM utilityfluent3DMeshToFoam.

To overcome inferior quality cells in thin cortical bone regions,smaller local cell sizes are required, and the minimum corticalbone thickness has been limited to 1.5 mm in troublesome areas.

To create the articular cartilage volume meshes, the femur andpelvis articular surface meshes are extruded in the surfacenormal direction by 0.6 mm using the OpenFOAM utilityextrudeMesh. The cartilage thickness, t, has been deter-mined using the approximate acetabulum radius, Ra, and theapproximate femoral head radius, Rf [4],

t ¼Ra " Rf

2(1)

where Ra ¼ 27:6 mm and Rf ¼ 26:4 mm have been determinedby manually fitting spheres.

Fig. 1 Volume conservative smoothing of the bone surfaces

Fig. 2 Final processed bone exterior surfaces embedded in afrontal CT slice

3In this context, castellated refers to the resemblance of the mesh to thebattlements on top of a medieval castle.

011006-2 / Vol. 136, JANUARY 2014 Transactions of the ASME

Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/21/2014 Terms of Use: http://asme.org/terms

bone is extracted by selecting pixels in the range 400–1585Hounsfield Units (HU), while the cancellous bone is extractedselecting pixels in the range 200–400 HU [48]. Subsequently, theexterior bone surfaces are clearly discernible, and with minimumuser effort, manual separation of the femur, pelvis and sacrum isperformed. However, the cortical-cancellous bone interface canbe much more difficult to distinguish necessitating time consum-ing manual segmentation. During the difficult task of distinguish-ing the cortical-cancellous bone interface, the MRI image set canbe combined with the CT images, using a fast rigid registrationprocedure [47], limiting the subjectively of the segmentation.

Once the bone pixels of interest have been selected, an enclos-ing triangulated surface is constructed using a marching cubesprocedure [47], producing a castellated surface mesh of the bone,3

illustrated in Fig. 1(a).To remove unwanted noise, the castellated surface meshes are

smoothed to ten iterations using a volume conserving Laplaciansmoothing algorithm (Fig. 1(b)) [49], as implemented in the open-source software Meshlab [50].

Decimation, the process of combining small faces together, isconducted using a quadric based edge collapse decimation proce-dure, making the surface files more manageable for subsequentmeshing procedures. A decimation factor of 0.2 is employedreducing the number of faces by a factor of 5, with negligibleeffect to the bone features. This has been verified using open-source software Metro [51] by examining the geometric deviationbetween the original surface mesh and the decimated mesh. Themean geometric deviation is 0.0059 mm and the maximum is0.1441 mm, which is considered acceptable.

Finally, cleaning operations are performed on the surface meshwhere close vertices are merged, short edges are removed, smallholes are filled, and isolated faces and vertices are eliminated[52]. The final surfaces (Fig. 2) are exported in stereolithography(STL) format, a facet-based surface composed of triangles, suita-ble for input to most volumetric meshing software.

2.2 Volume Meshing. Although, hexahedral meshes havebeen found to be more accurate than tetrahedral meshes [53,54],generation of fully hexahedral hip joint meshes is far from a trivialprocess. Consequently, tetrahedral meshes are often employed, asis the case in the current study.

The femur, pelvis, and cortical-cancellous STL surfaces areimported into ANSYS ICEM CFD [55], and partitioned intopatches of interest, distal femur, femur head, acetabulum, iliosac-ral joint, and pubic symphysis joint, for application of boundaryconditions. The cortical and cancellous bone volumes are meshedusing the patch independent Delaunay tetrahedral approach, andincrementally smoothed to improve the quality. Triangular prismsare grown from the boundary surface and cortical-cancellousinterface, which is favorable for accurate boundary stresses, and

the entire volume mesh is incrementally smoothed. The volumemeshes are exported via the ANSYS Fluent “.msh” format andconverted to the OpenFOAM format using the OpenFOAM utilityfluent3DMeshToFoam.

To overcome inferior quality cells in thin cortical bone regions,smaller local cell sizes are required, and the minimum corticalbone thickness has been limited to 1.5 mm in troublesome areas.

To create the articular cartilage volume meshes, the femur andpelvis articular surface meshes are extruded in the surfacenormal direction by 0.6 mm using the OpenFOAM utilityextrudeMesh. The cartilage thickness, t, has been deter-mined using the approximate acetabulum radius, Ra, and theapproximate femoral head radius, Rf [4],

t ¼Ra " Rf

2(1)

where Ra ¼ 27:6 mm and Rf ¼ 26:4 mm have been determinedby manually fitting spheres.

Fig. 1 Volume conservative smoothing of the bone surfaces

Fig. 2 Final processed bone exterior surfaces embedded in afrontal CT slice

3In this context, castellated refers to the resemblance of the mesh to thebattlements on top of a medieval castle.

011006-2 / Vol. 136, JANUARY 2014 Transactions of the ASME

Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/21/2014 Terms of Use: http://asme.org/terms

Castellated Surface Smoothened Surface

Patches for Application of Boundary Conditions created using Ansys ICEM.

Patch Creation

Pubic Symphysis

Joint

Iliosacral Joint

Distal Femur

Final Bone Surfaces

Meshing

cfMesh • cartesianMesh:

predominantly hexahedral cells with polyhedra in the transition regions between the cells of different size.

ICEM cfMesh

Cell Type Tetrahedral Predominately Hexahedral

Number Cells 569,418 ~6.5 million

10 times bigger.

Ankle Mesh

Including Articular Cartilage

Cartilage Thickness Calculation

Anderson, et al.

extrudeMesh

Material Properties

Sandwich Distribution

CT Based Distribution

OpenFOAM Utility: setYoungsModulusFromCt

Hounsfield Distribution

CT Slice

Air -1000

Water 0

Bone 1000

HU Scale

Volume Mesh

Material Distribution Utility

The Hounsfield Unit (HU) value is used to represent the density of tissue.

010

1000

-156

CT Voxels

Density Modulus Relationship

Hounsfield Unit Apparent Density Young’s Modulus

010

010

010

29GPa

96MPa

1000

-156 0.2 kg/m3

2.2 kg/m3

P. M. Cattaneo

010

29GPa

96MPa

12MPa 800MPa 17GPa

0 10100MPa 25GPa

1GPa 10GPa

Log Scale

Material Distribution Methods 3.5

Sandwich Model Distributed Model

0 10

29GPa12MPa

a) Heel Strike b) Mid-Stance c) Toe-off

Bergmann et al. Twice body weight - 1,611N2.38 body weight - 1,917N

Boundary Conditions

Pubic Symphysis

Joint

Iliosacral Joint Distal

Femur

Axial DisplacementFixed

Fixed

ContactFrictionless penalty method

Ankle Boundary Conditions

Mid-Stance Stress Predictions [MPa]

0 1010MPa0MPa

Contact Pressures [MPa]

Posterior View Lateral View Medial ViewAnterior View

von Mises Stress [MPa]

Total Hip Arthroplasty Modelling - Geometry Generation

Stem

Head

Insert

Cup

Total Hip Arthroplasty Modelling

Current work in progress…

• stitchMesh, non-conformal, conformal meshes.

• GGI (General Grid Interface).

Questions?

Acknowledgements

Supervisors Prof. Alojz Ivankovic

Dr. Philip Cardiff Clinical Supervisor

Prof. Rob Flavin