Finite element modelling and simulation of knee motion

1
Finite element modelling and simulation of knee
motion
Derek Bickerstaff Thornbury Hospital, Sheffield,
UK

• ACL STUDY GROUP MEETING
• MAY 29 JUNE 4, 2004, SARDINA

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AIMS

• Develop validate a high-quality 3-D finite
  element (FE) knee model
• To serve as a template for constructing
  patient-specific FE meshes
• Develop method to morph template model into
  patient-specific FE knee models
• To enable the investigation of kinematic motion
  of pathologic knees using finite element
  simulations

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Creating a Morphable Template
Acquire high resolution magnetic resonance (MR)
volume of knee
Identify label (segment) tissue structures
DONE ONCE
Template set of 3-D segments
Use segments to construct 3-D template finite
element knee mesh
20mins
3-D Register template segments to patient MR
images
RE-USED MANY TIMES
3-D Mapping function results
Apply mapping to template mesh to generate
patient FE mesh
lt 1 min
4
3-D MRI Sequence

• High-resolution MRI volume acquisition
• Developed for Simbio EU Project
• 0.35mm x 0.35mm x 2mm
• T2 TR47ms, TE15ms, Flip angle30º, gradient
  echo sequence
• Optimised for cartilage imaging
• Ensure accurate segmentation to generate smooth
  articulating surfaces

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Segmenting Template MRI Volume
Bones soft tissue structures segmented
manually from MR images
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Generating Template FE Mesh

• 3-D segments meshed using ANSYS and Matlab
  software
• Some optimisation of anatomy necessary to ensure
  good quality mesh
• Very low volume elements lead to numerical
  instability
• Thin / tapering anatomies truncated (e.g.
  meniscal horns)

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Final Template FE mesh

• Final template 3-D FE mesh consisted of
• 3,464 8-node solid elements (cartilages
  menisci
• 13,120 shell elements (mostly for rigid bones)
• 232 bar/beam elements (ligaments)

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Template to Patient-Specific FE knees
Template Red Patient Green
Registered yellow

• 3-D register template MR segment images to
  patient MR volume (set of images)
• using a non-linear algorithm (vreglocal3d)
  developed in-house
• Mapping function results

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Morphing the Template Mesh

• Mapping function from registration process used
  to morph the template mesh
• Inherent smoothness of template ? smooth patient
  mesh
• Necessary for FE simulations of articulating
  surfaces

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Sample Patient FE Meshes

• 11 patients scanned in total
• 5 meshes generated

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Meniscal FE meshes
MN07 partial medial meniscal injury MN02
partial medial meniscal injury MN03 partial
medial meniscal injury AC03 postero-lateral
corner injury
AC03
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Simulation of Template Knee

• FE simulation of flexing knee boundary
  conditions imposed by exercise rig
• Posterior view of ? knee cartilages menisci
• Performed using PAM-SAFE FE solver (ESI, Rungis,
  France)

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Method to Validate Motion

• Patient flexed knee under light load in custom
  designed MR compliant rig
• Quasi-dynamic cine MRI images acquired
• T1 cine sequence TR10ms, TE2.0ms, flip
  angle90?
• Interpolated 512 x 512 acquisition matrix
• 0.82 x 0.82 mm in-plane resolution
• 7 sagittal images for each flexion position
  total 42 (6 positions)

Pre-op motion partial lateral meniscal tear
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Dynamic Images Segmentation

• Bones segmented manually from dynamic MR images
• Drawbacks of acquired dynamic data
• Sparse images
• Often some degree of out-of-plane motion during
  flexion

Sample femoral slices shown for 1 flexion
position
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Dynamic Registration

• Rigid registration method
• Maps a fully segmented binary volume (3-D) onto
  the sparse dynamic binary slices (2-D)

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Euler Angles

• Resultant transformations can be resolved for
  Euler angles for rotation throughout motion
• 6 flexion positions
• Generate affine matrix for each flexion position
• Decompose matrices into Euler angles (order Z, X,
  Y) of femur w.r.t. static tibia
• Order of resolution is important for
  interpretation. We used
• Flexion/Extension (Z)
• Internal/External Rotation (Y)
• Varus/Valgus (X)
• A sensitivity analysis of simulated data
  demonstrated registration method to be stable
  reliable to accuracies of lt1 degree
• Quoted angles that follow are with respect to the
  static knee scanned at 15 º flexion hence
  starting angles of -15º at full extension
• Can apply the calculated angles back to the
  static volumes.

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Template Knee Motion
Both tibia and femur moving
Fixed tibia all motion shown at femur
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Patient Motion Results
flexion internal varus

• 45º flexion ROM
• External femoral rotation
• of 8º in 1st 15º of knee
• flexion (pre-op)
• External femoral rotation
• of 15º in 1st 23º of knee
• flexion (pre-op)

Postero-lateral corner injury pre/post op
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Patient Motion Results
flexion internal varus

• 40º flexion ROM
• External femoral rotation
• of 15º in 1st 25º of knee
• flexion

Partial lateral meniscal tear pre/post op
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Conclusions

• Mesh morphing method works well for generating
  patient-specific finite element knee meshes
• Ensures a smooth mesh sufficient for kinematic
  simulations
• Produces better automated segmentation for knee
  than intensity-based methods
• Further development required to account for major
  pathologies
• Examination of vector fields produced by
  registration process implementation of decision
  tree based on their properties
• Additional work required to model complex nature
  of cruciate collateral ligaments
• Current advances may permit solid modelling of
  the ligaments.
• Further work required to measure muscle forces
  pretension in ligaments ? improve in vivo type
  simulations
• Basis of work to develop pre-operative planning
  system to produce bespoke image of patients knee
  to reproduce
• anatomical attachments of ligaments (e.g. ACL) to
  plan surgery
• material properties of ligament to reproduce more
  accurately normal kinematics of knee

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Acknowledgements

• Dept. of Medical Physics, University of
  Sheffield, UK
• Dr. Rod Hose, Dr. Jill Van der Meulen, Mr David
  Chan
• Medical Physics, Sheffield Teaching Hospitals
  Trust, UK
• Prof. David Barber, Dr. Avril McCarthy, Dr.
  Steven Wood
• Academic Radiology, University of Sheffield, UK
• Dr. Iain Wilkinson, Mrs Gail Darwent
• Simbio EU Project for Funding
• Simbio A Generic Environment for Bio-numerical
  Simulation
• IST EU Programme, Project No. 10378
• www.simbio.de

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References

• McCarthy A.D., Hose D.R., Barber D.C., Wood S.,
  Darwent G., Chan D., Bickerstaff D.R. and
  Wilkinson I.D. A registration-based MR method
  for calculating in-vivo 3-D knee joint motion
  Validating finite element simulations.
  Proceedings of the International Society for
  Magnetic Resonance in Medicine, Toronto, July
  10-16, 2003
• S. Wood, D.C. Barber, A.D. McCarthy, D. Chan ,
  I.D. Wilkinson, G. Darwent and D.R. Hose, A
  novel image registration application for the
  in-vivo quantification of joint kinematics.",
  Proceedings of MIUA 2002 Conference, 22-23 July,
  Portsmouth, UK, 2002
• U. Hartmann, G. Lonsdale, G. Berti, J. Fingberg,
  A. Basermann, R. Grebe, P. Aimedieu, D. R. Hose,
  A. McCarthy, F. Kruggel, M. Tittgemeyer, C.
  Wolters, T. Hierl, Bio-numerical simulations
  with SimBio Selected Results, Proceedings of
  International Workshop on Deformable Modelling
  and Soft Tissue Simulation, Bonn, Germany, Nov.
  14-15, 2001

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• Extra slides to demo meshing limitations follow

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AC03 Cartilage meshes

• AC03
• Femoral cartilage
• Anterior
• Posterior
• Tibial cartilages

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Template Meshing limitations

• Registration process can crush elements
• may need minimal thickness flag
• could cause holes in mesh
• can warp elements by crushing

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Meshing limitations

• Registration process can warp elements by
  stretching