This is the archival of the developer site of the OpenKnee project - Generation 1. The development efforts for this generation of Open Knee were organized by Ahmet Erdemir and CoBi Core of the Cleveland Clinic. This study branched from a previous NIH funded study on multiscale modeling and simulation of the knee joint, J2C. For current activities (Generation 2), check FrontPage.

Previously:

-- aerdemir 2010-08-10 14:16:45 We are working on a User's and Developer's guide to prepare a tidy release of OpenKnee. Work on progress on this document can be found at https://simtk.org/websvn/wsvn/openknee/_gen1/doc/guide.odt in OpenOffice.org format.

-- -- siboles 2010-04-21 22:16:44 Python script, abq2feb.py and abq2feb.cnfg, is now available and can be downloaded at https://simtk.org/websvn/wsvn/openknee/_gen1/src

-- siboles 2010-10-05 22:19:34 New geometries have been generated from a reconstruction using ITK snap. These have been committed to the repository in a new directory ../dat/geo/version2geo/. Additions include: patella, patella cartilage, patella tendon, fibula, complete lcl, proximal and distal tibial mcl attachment, and meniscal horns. We are currently in the process of meshing these in TrueGrid this time with much more focus on the ability to edit mesh properties more easily.

Contents

  1. Goals
  2. Roadmap
    1. Version 1.0
    2. Version 2.0
    3. Long Term
  3. Release Notes
    1. Version 1.0
  4. Team Roles
  5. Specifications
    1. Geometry
    2. Mesh
    3. Material Properties
      1. Bone
      2. Cartilage
      3. Ligament
      4. Meniscus
    4. Interactions
    5. Loading & Boundary Conditions
    6. Output
  6. Solver
    1. Software
    2. Settings
  7. Data
    1. Specimen
    2. Imaging
    3. Mechanical Testing
  8. Documentation
  9. Simulations
    1. Test Suite
    2. Physiological
  10. Support
  11. References
    1. Literature on Finite Element Representation of the Knee Joint

Goals

Specific to our research interests:

Roadmap

Releases relies on the following numbering scheme:

version.major.minor.revision

version
numbering based on goals of the roadmap
major
implementation of a new feaure
minor
improvement of a feature or a bug fix
revision
revision number of the subversion repository on which the release is based on

Version 1.0

Version 2.0

Long Term

Release Notes

Version 1.0

Team Roles

Specifications

Geometry

Source: https://simtk.org/websvn/wsvn/openknee/_gen1/dat/geo/

Currently, the knee geometry relies on manual digitization generated from sagittal MR images. Volsuite was used for this purpose. This initial geometry set was generated by Craig Bennetts of CoBi Core at Cleveland Clinic. 3D spline curves were used to develop NURBS surfaces using the loft feature in the CAD package Rhinoceros. Due to poor visibility of the lateral collateral ligament in sagittal image sets, its geometry is an approximation. Geometries are provided in a coordinate system aligned with the first sagittal MR image:

Mesh

Source: https://simtk.org/websvn/wsvn/openknee/_gen1/dat/msh/

Current discretization relies on a fully hexahedral mesh generated using TrueGrid software (XYZ Scientific). The mesh file is a text based file conforming mesh definition convention of Abaqus.

A translator has been written to generate the complete model in FEBio with all materials, boundary conditions, and loads assigned. This also transforms the mesh into the widely used Grood & Suntay coordinate system. Grood & Suntay (1983)

Source: https://simtk.org/websvn/wsvn/openknee/_gen1/src

tf_joint-4-14.png

Element Sets:

Surface Sets:

Node Sets

Anterior, middle, and posterior ligament regions were defined for pre-strain definition based on data from literature. Pena et. al. 2006

Material Properties

All material formulations in FEBio use a decoupled formulation splitting deviatoric and dilatational stresses/strains. We therefore dropped the conventional ~ over all decoupled quantities for convenience. The reader should just assume all quantities are in their decoupled form.

Bone

Rigid

Cartilage

Incompressible, isotropic Mooney-Rivlin: latex(\begin{displaymath}C_{1}=0.856\end{displaymath}), latex(\begin{displaymath}C_{2}=0.0\end{displaymath}), and latex(\begin{displaymath}K=20.833\end{displaymath}) (E=5 MPa, latex(\begin{displaymath}\nu=0.46\end{displaymath})) Li (2001)

Strain Energy Function: latex(\begin{displaymath}W=C_{1}(I_{1}-3)+C_{2}(I_{2}-3)+\frac{K}{2}(ln(J))^2\end{displaymath})

Young's modulus and poisson ratio from linear elastic model were converted to shear and bulk modulus using relationships: latex(\begin{displaymath}\mu=\frac{E}{2(1+\nu)}\end{displaymath}) and latex(\begin{displaymath}K=\frac{2\mu(1+\nu)}{3(1-2\nu)}\end{displaymath}) with latex(\begin{displaymath}C_{1}=\frac{\mu}{2}\end{displaymath})

**Note: By setting C2 to zero Mooney-Rivlin reduces to the neo-Hookean model. Mooney-Rivlin was used since FEBio does not have a decoupled implementation of neo-Hookean.

Poroelastic representation of cartilage mechanical response is a future extension possibility.

Ligament

Incompressible, transversely isotropic Neo-Hookean:

Strain Energy Function: latex(\begin{displaymath}W=C_{1}(I_{1}-3)+F_{2}(I_{4})+\frac{1}{2}K(ln(J))^2\end{displaymath})

where latex(\begin{displaymath}I_{4}\frac{\partial F_{2}}{\partial I_{4}} = 0 \ \ I_{4} \le1 \end{displaymath}) ; latex(\begin{displaymath}I_{4}\frac{\partial F_{2}}{\partial I_{4}} = C_{3}(e^{C_{4}(I_{4}-1)}-1) \ \ 1 < I_{4} <\lambda\end{displaymath}) ; latex(\begin{displaymath}I_{4}\frac{\partial F_{2}}{\partial I_{4}} = C_{5}+C_{6}I_{4} \ \ I_{4} \ge \lambda \end{displaymath})

latex(\begin{displaymath}I_{4} = \mathbf{a_{0}}\cdot\mathbf{C}\cdot\mathbf{a_{0}}\end{displaymath}) where latex(\begin{displaymath}\mathbf{a_{0}}\end{displaymath}) is the initial fiber direction.

latex(\begin{displaymath}C_{6}\end{displaymath}) is set to ensure C1 continuity in F2.

MCL and LCL: C1=1.44 MPa, C3=0.57 MPa, C4=48, C5=467.1 MPa, lambda=1.062, K=397 MPa Gardiner (2003)

PCL: C1=3.25 MPa, C3=0.1196 MPa, C4=87.178, C5=431.063 MPa, lambda=1.035, K=122 MPa Pena (2006)

ACL: C1=1.95 MPa, C3=0.0139 MPa, C4=116.22, C5=535.039 MPa, lambda=1.046, K=73.2 MPa Pena (2006)

An ongoing problem in modeling of the knee is the identification of ligament slack lengths (if ligaments were modeled as line elements) or zero stress-strain state of the ligament (which dictates in situ strain at reference model configuration). Current ligament modeling is aimed towards providing an adequate overall joint stiffness characteristics. Therefore, in future, it may be possible to use line elements to simplify their representation.

Meniscus

Fung Orthotropic Hyperelastic:

E1 = 125 MPa (circumferential)

E2 = 27.5 MPa (radial)

E3 = 27.5 MPa (inferior-superior)

latex(\begin{displaymath}\nu_{12} = 0.1 \end{displaymath})

latex(\begin{displaymath}\nu_{23} = 0.33 \end{displaymath})

latex(\begin{displaymath}\nu_{31} = 0.1 \end{displaymath})

G12 = 2 MPa

G23 = 12.5 MPa

G31 = 2 MPa

c = 1

K = 10 MPa

Yao et. al. (2006)

Strain Energy Function: latex(\begin{displaymath}W=\frac{1}{2}c(e^Q-1)\end{displaymath})

where,

latex(\begin{displaymath}Q=c^{-1} \sum\limits^{3}_{a=1} [2\mu_{a}\mathbf{A_{a}}^0:\mathbf{E}^2+\sum\limits^{3}_{b=1}\lambda_{ab}(\mathbf{A_{a}}^0:\mathbf{E})(\mathbf{A_{b}}^0:\mathbf{E}]\end{displaymath})

E is the Green-Lagrange strain tensor

latex(\begin{displaymath}\mathbf{A_{a}}^0 = \mathbf{a_{a}}^0\otimes\mathbf{a_{a}}^0\end{displaymath}) is the material axis defined by the fiber's initial direction, latex(\begin{displaymath}\mathbf{a_{a}}^0\end{displaymath})

The orthotropic Lame parameters relate to Young's moduli, Poisson ratios, and shear moduli as follows:

latex(\begin{displaymath} \left[ \begin{array}{ccc}\lambda_{11}+2\mu_{1}&\lambda_{12}&\lambda_{13}\\\lambda_{12}&\lambda_{22}+2\mu_{2}&\lambda_{23}\\\lambda_{13}&\lambda_{23}&\lambda_{33}+2\mu_{3}\end{array}\right] = \left[ \begin{array}{ccc}\frac{1}{E_{1}}&\frac{-\nu_{12}}{E_{1}}&\frac{-\nu_{31}}{E_{3}}\\\frac{-\nu_{12}}{E_{1}}&\frac{1}{E_{2}}&\frac{-\nu_{23}}{E_{2}}\\\frac{-\nu_{31}}{E_{3}}&\frac{-\nu_{23}}{E_{2}}&\frac{1}{E_{3}}\end{array}\right]^{-1} \end{displaymath})

latex(\begin{displaymath} \mu_{1}=G_{12}+G_{31}-G_{23} \end{displaymath})

latex(\begin{displaymath} \mu_{2}=G_{12}-G_{31}+G_{23} \end{displaymath})

latex(\begin{displaymath} \mu_{3}=-G_{12}+G_{31}+G_{23} \end{displaymath})

Interactions

Ligaments are attached to bone via rigid interface definitions (interface nodes become part of rigid body).

Frictionless, sliding contact defined between tibial to femoral cartilage, cartilage to meniscus, ligament to bone, and ACL to PCL.

Loading & Boundary Conditions

The loading should allow prescription of tibiofemoral joint flexion and application of loads to the remainder of 5 degrees of freedom of the joint.

Output

Solver

Non-linear system is solved using a standard BFGS quasi-Newton algorithm or full Newton method implemented by Steve Maas in FEBio. The linear system at each iteration is solved using Pardiso, a sparse matrix solver for shared memory architecture. http://www.pardiso-project.org/

Software

For finite element analysis FEBio, a freely accessible package, will be used. This software is a product of significant efforts by Jeff Weiss and his group from the Musculoskeletal Research Laboratories at the University of Utah. Current version used in this project is FEBio 1.2, which can be downloaded from their site.

Settings

Data

Data for model development efforts are courtesy of van den Bogert Laboratory at the Cleveland Clinic. The information was collected is part of doctoral work conducted by Bhushan Borotikar.

Specimen

NDRI ID

08956 (Specimen acquired from National Disease Research Exchange)

MRMTC#

022508-03 (Specimen tested in Musculoskeletal Robotics and Mechanical Testing Facility at the Cleveland Clinic)

Side

Right

Donor Age

70 years

Donor Estimated Body Weight

170 lbs (77.1 kg)

Donor Heigt

5'6" (1.68 m)

Donor Gender

Female

Donor Cause of Death

Pneumonia/Cancer

Imaging

Source: https://simtk.org/websvn/wsvn/openknee/_gen1/dat/mri/

The knee specimen was imaged at the Biomechanics laboratory of the Cleveland Clinic using a 1.0T (Tesla) extremity MRI scanner (Orthone, ONI Medical Systems Inc, Wilmington MA). The scanner has the capability to scan upper and lower extremities of up to 180mm diameter. A scanning protocol that gave a good contrast for articular cartilage and ligaments in the same scan were used Borotikar (2009). The specifics of this protocol are detailed in following:

Setting for Magneric Resonance Imaging

Scan Parameters

Sagittal

Axial

Coronal

Pulse sequence

GE3D

GE3D

GE3D

TR

30

30

30

TE

8.9

8.9

8.9

Frequency

260

260

260

Phase

192

192

192

FOV

150

150

150

BW

20

20

20

Echo train

1

1

1

NEX

1

1

1

Flip angle

35

35

35

Time

5.03

3.19

3.30

Scan Options

Sagittal

Axial

Coronal

Graphics SL

Y

Y

Y

RF spoiling

Y

Y

Y

Fat suppression

N

N

N

Minimum TE

Y

Y

Y

Inversion recovery

N

N

N

Partial data

N

N

N

No phase wrap

Y

Y

Y

Spatial saturation

N

N

N

Flow comp

N

N

N

Magnetic transfer

N

N

N

Prescan Parameters

Sagittal

Axial

Coronal

Prescan

Auto

Auto

Auto

Center freq.

Peak

Peak

Peak

Slice Parameters

Sagittal

Axial

Coronal

Number of slices

70

45

60

Slice thickness (mm)

1.5

1.5

1.5

Gap (mm)

0

0

0

Range (mm)

105

67.5

90

The knee was kept in full extension position. Imaging technique utilizes 3D spoiled gradient echo sequence with fat suppression, TR = 30, TE = 6.7, Flip Angle = 200, Field of View (FOV) = 150mm X 150mm, Slice Thickness = 1.5mm. Scans in three anatomical planes, axial, sagittal, and coronal, were conducted. Total scanning time was approximately 18 minutes. Selecting these specific sequence parameters produced images that highlighted articular cartilage such that it could be easily discriminated from surrounding bone and tissue. The protocols and the image set reflect partial data from the doctoral work of Borotikar (2009).

Mechanical Testing

Documentation

Source: https://simtk.org/websvn/wsvn/openknee/_gen1/doc/guide.odt

The source location includes a draft of the User's and Developer's guide in OpenOffice.org format.

Simulations

tf_joint.feb@88 - 100 N compressive load applied from t=0..1. 90 degree (1.57 radian) rotation then applied from t=1..4 with 100 N compressive load held constant. Job randomly terminated without an exit flag.

51degreeflexion.zip

meniscectomy_45deg.cnfg@147 - 100N compressive load from t=0-1. 45 degree flexion t=1-2.5. Equilibrate from t=2.5-3.5. Meniscus-cartilage contact disabled.

meniscectomy_45deg.zip

tf_joint_45deg.cnfg@146 - 100N compressive load from t=0-1. 45 degree flexion t=1-2.5. Equilibrate from t=2.5-3.5.

tf_joint_45deg.zip

Test Suite

Physiological

Support

For questions or reporting bugs/problems with Open Knee please use the forums found here.

References

Grood ES, Suntay WJ. A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng. 1983 May;105(2):136-144.

Borotikar, Bhushan, Subject specific computational models of the knee to predict anterior cruciate ligament injury, Doctoral Dissertation, Cleveland State University, December 2009.

Gardiner JC, Weiss JA. Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading. J. Orthop. Res. 2003 Nov;21(6):1098-1106.

Peña E, Calvo B, Martínez MA, Doblaré M. A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech. 2006;39(9):1686-1701.

Li G, Lopez O, Rubash H. Variability of a Three-Dimensional Finite Element Model Constructed Using Magnetic Resonance Images of a Knee for Joint Contact Stress Analysis. J. Biomech. Eng. 2001;123(4):341-346.

Jiang Yao et al., Stresses and strains in the medial meniscus of an ACL deficient knee under anterior loading: a finite element analysis with image-based experimental validation. J, of Biomech. Eng. 2006;128(1):135-141.

Literature on Finite Element Representation of the Knee Joint

Results of a search with keywords ("finite element" AND knee) can be accessed:

http://www.ncbi.nlm.nih.gov/pubmed?term=%22finite%20element%22+knee

Review of finite element representation of the knee joint can be found in /LiteratureReviewKneeFea

GenerationOne (last edited 2016-05-04 22:09:51 by localhost)