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 20100810 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 20100421 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 20101005 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
Goals
 to provide a knee joint model (and related data) at various stages of its development
 for early testing and evaluation by any interested investigators
 to encourage collaborative work
 for reusability by others through open access
 as a learning tool for finite element analysis and knee biomechanics
Specific to our research interests:
 to develop a knee model representative of experimental overall joint response with the capability to predict cartilage stresses.
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
 Imaging data; DICOM files
 Geometry; STEP or IGES files
 Mesh; text based input deck
 Literature based material properties
 Frictionless contact between tissue structures
 Loading and boundary conditions representative of passive flexion
 Output at desired time increments
Version 2.0
Long Term
Release Notes
Version 1.0
Team Roles
 Bhushan Borotikar (data collection; MRI and mechanical testing)
 Ton van den Bogert (supervision of data collection; knee biomechanics)
 Steve Maas (development and support for finite element analysis software; FEBio)
 Jeff Weiss (supervision of FEBio development; tissue mechanics)
 Craig Bennetts (initial geometry generation)
 Ahmet Erdemir (project oversight)
 Scott Sibole (technical lead and work on modeling and simulation procedures)
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:
 origin  topleft corner
 xaxis  pointing towards right (anterior to posterior)
 yaxis  pointing downwards (superior to inferior)
 zaxis  pointing inwards (medial to lateral)
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)
 origin  most distal point on posterior femur midway between lateral and medial condyles
 xaxis  mediallateral flexion axis
 yaxis  posterioranterior of joint capsule
 zaxis  positive from distal femur to femoral head
Source: https://simtk.org/websvn/wsvn/openknee/_gen1/src
 python script: abq2feb.py
 configuration file: abq2feb.cnfg (comment with ##)
Element Sets:
 femur
 tibia
 femoral cartilage  fcart
 femoral cartilage w/o patella region  fcartr
 deep zone  fcartb
 transitional zone  fcartm
 superficial zone  fcartt
 tibial cartilage  tcart
 deep zone  tcartb
 transitional zone  tcartm
 superficial zone  tcartt
 medial meniscus  med meni
 lateral meniscus  lat meni
 medial collateral ligament  mcl
 anterior mcl  amc
 middle mcl  mmc
 posterior mcl  pmc
 lateral collateral ligament  lcl
 anterior lcl  alc
 middle lcl  mlc
 posterior lcl  plc
 anterior cruciate ligament  acl
 anterior acl  aac
 posterior acl  pac
 femoral insertion region (fibers defined by different nodal numbering due to need for different meshing technique)  aclfiber
 posterior cruciate ligament  pcl
 anterior pcl  apc
 posterior pcl  ppc
Surface Sets:
 femoral cartilage surface  fcs
 femoral cartilage surface w/o patella region  fcsr
 tibial cartilage surface  tcs
 femur surface contacting mcl  femmcl
 femur surface contacting lcl  femlcl
 tibia surface contacting mcl  mcltib
 tibia surface contacting lcl  lcltib
 mcl surface  mcl_surf
 only lateral side of mcl  mcls
 lcl surface  lcl_surf
 only medial side of lcl  lcls
 acl surface  aclsurf
 pcl surface  pclsurf
 lateral meniscus surface contact tibial cartilage  lmtib
 lateral meniscus surface contact femoral cartilage  lmfem
 medial meniscus surface contact tibial cartilage  mmtib
 medial meniscus surface contact femoral cartilage  mmfem
Node Sets
 Rigid interface nodes for femoral cartilage to femur attachment  f2fem
 Rigid interface nodes for tibial cartilage to tibia attachment  tc2tib
 Rigid interface nodes for ligament to femur attachment  femlig
 Rigid interface nodes for ligament to tibia attachment  tiblig
 Node set for anteriorlateral meniscal horn  lmant
 Node set for posteriorlateral meniscal horn  lmpost
 Node set for anteriormedial meniscal horn  mmant
 Node set for posteriormedial meniscal horn  mmpost
Anterior, middle, and posterior ligament regions were defined for prestrain 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 MooneyRivlin: 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(12\nu)}\end{displaymath}) with latex(\begin{displaymath}C_{1}=\frac{\mu}{2}\end{displaymath})
**Note: By setting C2 to zero MooneyRivlin reduces to the neoHookean model. MooneyRivlin was used since FEBio does not have a decoupled implementation of neoHookean.
Poroelastic representation of cartilage mechanical response is a future extension possibility.
Ligament
Incompressible, transversely isotropic NeoHookean:
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 stressstrain 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 (inferiorsuperior)
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
Strain Energy Function: latex(\begin{displaymath}W=\frac{1}{2}c(e^Q1)\end{displaymath})
where,
E is the GreenLagrange 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} \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
 Stress distribution
 Strain distribution
 Tibiofemoral joint kinematics (pose and orientation)
 Tibiofemoral joint kinetics (forces and moments)
 Contact stress
 Ligament forces
Solver
Nonlinear system is solved using a standard BFGS quasiNewton 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.pardisoproject.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# 
02250803 (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.
meniscectomy_45deg.cnfg@147  100N compressive load from t=01. 45 degree flexion t=12.5. Equilibrate from t=2.53.5. Meniscuscartilage contact disabled.
tf_joint_45deg.cnfg@146  100N compressive load from t=01. 45 degree flexion t=12.5. Equilibrate from t=2.53.5.
Test Suite
 Troubleshooting
 Mesh convergence
Physiological
 Passive knee flexion
 Anterior/posterior laxity
 Internal/external rotation laxity
 Varus/valgus laxity
 Gait like
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 threedimensional motions: application to the knee. J Biomech Eng. 1983 May;105(2):136144.
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. Subjectspecific finite element analysis of the human medial collateral ligament during valgus knee loading. J. Orthop. Res. 2003 Nov;21(6):10981106.
Peña E, Calvo B, Martínez MA, Doblaré M. A threedimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech. 2006;39(9):16861701.
Li G, Lopez O, Rubash H. Variability of a ThreeDimensional Finite Element Model Constructed Using Magnetic Resonance Images of a Knee for Joint Contact Stress Analysis. J. Biomech. Eng. 2001;123(4):341346.
Jiang Yao et al., Stresses and strains in the medial meniscus of an ACL deficient knee under anterior loading: a finite element analysis with imagebased experimental validation. J, of Biomech. Eng. 2006;128(1):135141.
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