Synopsis
The overall goal of this case study is to understand convergence characteristics of Open Knee(s) - Generation 1 model to conduct simulations in an efficient and effective manner.
Use Case
The case relies on simulations of varying levels of tibiofemoral joint loading to evaluate the performance of the model in terms of convergence while reasonably predicting joint mechanics. Convergence is defined by the ease and speed of simulations. Relative predictive accuracy evaluates changes in predicted joint kinematics and tissue stress-strain distributions.
Simulation Aims
- To understand the role of joint loading on convergence characteristics
- To understand the role of simulation (numerical analysis) parameters on convergence characteristics
- To understand model parameters on convergence characteristics
- To understand new model features on convergence characteristics
Model
The model is based on Open Knee(s) - Generation 1 model, which was updated for FEBio version 2.1:
Inputs
The loading and boundary conditions relies on prescribed time histories of movement and loading of the tibiofemoral joint (six degrees of freedom) for various loading scenarios (see Simulation Conditions):
- flexion
- internal/external rotation torque
- varus/valgus torque
- anterior/posterior force
- medial/lateral force
- compression/distraction force
Outputs
- Convergence metrics (primary)
- Completion of simulation (Yes/No)
- If not completed - time point at which the simulation crashed
- If completed - computation time (also provide computer specifications), number of iterations
- Time histories of kinematics-kinetics of the tibiofemoral joint (six degrees of freedom) (secondary)
- flexion torque
- internal/external rotation
- varus/valgus
- anterior/posterior translation
- medial/lateral translation
- compression/distraction
- Post-processed joint mechanics information (secondary)
- Comparison of tibia kinetics and femur kinetics
- Comparison of tibiofemoral joint kinematics to baseline simulation results
- Time histories of stress-strain behavior (secondary)
Simulation Conditions
- Simulation (numerical analysis) parameters (refer to FEBio manual for descriptions):
- Convergence tolerances
- dtol
- etol
- rtol
- lstol
- Time stepper properties
- dtmin
- dtmax
- max_retries
- opt_iter
- aggressiveness
- Newton/quasi-Newton parameters
- max_refs
- max_ups
- cmax
- min_residual
- Analysis type (static/dynamic)
- Convergence tolerances
- Model parameters
- Increase of menisci circumferential modulus
- Increase of cartilage modulus (relative to menisci)
- Increase of ligament fiber moduli
- Change in tibia and femur inertial properties (for dynamic simulations)
- Model changes
- Addition of transverse ligament
- Distributed attachment of meniscal horns
- Attachment of medial meniscus to medial collateral ligament
- Attachment of lateral and medial menisci to tibia
- Application of in situ ligament strain
- Additional ligaments
- Femur stabilization through low stiffness linear and torsional springs
- Use of different constitutive models
- Loading conditions
- passive flexion
- internal/external rotation laxity
- anterior-posterior translation laxity
- varus/valgus laxity
- pivot shift
Use Cases
max_retries & max_refs
Parameter permutations: max_retries = 5,10,20 max_refs = 5,10,20
Ranking: 1. max_retries = 5, max_refs = 20 1. max_retries = 20, max_refs = 20 both have similar results
Results: https://simtk.org/svn/openknee/app/Convergence/sol/max_retries_refs_1/
flexion angle & Anterior-Posterior (AP) force
Parameter permutations: flexion angle = 0,30,60,90 degrees AP force = -100 (P), 100 (A) N max_retries = 5 max_refs = 20
Converged: flexion angle = 0 degrees AP force = -100 (P)
Non-converged: all other permutations
Results: https://simtk.org/svn/openknee/app/Convergence/sol/flexion_AP_1/
flexion angle & Internal-External (IE) torque
SET 1
Parameter permutations: flexion angle = 0,30,60,90 degrees IE torque = -5 (I), 5 (E) N*mm = -0.005,0.005 N*m max_retries = 5 max_refs = 20
Converged: flexion angle = 0,30 degrees IE torque = -5,5 N*mm
Nonconverged flexion angle = 60,90 degrees IE torque = -5,5 N*mm
Results: https://simtk.org/svn/openknee/app/Convergence/sol/flexion_IE_1/
SET 2
Parameter permutations: flexion angle = 0,30,60,90 degrees IE torque = -5000 (I), 5000 (E) N*mm = -5,5 N*m max_retries = 5 max_refs = 20
Nonconverged: all permutations flexion angle = 0,30 degrees, completed flexion, began applying loading flexion angle = 60,90 degrees, didn't complete flexion
Results: https://simtk.org/svn/openknee/app/Convergence/sol/flexion_IE_2/
flexion angle & Varus-Valgus (VV) torque
SET 1
Parameter permutations: flexion angle = 0,30,60,90 degrees VV torque = -10 (Varus), 10 (Valgus) N*mm = -0.01,0.01 N*m max_retries = 5 max_refs = 20
Converged: flexion angle = 0,30 degrees VV torque = -10,10 N*mm
Nonconverged: flexion angle = 60,90 degrees VV torque = -10,10 N*mm
Results: https://simtk.org/svn/openknee/app/Convergence/sol/flexion_VV_1/
SET 2
Parameter permutations: flexion angle = 0,30,60,90 degrees VV torque = -10000 (Varus), 10000 (Valgus) N*mm = -10,10 N*m max_retries = 5 max_refs = 20
Converged: flexion angle = 0 degrees VV torque = -10,10 N*mm
Nonconverged: flexion angle = 30,60,90 degrees VV torque = -10,10 N*mm
flexion angle = 30,60 degrees, began loading flexion angle = 90 degrees, didn't finish flexion
Results: https://simtk.org/svn/openknee/app/Convergence/sol/flexion_VV_2/
Team Members
Ahmet Erdemir - study planning, assisting simulations, interpretation of results
Craig Bennetts - scripting for large scale analysis, execution of simulations, interpretation of results
Snehal Chokhandre - execution of simulations, interpretation of results
Progress
Source Code Repository
https://simtk.org/svn/openknee/app/Convergence/
Data
https://simtk.org/svn/openknee/app/Convergence/dat/
Model Customization
https://simtk.org/svn/openknee/app/Convergence/src/
Simulations
Post-Processing
https://simtk.org/svn/openknee/app/Convergence/sol/
Publications
https://simtk.org/svn/openknee/app/Convergence/doc/