Probabilistic Analysis: Applications to Biomechanics

1. Probabilistic Analysis: Applications to Biomechanics Students: Saikat Pal, Jason Halloran, Mark Baldwin, Josh Stowe, Aaron Fields, Shounak Mitra Collaborators: Paul Rullkoetter, Anthony Petrella, Joe Langenderfer, Ben Hillberry

2. The Question What do I learn from probabilistic modeling that I don’t already know from deterministic modeling? • Distribution of performance • Assessment includes variable interaction effects • Understanding of the probabilities associated with component performance • Probability of failure for a specific performance level • Minimum performance level for a specific POF • Sensitivity information Two common applications • Evaluation of existing components • Guidance for tightening/loosening the tolerances of specific dimensions • Design of future components • Predict performance and identify potential issues prior to prototyping and testing

3. Bounding predictions of TKR performance in a knee simulator Stanmore Wear Simulator Explicit FE Model

4. Research Question What impact does variability in component placement and experimental setup have on the kinematic and contact mechanics results? Wear? Approach • Experimental setup has inherent variability • To more rigorously validate the model • Scatter to setup parameters (m and s) is introduced • Distributions of results evaluated

5. Computational Model • Explicit FE model of Stanmore simulator (Halloran, Petrella, Rullkoetter) • Rigid body analysis with optimized pressure-overclosure relationship • Non-linear UHMWPE material • Simulated gait cycle • Profiles: AP load, IE torque, flexion angle, axial force • Computation time • Rigid-rigid 6-8 minutes/run • Rigid-deformable 6-8 hours/run

6. Model Variables FEax_IS Fem_IE ML Load Split FEax_AP Spring Constant (K) FE Axis Init_Fem_FE DML Insert_Tilt Insert_VV IE Axis IEax_AP Coefficient of Friction m IEax_ML

7. Probabilistic Approach • Deterministic Inputs • Component geometry • Gait profile (ISO) • Material behavior Probabilistic Model Performance Measures Deterministic Inputs Sensitivity Factors Probabilistic Inputs • Output Distributions • Kinematics • AP and IE position • Contact pressure • Wear • Probabilistic Inputs • 4 translational alignments • 4 angular alignments • 4 experimental/setup variables

8. Model Variables All variables assumed as normal distributions

9. AP Translation Model-predicted envelopes (1% to 99% confidence intervals) as a function of gait cycle Max. Range: 1.79 mm (Level A ), 3.44 mm (Level B)

10. IE Rotation IE Model-predicted envelopes (1% to 99% confidence intervals) as a function of gait cycle Max. Range: 2.17° (Level A ), 4.30° (Level B)

11. Peak Contact Pressure Model-predicted envelopes (1% to 99% confidence intervals) as a function of gait cycle Max. Range: 1.3 MPa (Level A ), 1.6 MPa (Level B) @ 40% Gait

12. Sensitivity Factors Normalized absolute average of sensitivity over the entire gait cycle Parameter sensitivities varied significantly throughout the gait cycle

13. Evaluating Measurement Uncertainty in Predicted Tibiofemoral Contact Positions using Fluoro-driven FEA

14. Evaluating Measurement Uncertainty in Predicted Tibiofemoral Contact Positions using Fluoro-driven FEA • Video fluoroscopy is widely used to obtainimplant kinematics in vivo • Evaluate performance measures (e.g. range of motion, cam-post interaction) • Uncertainty exists in spatial positioning of theimplants during the model-fitting process(Dennis et al., 1998) • Due to image clarity, operator experience, and differences in CAD and as-manufactured geometries • Errors up to 0.5 mm and 0.5° for in-plane translations and rotations (Dennis et al., 2003) • Objectives: • Develop an efficient method to account for measurement uncertainty in the model-fitting process • Evaluate the potential bounds of implant center-of-pressure contact estimates

15. Methods • Probabilistic analysis based on previous fluoro-driven FE model (Pal et al., 2004) • Fixed-bearing, semi-constrained, Sigma PS implant • Weight-bearing knee bend from 0° to 90° • Inputs: Six DOFs describing pose of each componentat each flexion angle (0° to 90°, at 10° intervals) • Gaussian distributions with mean based on model-fitting process • In-plane DOFs: SD = 0.17 mm and 0.17° • Out-of-plane DOFs: SD = 0.34 mm and 0.34° • To allow both condyles to contact throughout flexion, model loading conditions were: • Compressive force and in vivo kinematics (AP, IE and FE) • Unconstrained in ML and VV • Output: Distribution of contact location throughout flexion

16. + _ Medial Lateral 1% 99% Medial Lateral Results • Substantial variability in AP contact position observed • Average ranges: • Medial: 10.9 mm (0°-30°) 5.4 mm (30°-90°) • Lateral: 9.3 mm (0°-30°) 6.3 mm (30°-90°) • Maximum ranges: • 12.2 mm (M) and 10.7 mm (L) • Uncertainty in implant position affected cam-post interaction • Underscores the need for careful procedures when extracting kinematics using fluoroscopy Predicted tibiofemoral contact positions Contact patches at 90° flexion

17. Effects of Bone Mechanical Properties on Fracture Risk Assessment

18. Effects of Bone Mechanical Properties on Fracture Risk Assessment • CT scans are often used to create geometry and material properties of bone • Assess bone stresses • Predict fracture risk • Evaluate implant load transfer • Significant variability present in relationships between HU and Modulus and Strength • What effect does this variability have on predicted stress and risk assessment? Keller, 1994

19. Nessus CT data Material Relations BoneMat Stress Risk Abaqus Methods Proximal femur under stance loading (Keyak et al., 2001) Material relation variability (Keller, 1994)

20. 1R 1L 2L Results • Average bounds (1-99%) • Stress: 13.9 MPa • Risk: 0.25 • Potential to impact findings of bone studies • Computation time < 2 hours • Variability should be considered when applying lab-developed material relations to patient- specific bone models

21. Summary • Probabilistic analysis has been demonstrated as a useful computational tool in materials and biomechanics • Efficient MPP-based methods make probabilistic FE analysis quite feasible • Knowledge of bounds (distributions) of performance and important parameters useful in design decisions • Developed framework can be “easily” applied to most computational models