Using a Statistically Calibrated Biphasic Finite Element Model of the Human Knee Joint to Identify Robust Designs for a Meniscal Substitute

Abstract

This paper describes a methodology for selecting a set of biomechanical engineering design variables to optimize the performance of an engineered meniscal substitute when implanted in a population of subjects whose characteristics can be specified stochastically. For the meniscal design problem where engineering variables include aspects of meniscal geometry and meniscal material properties, this method shows that meniscal designs having simultaneously large radial modulus and large circumferential modulus provide both low mean peak contact stress and small variability in peak contact stress when used in the specified subject population. The method also shows that the mean peak contact stress is relatively insensitive to meniscal permeability, so the permeability used in the manufacture of a meniscal substitute can be selected on the basis of manufacturing ease or cost. This is a multiple objective problem with the mean peak contact stress over the population of subjects and its variability both desired to be small. The problem is solved by using a predictor of the mean peak contact stress across the tibial plateau that was developed from experimentally measured peak contact stresses from two modalities. The first experimental modality provided computed peak contact stresses using a finite element computational simulator of the dynamic tibial contact stress during axial dynamic loading. A small number of meniscal designs with specified subject environmental inputs were selected to make computational runs and to provide training data for the predictor developed below. The second experimental modality consisted of measured peak contact stress from a set of cadaver knees. The cadaver measurements were used to biascorrect and calibrate the simulator output. Because the finite element simulator is expensive to evaluate, a rapidly computable (calibrated) Kriging predictor was used to explore extensively the contact stresses for a wide range of meniscal engineering inputs and subject variables. The predicted values were used to determine the Pareto optimal set of engineering inputs to minimize peak contact stresses in the targeted population of subjects.