Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine.

The objective of this investigation was to develop probabilistic finite element (FE) models of the anterior longitudinal ligament (ALL) and posterior longitudinal ligament (PLL) of the cervical spine that incorporate the natural variability of biological specimens. In addition to the model development, a rigorous validation methodology was developed to quantify model performance. Experimental data for the geometry and dynamic properties of the ALL and PLL were used to create probabilistic FE models capable of predicting not only the mean dynamic relaxation response but also the observed experimental variation of that response. The probabilistic FE model uses a quasilinear viscoelastic material constitutive model to capture the time-dependent behaviour of the ligaments. The probabilistic analysis approach yields a statistical distribution for the model-predicted response at each time point rather than a single deterministic quantity (e.g. ligament force) and that response can be statistically compared to experimental data for validation. A quantitative metric that compares the cumulative distribution functions of the experimental data and model response is computed for both the ALL and PLL throughout the time histories and is used to quantify model performance.

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis.

Probabilistic analyses allow the effect of uncertainty in system parameters on predicted model performance measures to be determined. Furthermore, using performance functions to describe a failure event, the probability of failure can be quantified. The effect of three-dimensional prosthesis shape optimization on the probabilistic response and failure probability of a cemented hip prosthesis system is investigated. Random variables include joint and muscle loading, cortical and cancellous bone and PMMA bone cement elastic properties, and strength parameters describing failure of the bone cement and the prosthesis-bone cement interface. Several performance functions describing the bone cement and prosthesis-cement interface are used to compute the probability of failure. When evaluated deterministically, most performance functions indicated a safe design, with the exception of interface tensile failure. However, when evaluated probabilistically, finite probabilities of failure were computed, some significant. The most likely mode of failure before shape optimization was prosthesis-bone cement interface tensile failure with a predicted probability of failure of 97.9%. Deterministic prosthesis shape optimization reduced the probability of failure for all performance functions and reduced prosthesis-bone cement interface tensile failure by 31.7%. Probability sensitivity factors indicate that the uncertainty in the joint loading, cement strength, and implant-cement interface strength have the greatest effect on the computed probability of failure. Implant shape optimization results in a more robust implant design that is less sensitive to uncertainties in joint loading, which cannot be easily controlled, and more sensitive to cement and interface properties, which are easier to modify.