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.