Incorporating ligament laxity in a finite element model for the upper cervical spine

Predicting physiological range of motion (ROM) using a finite element (FE) model of the upper cervical spine requires the incorporation of ligament laxity. The effect of ligament laxity can be observed only on a macro level of joint motion and is lost once ligaments have been dissected and preconditioned for experimental testing. As a result, although ligament laxity values are recognized to exist, specific values are not directly available in the literature for use in FE models.

The purpose of the current study is to propose an optimization process that can be used to determine a set of ligament laxity values for upper cervical spine FE models. Furthermore, an FE model that includes ligament laxity is applied, and the resulting ROM values are compared with experimental data for physiological ROM, as well as experimental data for the increase in ROM when a Type II odontoid fracture is introduced.

The upper cervical spine FE model was adapted from a 50th percentile male full-body model developed with the Global Human Body Models Consortium (GHBMC). FE modeling was performed in LS-DYNA and LS-OPT (Livermore Software Technology Group) was used for ligament laxity optimization.

Ordinate-based curve matching was used to minimize the mean squared error (MSE) between computed load-rotation curves and experimental load-rotation curves under flexion, extension, and axial rotation with pure moment loads from 0 to 3.5 Nm. Lateral bending was excluded from the optimization because the upper cervical spine was considered to be primarily responsible for flexion, extension, and axial rotation. Based on recommendations from the literature, four varying inputs representing laxity in select ligaments were optimized to minimize the MSE. Funding was provided by the Natural Sciences and Engineering Research Council of Canada as well as GHMBC. The present study was funded by the Natural Sciences and Engineering Research Council of Canada to support the work of one graduate student. There are no conflicts of interest to be reported.

The MSE was reduced to 0.28 in the FE model with optimized ligament laxity compared with an MSE 0f 4.16 in the FE model without laxity. In all load cases, incorporating ligament laxity improved the agreement between the ROM of the FE model and the ROM of the experimental data. The ROM for axial rotation and extension was within one standard deviation of the experimental data. The ROM for flexion and lateral bending was outside one standard deviation of the experimental data, but a compromise was required to use one set of ligament laxity values to achieve a best fit to all load cases. Atlanto-occipital motion was compared as a ratio to overall ROM, and only in extension did the inclusion of ligament laxity not improve the agreement. After a Type II odontoid fracture was incorporated into the model, the increase in ROM was consistent with experimental data from the literature.

The optimization approach used in this study provided values for ligament laxities that, when incorporated into the FE model, generally improved the ROM response when compared with experimental data. Successfully modeling a Type II odontoid fracture showcased the robustness of the FE model, which can now be used in future biomechanics studies.