Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Abstract

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.

Figure 1. Mandible model used in the study.

Bal., balancing-side joint; Work., working-side joint; m1, lower first molar (carnassial); M.p., deep masseter; M.s., superficial masseter; P.i., internal pterygoid; T.p., deep temporalis; T.s., superficial temporalis; T.z., zygomatic part of temporalis; Z.m., zygomaticomandibularis. Temporalis and masseter muscle subgroups were used incrementally in the sensitivity test on number of muscles. All other models used a four-muscle input: temporalis-masseter-zygomaticomandibularis-pterygoid.

Figure 2. Sensitivity test on tetrahedral element quantity.

A. Element quantity plotted against solution time (in seconds), with exponential curve in background. B. Element quantity plotted against reaction force (in Newtons). C. Element quantity plotted against strain energy (in Joules), with linear regression line. D. von Mises stress distribution in the working-side dentary in test models; lateral view (in Megapascals).

Figure 3. Sensitivity test on balancing-working side ratio.

A. Ratio plotted against reaction force, with second-order polynomial curves fitted onto the working and balancing reaction forces. B. Ratio plotted against strain energy. C. von Mises stress distribution in the working-side dentary in test models.

Figure 4. Sensitivity test on musculature ratio.

A. Ratio plotted against reaction force. B. Ratio plotted against strain energy. C. von Mises stress distribution in the working-side dentary in test models. Ratios are given by temporalis-masseter-pterygoid sequences, with zygomaticomandibularis considered part of the masseter group.

Figure 5. Sensitivity test on number of muscle groups.

A. Number of groups plotted against reaction force, connected by lines to show trend. B. Number of groups plotted against strain energy. C. von Mises stress distribution in the working-side dentary in test models.

Figure 6. Sensitivity test on nodes at the bite point constraint.

A. Nodal constraints plotted against reaction force. B. Nodal constraints plotted against reaction force, showing components of the bite force vector. C. Nodal constraints plotted against strain energy. D. von Mises stress distribution in the working-side dentary in test models.

Figure 7. Sensitivity test on temporomandibular joint constraint.

A. Constraint type plotted against reaction force. B. Constraint type plotted against strain energy. C. Constraint type plotted against von Mises strain, showing mean and maximum strain for the working- and balancing-side joints, respectively. D. von Mises stress distribution in the working-side dentary in test models.

Figure 8. Sensitivity test on number of material properties.

A. Number of properties plotted against reaction force, connected by lines to show trend. B. Number of properties plotted against strain energy. C. von Mises stress distribution in the working-side dentary in test models.