Biomechanical Modeling of Squirrel Skulls

MDA models of the red and grey squirrel heads were created by importing the virtual reconstructions of the cranium and mandible to Adams View v. 2021 (MSC Software Corp., Irvine, CA, USA). The mass and inertial properties of the mandible were calculated based on volume and a standard tissue density of 1.05 g cm⁻³ [59 (link)]. The jaw-closing muscles, as listed above and in table 1, were added to the model. Each jaw adductor was modelled as a series of strands in order to capture the differing fibre directions present within a single muscle (figure 1). The masticatory system was completed by including a jaw opener (digastric muscle). Muscle wrapping was employed to enable accurate fibre excursions and to prevent muscle–bone and muscle–muscle intersections. This was particularly important for modelling the superficial masseter, anterior deep masseter, temporalis, lateral pterygoid and digastric.
Figure 1.

MDA model of the (a) red squirrel skull in right lateral view; and the grey squirrel skull in (b) right lateral; (c) ventral; and (d) frontal views. Muscles represented by coloured strands: sky blue, superficial masseter; royal blue, anterior deep masseter; midnight blue, posterior deep masseter; light green, anterior ZM; dark green, posterior ZM; red, temporalis; orange, medial pterygoid; yellow, lateral pterygoid; brown, digastric. Scale bar = 10 mm.

Biting was simulated through modelling a food bolus positioned between the cranium and mandible on the right side. The food bolus was modelled as two rigid plates separated by a translational spring damper which connected the two plates at a coincident location. A contact with a high friction coefficient was defined between the lower plate and the mandible to ensure there was minimal displacement between the two. The translational spring damper was defined with three orthogonal forces, all of which were proportional to the distance between the two plates. The height and position of the food bolus were both adjustable in order to simulate biting at gapes.
The muscles were activated through the application of a Dynamic Geometric Optimization (DGO) method [60 (link)], which estimates the muscle forces (taking into account the instantaneous strand orientations) to make the mandible follow a specific motion (see below). Each muscle was assigned a maximum muscle force (table 1), along with a small passive tension that is naturally developed in resistance to their elongation. A maximum passive tension of 0.15 N was assigned to each muscle strand to provide resistance during jaw opening and closing [60 (link)]. This passive tension was the same in all simulations for comparative purposes. Although consideration of the length-tension curve of the masticatory muscles would provide a greater degree of accuracy in the muscle forces applied across the jaw closing cycle, this data does not currently exist for squirrels. Moreover, previous research on rats [33 (link)] concluded that changes in isometric tension over the range of muscle extension generated during feeding would be very small. We believe this holds true for the squirrel models here as the maximum muscle stretch (approximately 35% in the anterior deep masseter) is similar to that reported in the rat (30% [33 (link)]).