Figure 4.

OpenSim head and neck impact model. The OpenSim musculoskeletal model is a 20 degree-of-freedom model that was based on the Mortensen 2018 model. (a) We added 80 individual cervical spine ligament sections representing 11 ligament groups to represent soft tissue stabilization force elements. The constitutive material model for the ligaments was represented with a (b) force–length and (c) force–velocity curve, which were identified previously in the literature. The force–length relationship of ligaments has a characteristic shape corresponding to the straightening (toe region), stretching (linear region) and breaking (yield region) of collagen fibres. Our constitutive model does not include a yield region, similar to how passive tendon is modelled. (d) The model also contains 84 muscle subvolumes over 15 muscle groups, which were defined in the original Mortensen 2018 model. Muscles were represented using the Hill-type muscle model, with a (e) force–length curve modelling myosin cross bridges in sarcomere functional units and a (f) force–velocity curve scaling force output depending on muscle fibre velocities. Ligament and muscle peak lengthening velocities are marked in (c,e) during experimental mild external loads and extrapolated median American football impacts. While the (e) muscle force–velocity scaling is similar in both load regimes, the (c) ligament force–velocity scaling is substantially larger during median American football impacts, resulting in greater moments produced by ligaments in the high-severity regime. (Online version in colour.)