Dynamics-based analysis of the anti-gravity functions of hindlimb muscles in Tyrannosaurus and other bipeds

We constructed three-dimensional musculoskeletal computer models to assess the capacities (per unit muscle force) of all major hindlimb muscles to generate vertical ground-reaction forces (GRF) at the foot, and thus support the body. To cover a broad size range and evolutionary spectrum, we modeled Tyrannosaurus, Gallus, and Struthio, among other bipeds. Musculoskeletal geometry was derived from phylogenetically-constrained published reconstructions or from dissection. Analysis of our models showed how limb orientation influences support provided by the skeleton rather than by muscles. For Tyrannosaurus, joint contact forces support ~25% of body weight (BW) in a straight-legged pose, versus only ~4% BW in more crouched poses. Thus a crouched pose dramatically increases the support that must be provided by muscles. In the Tyrannosaurus crouched pose, when muscles act in isolation, ankle and toe muscles provide much more vertical GRF (e.g., M. flexor digitorum longus: 1.2 N vertical GRF/1 N muscle force) than knee extensors (e.g., M. femorotibialis externus: 0.27 N/1 N), which in turn are more effective than hip extensors (e.g., M. caudofemoralis longus: 0.14 N/1N). These results demonstrate that more distal muscles are more effective in generating vertical GRF than proximal muscles when the muscles act in isolation. However, proximal muscles are very effective in generating vertical GRF when they are activated synergistically with ankle extensors and toe flexors, which stiffen the distal joints and help transfer energy from proximal muscles to the ground. Our simulations show that these general principles hold not only for Tyrannosaurus, but also for chickens, ostriches, and other bipeds, including humans.