Physically-based modelling of musculoskeletal systems

In recent years, we have seen several anatomically-inspired, modeling systems, such as those created by Scheepers et al.[5] and Wilhelms and van Gelder[6]. Although these modeling systems may be suitable for de ning super cial body shape, the choice of shape primitives are not suÆciently accurate for medical applications because they do not capture details of muscle ber architecture nor allow speci cation of complex attachment areas of musculotendon to bone. Furthermore, these muscles are merely shape primitives which are incapable of generating forces for physical simulation. In biomechanics, numerous muscle force models have been developed, largely derived from the work of Hill[3]. The forces produced by these models can be applied along lines of action that are represented as piecewise line segments attached to bones[2]. However, the muscle's 3-D geometric shape and inter-muscular forces are often overlooked or simpli ed. We are developing an anatomically-based modeling system that integrates both the physical and geometric properties of muscle and tendon for the purpose of constructing and simulating musculoskeletal systems. Our goal is to choose a muscle model that can be embedded with physical properties to enable animation of active muscle contraction and other inertial e ects as the muscles move with their underlying bones. Essentially, we are incorporating lowlevel, physically-based muscle models, such as those used by Chen and Zeltzer[1], with the concept of 3-D shape modelling from computer graphics. The key component is a volumetric muscle primitive that can capture accurate muscle architectural details while being able to maintain global and local constraints such as volume-preservation, bone attachment, and non-interpenetration between other bones and muscles.