LIE–LAGRANGIAN MODEL FOR REALISTIC HUMAN BIODYNAMICS

Abstract

We present a sophisticated Lagrangian model for anatomically and physiologically realistic human biodynamics (RHB), to accompany the recently reported Hamiltonian formulation.1 The present RHB formulation is designed around three main modules: (i) A Riemannian configuration manifold, composed of gauge Lie groups of constrained 3D rotations and translations, which includes more than 300 degrees of freedom (DOF); (ii) exterior Lagrangian dynamics of the human musculo-skeletal system, including all natural conservative, dissipative and driving forces, powered by 600 equivalent muscles; and (iii) hierarchical nonlinear control, based on an iterative Lie derivative formalism, resembling both spinal reflexes and coordination-control of the human cerebellum. RHB is driven by individual, user supplied musculo-skeletal data. It is modeled in the computer algebra system Mathematica™, simulated in Delphi™ and animated in the 3DS Max™ graphical environment. As an applied example of RHB, we present the full spine simulator, with 150 DOF (25 movable joints each with three constrained rotations and translations), muscular excitation and contraction dynamics, spring-and-damper ligament-like dynamics, spinal-like and cerebellar-like control, and external torques and forces (including inertial, gravitational, viscous, elastic and various types of impacts).