Mathematical modelling of energy storage and return prostheses

Abstract

Lower-limb energy storage and return (ESAR) prostheses are constructed of carbon-fibre composite to approximately replicate the lower-limb of an able-bodied athlete during the stance phase of dynamic activities, such as running and jumping. However, the dynamic properties of ESAR prostheses means they adhere poorly to the underlying rigid body assumptions of conventional link segment models, and the associated impact on calculated mechanical behaviour is not well documented. As such, the purpose of this thesis was to investigate the types and limitations of existing mathematical models of lower-limb prostheses, and then develop alternative models of ESAR prosthesis mechanical behaviour - both independent from and during gait.

Firstly, mathematical models of prosthetic feet independent from gait were developed. Finite element (FE) models of four ESAR prostheses were developed from mechanical testing, presenting a new and robust method of comparing the dynamic behaviour of different ESAR prostheses without resorting to destructive testing. To describe prosthesis behaviour with reduced computational cost compared to FE models, three lumped-parameter models of four ESAR prostheses were also developed that enable the simulation of ground reaction force for a given prosthesis translation and rotation.

Mathematical models of prosthesis behaviour during gait were then developed. A multibody FE model was proposed, using experimental marker trajectories to prescribe the displacement of the rigid skeletal bodies as well as the proximal and distal ends of the prosthesis. Additionally, the effect of a link segment model’s marker-set and geometry on calculated lower-limb kinematics, kinetics and energetics during amputee sprinting was investigated. Five different link segment models of the Ottobock 1E90 Sprinter were developed and statistically compared. The results indicated that the omission of prosthesis-specific spatial, inertial and elastic properties from full-body models significantly influence the calculated amputee gait characteristics.

The newly developed methodologies enable the analysis of ESAR prostheses without using a two-link segment model to describe the mechanical behaviour. This research has the potential to optimise sporting technique as well as to provide more accurate data for health care professionals, improving the athletic performance and well-being of individuals with lower-limb amputation.