Title: Modelling three-dimensional human strength capacity: logistic vs. polynomial surface equations

Authors: John M. Looft; Laura A. Frey-Law

Addresses: Virtual Soldier Research Group, Center for Computer-Aided Design, College of Engineering, University of Iowa, Iowa City, IA 52242, USA ' Department of Physical Therapy and Rehabilitation Science, Carver College of Medicine, University of Iowa, 1-252 Medical Education Bldg., Iowa City, IA 52242, USA

Abstract: One approach to modelling muscle strength is to represent peak torque as three-dimensional (3D) torque-angle-velocity surfaces at the joint level. These nonlinear relationships have been modelled using polynomial equations. However, we hypothesised logistic equations would better represent 3D peak strength based on known 'S-shaped' relationships between torque and velocity. To compare the two approaches, we modelled eight 3D strength surfaces based on previously published data, elbow and knee strength, using polynomial and logistic equations. Both models fit the strength data well, with median R² values of 0.983 and 0.971 for polynomial and logistic equations, respectively. However, when extrapolating the models to a full normal range of motion (0° to 140°) 100% of the polynomial surfaces, but only 25% of the logistic surfaces, displayed non-physiologic strength estimates (i.e., crossed zero). Accordingly, logistic equations may provide equal or better representations of 3D joint strength surfaces for digital human modelling.

Keywords: torque-velocity-angle; muscle strength; 3D strength surfaces; three-dimensional strength surfaces; peak torque; knee strength; elbow strength; normative strength; mathematical modelling; ergonomics; muscle force; torque-angle relationship; torque-velocity relationship; logistic equations; polynomial equations; polynomial surfaces; logistic surfaces; digital human modelling.

DOI: 10.1504/IJHFMS.2015.068122

International Journal of Human Factors Modelling and Simulation, 2015 Vol.5 No.1, pp.5 - 18

Received: 09 Jan 2014
Accepted: 17 Sep 2014
Published online: 18 Mar 2015 *

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