An integrative modeling approach for the efficient estimation of cross sectional tibial stresses during locomotion

Abstract

The purpose of this research was to utilize a series of models to estimate the stress in a cross section of the tibia, located 62% from the proximal end, during walking. Twenty-eight male, active duty soldiers walked on an instrumented treadmill while external force data and kinematics were recorded. A rigid body model was used to estimate joint moments and reaction forces. A musculoskeletal model was used to gather muscle length, muscle velocity, moment arm and orientation information. Optimization procedures were used to estimate muscle forces and finally internal bone forces and moments were applied to an inhomogeneous, subject specific bone model obtained from CT scans to estimate stress in the bone cross section. Validity was assessed by comparison to stresses calculated from strain gage data in the literature and sensitivity was investigated using two simplified versions of the bone model-a homogeneous model and an ellipse approximation. Peak compressive stress occurred on the posterior aspect of the cross section (−47.5±14.9MPa). Peak tensile stress occurred on the anterior aspect (27.0±11.7MPa) while the location of peak shear was variable between subjects (7.2±2.4MPa). Peak compressive, tensile and shear stresses were within 0.52MPa, 0.36MPa and 3.02MPa respectively of those calculated from the converted strain gage data. Peak values from a inhomogeneous model of the bone correlated well with homogeneous model (normal: 0.99; shear: 0.94) as did the normal ellipse model (r=0.89–0.96). However, the relationship between shear stress in the inhomogeneous model and ellipse model was less accurate (r=0.64). The procedures detailed in this paper provide a non-invasive and relatively quick method of estimating cross sectional stress that holds promise for assessing injury and osteogenic stimulus in bone during normal physical activity.