Stochastic description of the peak hip contact force during walking free and going upstairs

Uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element (FE) models in clinical applications. Reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor. We therefore analyze the in-vivo available data of seven individuals from HIP98 and OrthoLoad with the objective of characterizing the variability of the peak hip contact force magnitude and two corresponding spatial angles (in sagittal and frontal plane) during walking free and going upstairs. Regression analyses with linear mixed-effects models were performed resulting in six normal random variables, one for each force component and activity. Importantly, the statistical analysis accounts for the fact that same individuals performed both activities. The mean of the peak force magnitude was found to be linearly dependent on the body weight with an additional, activity-specific intercept and all variances were dominated by the inter-patient variability. No distinct correlation was found between the two angles and the force magnitude. The proposed stochastic description of the peak hip contact force during walking free and going upstairs contributes towards future uncertainty quantification of patient-specific FE models.