Estimating in vivo midfoot and hindfoot joint locations using external skin markers

Musculoskeletal modeling offers a non-invasive approach to analyze human movement, enabling estimation of forces that are difficult to measure experimentally. In musculoskeletal modeling, the human body is represented as rigid segments connected by joints. Complex structures (i.e., the foot) are often modeled as a single rigid segment due to challenges in capturing the motion of individual bones with conventional gait analysis. Additionally, internal joint locations typically require invasive imaging to be accurately determined. Here, we propose a regression-based method to locate the in vivo positions of mid- and hindfoot joint centers using three-dimensional surface markers. Simulated weight-bearing computed tomography (SWCT) scans of 20 individuals were randomly assigned to training (n = 16) and validation (n = 4) datasets. Surface models of each foot were generated, and anatomical markers identified in Avizo Lite 9.0.1. Forty additional landmarks were placed within each foot to represent internal joint centers of 20 mid- and hindfoot joints. Best-fit models for each joint center were generated using stepwise regressions on the training set and evaluated on the validation set. Regression models showed strong predictive performance for all mid- and hindfoot joints based on external skin markers, with r² values ranging from 0.79 to 0.98 and generally low standard errors of estimate (X: r² = 0.91-0.99; SEE: 0.002-0.6 mm; Y: r² = 0.93-0.99; SEE: 0.004-0.6 mm; Z: r² = 0.70-0.96, SEE: 0.02-0.5 mm). These predictive equations thus provide a practical tool for researchers aiming to develop and validate detailed musculoskeletal models of the foot.