Estimating foot inertial parameters: A new regression approach

Abstract Background Estimating the inertial parameters for the foot (mass, center of mass position and inertia tensor) is important for applications involving the ankle joint such as inverse dynamics or stiffness measurement techniques (e.g. Quick-release). Scaling equations relying on foot length and body mass are widely used. However, because of the complex foot geometry, such equations may represent an oversimplified solution. Our aim was to evaluate these approaches and propose a new method. Methods Thirty-four right feet (17 Males, mean age and weight 30 years, 75 kg; 17 Females, 32 years, 61.5 kg) were reconstructed using a 3D surface scanner and used as geometrical references. Associated inertial parameters were calculated directly on each reference assuming a uniform density distribution and were compared to corresponding scaling and multiple regression estimates. Finally, an alternative method, based on multiple non-linear regressions, was proposed considering both foot length (L) and ankle width (W). Findings Comparisons showed that reference mass and moments of inertia were greater than scaling predictions with mean difference up to 33 and 16% for mass and moments of inertia respectively. The maximum standard errors of estimate for scaled moments of inertia reached 26%. The alternative solution involving ankle width in the equations lowered the gap with reference data (8.7% max standard errors of estimate) for both genders. Interpretation This strategy, requiring two simple and accessible measurements, may offer a better practicality/relevance compromise for clinical routine use, in regards to existing scaling and regression equations.