The Effects of Prosthesis Inertial Parameters on Inverse Dynamics: A Probabilistic Analysis

Abstract

Joint kinetic measurement is a fundamental tool used to quantify compensatory movement patterns in participants with transtibial amputation (TTA). Joint kinetics are calculated through inverse dynamics (ID) and depend on segment kinematics, external forces, and both segment and prosthetic inertial parameters (PIPS); yet the individual influence of PIPs on ID is unknown. The objective of this investigation was to assess the importance of parameterizing PIPs when calculating ID using a probabilistic analysis. A series of Monte Carlo simulations were performed to assess the influence of uncertainty in PIPs on ID. Multivariate input distributions were generated from experimentally measured PIPs (foot/shank: mass, center of mass (COM), moment of inertia) of ten prostheses and output distributions were hip and knee joint kinetics. Confidence bounds (2.5–97.5%) and sensitivity of outputs to model input parameters were calculated throughout one gait cycle. Results demonstrated that PIPs had a larger influence on joint kinetics during the swing period than the stance period (e.g., maximum hip flexion/extension moment confidence bound size: stance = 5.6 N·m, swing: 11.4 N·m). Joint kinetics were most sensitive to shank mass during both the stance and swing periods. Accurate measurement of prosthesis shank mass is necessary to calculate joint kinetics with ID in participants with TTA with passive prostheses consisting of total contact carbon fiber sockets and dynamic elastic response feet during walking.

The association between periacetabular osteotomy reorientation and hip joint reaction forces in two subgroups of acetabular dysplasia

“…Sensitivity factors were calculated by correlating the individual PAO DOFs to the JRFs and muscle moment arms using Pearson product-moment correlation coefficients (r) at JRF1 and JRF2. Sensitivity factors were categorized as weak (0.2 ≤ r < 0.4), moderate (0.4 ≤ r < 0.6), or strong (0.6 ≤ r < 1.0) (Gaffney et al, 2017;Myers et al, 2015). Positive sensitivity factors indicate a reduction in JRF.…”

A screening method to analyse the sensitivity of a lower limb multibody kinematic model

“…Whatever the approach used to identify the influential parameters, it seems important to analyse the evolution of the sensitivity measures or indices over the gait cycle as they may be different between the stance and swing phases or may vary with the joint amplitude, as it appears in the present study, depending on the knee flexion-extension. Some previous sensitivity analyses of a lower limb models have reported time averages [4,12,15,35,41], time integrals [9,29,43] as well as correlation coefficients [17,25,26,38] or root mean square differences [1] computed on the whole gait cycle. One study has reported partial derivatives of the output with respect to the parameters (calculated using a finite-difference approximations) at each instant of time of the gait cycle [36] and demonstrated varying influence of some parameters on the lower limb joint moments.…”

“…This number is already associated to a high numerical cost, but the converged value of the sensitivity indices S T i may not be reached: probably that a number larger 10000 should have been used, but the numerical cost would have been too high. Yet, n s = 10000 can be considered quite high in comparison to a number of samples in the range more generally used in biomechancis [1,4,17,20,22,25,26,40].…”