Least-Squares Matrix Correlations Between Stump Stresses and Prosthesis Loads for Below-Knee Amputees

Abstract

Stump stresses were correlated to prosthesis loads for two unilateral, below-knee amputees over a range of flexion-extension angular adjustments. Normal stresses on the patellar tendon and gastrocnemius were related to the axial force and flexion-extension moment of the prosthesis via a matrix equation. Elements of this matrix, influence factors calculated by least-squares algorithms, identified the contributions of each time-dependent load component acting to produce the time-dependent normal stresses. The flexion-extension angular sensitivity of the way these sagittal plane loads combined to produce normal stresses was included in the matrix equation via a first-order Maclaurin series. Highly favorable correlation coefficients between empirically measured and theoretically predicted stump stresses were calculated. This demonstrated that, in future studies, using an influence-factor matrix holds promise for quantifying sensitivities of normal stresses of the stump to multiple adjustments in prostheses.