First-order model for the analysis of stump stresses for below-knee amputees.

This study extends what had been a purely numerical model that used influence-factor matrices to relate the stump stresses to prosthesis loads for unilateral, below/knee amputees. Previously published influence-factor matrices are now factored into a coefficient matrix times the inverse of a stump geometry matrix. Using actual stump parameters, new information is learned about how the resistive moment of the stump balances the flexion-extension moment of the prosthesis and why certain normal stresses reach a maximum during a specific portion of the stance phase of the prosthesis.

Analytical description of minimum energy expenditure surfaces.

Mechanical energy expenditure during level walking was evaluated and graphed for two unilateral, below-knee amputees over time and a range of adjustments of the flexion-extension alignment angle. The resulting mechanical energy surfaces were then least-squared fitted with an analytical function that was linear in time and quadratic in flexion-extension alignment angle. The least-squares analysis showed that there was a flexion-extension adjustment that minimized the mechanical energy expenditure and that this optimal adjustment was very close to the design point set by certified prosthetists.

Least-squares matrix correlations between stump stresses and prosthesis loads for below-knee amputees.

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.