A new method for estimating subject-specific muscle-tendon parameters of the knee joint actuators: a simulation study

A new method for the estimation of subject-specific muscle-tendon parameters of the knee actuators based on dynamometry experiments is presented. The algorithm aims at estimating the tendon slack length and the optimal muscle fiber length by minimizing the difference between experimentally reproduced and model-based joint moments. The key innovative features are as follows: (i) the inclusion of a priori physiological knowledge to define a physiologically feasible set, the hot start for the optimization, and constraints for the optimization and (ii) the introduction of a new (affine) transformation of the muscle-tendon parameters, which greatly improves the numerical condition of the optimization. The influence of the initial guess and of measurement noise was studied in a simulation environment, and the performance was compared with that of the method presented earlier by Garner and Pandy for the upper limb. The tendon slack length was estimated for 97.5/63% (extensors/flexors) of all initial guesses within 2% of the ground truth. The optimal fiber length was estimated for 89/90% (extensors/flexors) of all initial guesses within 2% of the ground truth. When 10 Nm measurement noise was added, the mean value of the estimated tendon slack length deviated at most 1.9/1.6% (extensors/flexors) from the ground truth whereas the standard deviations were at most 5.1/3.9%. The mean value of the estimated optimal fiber length deviated at most 4.3/3.0% (extensors/flexors) from the ground truth whereas the standard deviations were at most 10.2/15.5%. In comparison, mean values resulting from the method of Garner and Pandy deviated up to 181% ( ± 123%) and 119% ( ± 30%) from the ground truth for, respectively, optimal fiber length and tendon slack length of rectus femoris. We concluded that the presented method had a low dependency on the initial guess and outperformed the method of Garner and Pandy in terms of accuracy by at least one order of magnitude when parameters were estimated from noisy data. The improvements open new perspectives for subject-specific modelling of muscles and tendons, which is beneficial for the accuracy of human motion simulations.