Optimization of Active Muscle Force–Length Models Using Least Squares Curve Fitting

The objective of this paper is to propose an asymmetric Gaussian function as an alternative to the existing active force-length models, and to optimize this model along with several other existing models by using the least squares curve fitting method. The minimal set of coefficients is identified for each of these models to facilitate the least squares curve fitting. Sarcomere simulated data and one set of rabbits extensor digitorum II experimental data are used to illustrate optimal curve fitting of the selected force-length functions. The results shows that all the curves fit reasonably well with the simulated and experimental data, while the Gordon-Huxley-Julian model and asymmetric Gaussian function are better than other functions in terms of statistical test scores root mean squared error and R-squared. However, the differences in RMSE scores are insignificant (0.3-6%) for simulated data and (0.2-5%) for experimental data. The proposed asymmetric Gaussian model and the method of parametrization of this and the other force-length models mentioned above can be used in the studies on active force-length relationships of skeletal muscles that generate forces to cause movements of human and animal bodies.