A simple Hill element-nonlinear spring model of muscle contraction biomechanics

The purpose of this study was to develop a model to predict the mechanical response of muscles during isometric tetanic, afterloaded isotonic and isovelocity shortening contractions. Two versions of the model were developed. Both incorporated a contractile element that obeyed a Hill force-velocity relationship and a series elastic element. In a quadratic spring version, the series elastic element force was represented as proportional to the square of the stretch; in a cubic spring version, it was represented as proportional to the cube of the stretch. Both versions provided closed-form equations for response predictions that involved four independent parameters. Once the four parameters were chosen, each of these responses could be predicted. Model validity was established by comparing predicted and observed responses in slow and fast hindlimb muscles of rodents. Significant model-predicted responses seldom differed by more than 15% from experimental values. The model can provide insights into how changes in individual properties affect the overall mechanical behavior of muscles in a variety of circumstances and reduce the need for collection of experimental data.