Determining all parameters necessary to build Hill-type muscle models from experiments on single muscles

Characterizing muscle requires measuring such properties as force-length, force-activation, and force-velocity curves. These characterizations require large numbers of data points because both what type of function (e.g., linear, exponential, hyperbolic) best represents each property, and the values of the parameters in the relevant equations, need to be determined. Only a few properties are therefore generally measured in experiments on any one muscle, and complete characterizations are obtained by averaging data across a large number of muscles. Such averaging approaches can work well for muscles that are similar across individuals. However, considerable evidence indicates that large inter-individual variation exists, at least for some muscles. This variation poses difficulties for across-animal averaging approaches. Methods to fully describe all muscle's characteristics in experiments on individual muscles would therefore be useful. Prior work in stick insect extensor muscle has identified what functions describe each of this muscle's properties and shown that these equations apply across animals. Characterizing these muscles on an individual-by-individual basis therefore requires determining only the values of the parameters in these equations, not equation form. We present here techniques that allow determining all these parameter values in experiments on single muscles. This technique will allow us to compare parameter variation across individuals and to model muscles individually. Similar experiments can likely be performed on single muscles in other systems. This approach may thus provide a widely applicable method for characterizing and modeling muscles from single experiments.