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

A neuro-mechanical model for the switching of stepping direction and transitions between walking gaits in the stick insect

In this study, a mathematical model for the locomotion of the stick insect is developed. This model takes physiological conditions into account and it is capable of mimicking biological relevant features. The model is predicated on the crucial role, that sensory feedback plays in the coordination of limbs during walking. Central Pattern Generators (CPGs), which produce the rhythm of locomotion, are affected by sensory influences between the segments. The activities of the CPGs are transferred by the motoneurons to the muscles. Starting with existing neuron models and neuronal network models, a neuro-mechanical model is developed that includes the coupling of segments inside of a leg as well as the coupling of multiple legs. Firstly, mechanical models concerning the motion of the three isolated main joints are derived. These mechanical models are fused with the neuronal one. Thus, they represent neuro-mechanical models for the single joints that are coupled via sensory feedback. By means of the introduction of a switching mechanism the model is able to produce forward, backward and sideward stepping of a middle leg. Through the junction of two stepping middle legs to the body of the modeled stick insect, curve walking sequences with different curvatures can be produced. By extending the model to the front and the hind leg, the structure of intersegmental connection between the legs during the tripod and tetrapod gait can be generated. The change of stepping direction can be brought about by changing one single central command. If the middle leg is stepping backwards, the curvature during turning is smaller than in the case of sideward stepping. Weakly inhibitory intersegmental connections show the most accommodating leg coordination during both the tetrapod and the tripod gait