Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force-length and force-velocity relationship, excitation-contraction coupling and series and parallel elastic force-elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force-velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling.

Skeletal muscles are surrounded by other muscles, connective tissue and bones, which may transfer transversal forces to the muscle belly. Simple Hill-type muscle models do not consider transversal forces. Thus, the aim of this study was to examine and model the influence of transversal muscle loading on contraction dynamics, e.g. on the rate of force development and on the maximum isometric muscle force (Fim). Isometric experiments with and without transversal muscle loading were conducted on rat muscles. The muscles were loaded (1.3 N cm⁻²) by a custom-made plunger which was able to move in transversal direction. Then the muscle was fully stimulated, the isometric force was measured at the distal tendon and the movement of the plunger was captured with a high-speed camera. The interaction between the muscle and the transversal load was modelled based on energy balance between the (1) work done by the contractile component (CC) and (2) the work done to lift the load, to stretch the series elastic structures and to deform the muscle. Compared with the unloaded contraction, the force rate was reduced by about 25% and Fim was reduced by 5% both in the experiment and in the simulation. The reduction in Fim resulted from using part of the work done by the CC to lift the load and deform the muscle. The response of the muscle to transversal loading opens a window into the interdependence of contractile and deformation work, which can be used to specify and validate 3D muscle models.

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