B.J.J.J. van der Linden

A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects

The aim of the present study was to develop a Hill type muscle model that accounts for the effects of shortening history. For this purpose, a function was derived that relates force depression to starting length, shortening amplitude and contraction velocity. History parameters were determined from short-range isokinetic experiments on rat medial gastrocnemius muscle (GM). Simulations of isokinetic as well as isotonic experiments were performed with the new model and a standard Hill type model. The simulation results were compared with experimental results of rat GM to evaluate if incorporation of history effects leads to improvements in model predictions. In agreement with the experimental results, the new model qualitatively described force reduction during and after isokinetic shortening as well as the experimental observation that isometric endpoints of isotonic contractions are attained at higher muscle lengths than is expected from the fully isometric length-force curve. Consequently, the new model gave a better quantitative prediction of the experimental results compared to the standard model. It was concluded that incorporation of history effects can improve the predictive power of a Hill type model considerably. The applicability of the model to conditions other than those described in the present paper is discussed.

Modelling functional effects of muscle geometry.

Muscle architecture is an important aspect of muscle functioning. Hence, geometry and material properties of muscle have great influence on the force-length characteristics of muscle. We compared experimental results for the gastrocnemius medialis muscle (GM) of the rat to model results of simple geometric models such as a planimetric model and three-dimensional versions of this model. The capabilities of such models to adequately calculate muscle geometry and force-length characteristics were investigated. The planimetric model with elastic aponeurosis predicted GM muscle geometry well: maximal differences are 6, 1, 4 and 6% for fiber length, aponeurosis length, fiber angle and aponeurosis angle respectively. A slanted cylinder model with circular fiber cross-section did not predict muscle geometry as well as the planimetric model, whereas the geometry results of a second slanted cylinder model were identical to the planimetric model. It is concluded that the planimetric model is capable of adequately calculating the muscle geometry over the muscle length range studied. However, for modelling of force-length characteristics more complex models are needed, as none of the models yielded results sufficiently close to experimental data. Modelled force-length characteristics showed an overestimation of muscle optimum length by 2 mm with respect to experimental data, and the force at the ascending limb of the length force curve was underestimated. The models presented neglect important aspects such as non-linear geometry of muscle, certain passive material properties and mechanical interactions of fibers. These aspects may be responsible for short-comings in the modelling. It is argued that, considering the inability to adequately model muscle length-force characteristics for an isolated maximally activated (in situ) muscle, it is to be expected that prediction will fail for muscle properties in conditions of complex movement with many interacting factors. Therefore, modelling goals should be limited to the heuristic domain rather than expect to be able to predict or even approach medical or biological reality. However, the increased understanding about muscular mechanisms obtained from heuristic use of such simple models may very well be used in creating progress in, for example, clinical applications.

Revised planimetric model of unipennate skeletal muscle: a mechanical approach

OBJECTIVE: Planimetric models which are simple, in the sense that small numerical effort is needed, are used to study functional consequences of skeletal muscle architecture. This paper argues with the approach to derive force of a unipennate muscle based on only equilibrium of the aponeurosis (tendon-sheet). In such an approach intramuscular pressure gradients are neglected and no suitable aponeurosis force can be determined. METHOD: The approach presented in this paper is based on mechanical equilibrium of whole muscle. A volume-related force is introduced to keep muscle volume constant. Mechanical equilibrium of whole muscle yields a different relation between fiber and muscle force as well as length changes as a consequence of pennation, compared with relations derived when only equilibrium of aponeurosis is considered. RESULTS: The newly derived relation improved prediction of the rat gastrocnemius medialis muscle force-length characteristics. CONCLUSION: The prediction of muscle geometry and the prediction of force-length characteristics are very good with a simple model such as a planimetric model. This conclusion suggests that the influence of properties neglected in such a simple model are either small or are internally compensated for in the net effects.

Is high-frequency stiffness a measure for the number of attached cross-bridges?

Muscle stiffness is an important property for movement control. Stiffness is a measure for the resistance against mechanical disturbances in muscular-skeletal systems. In general muscle stiffness is assumed to depend on the number of attached cross-bridges. It is not possible to measure this number in vivo or vitro. In experiments, high frequency perturbations are used to obtain a measurement of stiffness. In this paper a simulation study is presented concerning the correlation between the number of attached cross-bridges and high-frequency stiffness. A model based on the sliding-filament theory was used for the simulation of dynamic contractions. It is concluded that these two methods of muscle stiffness determination do not yield compatible results during lengthening.