The influence of inhomogeneity in architecture on the modelled force-length relationship of muscles

Abstract

In this study a model has been developed to assess the length-force relationship of skeletal muscle, accounting for inhomogeneity in the muscular architecture. The muscle was modelled as a number of parallelepipeds parallel to but geometrically different from each other. For each of the parallelepipeds the force at a given length was calculated. The force-length relationship of the whole muscle was obtained by summing the forces of each of the parallelepipeds. Four kinds of inhomogeneities were simulated using this model: (i) variation of the aponeuroses lengths over the parallel parallelepipeds; (ii) variation of the muscle fibre lengths; (iii) variation of the pennation angles; (iv) variation of the fibre lengths keeping the pennation angle constant. By varying geometry parameters a total of 1000 inhomogeneous muscles was created. The force-length relationships were also calculated neglecting the inhomogeneities, by taking the extreme, or the median of the inhomogeneous parameter value, as descriptive for a homogeneous model. It was found that an inhomogeneity of the aponeuroses length has only minimal influence on the calculated force-length relationship. In the cases of the three other inhomogeneities simulated considerable differences were found. Especially when in the model neglecting inhomogeneities one of the extreme architectural variables was used, unacceptable large differences with the model considering the inhomogeneities occurred. The model was also applied to the equine M. flexor carpi radialis. Considerable differences in the calculated force-length relationship were found after incorporating inhomogeneity. These appeared to depend largely on the pennation angles, either being kept constant, or changing with varying fibre lengths over the parallel parallelepipeds.