Effects of muscle model parameter dispersion and multi-loop segmental interaction on the neuromuscular system performance

The effects of parameter dispersion among motor units on the neuromuscular system performance as well as interaction between muscle segments and spinal cord mechanisms are investigated. Elementary components of the system are modeled to simulate with simple models their input-output characteristics. A leaky SS-IPFM encoder with a time-dependent threshold simulates the motor-neuron encoding characteristics. An amplitude and time dependent nonlinear model represent the motor unit mechanical output to neuronal input relationship. The dispersion of parameters in the components of the whole muscle control model is investigated in the open loop mode. It is shown that the dispersion of parameters in the multi-efferent channels converging on a common tendon provides a spatial filtration generating a smoother muscle force in addition to extending the linear dynamic range compared to a similar system having identical motor units. Muscle segmental interaction is investigated in this distributed model by closing the loop through a coupling matrix, representing afferent-motorneuron interaction on the spinal cord level. A diagonal matrix represents no segmental interaction and a uniform matrix represents a uniform interaction between segments through the muscle spindles and Golgi tendon feedback elements. The close loop simulation studied shows that (a). The type of segmental interaction has little effect on the overall system performance, i.e., range of linerity and stability, which is the result of having a muscle system with a large number of motor units. (b) There are only minor differences in results between the uniform and normal parameter distributions tested. (c) A loop gain of 4 divided by 8 in the distributed model can provide linearity through the full physiological force range. (d) Type of segmental interaction has significant effects on the individual segment. A uniform matrix provides a more stable segment due to the spatial filtration resulting from the segmental interaction, while the diagonal noninteracting matrix shows instabilities on the local segmental level despite global stability. The more realistic exponentially decaying spatial interaction matrix yields both global neuromuscular and local segmental stability with the same linear dynamic range generated with the uniform or diagonal matrices.