運動単位の活動様式を模擬する筋張力制御のためのニューラルネットワークモデルの構築(3部 モデルによる探索)  [in Japanese] NEURAL NETWORK MODEL FOR MUSCLE FORCE CONTROL : RELATION BETWEEN FIRING RATE OF ALPHA MOTONEURON AND FORCE  [in Japanese]

We proposed a neural network model for force control of skeletal muscles. The model consisted of a single motor cortex output cell, α motoneurons (MNs), Renshaw cells, and muscle units. The model was based on the size principle and had recurrent inhibition by Renshaw cells. The first purpose of this study was to construct a neural network model whose relation between the firing rate of αMNs and force is similar to that observed in human muscles. The second purpose was to investigate the mechanism for force control. The number of motor units used for models of human brachialis muscle, extensor digitorum muscle, and first dorsal interosseous muscle were 101, 99, and 101, respectively. We made the following simplification and assumptions: (1) all the motor cortex output cells (CMN) innervating one muscle were simply modeled as a single CMN; (2) a Renshaw cell, RC_M (M=1,..., n) receives excitatory impulses from all αMN and sends inhibitory impulses back to all or some of them; (3) an RC_M is located adjacent to, or is strongly connected to, an MN_M; (4) afferent impulses from various kinds of receptors are ignored while αMNs receive them. Many neural network models were constructed with various numbers of recurrent inhibitory connections from Renshaw cells to αMNs and various ranges of RIPSP, which were determined empirically considering the physiological values. For all muscles, only small αMNs fired when the force was small. Large αMNs began to fire as the force increased. This was consistent with the size principle. When the appropriate number of connections between Renshaw cells and αMNs and magnitude of RIPSP were utilized, the neural network models provided the following relationships. For brachialis muscle, the firing rate of the small and medium-sized αMNs increased rapidly after the αMNs began to fire. Then they increased gradually. Subsequently, the firing rate of the medium-sized αMNs increased rapidly once again. The neural network model of the first dorsal interosseous muscle provided an almost linear relation between the firing rate of αMNs and force. For extensor digitorum muscle, the firing rate of αMNs increased, first rapidly and then gradually, as muscle force increased. These findings agree with those for human muscles. In conclusion, the size distribution of motor units has a dominant effect on the relation between firing rate of αMNs and force. The details of the relationship were inconsistent with those observed in human muscles. In constructing the model, we need to take into account the afferent input from muscle spindle and tendon or the nonlinear inhibition by Renshaw cells. Further study is needed.