膀胱平滑筋興奮伝播過程の数理的解析

抄録

It has been reported that the impulse propagation in the smooth muscle is greatly affected by the temporal and spatial characteristics of a single muscle cell. Although there have been many papers which investigated the characteristics of a single cell by means of microelectrode technique, the impulse propagation along the network of cellular structure in the smooth muscle of the bladder has not been quantitatively analysed. In the present study, the author presents the mathematical method to analyse the random construction of the cellular network using the analog neuron-like elements model proposed by Amari in 1972. The model has been slightly modified so as to insert an external input and to be stimulated by the repeative external pulse. The simultaneous differential equations expressing the “macroscopic state” are introduced, which express the relation between dU/dt and dV/dt, where : U is the macroscopic internal state of the smooth muscle cells, V : the variance of U and t : time. The simulation study using a digital computer has been carried out on the model in order to obtain the relations between the macroscopic output (the isometric intravesical pressure of the bladder) and the parameters such as the input pulse frequency, pulse width and pulse amplitude. From the analysis of the former two relations, it was demonstrated that there are convex characteristics, while there is a sigmoid characteristic in the third relation. The author has suggested that the reason for decrease in the macroscopic output in the high frequency range may be caused by the increase in the variance V rather than the increase in U.
In 10 dogs, the author has measured the isometrical intravesical pressure of the bladder by stimulating it with repeative electrical pulses. The results obtained from the animal are the same as those obtained from the model.