Mathematical equation of fusion index of tetanic contraction of skeletal muscles

The fusion index (FI) is an index that can evaluate the tetanic progression of the skeletal muscles. Although the FI-frequency curve (FFC), which is obtained by changing the stimulation frequency, is greatly affected by muscle fiber type and fiber compositions, there are no reports of a mathematical equation that can express the FFC. In this study, the FFC was measured for the gastrocnemius, vastus intermedius, and soleus muscles of rats, and the mathematical equation (FFC-equation) was proposed. The FFC-equation (FI(f)) was proportional to the h-th power of f, and was in inverse proportion to the sum of the h-th power of k and the h-th power of f. f was the stimulation frequency, k was the stimulation frequency at 50% of FI, and h reflected the gradient of FFC. As a result, the approximated curve produced by the FFC-equation corresponded with the measured FFC. k reflected the fiber compositions and h represented the ratio of relaxation time to contraction time of the twitch contraction. The calcium ion fluctuation in muscle plasma may be described by the FFC-equation obtained from the experimental data.