Exponential hyperbolic sine function fitting of heart rate response to constant load exercise

We attempted to fit heart rate (HR) changes induced by constant exercise loads of different intensities to an exponential hyperbolic sine curve by the least-squares method, and we compared the results with the fitting of the changes to exponential curves. Seven healthy male volunteers performed three different intensities of constant-load exercise on a bicycle ergometer. The exponential hyperbolic sine function adequately fitted the HR responses induced by all three different intensities of loads: low (30 W: correlation coefficient, r = 0.68 +/- 0.13, mean +/- SD), moderate (75 W: r = 0.93 +/- 0.07) and high (125 W: r = 0.97 +/- 0.02). The first-order exponential curve fitted only the moderate load response. Although the second-order exponential equation fitted the HR response for both the moderate and high loads, the equation did not fit the low-load response (r = 0.43 +/- 0.26). In low-load exercise, the sum of the power of the residuals for the exponential hyperbolic sine curve fitting was significantly smaller than that for the first- or second-order exponential curve fitting. In conclusion, the exponential hyperbolic sine function is useful for quantitative analyses of the HR response to exercise loads of various intensities.