Decremental oscillation curve fitting of heart rate response following face immersion into cold water

Using 18 healthy volunteers, we attempted to fit the heart rate response to a decremental oscillation curve by the least-squares method following facial immersion into cold water. The decremental oscillation equation was as follows: HR = alpha.e(-betat) sin omegat + gamma, where HR is the instantaneous heart rate at t s, alpha the maximum amplitude of the decremental oscillation, beta the decremental rate, omega the angular velocity and gamma the basal heart rate. Each subject immersed his/her face fully in a basin filled with ice-cold water (4 degrees C) for 30 s. The heart rate response to facial immersion was significantly fitted to the decremental oscillation curve with a correlation coefficient > 0.75 in all the trials. Double trials with a 15-min intertrial interval did not show any significant change in the coefficients. Atropine sulfate decreased the value of coefficient omega and increased that of gamma but did not change alpha or beta, indicating that omega is determined mainly by parasympathetic tone. There were no differences for any coefficient between men and women. The coefficients beta and gamma increased in association with age. Given the significant fitting to the decremental oscillation curve of the heart rate response, we propose that the corresponding electrical circuit consists of a resistance and an inductor connected in series, with a condenser in a parallel circuit with a direct current impulse. This method of fitting with the corresponding electric circuit may be useful for analysis of the heart rate response to physiological stimulus.