Consideration on parameter determination of a new model describing dynamic vagal heart rate control in rats

The dynamic characteristics of vagal heart rate control can be approximated by a first-order low-pass filter with pure dead time in rabbits. However, this model may not necessarily be the best approximation of the vagal transfer function of the heart rate control in rats, because a flatter portion exists in the gain plot above approximately 0.3 Hz. We developed a new model that includes a frequency-independent gain term to reproduce the flatter portion of the gain plot seen in the vagal transfer function in rats. The inclusion of the new term increased the coefficient of determination in an external validation of the linear regression relationship between measured and predicted heart rate responses to vagal stimulation, and made the slope of the regression line closer to unity. The parameters of mathematical transfer functions were determined in both the frequency and time domains. The frequency-domain fitting provided a set of parameters that was also able to reproduce the time-domain step response reasonably well. In contrast, the time-domain fitting provided a set of parameters that reproduced the frequency-domain transfer function only up to 0.2 Hz. Determination of proper model parameters was crucial for the development of a new model to describe the dynamic heart rate response to vagal stimulation in rats.