Computer-controlled heart rate increase by isoproterenol infusion: Mathematical modeling of the system

The purpose of this study was mathematical modeling of the heart rate (HR) response to isoproterenol (Iso) infusion. We developed a computerized system for the controlled increase of HR by Iso, based on a modified proportional-integral controller. HR was measured in conscious, freely moving rats. We found that the steady-state HR can be described as a hyperbolic power function of the steady-state Iso flow rate. This dependence was coupled with a first-order difference equation to form a pharmacodynamic model that reliably describes the relationship between HR and Iso flow for any arbitrary form of Iso flow function. In simulation studies, we showed that the model continued to follow the HR curve from real-time experiments far beyond the initial 'learning interval' from which its parameters were calculated. Our results suggest that the predictive ability and the simplicity of calculating the parameters render this pharmacodynamic model appropriate for use within future advanced, model-based, adaptive control systems and as a part of larger cardiovascular models.