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 syste m for the controlled increase of HR by Iso, based on a modified proportiona l-integral controller. HR was measured in conscious, freely moving rats. We found that the steady-state HR can be described as a hyperbolic power func tion of the steady-state Iso flow rate. This dependence was coupled with a first-order difference equation to form a pharmacodynamic model that reliab ly describes the relationship between HR and Iso flow for any arbitrary for m of Iso flow function. In simulation studies, we showed that the model con tinued to follow the HR curve from real-time experiments far beyond the ini tial "learning interval" from which its parameters were calculated. Our res ults 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 la rger cardiovascular models.