A mathematical model for dynamics of cardiovascular drug action: Application to intravenous dihydropyridines in healthy volunteers

Abstract

A physiologically based mathematical model was built to describe the pharmacodynamic effects in response to the administration of intravenous (iv)dihydropyridine drugs in healthy volunteers. This model incorporates a limited number of hemodynamic variables, namely, mean arterial blood pressure (MAP),cardiac output (CO)or heart rate (HR),stroke volume (SV),and total peripheral resistance (TPR),into a closed-loop system supposed to represent essential features of the cardiovascular regulation. We also defined an additional auxiliary control variable (U)which is thought to represent primarily the role of the baroreceptor reflex. It was assumed that the variable Uwas related to MAPchanges through both deviation- and ratesensitive mechanisms. Other model parameters are the baseline levels for MAP, CO(or HR),and TPR,as well as time constants to account for further temporal aspects of the regulation. Finally, TPRwas assumed to be linked to the plasma concentrations of dihydropyridine drugs via a conventional pharmaco-kinetic/pharmacodynamic (PK/PD) model, relying upon an effect compartment and a linear, hyperbolic, or sigmoidal relationship between the reduction in TPRand the drug concentrations at the effect site. The model characteristics were explored by studying the influence of various parameters, including baseline levels and deviation- and rate-sensitive control parameters, on the hemodynamic responses to a fictive constant rate ivinfusion of a vasodilator drug. Attempts were also made to mimic literature data with nifedipine, following ivadministration under both constant and exponentially decreasing infusion rates. The applicability of the model was demonstrated by fitting hemodynamic data following ivinfusion of nicardipine to healthy volunteers, under experimental conditions similar to those described above for nifedipine. The effect model for the action of nicardipine on TPR,combined with the physiological model including a feedback control loop, allowed an adequate quantitative description of time profiles for both cardiac output and mean arterial pressure. The suggested model is a useful tool for integrated data analysis of hemodynamic responses to vasodilator drugs in healthy volunteers. Computer simulations suggest that a graded variation of a few model parameters-including baseline levels of TPRand MAPand the deviaion-sensitive parameter of the arterial pressure control-would also be able to account for the pattern of hemodynamic response observed in hypertensive patients, which is qualitatively different to that seen in normotensive subjects. Extrapolation of drug response from the healthy volunteer to the hypertensive patient is allowed by our model. Its usefulness for an early evaluation of drug efficacy during drug development is under current investigation.