Pharmacokinetic-pharmacodynamic modelling of the cardiovascular effects of drugs – method development and application to magnesium in sheep

BACKGROUND: There have been few reports of pharmacokinetic models that have been linked to models of the cardiovascular system. Such models could predict the cardiovascular effects of a drug under a variety of circumstances. Limiting factors may be the lack of a suitably simple cardiovascular model, the difficulty in managing extensive cardiovascular data sets, and the lack of physiologically based pharmacokinetic models that can account for blood flow changes that may be caused by a drug. An approach for addressing these limitations is proposed, and illustrated using data on the cardiovascular effects of magnesium given intravenously to sheep. The cardiovascular model was based on compartments for venous and arterial blood. Blood flowed from arterial to venous compartments via a passive flow through a systemic vascular resistance. Blood flowed from venous to arterial via a pump (the heart-lung system), the pumping rate was governed by the venous pressure (Frank-Starling mechanism). Heart rate was controlled via the difference between arterial blood pressure and a set point (Baroreceptor control). Constraints were made to pressure-volume relationships, pressure-stroke volume relationships, and physical limits were imposed to produce plausible cardiac function curves and baseline cardiovascular variables. "Cardiovascular radar plots" were developed for concisely displaying the cardiovascular status. A recirculatory kinetic model of magnesium was developed that could account for the large changes in cardiac output caused by this drug. Arterial concentrations predicted by the kinetic model were linked to the systemic vascular resistance and venous compliance terms of the cardiovascular model. The kinetic-dynamic model based on a training data set (30 mmol over 2 min) was used to predict the results for a separate validation data set (30 mmol over 5 min). RESULTS: The kinetic-dynamic model was able to describe the training data set. A recirculatory kinetic model was a good description of the acute kinetics of magnesium in sheep. The volume of distribution of magnesium in the lungs was 0.89 L, and in the body was 4.02 L. A permeability term (0.59 L min(-1)) described the distribution of magnesium into a deeper (probably intracellular) compartment. The final kinetic-dynamic model was able to predict the validation data set. The mean prediction error for the arterial magnesium concentrations, cardiac output and mean arterial blood pressure for the validation data set were 0.02, 3.0 and 6.1%, respectively. CONCLUSION: The combination of a recirculatory model and a simple two-compartment cardiovascular model was able to describe and predict the kinetics and cardiovascular effects of magnesium in sheep.