Figure 12
Overview of the kinetic-dynamic model linking process. A schematic representation of how the final model was derived from Data set 1. The pharmacokinetic (PK) component of the model was developed by fitting the observed arterial magnesium concentrations (Fig. 10, middle). As cardiac output was a parameter of the recirculatory model, the magnesium induced changes in cardiac output were represented as a forcing function during fitting (Fig. 10, top). In the final model, this forcing function was replaced by the cardiac output predicted by the cardiovascular (CV) model. For the CV model, target baseline cardiovascular variables were derived from previous measurements and the literature (Table 1). A unique parameter set for the CV model was found that reproduced these values (Table 2). To account for the changes in cardiovascular variables from baseline following magnesium, four parameters (SVR, CPLv, CNT and S2) were fitted to the observed magnesium CV data (expressed as change from baseline) at selected time-points (Fig. 8; Table 3). Of these, two parameters (SVR, CPLv) showed concentration dependent changes that could be related via link functions to the time-course of magnesium concentrations (Fig. 11). The other parameters of the CV model were fixed at their baseline values. The final model was able to predict the concentrations and CV effects of magnesium for a different dose regimen (Data set 2, Fig. 13).