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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.

Background Tramadol is an atypical centrally acting analgesic agent available as both oral and parenteral preparations. For patients who are unable to take tramadol orally, the subcutaneous route of administration offers an easy alternative to intravenous or intramuscular routes. This study aimed to characterise the absorption pharmacokinetics of a single subcutaneous dose of tramadol in severely ill patients and in healthy subjects. Methods/design Blood samples (5 ml) taken at intervals from 2 minutes to 24 hours after a subcutaneous dose of tramadol (50 mg) in 15 patients (13 male, two female) and eight healthy male subjects were assayed using high performance liquid chromatography. Pharmacokinetic parameters were derived using a non-compartmental approach. Results There were no statistically significant differences between the two groups in the following parameters (mean ± SD): maximum venous concentration 0.44 ± 0.18 (patients) vs. 0.47 ± 0.13 (healthy volunteers) mcg/ml (p = 0.67); area under the plasma concentration-time curve 177 ± 109 (patients) vs. 175 ± 75 (healthy volunteers) mcg/ml*min (p = 0.96); time to maximum venous concentration 23.3 ± 2 (patients) vs. 20.6 ± 18.8 (healthy volunteers) minutes (p = 0.73) and mean residence time 463 ± 233 (patients) vs. 466 ± 224 (healthy volunteers) minutes (p = 0.97). Conclusions The similar time to maximum venous concentration and mean residence time suggest similar absorption rates between the two groups. These results indicate that the same dosing regimens for subcutaneous tramadol administration may therefore be used in both healthy subjects and severely ill patients. Trial registration ACTRN12611001018909