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Project: Blood serum drug concentration profile optimization

Given a pharmacokinetic or pharmacodynamic (PK/PD) model for the metabolism of a drug, consider the related problems of matching a desired blood concentration profile for a drug over a specified time period and maintaining a constant blood concentration of a drug over a prolonged period of time. These problems are constrained by the metabolic loss of the drug from a vascular (blood circulation) compartment  and drug transfer between the vascular compartment and at least one tissue compartment.

These problems are important for several reasons. First, it may be necessary to maintain a constant blood concentration of a drug over an extended period of time to achieve a specific therapeutic effect, possibly due to transfer of the drug to one or more tissue compartments. Second, it may be desirable to follow a specific drug concentration input profile to minimize negative aspects of a drug, e.g., nausea, pain, headache, etc., while approaching a therapeutic level of the drug concentration in the blood. Third, the therapeutic blood concentration level of a drug may be a significant fraction of the toxic level, requiring a tightly controlled delivery of the drug to the vascular compartment and affected tissue compartments.

A procedure for estimating constant drug input rates over predetermined time intervals, e.g. via intravenous drip, has been developed. The procedure is demonstrated using a one compartment model for the vascular system, a well stirred tank model, with linear or proportional metabolic loss, and a two compartment model representing the drug concentration of a vascular compartment and a tissue compartment. Drug transfer is assumed to occur at different rates between the compartments and metabolic loss was assumed to be from only the vascular compartment. In both examples the numbers are in arbitrary units and there has been no attempt to make the values biologically meaningful. The intent is simply to demonstrate the feasibility of the procedures.