An integer programming approach for optimal drug dose computation

In this paper, we study the problem of determining the optimal drug administration strategy when only a finite number of different dosages are available, a lower bound is posed on the time intervals between two consecutive doses, and drug concentrations should not exceed the toxic concentration levels. The presence of only binary variables leads to the adoption of an integer programming (IP) scheme for the formulation and solution of the drug dose optimal control problem. The proposed method is extended to account for the stochastic formulation of the optimal control problem, so that it can be used in practical applications where large populations of patients are to be treated. A Finite Impulse Response (FIR) model derived from experimental pharmacokinetic data is employed to correlate the administered drug dose with the concentration-time profiles of the drug in the compartments (organs) of the body.