OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

Abstract

Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic–pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic–pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic–pharmacodynamic examples.

Computing optimal drug dosing with OptiDose: implementation in NONMEM

“…The tolerances for the solving the differential equation ranged from TOL = 6 to TOL = 12. All solutions were verified by the Opti-Dose implementation [15] in MATLAB [24] which was also utilized to create the figures. All computations were performed on an ASUSTek computer with Intel(R) Core(TM) i7-7700HQ CPU processor with 2.80GHz and 16GB RAM.…”

“…For a given D the so-called state equation Eq. ( 1) admits a unique solution y(D) : [0, T ] → R n (under smoothness assumptions on the right-hand side, see [15]).…”

“…with a nonlinear function L : R n+1 → R and an additional term R : R m → R depending on the administered doses, compare [15] where R(D) = m i=1 α i n i D i with weights α i and the number n i of repeated administrations of each dose D i in favor of a linear dependency [5] to lower drug doses.…”

“…The optimal dosing algorithm OptiDose [15] solves an optimal control problem (OCP) to compute the doses which bring the associated response of the PKPD model as closely as possible to a desired therapeutic goal. Op-tiDose was specifically designed for optimal dosing tasks in PKPD modeling since (i) it optimizes the drug doses, the control variables, which generate the drug level according to the dosing scenario which then drives the model response, and (ii) it is robust with respect to jumps in the model solution occuring for intravenous (IV) bolus, oral and subcutaneous dose administration.…”

“…Second, the dosing scenario must be defined, i.e., (i) dosing time points, (ii) route of administration, (iii) maximal tolerable doses, and (iv) how often the dose can vary, e.g., daily, weekly, etc. Third, the therapeutic goal needs to be characterized by a mathematical function called the reference function in [15].…”