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.
Highlights
An optimal drug dosing regimen is a prerequisite to provide the best possible care for every individual patient
We develop a mathematical optimal control problems (OCP) that is especially designed for PKPD models and name the software OptiDose
The existence of an optimal control uthen follows from the compactness of Uad ⊂ Rm and the Weierstraß theorem, since the map J : Uad → R is continuously differentiable as the solution operator of the state equation u ∈ U → y(u) ∈ Y is continuously differentiable by the implicit function theorem and the assumptions of the OCP
Summary
An optimal drug dosing regimen is a prerequisite to provide the best possible care for every individual patient. E.g., many drugs are promoted as “one size fits all,” and individual patient characteristics are completely ignored Another reason might be much simpler; currently, to our knowledge no software for solving optimal control problems (OCP) is available that is custom-built for PKPD models and addresses the needs in daily clinical application. We will apply nonlinear model predictive control (NMPC), in engineering called closed-loop strategy, see [17] for theoretical details and [18] for an application to hemodialysis This meets clinical needs as it allows to adapt patient parameters during the optimization if the covariates change over time, e.g., due to maturation processes or sudden changes in the disease characteristics, or if more clinical measurements are available. We present three examples of different complexity, a biomarker indirect response model, a tumor growth inhibition model and a model characterizing various binding dynamics of a bispecific monoclonal antibody from immuno-oncology
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