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.

为个体患者提供最佳药物剂量策略是药物科学和日常临床应用中的一项重要任务。我们开发并验证了最佳给药算法（OptiDose），该算法通过解决最佳控制问题，在不同给药途径的不同场景下计算药代动力学-药效模型的最佳个体化给药方案。目的是计算一个控制，通过最小化成本函数，使底层系统尽可能接近所需的参考函数。在药代动力学-药效学模型中，对照是给药剂量，参考函数可以是疾病进展。在某些时间点的药物给药提供了有限数量的离散控制、药物剂量，确定药物浓度及其对疾病进展的影响。因此，重写成本函数给出了仅取决于剂量的有限维最优控制问题。伴随技术可以有效地计算成本函数的梯度。这允许使用鲁棒算法解决最优控制问题，例如有限维优化的拟牛顿方法。 OptiDose 适用于三个相关但实质上不同的药代动力学-药效学示例。