OptiDose: computing the individualized optimal drug dosing regimen using optimal control. (English) Zbl 1466.92071
Summary: 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.
MSC:
| 92C50 | Medical applications (general) |
| 93B45 | Model predictive control |
| 49M15 | Newton-type methods |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
Keywords:
optimal control; model predictive control; quasi-Newton methods; individualized optimal drug dosing; pharmacokinetic-pharmacodynamic modelsReferences:
| [1] | Van Donge, T.; Evers, K.; Koch, G.; van den Anker, J.; Pfister, M., Clinical Pharmacology and Pharmacometrics to Better Understand Physiological Changes During Pregnancy and Neonatal Life. Handbook of Experimental Pharmacology (2019), Berlin: Springer, Berlin |
| [2] | Kearns, GL; Abdel-Rahman, SM; Alander, SW; Blowey, DL; Leeder, JS; Kauffman, RE, Developmental pharmacology—drug disposition, action, and therapy in infants and children, N. Engl. J. Med., 349, 1157-1167 (2003) · doi:10.1056/NEJMra035092 |
| [3] | Koch, G.; Datta, DN; Jost, K.; Schulzke, SM; van den Anker, J.; Pfister, M., Caffeine citrate dosing adjustments to assure stable caffeine concentrations in preterm neonates, J. Pediatr., 191, 50-56 (2017) · doi:10.1016/j.jpeds.2017.08.064 |
| [4] | Gobburu, JVS; Marroum, PJ, Utilisation of pharmacokinetic-pharmacodynamic modeling and simulation in regulatory decision making, Clin. Pharmacokinet, 40, 883-892 (2001) · doi:10.2165/00003088-200140120-00001 |
| [5] | Gibaldi, M.; Perrier, S., Pharmacokinetics (1982), Boca Raton: CRC Press Tayler & Francis Group, Boca Raton · doi:10.1201/b14095 |
| [6] | Mager, D.; Wyska, E.; Jusko, W., Diversity of mechanism-based pharmacodynamics, Drug Metab. Dispos., 31, 510-519 (2003) · doi:10.1124/dmd.31.5.510 |
| [7] | Koch, G.; Schropp, J.; Kloeden, P.; Pötzsche, C., Mathematical concepts in pharmacokinetics and pharmacodynamics with application to tumor growth, Nonautonomous Dynamical Systems in the Life Sciences, 225-250 (2013), New York: Springer, New York · Zbl 1311.37076 · doi:10.1007/978-3-319-03080-7_7 |
| [8] | Bonate, P., Pharmacokinetic-Pharmacodynamic Modeling and Simulation (2011), Berlin: Springer, Berlin · doi:10.1007/978-1-4419-9485-1 |
| [9] | Gabrielsson, M.; Weiner, D., Pharmacokinetic and Pharmacodynamic Data Analysis (2017), Sweden: Swedish Pharmaceutical Press, Sweden |
| [10] | Pfister, M.; D’Argenio, DZ, The emerging scientific discipline of pharmacometrics, special issue, Clin. Pharmacol., 50, 1-6 (2010) |
| [11] | Schättler, H.; Ledzewicz, U., Optimal Control for Mathematical Models of Cancer Therapies (2015), New York: Springer, New York · Zbl 1331.92008 · doi:10.1007/978-1-4939-2972-6 |
| [12] | Moore, H., How to mathematically optimize drug regimens using optimal control, J. Pharmacokinet Pharmacodyn., 45, 127-137 (2018) · doi:10.1007/s10928-018-9568-y |
| [13] | Schropp, J.; Khot, A.; Dhaval, SK; Koch, G., Target-mediated drug disposition model for bispecific antibodies: properties, approximation, and optimal dosing strategy, CPT Pharmacomet. Syst. Pharmacol., 8, 3, 177-187 (2019) · doi:10.1002/psp4.12369 |
| [14] | Pontryagin, LS, Mathematical Theory of Optimal Processes (1987), CRC Press: Classics in Soviet Mathematics, CRC Press |
| [15] | Irurzun-Arana, I.; Janda, A.; Ardanza-Trevijano, S.; Troconiz, IF, Optimal dynamic control approach in a multiobjective therapeutic scenario: application to drug delivery in the treatment of prostate cancer, PLoS Comput. Biol., 14, 4, e1006087 (2018) · doi:10.1371/journal.pcbi.1006087 |
| [16] | Abboubakar, H.; Kamgang, JC; Nkague Nkamba, L.; Tieudjo, D., Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases, J. Math. Biol., 76, 379-427 (2018) · Zbl 1393.37098 · doi:10.1007/s00285-017-1146-1 |
| [17] | Grüne, L.; Pannek, J., Nonlinear Model Predictive Control (2011), New York: Springer, New York · Zbl 1220.93001 · doi:10.1007/978-0-85729-501-9 |
| [18] | Rogg, S.; Fuertinger, DH; Volkwein, S.; Kappel, F.; Kotanko, P., Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach, J. Math. Biol., 79, 2281-2313 (2019) · Zbl 1430.92039 · doi:10.1007/s00285-019-01429-1 |
| [19] | Chahim, M.; Hartl, RF; Kort, PM, A tutorial on the deterministic impulse control maximum principle: necessary and sufficient optimality conditions, Eur. J. Oper. Res., 219, 1, 18-26 (2012) · Zbl 1244.49032 · doi:10.1016/j.ejor.2011.12.035 |
| [20] | Hackbusch, W., Elliptic Differential Equations, Theory and Numerical Treatment. Computational Mathematics 18 (2003), New York: Springer, New York |
| [21] | Hinze, M.; Pinnau, R.; Ulbrich, M.; Ulbrich, S., Optimization with PDE Constraints. Mathematical Modelling: Theory and Applications (2009), Berlin: Springer, Berlin · Zbl 1167.49001 |
| [22] | Renardy, M., Rogers, R.C.: An introduction to partial differential equations. Texts in Applied Mathematics 13 (Second ed.). Springer, New York (2004) · Zbl 1072.35001 |
| [23] | Kelley, C., Iterative Methods for Optimization. Frontiers in Applied Mathematics (1999), Philadelphia: SIAM, Philadelphia · Zbl 0934.90082 · doi:10.1137/1.9781611970920 |
| [24] | The Math Works, I.: MATLAB Release (2018a). The MathWorks, Inc., Natick, MA (2018) |
| [25] | Dayneka, NL; Garg, V.; Jusko, WJ, Comparison of four basic models of indirect pharmacodynamic responses, J. Pharmacokinet Biopharm., 21, 4, 457-478 (1993) · doi:10.1007/BF01061691 |
| [26] | Koch, G.; Schropp, J., Delayed logistic indirect response models: realization of oscillating behavior, J. Pharmacokinet Pharmacodyn., 45, 1, 49-58 (2018) · doi:10.1007/s10928-017-9563-8 |
| [27] | Koch, G.; Schropp, J.; Jusko, WJ, Assessment of non-linear combination effect terms for drug-drug interactions, J. Pharmacokinet Pharmacodyn., 43, 5, 461-479 (2016) · doi:10.1007/s10928-016-9490-0 |
| [28] | Simeoni, M.; Magni, P.; Cammia, C.; De Nicolao, G.; Croci, V.; Pesenti, E.; Germani, M.; Poggesi, I.; Rocchetti, M., Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents, Cancer Res., 64, 1094-1101 (2004) · doi:10.1158/0008-5472.CAN-03-2524 |
| [29] | Koch, G.; Walz, A.; Lahu, G.; Schropp, J., Modeling of tumor growth and anticancer effects of combination therapy, J. Pharmacokinet Pharmacodyn., 36, 2, 179-197 (2009) · doi:10.1007/s10928-009-9117-9 |
| [30] | Koch, G.; Krzyzanski, W.; Perez-Ruixo, JJ; Schropp, J., Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations, J. Pharmacokinet Pharmacodyn., 41, 4, 291-318 (2014) · doi:10.1007/s10928-014-9368-y |
| [31] | Jiang, X.; Chen, X.; Carpenter, TJ; Wang, J.; Zhou, R.; Davis, HM; Heald, DL; Wang, W., Development of a target cell-biologics-effector cell (TBE) complex-based cell killing model to characterize target cell depletion by T cell redirecting bispecific agents, MAbs, 10, 6, 876-889 (2018) · doi:10.1080/19420862.2018.1480299 |
| [32] | Doldan-Martelli, V.; Guantes, R.; Miguez, DG, A mathematical model for the rational design of chimeric ligands in selective drug therapies, CPT Pharmacometrics Syst. Pharmacol., 2, 2, 26-33 (2013) · doi:10.1038/psp.2013.2 |
| [33] | Rhoden, JJ; Dyas, GL; Wroblewski, VJ, A modeling and experimental investigation of the effects of antigen density, binding affinity, and antigen expression ratio on bispecific antibody binding to cell surface targets, J. Biol. Chem., 291, 11337-11347 (2016) · doi:10.1074/jbc.M116.714287 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
