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Technical Brief

A Control-Theoretic Approach to Neural Pharmacology: Optimizing Drug Selection and Dosing

[+] Author and Article Information
Gautam Kumar

Department of Electrical and Systems Engineering,
Washington University,
St. Louis, MO 63130
e-mail: gautam.kumar@wustl.edu

Seul Ah Kim

Department of Biomedical Engineering,
Washington University,
St. Louis, MO 63130
e-mail: seulah.kim@wustl.edu

ShiNung Ching

Department of Electrical and Systems Engineering,
Division of Biology and Biomedical Sciences,
Washington University,
St. Louis, MO 63130
e-mail: shinung@wustl.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 24, 2015; final manuscript received March 2, 2016; published online May 25, 2016. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 138(8), 084501 (May 25, 2016) (8 pages) Paper No: DS-15-1342; doi: 10.1115/1.4033102 History: Received July 24, 2015; Revised March 02, 2016

The induction of particular brain dynamics via neural pharmacology involves the selection of particular agonists from among a class of candidate drugs and the dosing of the selected drugs according to a temporal schedule. Such a problem is made nontrivial due to the array of synergistic drugs available to practitioners whose use, in some cases, may risk the creation of dose-dependent effects that significantly deviate from the desired outcome. Here, we develop an expanded pharmacodynamic (PD) modeling paradigm and show how it can facilitate optimal construction of pharmacologic regimens, i.e., drug selection and dose schedules. The key feature of the design method is the explicit dynamical-system based modeling of how a drug binds to its molecular targets. In this framework, a particular combination of drugs creates a time-varying trajectory in a multidimensional molecular/receptor target space, subsets of which correspond to different behavioral phenotypes. By embedding this model in optimal control theory, we show how qualitatively different dosing strategies can be synthesized depending on the particular objective function considered.

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References

Chou, T.-C. , 2006, “ Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies,” Pharmacol. Rev., 58(3), pp. 621–681. [CrossRef] [PubMed]
Campillos, M. , Kuhn, M. , Gavin, A.-C. , Jensen, L. J. , and Bork, P. , 2008, “ Drug Target Identification Using Side-Effect Similarity,” Science, 321(5886), pp. 263–266. [CrossRef] [PubMed]
Dumont, G. A. , and Ansermino, J. M. , 2013, “ Closed-Loop Control of Anesthesia: A Primer for Anesthesiologists,” Anesth. Analg., 117(5), pp. 1130–1138. [CrossRef] [PubMed]
Syafiie, S. , Rami, M. A. , and Tadeo, F. , 2010, “ Positive Infusion of Propofol Drug During Induction,” IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Macao, China, Dec. 7–10, pp. 325–328.
Hahn, J.-O. , Dumont, G. , and Ansermino, J. M. , 2011, “ Closed-Loop Anesthetic Drug Concentration Estimation Using Clinical-Effect Feedback,” IEEE Trans. Biomed. Eng., 58(1), pp. 3–6. [CrossRef] [PubMed]
Ching, S. , Liberman, M. Y. , Chemali, J. J. , Westover, M. B. , Kenny, J. D. , Solt, K. , Purdon, P. L. , and Brown, E. N. , 2013, “ Real-Time Closed-Loop Control in a Rodent Model of Medically Induced Coma Using Burst Suppression,” Anesthesiology, 119(4), pp. 848–860. [CrossRef] [PubMed]
Hopkins, A. L. , 2008, “ Network Pharmacology: The Next Paradigm in Drug Discovery,” Nat. Chem. Biol., 4(11), pp. 682–690. [CrossRef] [PubMed]
Tang, J. , and Aittokallio, T. , 2014, “ Network Pharmacology Strategies Toward Multi-Target Anticancer Therapies: From Computational Models to Experimental Design Principles,” Curr. Pharm. Des., 20(1), pp. 23–36. [CrossRef] [PubMed]
Kirk, D. E. , 2004, Optimal Control Theory: An Introduction, Dover, Mineola, NY.
West, N. , Dumont, G. A. , van Heusden, K. , Petersen, C. L. , Khosravi, S. , Soltesz, K. , Umedaly, A. , Reimer, E. , and Ansermino, J. M. , 2013, “ Robust Closed-Loop Control of Induction and Maintenance of Propofol Anesthesia in Children,” Pediatr. Anesth., 23(8), pp. 712–719. [CrossRef]
Ingole, D. D. , Sonawane, D. N. , Naik, V. V. , Ginoya, D. L. , and Patki, V. V. , 2013, “ Linear Model Predictive Controller for Closed-Loop Control of Intravenous Anesthesia With Time Delay,” ACEEE Int. J. Control Syst. Instrum., 4(1), pp. 8–15.
Shanechi, M. M. , Chemali, J. J. , Liberman, M. , Solt, K. , and Brown, E. N. , 2013, “ A Brain-Machine Interface for Control of Medically-Induced Coma,” PLoS Computat. Biol., 9(10), pp. 1–17. [CrossRef]
Derendorf, H. , and Meibohm, B. , 1999, “ Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives,” Pharm. Res., 16(2), pp. 176–185. [CrossRef] [PubMed]
Schumacher, P. M. , Dossche, J. , Mortier, E. P. , Luginbuehl, M. , Bouillon, T. W. , and Struys, M. M. R. F. , 2009, “ Response Surface Modeling of the Interaction Between Propofol and Sevoflurane,” Anesthesiology, 111(4), pp. 790–804. [CrossRef] [PubMed]
Minto, C. F. , Schnider, T. W. , Short, T. G. , Gregg, K. M. , Gentilini, A. , and Shafer, S. L. , 2000, “ Response Surface Model for Anesthetic Drug Interactions,” Anesthesiology, 92(6), pp. 1603–1616. [CrossRef] [PubMed]
Shaffer, C. L. , Osgood, S. M. , Smith, D. L. , Liu, J. , and Trapa, P. E. , 2014, “ Enhancing Ketamine Translational Pharmacology Via Receptor Occupancy Normalization,” Neuropharmacology, 86, pp. 174–180. [CrossRef] [PubMed]
Aradi, I. , and Erdi, P. , 2006, “ Computational Neuropharmacology: Dynamical Approaches in Drug Discovery,” Trends Pharmacol. Sci., 27(5), pp. 240–243. [CrossRef] [PubMed]
Ching, S. , and Brown, E. N. , 2014, “ Modeling the Dynamical Effects of Anesthesia on Brain Circuits,” Curr. Opin. Neurobiol., 25, pp. 116–122. [CrossRef] [PubMed]
Brown, E. N. , Purdon, P. L. , and Van Dort, C. J. , 2011, “ General Anesthesia and Altered States of Arousal: A Systems Neuroscience Analysis,” Annu. Rev. Neurosci., 34(1), pp. 601–628. [CrossRef] [PubMed]
Ching, S. , Cimenser, A. , Purdon, P. L. , Brown, E. N. , and Kopell, N. J. , 2010, “ Thalamocortical Model for a Propofol-Induced Alpha-Rhythm Associated With Loss of Consciousness,” Proc. Natl. Acad. Sci. U.S.A., 107(52), pp. 22665–22670. [CrossRef] [PubMed]
Vijayan, S. , Ching, S. , Purdon, P. L. , Brown, E. N. , and Kopell, N. J. , 2013, “ Thalamocortical Mechanisms for the Anteriorization of α Rhythms During Propofol-Induced Unconsciousness,” J. Neurosci., 33(27), pp. 11070–11075. [CrossRef] [PubMed]
Trescot, A. M. , Datta, S. , Lee, M. , and Hansen, H. , 2008, “ Opioid Pharmacology,” Pain Physician, 11(Suppl. 2), pp. S133–S153. [PubMed]
Holz, M. , and Fahr, A. , 2001, “ Compartment Modeling,” Adv. Drug Delivery Rev., 48(2–3), pp. 249–264. [CrossRef]
Haddad, W. M. , Chellaboina, V. , and Hui, Q. , 2010, Nonnegative and Compartmental Dynamical Systems, Princeton University Press, Princeton, NJ.
Danhof, M. , de Jongh, J. , Lange, E. C. D. , Pasqua, O. D. , Ploeger, B. A. , and Voskuyl, R. A. , 2007, “ Mechanism-Based Pharmacokinetic-Pharmacodynamic Modeling: Biophase Distribution, Receptor Theory, and Dynamical Systems Analysis,” Annu. Rev. Pharmacol. Toxicol., 47(1), pp. 357–400. [CrossRef] [PubMed]
Schuler, S. , Ebenbauer, C. , and Allgöwer, F. , 2011, “ L0-System Gain and l1-Optimal Control,” 18th IFAC World Congress, Milan, Italy, Aug. 28–Sept. 2, Vol. 18, pp. 9230–9235.
Gallieri, M. , and Maciejowski, J. M. , 2012, “ ℓ asso MPC: Smart Regulation of Over-Actuated Systems,” American Control Conference (ACC), Montreal, Canada, June 27–29, pp. 1217–1222.
Nagahara, M. , Quevedo, D. E. , and Nesic, D. , 2013, “ Maximum Hands-Off Control and L1 Optimality,” IEEE 52nd Annual Conference on Decision and Control (CDC), Firenze, Italy, Dec. 10–13, pp. 3825–3830.
Kwon, W. H. , and Han, S. H. , 2005, “ Receding Horizon Control: Model Predictive Control for State Models,” Advanced Textbooks in Control and Signal Processing, Springer, London.
Mayne, D. Q. , Rawlings, J. B. , Rao, C. V. , and Scokaert, P. O. M. , 2000, “ Constrained Model Predictive Control: Stability and Optimality,” Automatica, 36(6), pp. 789–814. [CrossRef]
Qin, S. , and Badgwell, T. A. , 2003, “ A Survey of Industrial Model Predictive Control Technology,” Control Eng. Pract., 11(7), pp. 733–764. [CrossRef]
Sawaguchi, Y. , Furutani, E. , Shirakanmi, G. , Araki, M. , and Fukuda, K. , 2003, “ A Model-Predictive Hypnosis Control System Under Total Intravenous Anesthesia,” IEEE Trans. Biomed. Eng., 55(3), pp. 874–887. [CrossRef]
Luginbühl, M. , Bieniok, C. , Leibundgut, D. , Wymann, R. , Gentilini, A. , and Schnider, T. W. , 2006, “ Closed-Loop Control of Mean Arterial Blood Pressure During Surgery With Alfentanil: Clinical Evaluation of a Novel Model-Based Predictive Controller,” Anesthesiology, 105(3), pp. 462–470. [CrossRef] [PubMed]
Hovorka, R. , 2011, “ Closed-Loop Insulin Delivery: From Bench to Clinical Practice,” Nat. Rev. Endocrinol., 7(7), pp. 385–395. [CrossRef] [PubMed]
Maguire, P. , Tsai, N. , Kamal, J. , Cometta-Morini, C. , Upton, C. , and Loew, G. , 1992, “ Pharmacological Profiles of Fentanyl Analogs at Mu, Delta and Kappa Opiate Receptors,” Eur. J. Pharmacol., 213(2), pp. 219–225. [CrossRef] [PubMed]
McCarthy, M. M. , Brown, E. N. , and Kopell, N. , 2008, “ Potential Network Mechanisms Mediating Electroencephalographic Beta Rhythm Changes During Propofol-Induced Paradoxical Excitation,” J. Neurosci., 28(50), pp. 13488–13504. [CrossRef] [PubMed]
Eghbali, M. , Gage, P. W. , and Birnir, B. , 2003, “ Effects of Propofol on GABAa Channel Conductance in Rat-Cultured Hippocampal Neurons,” Eur. J. Pharmacol., 468(2), pp. 75–82. [CrossRef] [PubMed]
Jin, Y.-H. , Zhang, Z. , Mendelowitz, D. , and Andresen, M. C. , 2009, “ Presynaptic Actions of Propofol Enhance Inhibitory Synaptic Transmission in Isolated Solitary Tract Nucleus Neurons,” Brain Res., 1286, pp. 75–83. [CrossRef] [PubMed]
Yildirim, M. A. , Goh, K.-I. , Cusick, M. E. , Barabási, A.-L. , and Vidal, M. , 2007, “ Drug-Target Network,” Nat. Biotechnol., 25(10), pp. 1119–1126. [CrossRef] [PubMed]
Kern, S. E. , and Stanski, D. R. , 2008, “ Pharmacokinetics and Pharmacodynamics of Intravenously Administered Anesthetic Drugs: Concepts and Lessons for Drug Development,” Clin. Pharmacol. Ther., 84(1), pp. 153–156. [CrossRef] [PubMed]
Absalom, A. R. , Mani, V. , De Smet, T. , and Struys, M. M. R. F. , 2009, “ Pharmacokinetic Models for Propofol—Defining and Illuminating the Devil in the Detail,” Br. J. Anaesth., 103(1), pp. 26–37. [CrossRef] [PubMed]
Bai, D. , Pennefather, P. S. , MacDonald, J. F. , and Orser, B. A. , 1999, “ The General Anesthetic Propofol Slows Deactivation and Desensitization of GABAa Receptors,” J. Neurosci., 19(24), pp. 10635–10646. [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of optimal drug selection and dosing to achieve a desired endpoint in the receptor space. (a) Conventional PK–PD modeling approach. (b) Receptor dynamics based modeling approach wherein a particular dosing strategy leads to a time-varying trajectory indicating the fraction of bound receptors. (c) An optimal controller designs dosing of n available drugs by minimizing an appropriately defined cost function. The drug PK then determines time-varying effect site concentrations, and the dynamic receptor-binding model subsequently generates a trajectory in the multidimensional receptor space. The control objective is to drive this trajectory to some endpoint, corresponding to a desired behavioral outcome.

Grahic Jump Location
Fig. 2

Comparison of various cost functions in optimal selection and dosing of fentanyl, sufentanil, alfentanil, and remifentanil (top: low-price per unit fentanyl and bottom: high-price per unit fentanyl). (a) Bolus-type (sparse) dosing of drugs using an L1 cost function, (b) smooth dosing of drugs using an L2 quadratic cost function, and (c) smooth but spatially sparse dosing of drugs using L2 − L1 norm minimization. (d) Trajectories of bound μ and κ receptors for each of these dosing designs in the receptor space (solid: low-price per unit fentanyl and dashed: high-price per unit fentanyl). Note that u(t) represents the quantity (dimensionless) administered per minute.

Grahic Jump Location
Fig. 4

Circumventing constraints in the receptor space. (a) Optimally designed sparse dosing of three drugs, namely, fentanyl, alfentanil, and remifentanil (shown in (b)) fails to circumvent the region corresponding to a hypothetical paradoxical effect (shaded region in (a)) in the receptor space in (a). Adding another drug sufentanil in the optimal control design (shown in (c)) allows the system to achieve the desired state in the receptor space by circumventing the region corresponding to a hypothetical paradoxical effect in the receptor space.

Grahic Jump Location
Fig. 3

Design of optimal dosing to target paradoxical excitation with propofol. (a) Spectrogram of the model output as a function of the fraction of GABAA receptors bound by propofol. (b) The model consists of reciprocally coupled excitatory and inhibitory neurons, each modeled using voltage-gated conductance equations. The fraction of receptors bound modulates the GABA-ergic synaptic conductance and decay time. The design objective here is to induce the paradoxically elevated firing rate, corresponding to approximately 70% of receptors bound. (c) The optimal dose trajectories, (d) model output frequency, and (e) fraction bound trajectories are shown for L1- and L2-based cost functions.

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