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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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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.

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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.

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.

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