Abstract
Control theory provides a powerful conceptual framework and mathematical armamentarium for modeling addictive behavior. It is particularly appropriate for repetitive, rhythmic behavior that occurs over time, such as drug use. We reframe seven selected theories of addictive behavior in control theoretic terms (heroin addiction model, opponent process theory, respondent conditioning, evolutionary theory, instrumental conditioning, incentive sensitization, and autoshaping) and provide examples of quantitative simulations for two of these models (opponent process theory and instrumental conditioning). This paper discusses theories of addiction to lay the foundation for control theoretic analyses of drug addiction phenomena, but does not review the empirical evidence for or against any particular model. These seven addiction models are then discussed in relation to the addictive phenomena for which they attempt to account and specific aspects of their feedback systems.
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Notes
- 1.
We do not model pharmacokinetic functions in this discussion, although we recognize that physiologically based pharmacokinetic modeling (e.g., Umulis et al. 2005) is needed to complete the modeling process. For simplicity, drug metabolism and excretion is modeled here simply as “time elapsed since drug administration.”
- 2.
From Wiener’s (1948) introduction to Cybernetics: “The mathematician need not have the skill to conduct a physiological experiment, but he must have the skill to understand one, to criticize one, and to suggest one. The physiologist need not be able to prove a certain mathematical theorem, but he must be able to grasp its physiological significance and to tell the mathematician for what he should look.”
- 3.
If self-administration were at a constant dose of the drug, then one might construe several addiction models herein as hybrid control models because the actual self-administration appeared binary (either take the drug or not). However, using a longer time frame, such as weeks or months, the rate and dose can be viewed as continuous measures, making hybrid modeling unnecessary.
- 4.
In its original formulation (Siegel 1975), Siegel’s associative model of morphine tolerance assumed that the unconditioned response was the drug effect, itself. However, this was revised (Eikelboom and Stewart 1982) to acknowledge that the drug effect (analgesia) is actually the unconditioned stimulus, and the adaptive, counter-directional response to the drug effect is the unconditioned response. In this sense, the conditioned and unconditioned responses are actually in the same direction, in this case hyperalgesia. For the purposes of this discussion, we will revert to Siegel’s terminology, keeping in mind that these psychobiological systems are themselves controlled systems for which the issue of whether the response is part of an afferent or efferent response can be critical (Eikelboom and Stewart 1982).
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Acknowledgements
The authors are particularly indebted to Thomas Piasecki for invaluable comments on two separate drafts of this manuscript. We thank Daniel Shapiro, Kevin Strubler and Rachael Renton for editorial assistance and Diane Philyaw for extensive graphics work. The authors have no conflicts of interest in this research. This research was supported in part by NIAAA grant 1R21AA015704 and NIDA grant 1R21DA020592 to DBN and by RTI International.
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Newlin, D.B., Regalia, P.A., Seidman, T.I., Bobashev, G. (2012). Control Theory and Addictive Behavior. In: Gutkin, B., Ahmed, S. (eds) Computational Neuroscience of Drug Addiction. Springer Series in Computational Neuroscience, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0751-5_3
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