Abstract
Rationale
Behavioral–economic demand curve analysis offers several useful measures of drug self-administration. Although generation of demand curves previously required multiple days, recent within-session procedures allow curve construction from a single 110-min cocaine self-administration session, making behavioral–economic analyses available to a broad range of self-administration experiments. However, a mathematical approach of curve fitting has not been reported for the within-session threshold procedure.
Objectives
We review demand curve analysis in drug self-administration experiments and provide a quantitative method for fitting curves to single-session data that incorporates relative stability of brain drug concentration.
Methods
Sprague–Dawley rats were trained to self-administer cocaine, and then tested with the threshold procedure in which the cocaine dose was sequentially decreased on a fixed ratio-1 schedule. Price points (responses/mg cocaine) outside of relatively stable brain cocaine concentrations were removed before curves were fit. Curve-fit accuracy was determined by the degree of correlation between graphical and calculated parameters for cocaine consumption at low price (Q 0) and the price at which maximal responding occurred (P max).
Results
Removing price points that occurred at relatively unstable brain cocaine concentrations generated precise estimates of Q 0 and resulted in P max values with significantly closer agreement with graphical P max than conventional methods.
Conclusion
The exponential demand equation can be fit to single-session data using the threshold procedure for cocaine self-administration. Removing data points that occur during relatively unstable brain cocaine concentrations resulted in more accurate estimates of demand curve slope than graphical methods, permitting a more comprehensive analysis of drug self-administration via a behavioral–economic framework.
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Notes
P max and O max refer to non-normalized variables, and nP max and nO max, as defined later, are respectively used to refer to the normalized variables.
The terms “cost” and “price” will be used interchangeably to refer to the variable C in Eq. 1.
P max is found here in units of C. P max in standardized units could be determined by multiplying the result by Q 0 or in normalized units by multiplying the result by Q 0 and dividing by 100.
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Acknowledgments
We thank Rebecca Fallon and Erik Oleson for assistance with implementing the within-session threshold procedure. These experiments were supported by PHS grants R37 DA06214 and T32 GM008716.
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Bentzley, B.S., Fender, K.M. & Aston-Jones, G. The behavioral economics of drug self-administration: A review and new analytical approach for within-session procedures. Psychopharmacology 226, 113–125 (2013). https://doi.org/10.1007/s00213-012-2899-2
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DOI: https://doi.org/10.1007/s00213-012-2899-2