Methodological and analytical issues of progressive ratio schedules: Definition and scaling of breakpoint

Abstract

Background: The break point (BP) of the progressive ratio (PR) schedule of drug delivery is a well-recognized parameter in self-administration studies. Nonetheless, two problems remain unresolved: there is no rationally justified criterion for the last response at BP; the both commonly used definitions of BP as the number of deliveries or the last complete progressive ratio requirement are not the best assuming that BP is a measure of motivation.

New method: A criterion for the last lever press is proposed in this study using intravenous cocaine self-administration in rats. The rationale is based on the finding that long inter-press intervals have initially very low probability to occur during the self-administration phase of the session under the PR schedule. But this probability dramatically increases when inter-injection intervals increase due to high ratio requirements.

Results: For cocaine these critical inter-press intervals were 7.5 min and longer. This novel criterion was applied to measure BP according to all four theoretically plausible definitions of BP including the new one: the higher of the two numbers of presses before or after the last delivery of the reinforcer.

Comparison with existing method: The conventionally defined BP is significantly lower (by 12 %) than BP defined according to the new proposed definition. The new definition of BP provides not only a more accurate value of BP but now the variance of BP at different cocaine doses is homogeneous as required by many statistical tests.

Conclusion: These new definitions of the last press and BP provide more accurate and statistically homogenous measure of BP.

Keywords: Breakpoint; Cocaine; Definitions; Drug addiction; Inter-press intervals; Progressive ratio schedule; Self-administration.

Fig. 1.

Comparison of probability density functions of IPIs before and after the last cocaine injection in a representative rat. Both distributions were lognormal and bimodal. Lines represent the best fit of non-linear regression analysis before (solid blue lines) and after (long-dashed red lines) the last injection. Longest IPIs were observed at the end of the sessions.

Fig. 2.

The probability of IPIs to occur during the last completed progression requirement as a function of the IPI duration. Symbols (⦁) represent probability of a few arbitrary selected IPI durations. Line represents the best fit of regression analysis according to exponential function: y = a · exp(−b·x), where a = 100 and b = 0.78. Star represents the IPI = 7.5 min (450 s) with calculated probability to occur equal to 0.29 %. Data collected from 126 sessions from 6 rats.

Fig. 3.

Survival analysis of the first IPI ≥ 7.5 min which occurred after the last injection. Symbols (•) represent probability for arbitrary selected IPI durations. Line represents the best fit of regression analysis according to exponential function: y = y₀ + a · exp(−b·x), where y₀ =45.9 s, a = 81.6 and b = 0.05. Star represents the probability of 50 % that the first longer than 7.5 min IPI will be also longer than 56.5 min. Data are collected from 120 sessions. In 6 sessions experiment was accidently terminated before the first IPI = 7.5 min.

Fig. 4.

Relationship between the cocaine unit dose and BP (mean ± SEM) determined according to four definitions. Note that BP values measured by the number of injections are on the right y-axis.