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Optimal Dosing Schedules for Substances Inducing Tolerance

Golrokh Nouri, Paul Tupper

TL;DR

This work provides a simple mathematical model of response to consumption and tolerance that can be fit from data on substance administration and response and determines optimal consumption schedules to maximize a given objective.

Abstract

Many drugs used therapeutically or recreationally induce tolerance: the effect of the substance decreases with repeated use. This phenomenon may reduce the efficacy of the substance unless dosage is increased beyond what is healthy for the individual. Restoring the effect of the substance can often be obtained by taking a break from consumption. We propose designing dosing schedules that maximize the desired effect of the substance with a given total consumption, while factoring in the effect of tolerance. We provide a simple mathematical model of response to consumption and tolerance that can be fit from data on substance administration and response. Using this model with given parameters, we determine optimal consumption schedules to maximize a given objective. We illustrate with the example of caffeine, where we provide a schedule of consumption for a user who values the effects of caffeine on all days but needs extra alertness on some days of the week.

Optimal Dosing Schedules for Substances Inducing Tolerance

TL;DR

This work provides a simple mathematical model of response to consumption and tolerance that can be fit from data on substance administration and response and determines optimal consumption schedules to maximize a given objective.

Abstract

Many drugs used therapeutically or recreationally induce tolerance: the effect of the substance decreases with repeated use. This phenomenon may reduce the efficacy of the substance unless dosage is increased beyond what is healthy for the individual. Restoring the effect of the substance can often be obtained by taking a break from consumption. We propose designing dosing schedules that maximize the desired effect of the substance with a given total consumption, while factoring in the effect of tolerance. We provide a simple mathematical model of response to consumption and tolerance that can be fit from data on substance administration and response. Using this model with given parameters, we determine optimal consumption schedules to maximize a given objective. We illustrate with the example of caffeine, where we provide a schedule of consumption for a user who values the effects of caffeine on all days but needs extra alertness on some days of the week.
Paper Structure (9 sections, 9 equations, 3 figures, 2 tables)

This paper contains 9 sections, 9 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model
  3. A single rapid dose, with no tolerance
  4. Constant Dosage, Long-Term Tolerance
  5. Examples
  6. Nicotine
  7. Caffeine
  8. Optimization of Dosing Schedule
  9. Discussion

Figures (3)

  • Figure 1: A fit of the model to experimental data from Porchet et al. porchet1988pharmacodynamic. Parameters are listed in Table \ref{['table: CafNicParameters']}.
  • Figure 2: Caffeine plasma level $C(t)$, alertness $E(t)$, and baseline alertness $E_b(t)$ over a four-week period for three dosing regimens.
  • Figure 3: Alertness versus time over the course of a week of caffeine consumption with optimized schedules. Left column, results for the model without tolerance; right column, with tolerance. Top row, consumption restricted to at most two cups of coffee a day; bottom row, consumption restrictred to ten cups of coffee a week.