Abstract
The dose-response relationship in a pharmacologic system is analyzed using basic concepts of drug-receptor interaction and the theory of stochastic processes. Response is viewed as resulting from additive recruitment of tissue receptor-effector units. A Fokker-Planck (continuity) equation is written relating response to drug dosage in time. The solution to this equation is recalled from a previous paper. An expression relating response at equilibrium to drug dose follows, and easy methods for evaluation of experimental parameters are developed. Another mode of solution of the Fokker-Planck equation using Laplace transforms is presented, and simple equations are derived permitting straightforward evaluation of experimental parameters in transient states. These equations are adapted to "relaxation" type experiments.
| Original language | English |
|---|---|
| Pages (from-to) | 307-317 |
| Number of pages | 11 |
| Journal | Mathematical Biosciences |
| Volume | 19 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - 1974 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics
Cite this
Stochastic dose response. / Rendell, Marc.
In: Mathematical Biosciences, Vol. 19, No. 3-4, 1974, p. 307-317.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stochastic dose response
AU - Rendell, Marc
PY - 1974
Y1 - 1974
N2 - The dose-response relationship in a pharmacologic system is analyzed using basic concepts of drug-receptor interaction and the theory of stochastic processes. Response is viewed as resulting from additive recruitment of tissue receptor-effector units. A Fokker-Planck (continuity) equation is written relating response to drug dosage in time. The solution to this equation is recalled from a previous paper. An expression relating response at equilibrium to drug dose follows, and easy methods for evaluation of experimental parameters are developed. Another mode of solution of the Fokker-Planck equation using Laplace transforms is presented, and simple equations are derived permitting straightforward evaluation of experimental parameters in transient states. These equations are adapted to "relaxation" type experiments.
AB - The dose-response relationship in a pharmacologic system is analyzed using basic concepts of drug-receptor interaction and the theory of stochastic processes. Response is viewed as resulting from additive recruitment of tissue receptor-effector units. A Fokker-Planck (continuity) equation is written relating response to drug dosage in time. The solution to this equation is recalled from a previous paper. An expression relating response at equilibrium to drug dose follows, and easy methods for evaluation of experimental parameters are developed. Another mode of solution of the Fokker-Planck equation using Laplace transforms is presented, and simple equations are derived permitting straightforward evaluation of experimental parameters in transient states. These equations are adapted to "relaxation" type experiments.
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U2 - 10.1016/0025-5564(74)90046-7
DO - 10.1016/0025-5564(74)90046-7
M3 - Article
VL - 19
SP - 307
EP - 317
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 3-4
ER -