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The solution of this differential equation is useful in calculating the concentration after the administration of a single dose of drug via IV bolus injection: = C t is concentration after time t; C 0 is the initial concentration (t=0) K is the elimination rate constant
Pharmacodynamics (PD) is the study of the biochemical and physiologic effects of drugs (especially pharmaceutical drugs). The effects can include those manifested within animals (including humans), microorganisms , or combinations of organisms (for example, infection ).
PK/PD relationships can be described by simple equations such as linear model, Emax model or sigmoid Emax model. [5] However, if a delay is observed between the drug administration and the drug effect, a temporal dissociation needs to be taken into account and more complex models exist: [6] [7] Direct vs Indirect link PK/PD models
The Lotka–Volterra equations describe dynamics of the predator-prey systems. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this rate is evaluated as xy, where x is the number of prey, y is the number of predator. This is a typical example of the law of mass action.
An example for a simple case (mono-compartmental) would be to administer D=8 mg/kg to a human. A human has a blood volume of around V b l o o d = {\displaystyle V_{blood}=} 0.08 L/kg . [ 7 ] This gives a C 0 = {\displaystyle C_{0}=} 100 μg/mL if the drug stays in the blood stream only, and thus its volume of distribution is the same as V b l o ...
The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs. ligand concentration. [9] Dose is usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures. Other dose units include moles ...
The plateau principle is a mathematical model or scientific law originally developed to explain the time course of drug action (pharmacokinetics). [1] The principle has wide applicability in pharmacology, physiology, nutrition, biochemistry, and system dynamics.
For an example, one might consider the hypothetical drug foosporin. Suppose it has a long lifetime in the body, and only ten percent of it is cleared from the blood each day by the liver and kidneys. Suppose also that the drug works best when the total amount in the body is exactly one gram.