The Compartment Model and Definitions

Pharmacokinetics - the study of absorption, distribution, metabolism and excretion of injected and inhaled drugs and their metabolites - what the body does to the drug

• Determines the concentration of drug at its sites of action and the intensity of the drug's effects with time
• Also determines variability in drug responses between patients

The Compartment Model

• The body can be simplified to be thought of as a number of compartments representing theoretical spaces
• A two-compartment model can be used to illustrate pharmacokinetics:
• Drug is introduced by IV injection directly into the central compartment
• The drug subsequently distributes to the peripheral compartment, before returning to the central compartment where clearance from the body occurs from
• The central compartment includes intravascular fluid and highly perfused tissues such as lungs/heart/brain/kidneys - into which uptake of the drug is rapid
• These tissues recieve 75% of the cardiac output, but represent only 10% of the body mass
• Compartments are considered in terms of calculated volume, not actual anatomical volume
• Large calculated volume for the peripheral compartment suggests extensive uptake of drug by the tissues making up the peripheral compartment
• Rate of drug transfer (rate constant = K) may decrease with aging, causing higher plasma concentrations of drugs such as thiopental in elderly patients
• Residual drug in the peripheral compartment will diminish the effect of distributive processes in the reduction of the plasma concentration and lead to exaggerated repeat dose effects
• Degree of cumulative drug effect can be calculated knowing the drug's dosing interval and elimination half-time
• The two compartment model doesn't always hold:

• Doesn't work with rapid IV injection of drugs which attain maximum effect in <2 minutes
• Doesn't hold with drugs which don't depend on nonorgan clearance mechanisms eg. atracurium and cisatracuruim which are eliminated by Hoffman elimination/ester hydrolysis
• Elimination half-time is based on drug disposition in a single compartment model is of limited value in multicompartmental models

Plasma Concentration Curves

• A graphic plot of the logarithm of the decrease in the plasma concentration of a drug versus time after a rapid IV bolus characterises the:

• Alpha - distribution of a drug - begins immediately after IV injection, reflects the drugs distribution from the circulation to peripheral tissues
• Beta - elimination of a drug - occurs after the initial distribution phase - a more gradual decline in the drug's plasma concentration as the drug is cleared by the renal and hepatic clearance mechanisms

• Logarithms are used because they allow a large range of plasma concentrations to be plotted after the IV injection of a drug, especially in 1st order kinetics which occur in most drugs
• The traditional concept holds that a drug's effect parallels plasma concentration - however with cisatracurium, plasma concentration is already decreasing while the pharmacologic effect is still increasing - can consider this as a third compartment linked to plasma by a rate constant - this is called effect compartment modeling

Elimination Half-Time

• The time necessary for the plasma concentration of a drug to decrease to 50% during the elimination phase
• The term most often used to characterize a drug's pharmacokinetic behavior
• Directly proportional to volume of distribution Vd, and inversely proportional to clearance
• About 5 elimination half-times are required for nearly total (96.9%) elimination of drug from the body
• Drug accumulation is predictable if dosing intervals are less than 5 elimination half-times
• Less useful in multi-compartmental models
• Rate constant K (/min) = 1 / Time constant (min)
• Half-life = 0.693 x Time constant

Elimination Half-Life

• The time necessary to eliminate 50% of the drug from the body after its rapid IV injection

Clearance - the volume of plasma cleared of drug by renal excretion and/or metabolism in the liver or other organs

First Order Kinetics - the rate of change of drug concentration by any process is directly proportional to the drug concentration remaining to undertake that process. Remember first order kinetics is an assumption of a linear model not a one compartment model

Zero Order Kinetics - rate of elimination of a drug is constant regardless of Cp (i.e. constant amount of drug eliminated per unit time). Cp decreases linearly with time. A drug normally displaying first order kinetics can display zero order kinetics at high doses due to saturation of clearance pathways

Volume of Distribution - also known as apparent volume of distribution, is a pharmacological, theoretical volume that a drug would have to occupy (if it were uniformly distributed), to provide the same concentration as it currently is in blood plasma = total amount of drug in body / drug blood plasma concentration

Bioavailability - the fraction of an administered dose of unchanged drug that reaches the systemic circulation - by definition IV bioavailability is 100%

Area Under the Plasma Drug Concentration-Time Curve (AUC) - reflects the actual body exposure to drug after administration of a dose of the drug and is expressed in mg*h/L

Extraction Ratio - rate of plasma drug removal by an organ of elimination, divided by the rate at which it is presented to this organ - E = (C_A - C_V) / C_A