Two-compartment model Mohammad Issa Saleh

y axis: logarithmic scale Typical plasma concentration (Cp) versus time profiles for a drug that obeys a two-compartment model following intravenous bolus administration y axis: normal scale y axis: logarithmic scale

A schematic representation of three types of two-compartment models consisting of a central and a peripheral compartment. Please note the difference in each type is reflected in the placement of an organ responsible for the elimination of the drug from the body. K12, K21, transfer rate constants; K10, K20, elimination rate constants. X1 X2 X1 X2 X1 X2

Assumptions of the model Upon drug absorption there is instantaneous distribution of drug throughout the central compartment (sampling compartment) having a volume V1 (Vc) Transfer of drug from the central compartment to the peripheral compartment is by a first-order process Transfer of drug from of drug from the peripheral compartment to the central compartment is by a first-order process

One Compartment Two Compartments Rapid or prompt equilibrium is attained. Distribution equilibrium is slow (takes finite time). There is a single disposition phase Distribution and post-distribution are two distinct phases. Linear: drug elimination follows first order kinetics Linear: distribution and elimination both follow first order

Drug concentrations in the two compartments following a single i. v Drug concentrations in the two compartments following a single i.v. bolus injection We start with virtually no drug in the second compartment, but re-equilibration moves drug in – levels rise A brief equilibrium - no net movement – at the peak of the curve, levels are neither rising nor falling Re-equilibration moves into reverse and drug leaves the second compartment – levels fall

X1 X2 K12 K21 K10 Distribution rate from X1 to X2 = Elimination rate =

Amount in the central compartment Conc in the central compartment VC is the volume of the central compartment Amount in the peripheral compartment

Postdistribution phase to determine: Determination of the postdistribution rate constant (β) and the coefficient (B) Postdistribution phase to determine: Determine β from the graph by using the slope The y-axis intercept of the extrapolated line is B

Determination of the distribution rate constant (α) and the coefficient (A) Method of residuals: The difference between measured concentrations and those obtained by extrapolation of the post-distribution line is plotted vs time Determine α from the graph by using the slope The y-axis intercept of the extrapolated line is A

Determination of micro rate constants: the inter-compartmental rate constants (K21 and K12) and the pure elimination rate constant (K10)

Volume of distribution of the central compartment (VC) Volume of distribution of the central compartment (VC). This is a proportionality constant that relates the amount of drug and the plasma concentration immediately (i.e. at t=0) following the administration of a drug.

Volume of distribution during the terminal phase (Vb or Vβ) This is a proportionality constant that relates the plasma concentration and the amount of drug remaining in the body at a time following the attainment of distribution equilibrium, or at a time on the terminal linear portion of the plasma concentration time data

Volume of distribution at steady state (Vss) This is a proportionality constant that relates the plasma concentration and the amount of drug remaining in the body at a time, following the attainment of practical steady state. This volume of distribution is independent of elimination parameters such as K10 or drug clearance.

The area under the plasma concentrationtime curve (AUC) Model independent: Trapezoid method Model dependent:

From these data, calculate: a. The volume of the central compartment Example: The pharmacokinetics of amrinone after a single IV bolus injection (75 mg) in 14 healthy adult male volunteers followed a two-compartment open model and fit the following parameters: A = 4.62 ± 12.0 µg/mL B = 0.64 ± 0.17 µg/mL  = 8.94 ± 13 hr–1  = 0.19 ± 0.06 hr–1 From these data, calculate: a. The volume of the central compartment b. The volume of the tissue compartment c. The transfer constants k12 and k21 d. The elimination rate constant from the central compartment e. The elimination half-life of amrinone after the drug has equilibrated with the tissue compartment

Two Compartment Extravascular Xa X1 X2 Ka K12 K21 K10

Two Compartment Extravascular Xa X1 X2 Ka K12 K21 K10