Hawler Medical University Pharmacokinetics 4th stage Distribution of the drug in the body (Volume of Distribution) Lec. -1- By: Dr. Raad A. Kaskoos Ph. D. Pharmaceutics Pharmaceutics Dept. Hawler Medical University College of Pharmacy

Volume of distribution (Vd) Is a useful parameter that relates plasma drug concentration to the amount of drug in the body In multiple compartment kinetics there are several volume of distribution

Volume of distribution (Vd), cont. There are several volume of distribution that may be considered for a drug that assumes a two compartment open model such as volume of the central compartment and the volume of the peripheral or tissue compartment.

Apparent volume of the central compartment Vc It is useful for describing changes in drug concentration In the determination of drug clearance The magnitude of Vc gives an indication of the distribution of the drug in the body water

Apparent volume of the central compartment Vc , cont. As in the case of one compartment model, Vc may be determined from the dose and the instantaneous plasma drug concentration Cc Vc can be calculated by the following equation: Vc = X0 / Cc

Apparent volume of the central compartment Vc , cont. Vc = X0 / Cc Where: Vc = Volume of distribution of the central compartment X0 = Amount of the drug at zero time Cc = Plasma drug concentration

Apparent volume of distribution at steady state At steady state conditions the rate of drug entry into the tissue compartment from the central compartment is equal to the rate of drug exit from the tissue compartment into the central compartment The rate of drug transfer are described by the following eqation: Xp K21 = Xc K12

Apparent volume of distribution at steady state, cont. Xp K21 = Xc K12 Xp = Xc K12 / K21 And the amount of drug in the central compartment Xc is equal to Vc Cc , then by substitution in the above equation: Xp = K12 Vc Cc / K21

Apparent volume of distribution at steady state, cont. The total amount of drug in the body at steady state is equal to the sum of the amount of drug in the tissue compartment Xp , and the amount of drug in the central compartment Xc Therefore, at steady state, the apparent volume of drug (Vd)ss may be calculated by dividing the total amount of drug in the body by the concentration of drug in the central compartment at steady state: (Vd)ss = Xc + Xp / Cc

Extrapolated volume of distribution (Vd)exp can be calculated by the following equation: (Vd)exp = X0 B Where: (Vd)exp = Extrapolated volume of distribution X0 = Amount of the drug B = is the intercept

Volume of distribution by area (Vd) It is also known as (Vd)ß It is obtained through calculation similar to those used to find Vc , except that the rate constant ß is used instead of elimination rate constant Ke (Vd)area = (Vd)ß = X0 / ß (AUC)0

Significance of the volume of distribution Volume of distribution is affected by changes in the overall elimination rate and by the change in the total body clearance of the drug After the drug is distributed, the total amount of drug in the body during the elimination of ß phase is calculated by using (Vd) area

Significance of the volume of distribution, cont. Whereas (Vd)ss is not affected by changes in drug elimination, (Vd)ss reflects the true distributional volume changes due to renal function Vc represent the apparent volume of the central compartment and is useful in the calculation of drug clearance

Significance of the volume of distribution, cont. The magnitude of the various apparent volumes of distribution have the following relationship to each other: (Vd)exp > (Vd)area > Vc For drugs that follow two compartment model kinetics, changes in disease states may not result in different pharmacokinetic parameters

Significance of the volume of distribution, cont. Conversely, changes in pharmacokinetc parameters should not be attributed to physiologic changes without careful consideration of method of curve fitting and intersubject difference The terms K12 and K21 often fluctuate due to minor fitting and experimental difference and may affect calculation of other parameters

Drugs in the tissue/peripheral compartment The apparent volume of the tissue compartment Vp is a conceptual volume only and does not represent true anatomic volumes The Vp may be calculated from the knowledge of the transfer rate and Vc as follows: Vp = Vc K12 / K21 The calculation of the amount of drug in the tissue compartment does no entail the use of Vp

Drugs in the tissue/peripheral compartment, cont. Calculation of the drug concentration in the tissue compartment is useful, since the pharmacologic activity may correlate better with the tissue drug level time curve The amount of drug in the tissue compartment is also related to the amount of drug in the central compartment and the transfer constants

Elimination rate constant In the two compartment model (I.V administration) the elimination rate constant Ke represents the elimination of drug from the central compartment Whereas ß represents the elimination of drug from the entire body after the diffusable drug has established an equilibrium Therefore, ß is useful in calculating t1/2 and multiple dosage regimens

Two compartment open model intravenous infusion

Two compartment open model intravenous infusion, cont.

Two compartment open model-extravascular administration

Two compartment open model-extravascular administration, cont.

Three compartment open model It is an extension of the two compartment model with an individual deep tissue compartment The drug is distributed most rapidly to a highly perfused central compartment, less rapidly to the second or tissue compartment and very slowly to the third or deep tissue compartment

Three compartment open model, cont.

Three compartment open model, cont.

Determination of compartment models Models based on compartmental analysis use the fewest number of compartments necessary to adequately describe the experimental data Once an empirical equation is derived from the experimental observations, it becomes necessary to examine how well the theoretical values calculated from the derived equation fit the experimental data

Determination of compartment models, cont. Depending on the sampling intervals, it is also possible to miss a compartment Samples may be taken too late after administration of the dose to observe a possible distributive phase For example the following data plotted could easily mistaken for those of one compartment model as follows:

Determination of compartment models, cont.

Determination of compartment models, cont. In describing compartments each new compartment requires an additional first-order plot Compartment models having more than three compartments are rarely of pharmacologic significance In certain cases it is possible to lump a few compartments together to get a smaller number of compartments which together will describe the data adequately

Determination of compartment models, cont. An adequate description of several tissue compartments may be difficult Addition of a compartment to the model seems necessary It is important to realise that the drug may be retained or slowly concentrated in a deep tissue compartment

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