Volume of Distribution Presented by: Santosh Kumar Gupta Reg no: 11MSY0009 1

Introduction :

Introduction Volume of Distribution (V D ), is defined as the volume in which the amount of drug would be uniformly distributed to produce the observed blood concentration. The Volume of distribution (V D ), also known as Apparent volume of distribution , is used to quantify the distribution of a drug between plasma and the rest of the body after oral or parenteral dosing. It is called as Apparent Volume because all parts of the body equilibrated with the drug do not have equal concentration. 2

The real volume of distribution has physiological meaning and is related to the Body Water.:

The real volume of distribution has physiological meaning and is related to the Body Water. 3

The volume of each of these compartments can be determined by use of specific markers or tracers.:

The volume of each of these compartments can be determined by use of specific markers or tracers. Physiological Fluid Compartments the Markers Used Approximate volume (liters) Plasma Evans Blue, Indocyanine Green 4 Extracellular fluid Inulin , Raffinose , Mannitol 14 Total Body Water D 2 O, Antipyrine 42 4

Drugs which bind selectively to Plasma Proteins, e.g. Warfarin have apparent Volume of Distribution smaller than their Real volume of distribution. The Vd of such drugs lies between blood volume and total body water i.e. b/w 6 to 42 liters. :

Drugs which bind selectively to Plasma P roteins, e.g. Warfarin have apparent V olume of Distribution smaller than their Real volume of distribution. The Vd of such drugs lies between blood volume and total body water i.e. b/w 6 to 42 liters. Drugs which bind selectively to Extravascular Tissues e.g. Chloroquine have Apparent volume of distribution larger than their Real volume of distribution. The Vd of such drugs is always greater than 42 liters. 5

Vd of Some Drugs :

Vd of S ome Drugs Factors affecting the Vd of a drug: Lipid solubility of drug. Degree of PPB(Plasma Protein Binding) ---- high PPB drugs have smaller Vd . Affinity for different tissue proteins. Fat : lean body mass. Disease like Congestive Heart Failure (CHF), uremia, cirrhosis. Drugs Vd ( L/70 Kg) Heparin 5 Aspirin 11 Digoxin 420 Chloroquine 13000 6

Classification of Vd:

Classification of Vd Volume of the central compartment (V c). Volume of distribution calculated by the area method (V area). Steady State Volume of Distribution (V ss ). 7

Volume of the central compartment (Vc):

Volume of the central compartment ( V c ) In the framework of a compartmental analysis, the initial volume of distribution is termed volume of central compartment and is obtained by mean which is given by equation: V c = Dose ⁿ∑ Y i i =1 where, Y i are the intercepts of different phases of kinetic disposition obtained by fitting the plasma drug concentration Vs time profile. Therefore, Vc can be viewed as the apparent volume for which drug elimination occurs because kidney and liver are two main clearing organs belonging to the central compartment. Vc can be useful to predict the initial maximum conc. for an I.v . bolus administration and also used to estimate the plasma volume when using a compound which is restricted to plasma such as Evans blue. 8

Volume of distribution calculated by area method(V area):

Volume of distribution calculated by area method(V area) V area is the asymptotic value where Vd increases progressively until it reaches this value, where the pseudo equilibrium is achieved. When the distribution of pseudo equilibrium is reached, the net exchange between plasma (central compartment) and the tissue (peripheral compartments) is null, and the decrease of plasma concentration is now only because of irreversible drug elimination, which is proportional to the body (total) clearance which is given by equation: Rate of drug elimination= Cl tot ×C plasma Where Cl tot is the plasma clearance V area is used to eliminate the residual amount of drug in the body when the drug decreases according to its elimination phase. 9

The relationship between plasma concentration and the amount of drug in the body during the elimination phase is given by equation ::

The relationship between plasma concentration and the amount of drug in the body during the elimination phase is given by equation : V area = Amount of drug in the body during the terminal phase Plasma concentration during the terminal phase The amount of drug present in the body at a given time t during the elimination phase is equal to the amount of drug which remains to be eliminated, i.e. equation : Amount of drug in the body at time t i = ʃ Cl × C (t) dt where ti is a time during the elimination phase .Integration of this eqution gives eq : Amount of drug at time t i = Cl × [AUC ( t i - ∞) ] Where AUC ( t i -∞) is the area under the plasma concentration vs. time curve between t i and infinity. When V area is computed after extra vascular drug administration and when the amount of drug that gains access to the systemic circulation is unknown, what is actually estimated is V area/F ,not V area. V area/F = Dose/AUC ×1/ λ Z Where F is the bioavailability factor from 0 to 1. 10

PowerPoint Presentation:

According to the principle of mass balance, the total amount of drug in the body is equal to the amount in plasma (V P C P ) plus the amount in tissue (V T C T ). By definition of volume of distribution Vd = V P C P + V T C T /C P or Vd = V P + V T ×C T /C P or Vd = V P + V T × fu,P / fu,T 11

Steady State Volume of Distributio(Vss):

Steady State Volume of Distributio ( Vss ) V ss is a clearance independent volume of distribution that is used to calculate the drug amount in the body under equilibrium conditions, i.e. during a drug i.v . infusion and also during multiple drug administration once the steady-state conditions are achieved. Vss = Amount of drug in the body in equilibrium conditions Steady state plasma concentration ( Css ) V ss can be derived using the statistical moments approach described by Benet and Galeazzi (1979) Vss = Dose i.v . × AUMC/(AUC)² = Cl × MRT where AUMC is the area under the first moment of the disposition curve, Cl the plasma clearance, and MRT the mean residence time in the system. V ss is the most useful V d because it allows computation of a loading dose . Loading dose = Vss × Css F where C ss is the expected (desired) plasma concentration at steady-state and F (0–1), is the bioavailability factor. 12

PowerPoint Presentation:

A loading dose can be required for some drugs when it is desirable to reach immediately or rapidly the C ss [e.g. under life threatening conditions for anti-coagulant, anti-epileptic, anti-arrhythmic ( Lidocaine ), antimicrobial therapy,…]and when the drug has a long terminal half-life. V ss can also be used to predict the fluctuation of plasma concentrations during a dosage interval for an intermittent dosage regimen. In the equilibrium condition, the plasma concentration is decreased from the peak (maximum) plasma concentration ( Cmax ) to a trough (minimum) concentration ( Cmin ). The amplitude of the fluctuation can be approximately given by: Cmax - Cmin =F(Dose)/ Vss Therefore, the larger the Vss the smaller the fluctuation and vice versa. 13

Terminal Half Life:

Terminal Half Life After an i.v . bolus administration, the terminal half-life (t 1/2 ) is a hybrid parameter which can be interpreted in terms of both clearance and volume of distribution according to eqn : t ½ = (0.693/Clearance)V area A long t 1/2 may be associated either with a large V d or/and a low clearance. The influence of V d (or more exactly of the drug distribution) is because of the fact that only drug in the vascular system can be presented to the eliminating organs (kidney and liver). The larger the V d , the lower the fraction of the drug that can be eliminated over time and the longer the half-life. 14

Conclusion:

Conclusion Clearance is the relevant parameter to compute the maintenance dose, whilst V ss is the pharmacokinetic parameter to compute a loading dose. Using an appropriate model for the interpretation/prediction, the volume of distribution can be predicted in drug development and can assist drug companies in designing drugs with a long terminal half-life, and in anticipating a persistence of drug residues. 15

References:

References Toutain , P.L.,Bousquet-Melou , A. Volumes of distribution . J. vet. Pharmacol . Therapy. 27, 441-453. Biopharmaceutics and Pharmacokinetics By G.R.Chatwal . Biopharmaceutics and Pharmacokinetics By Brahmankar . 16

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