School of Pharmacy, University of Nizwa Half Life of Drug, Volume of Distribution and Therapeutic Drug Monitoring Course Coordinator Jamaluddin Shaikh, Ph.D. School of Pharmacy, University of Nizwa Lecture-11 October 19, 2011

Half Life of Drug The duration of action of a drug is known as its half life It is the time taken for a drug to become 50% of concentration Biological half-life is an important pharmacokinetic parameter and is usually denoted by the abbreviation t½

Half Life of Drug 2 4 6 8 10 7.5 Conc. (mg/L) 5 2.5 time (h) 1.25 2.5 5 7.5 10 2 4 6 8 time (h) Conc. (mg/L) 1.25 0.625

Use of Half Life To predict how long it will take from the start of dosing to reach steady state levels (CSS) Time for a drug to be removed from the body. It takes about 6 t½ for near complete elimination Means to estimate the appropriate dosing interval Can be used to predict how long it will take a drug concentration to decline from one specific value to another

Steady State Drug Levels CSS of a drug is the concentration of the drug where the rate of absorption of drug into the systemic circulation is equal to the rate of elimination from the body Two questions can be asked about achieving the steady-state what is the relationship between the rate of drug infusion and the plasma concentration of drug achieved at the steady state? Second, what length of time is required to reach the steady state drug concentration?

Multiple i.v. bolus dose administration : drug accumulation in plasma until the steady state is achieved During multiple dosing or continuous IV infusion, it takes 4 t½ to reach CSS.

Immediately effective treatment Use of a loading dose Immediately effective treatment The delay in reaching the CSS can be overcome by giving a loading dose e.g. digoxin. Loading Dose= Vd x desired Css

Volume of Distribution (Vd) The Vd is a hypothetical volume of fluid into which the drug is disseminated The apparent Vd: A drug rarely distribute into one of the water compartments of the body. Instead, the vast majority of drugs distribute into several compartments. Therefore, the volume into which drugs distribute is called the apparent Vd

Vd = Amount / Concentration in plasma Vd=D/C, where D= total amount of drug in the body and C= concentration of drug in the plasma Most drugs are distributed unevenly into the body. Some drugs (digoxin) are extensively distributed and bound in tissues, leaving low concentrations in the plasma, thus the body as a whole appears to have a large volume of distribution.

Water Compartments in the Body Once a drug enters the body, it has the potential to distribute into any one of three functionally distinct compartments of body water Plasma compartment Extracellular fluid Total body water

Plasma Compartment If a drug has a very large molecular weight or binds to plasma proteins, it is too large to move out through the endothelial slit junctions of the capillaries and thus is effectively trapped within the plasma compartment. Plasma volume is about 4% of the body weight or, in a 70-kg individual, about 3 L of body fluid.

Extracellular Fluid If the drug has a low molecular weight, but is hydrophilic, it can move through the endothelial slit junctions of the capillaries into the interstitial fluid However, hydrophilic drugs cannot move across the membranes of cells to enter the water phase inside the cell. Extracellular fluid= Plasma water + Interstitial fluid This is about 20% of the body weight, or about 14 L in a 70-kg individual

Total Body Water If the drug has a low molecular weight and is hydrophobic, it can not only move through the slit junctions but can also move thought the cell membranes into the intracellular fluid Total body water= Plasma water + Interstitial fluid + Intracellular fluid This volume is about 60% of body weight, or about 42 L in a 70-kg individual.

Body water Intra-vascular Interstitial Intra-cellular

Distribution - Evan’s Blue Intra-vascular space only

Distribution - Inulin Extracellular water

Distribution - Ethanol All water

Distribution - Evan’s Blue Intra-vascular space only V = D/C C is very high, so V is small (3 L) Small V tells us drug does not tend to spread beyond the blood.

Distribution - Inulin Extracellular water V = D/C C is lower, so V is higher (14 L) Higher V tells us some of the drug leaves the blood.

Distribution - Ethanol All water V = D/C C is even lower, so V is now quite high (42 L) High V tells us much of the drug leaves the blood.

Distribution - Quinacrine Concentration into cells V = D/C C is very low, so V is enormous Huge V tells us most of the drug leaves the blood.