Pharmacokinetic parameters

Pharmacokinetics assumes that a relationship exists between the concentration of drug in an accessable site, such as the blood, and the pharmacological or toxic response. The concentration of drug in the systemic circulation is related to the concentration of drug at the site of action. Pharmacokinetics attempts to quantify the relationship between dose and drug disposition and provide the framework, through modeling, to interprete measured concentrations in biological fluids.3 Several pharmacokinetic parameters are utilized to explain various phar-macokinetic processes. It is often changes in these parameters, through disease, genetic abnormalities, or drug interactions, which necessitate modifications of dosage regimens for therapeutic agents. The most important parameters are clearance, the ability of the body to eliminate drug, volume of distribution, a measure of the apparent volume of the body available to occupy the drug, bioavailability, the proportion of drug absorbed into the systemic circulation, and half-life, a measure of the rate of drug elimination from the blood. These concepts are discussed below.

3.1.4.1 Clearance

Clearance is defined as the proportionality factor that relates the rate of drug elimination to the blood or plasma drug concentration:16

Clearance = Rate of elimination/Concentration

In the above equation, the concentration term refers to drug concentration at steady state. The units of clearance are volume per unit time and, therefore, this parameter measures the volume of biological fluid, such as blood, that would have to have drug removed to account for drug elimination. Therefore, clearance is not a measure of the amount of drug removed.

The concept of clearance is useful in pharmacokinetics because clearance is usually constant over a wide range of concentrations, providing that elimination processes are not saturated. Saturation of biotransformation and excretory processes may occur in overdose and toxicokinetic effects should be considered. If a constant fraction of drug is eliminated per unit time, the elimination follows first order kinetics. However, if a constant amount of drug is eliminated per unit time, the elimination is described by zero order kinetics. Some drugs, for example, ethanol, exhibit zero order kinetics at "normal" or non-intoxicating concentrations. However, for any drug that exhibits first order kinetics at therapeutic or non-toxic concentrations, once the mechanisms for elimination become saturated, the kinetics become zero order and clearance becomes variable.3

Clearance may also be viewed as the loss of drug from an organ of elimination such as the liver or kidney. This approach enables evaluation of the effects of a variety of physiological factors such as changes in blood flow, plasma protein binding, and enzyme activity. Therefore, total systemic clearance is determined by adding the clearance (CL) values for each elimination organ or tissue:

CLsystemic = CLrenal + CLhepatic + CLlung + CLother

Clearance from an individual organ is a product of blood flow and the extraction ratio. The extraction ratio is derived from the concentration of drug in the blood entering the organ and the concentration of drug in the blood leaving the organ. If the extraction ratio is zero, no drug is removed. If it is 1, then all the drug entering the organ is removed from the blood. Therefore, the clearance of an organ may be determined from the following equation:

where

Q = blood flow

CA = arterial drug concentration CV = venous drug concentration E = extraction ratio

3.1.4.2 Volume of Distribution

The plasma drug concentration reached after distribution is complete is a result of the dose and the extent of uptake by tissues. The extent of distribution can be described by relating the amount of drug in the body to the concentration. This parameter is known as the volume of distribution. This volume does not indicate a defined physiological dimension but the volume of fluid required to contain all the drug in the body at the same concentration as in the plasma or blood. Therefore, it is often called the apparent volume of distribution (V) and is determined at steady state when distribution equilibrium has been reached between drug in plasma and tissues.

V= Amount in body/ Plasma drug concentration

The volume of distribution depends on the pKa of the drug, the degree of plasma protein and tissue binding, and the lipophilicity of the drug. As would be expected, drugs that distribute widely throughout the body have large volumes of distribution. In the equation above, the body is considered one homogeneous unit and therefore exhibits a one compartment model. In this model, drug administration occurs in the central compartment, and distribution is instantaneous throughout the body. For most drugs, the simple one compartment model does not describe the time course of drug in the body adequately and drug distribution and elimination is more completely described in multiple exponential terms using multicompartmental models. In these models, the volume of distribution, Varea, is calculated as the ratio of clearance to the rate of decline of the concentration during the elimination phase:

Varea= CL/k where k= rate constant.

3.1.4.3 Bioavailability

The bioavailability of a drug refers to the fraction of the dose that reaches the systemic circulation. This parameter is dependent on the rate and extent of absorption at the site of drug adminsitration. Obviously, it follows that drugs administered intravenously do not undergo absorption, but immediately gain access to the systemic circulation and are considered 100% bioavailable. In the case of oral administration, if the hepatic extraction ratio is known, it is possible to predict the maximum bioavailability of drug by this route assuming first order processes, according to the following equation:3

Fmax = 1-E= 1-(CLhepatic/Qhepatic)

The bioavailability of a drug by various routes, may also be determined by comparing the area under the curve (AUC) obtained from the plasma concentration vs. time curve after intravenous and other routes of administration:9

Bioavailability= AUCoral/AUCIV

3.1.4.4 Half-Life

The half-life is the time it takes for the plasma drug concentration to decrease by 50%. Half-life is usually determined from the log-terminal phase of the elimination curve. However, it is important to remember that this parameter is a derived term and is dependent on the clearance and volume of distribution of the drug. Therefore, as CL and V change with disease, drug interactions, and age, so a change in the half-life should be expected. The half-life is typically calculated from the following equation:

t1/2 = 0.693/k where t1/2= half life k= elimination rate constant

Because k = CL/V, the inter-relationship between these parameters is clearly evident.

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