Download Pharmacokinetics Introduction and more Lecture notes Biopharmaceutics and Pharmacokinetics in PDF only on Docsity!
Pharmacokinetics
What is Pharmacokinetics? It is the study of kinetics of Absorption, distribution, metabolism and excretion (ADME) of drug and its corresponding pharmacologic, therapeutic or toxic response in humans and animals. Actually the word pharmacokinetics is derived from the two Greek terms โ Pharmakon meaning drug and kinetikos meaning motion. The word kinetics means motion or movement. Therefore Pharmacokinetics can also be defined as the time course (i.e. time taken) for absorption, distribution, metabolism and excretion of drug. The primary goal of Pharmacokinetics is increasing the efficacy and reducing the toxicity of a drug therapy.
Application of Pharmacokinetics
- Bioavailability measurement
- Effect of physiological and pathological conditions on drug disposition and absorption.
- Dose calculation and dose adjustment in case of disease conditions
- To study drug interaction
- To establish correlation between pharmacological response and dose administered.
Mathematical considerations of Pharmacokinetics
The mathematics of Pharmacokinetics is very much same that of chemical kinetics of enzyme kinetics. It is necessary to study some of the basic mathematical concepts as models of pharmacokinetics (which we will see in the next section) consider the drug in the body to be in dynamic state. Calculus is the most important tool to analyze the quantitative drug movement in the body.
Differential calculus โ It is used to determine the rate at which a particular variable quantity is changing. In biopharmaceutics the variable quantity is the concentration of drug in the body. Let us understand it this way that when the drug is administered the amount of the drug in the blood is zero after some time when the drug is released from the formulation the process of absorption starts and the concentration of the drug in the blood slowly increases with time and reaches the peak level (peak plasma concentration). The concentration of the drug after peak plasma concentration is reached slowly decreases as the process of elimination starts. Thus the variable quantity in biopharmaceutics is the concentration of the drug in the blood. Differential calculus is used to determine the rate at which the drug is absorbed and eliminated from the body.
Let us understand this by using a simple example โ if a specific amount of the drug โXโ is placed in the beaker filled with water the drugs starts to dissolve. The variable quantity is the amount of drug getting in the solution. The rate at which the drug dissolves is given by Noyes-whitney equation:
In equation (1) d = denotes very small change; X = drug X; t= time; D = diffusion coefficient; A = effective surface area of the drug; l = is the length of diffusion layer; C 1 = is the concentration of the drug in the diffusion layer; C 2 = is the concentration of the drug in the bulk of solution.
The derivative is the very small change in the concentration of drug with respect to change in the time t.
In the study of Pharmacokinetics the concentration of the drug in the body is variable quantity i.e. dependent variable. From this it is understood the change in the concentration of drug in body is the function of time, t. The time is thus independent variable. Thus in pharmacokinetics the amount of drug in the body varies with time.
This can be written in the equation form as
eq. 2
It can be seen from equation 2 that the concentration of drug C is the function of time t.
To consider the above let us see the following data
Time (hr) Plasma concentration of
drug C (ฮผg/ml) 0 12 1 10 2 8 3 6 4 4 5 2
If closely observe the data it can be seen that plasma concentration of drug C is decreasing with time t i.e. the change in the concentration of drug C is the function of time t. The rate of change of drug is 2 ฮผg/ml for each hour. The rate of change of drug concentration with respect of time can be expressed as โ
This can be further solved as
Integrating the above equation we have
Two types of Logarithms are used in the study of biopharmaceutics โ (1) Common logarithm and (2) Natural logarithm.
In mathematics, the common logarithm is the logarithm with base 10. When we simply write log X it means that log 10 X^ similarly log 10 = log 1010 = 1. Log 10100 = 2 this means that when 10 is raised to power 2 we get 100. Thus number 100 is considered the antilogarithm of 2.
Natural logarithm of a number is its logarithm to the base e where e has the value approximately equal to 2.718282. The natural logarithm of a number X is written as ln X or log (^) eX.
Log is commonly represented in base-10 whereas natural log or Ln is represented in base e. Now e has a value of 2.71828. So e raised to the power of 2.303 equals 10 ie 2.71828 raised to the power of 2.303 equals 10 and hence ln 10 equals 2.303 and so we multiple 2.303 to convert ln to log. The following equation is used to relate natural log to common log. The natural log of 10; Ln 10 = 2.
2.303 log N = ln N
Laws of logarithm
Lne-x^ = -x
Log10-2^ = -
Rate of reaction:
The rate of reaction is the speed at which reactants are converted into products and it is often represented mathematically as a differential expression dc/dt. That is the change in the variable quantity C with respect to time. While studying biopharmaceutics it is important to understand the concept of rate as the process of drug absorption and elimination is described by the rate.
If the amount of drug A is decreasing with respect to time then the rate of reaction is given as
If the amount of B is increasing with time the rate of reaction is expressed by the following differential term
The rate process is further specified by order. In pharmacokinetics two orders are of importance
- Zero order and first order.
Zero order process
The zero order process rate is the once that proceeds with time (t) and independent of concentration (c). If the amount of drug A is decreasing at a constant time interval (t) then the rate of disappearance of drug A is expressed as
Where k 0 is the zero order rate constant. The unit is mass/time (mg/min).
Rearranging the above equation gives
Integrating the above equation
Solving the above equation we have
Rearranging the above equation we have
OR
In the above equation A 0 is the amount of drug at time t=0. The above equation is similar to equation of straight line y=mx+c; hence โk 0 is the slope of the line i.e. the rate of process. A 0 is
the y intercept i.e. the concentration of drug at time t=0.
Let us understand this by the following example โ if 10 mg of drug is dissolved in 100 ml of water at room temperature and the samples are withdrawn at definite time interval and the following data is obtained.
Time (hrs) Concentration
(mg/ml) 0 100 2 95 4 90 6 85 8 80 10 75 12 70
From the above data if the graph is plotted โ concentration versus time
