Course: Biopharmaceutics and Pharmacokinetics Course code: 0510423

Dr. Qutaiba Ahmed Al Aga

Assistant Professor

Faculty of Pharmacy

Philadelphia University-Jordan

At the end of this lesson students will be able to * Differentiate between the first and second order of reaction.

* Using equations and figures to determine the order of reaction.

* Clinical application of mathematic problem solving.

*  Calculating pharmacokinetic parameters eg: biological half life for first and zero order reaction.

*  application of knowledge to answer practical questions

* The order of a reaction refers to the way in which the concentration of drug or reactants influences the rate of a chemical reaction or process.

* 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: …..(1) * The term k0 is the zero-order rate constant and is expressed in units

of mass/time (eg, mg/min). Integration of Equation (1) yields the following expression:

…..(2) * Where A0 is the amount of drug at t = 0. Based on this expression

(Eq. 2), a graph of A versus t yields a straight line. The y intercept is equal to A0, and the slope of the line is equal to k0.

* Equation 2 may be expressed in terms of drug concentration, which

can be measured directly.

*  …..3

* C0 is the drug concentration at time 0, C is the drug concentration at time t, and k0 is the zero-order decomposition constant.

EXAMPLE

*  A pharmacist weighs exactly 10 g of a drug and dissolves it in 100 mL of water. The solution is kept at room temperature, and samples are removed periodically and assayed for the drug. The pharmacist obtains the following data:

*  From these data, a graph constructed by plotting the concentration of drug versus time will yield a straight line. Therefore, the rate of decline in drug concentration is of zero order.

The zero-order rate constant k0 may be obtained from the slope of the line or by proper substitution into Equation 3. If C0 = concentration of 100 mg/ml at t = 0 And C = concentration of 90 mg/ ml at t =4 hr Then 90= -k0 (4) + 100 And k0 = 2.5 mg/ml. hr Careful examination of the data will also show that the concentration of drug declines 5 mg/mL for each 2-hour interval. Therefore, the zero-order rate constant may be obtained by dividing 5 mg/mL by 2 hours:

* If the amount of drug A is decreasing at a rate that is proportional to

the amount of drug A remaining, then the rate of disappearance of drug A is expressed as:

*  .......4

* Where k is the first-order rate constant and is expressed in units of time -1 (eg, hr-1). Integration of Equation 4 yields the following expression:

*  …….5

* Equation 5 may also be expressed as:

*  ……6

* Because ln = 2.3 log, Equation 5 becomes

…..7

* When drug decomposition involves a solution, starting with initial concentration C 0, it is often convenient to express the rate of change in drug decomposition, dC/dt, in terms of drug concentration, C, rather than amount because drug concentration is assayed. Hence,

* This equation may be expressed as

*  ….8

* Because ln = 2.3 log, Equation 8 becomes

* According to Equation 7, a graph of log A versus t will yield a straight line, the y intercept will be log A0, and the slope of the line will be -k/2.3. Similarly, a graph of log C versus t will yield a straight line according to Equation 9. The y intercept will be log C0, and the slope of the line will be -k/2.3.

* Half-life (t1/2) expresses the period of time required for the amount or concentration of a drug to decrease by one-half.

* FIRST-ORDER HALF-LIFE

* The t1/2 for a first-order reaction may be found by means of the following equation:

* It is apparent from this equation that, for a first-order reaction, t1/2 is a constant. No matter what the initial amount or concentration of drug is, the time required for the amount to decrease by one-half is a constant.

* In contrast to the first-order t1/2, the t1/2 for a zero-order process is

not constant. The zero-order t1/2 is proportional to the initial amount or concentration of the drug and is inversely proportional to the zero-order rate constant k0:

* Because the t1/2 changes as drug concentrations decline, the zero-order t1/2 has little practical value.

* EXAMPLE

* A pharmacist dissolves exactly 10 g of a drug into 100 mL of water. The solution is kept at room temperature, and samples are removed periodically and assayed for the drug. The pharmacist obtains the following data:

* With these data, a graph constructed by plotting the logarithm of the drug concentrations versus time will yield a straight line on rectangular coordinates. More conveniently, the drug concentration values can be plotted directly at a logarithmic axis on semilog paper against time, and a straight line will be obtained. The relationship of time versus drug concentration in indicates a first-order reaction.

* The t1/2 for a first-order process is constant and may be obtained from any two points on the graph that show a 50% decline in drug concentration. In this example, the t 1/2 is 4 hours. The first-order rate constant may be found by (1) obtaining the product of 2.3 times the slope or (2) by dividing 0.693 by the t1/2, as follows:

* 

ü  Applied Biopharmaceutics and Pharmacokinetics., Shargel and A.B.C. Yu., Appleton & Lange/MacGraw-Hill, New York., 4th edition 1999. ISBN 0-8385-0129-X

ü  Applies clinical pharmacokinetics, Bauer, Larry A. Appleton & Lange/MacGraw-Hill, New York., 2nd edition 2008. 10.1036/0071476288

ü  Clinical Pharmacokinetics Concepts and Application s. MALCOlM ROWlAND and THOMASN. TOZER., 1994, 3rd edition. LIpPINCOTT WILLIAMS&WILKINS