Stability Of Drugs:Rate Kinetics

From Pharmpedia

The rate of decomposition then, depends on the frequency and intensity of the collisions of the molecules. This in turn is dependent on the nature and concentration of the chemicals involved or more specifically on their activation energy , collision frequency and what is called as a orientation factor. They can be predicted because they are happening due to molecular collisions which in turn are dependant on temperature, pH and light. The science that deals with these rates is called “kinetics” and as it describes decomposition it is called the kinetics of decomposition.

When we talk about kinetics, several ‘orders’ of kinetics can be there, such as zero order, first order, second order and so on, but fortunately for all of us drug decomposition rates do not follow complex orders; they are mostly of zero order or first order.

Rate kinetics is discussed in four different contexts;1. drug stability 2. drug release from dosage forms in dissolution studies 3. absorption, distribution, and elimination studies on the drugs in the body and 4. explaining the drug action at the molecular level when the response is a rate process. In all the cases the concepts are the same and the equations are also same.

At this stage it is imperative for us to get the concepts about zero order and first order because they are very important. These are explained most beautifully by Alfred Martin in his Physical Pharmacy book.

A man called A decides to go by car from a town called Anakapalli to a city called Visakhapatnam . Let us assume they are separated by a distance of 40 Km. The man A declares that he will proceed from Anakapalli to Visakhapatmam at a steady speed of 10 Km/hr. So if he starts at 10 a.m. in Anakapalli he will reach Visakhapatnam at 2 p.m. In his journey he will neither accelerate nor decelerate. We can say that A is making a journey at a zero order rate.

A man called B also decides to make the same journey by his car; but he declares that his speed at any given time is one fourth of the distance to be covered in Km/hr. For the sake of easy calculation let us assume B breaks down his time periods into half hours. Then in the first half hour he travels a distance of 40/8 i.e. 5 km; in the second half hour 35/8 i.e. 4.375; in the third half hour 30.625/8 i.e. 3.828; in the fourth half hour 26.797/8 i.e. 3.349 and so on. So as the destination nears his speed will go on decreasing because his speed is one fourth of the distance to be covered. So theoretically speaking B will never reach his destination.

B is traveling by first order kinetics!

You must all have seen a nurse arrange an infusion into a patient’s vein at a fixed number of drops per minute; the infusion is flowing by zero order.

Suppose you throw a big rock into a stagnant pool of water, suddenly there are waves, and the extent of waves go down with each passing moment, but it will take a lot of time for the pool to become still again. This phenomenon is following a first order kinetics

The rate of decomposition is proportional to some power of the concentration of the reactants and it can be shown like this -dc/dt=KCⁿ different values to n we will get equations for different orders. If n = 0 then -dc/dt=KC .If n = 1 then -dCa/dt=KCa where Ca is the concentration of the reactant.

Let us understand these two orders and let us also learn how to differentiate between these two.

For zero order reaction a plot of time vs % drug remaining will be like this

If the drug decomposition is following first order kinetics then plot of time Vs % drug remaining will be like this:

If we plot log % remaining Vs time, the plot will be like this,

By looking at all these differences you may feel it is very easy to find the order of the reaction by looking at the data, it is not so easy practically though theoretically it may look like that. The reason is when we actually follow the decomposition of some drugs the data appear as though they are satisfying criteria of both the orders. In such a situation to find the order of the reaction we have to follow the least square method of linear regression.

Second order, third order and more complex reactions are there but drug decomposition usually follows zero order or first order. When we know the order and the reaction rate constant we can predict the expiry date. In the case of vitamins, this data helps in determining the amount of overages we want to add to prolong the shelf life by a particular period of time. By knowing kinetic data and using some statistical methods we can also draw a stability line and 95% and 99% confidence limits to that line. Thus understanding rate kinetics is a key element in understanding the stability of drugs