A sample pharmacokinetic model.

In the previous post (link), I gave one of the reasons why one should prepare a mathematical model - so that we can predict if the drug concentration in the body is within the levels we desire. This kind of modeling is also called pharmacokinetic modeling. In this post, we will explore in further detail what form pharmacokinetic predictions will take.

As we learnt before, there are four key processes a drug undergoes after it is administered to the human body. These are Absorption, Distribution, Metabolism, and Excretion, in short known as (ADME). We will understand the effects of these processes in the context of a very simple mathematical model. Assume for a moment that a patient was given a pill with an active ingredient. On taking a pill, the first event that the pill would undergo is disintegration in the gastrointestinal tract of the subject. The liberated drug ingredients are absorbed by the bloodstream. During this time, the drug concentration rises in the blood stream.

Figure: A typical plasma drug concentration time curve (Ref: link)

As the blood is transported across the body, the drug leaves the blood stream and drug concentration in the blood starts falling. This is the distribution and metabolism phase of the drug life in the body. During this time, as the drug passes through excretory organs such as the kidney or the liver, the drug is also getting eliminated from the blood. However, this process gets more prominent as the drug concentration falls below a certain limit. The figure above shows a typical drug concentration curve in the blood. Also shown are the minimum effective concentration and the maximum safe concentration (minimum toxic concentration) that we saw in the last post (link). Analyzing various parts of the curve gives among others, the following parameters:

ka : Absorption rate constant : - Parameters like these give the rising shape of the curve above.
Q: Intercompartmental clearance: - Parameters like these explain the post absorption phase of the curve. They explain how the drug gets taken up by other organs in the body.
Cl: Clearance: - Parameters like these explain the elimination phase of the curve.
V: Volume of distribution: Parameters like these help give the volume in which the drug is distributed. Depending on the drug, these can range from the volume of the blood in the human body to a range determined by the protein binding of drug in the body.

If C is the concentration of drug in the blood, then we can write the following equations to predict C:

dA/dt = -ka*A
dC/dt = ka*A/Vc - Q*C - Cl*C

where A is amount of drug administered and dA/dt and dC/dt indicate miniscule changes in A and C over miniscule changes in time (for more info on above equations, see link).

There are several other pharmacokinetic parameters of importance and we will see them in the context of the models discussed in the future. Plasma drug curves as the one shown above are supported by rigorous clinical data with drug sampling done at short intervals so as to be create a virtual facsimile of the drug processes. Studying ayurvedic drugs in similar context gets possible if after identification of active ingredients of the drug repeated sampling is done in the blood to assess the blood levels of the drug as it travels through the body. One example is turmeric which is widely used spice in Indian cooking. Curcumin, one of the chemical compounds found in turmeric is currently receiving a lot of focus because of its anti-oxidant and anti-inflammatory properties. In the next post, we will look at a hypothetical model for Curcumin.