Last post we have already talked about physiologically based pharmacokinetics example part 1 and part 2. These two posts give example on how to calculate the concentration of a suspected toxic chemicals within our digestive tract inside our body. They include the scheme starting from stomach and flow blood and kidneys. Just to refresh memory, this chemical enters the body, goes passing stomach before actually absorbed by blood for metabolism and the rest is sent to kidneys to be urinated.

This post will give a bit complicated example as it will involve the presence of liver. We know that liver is the most crucial organ inside our body since liver control the metabolism mechanism. Before we move on, it is better to visit the simple digestion scheme I made in word document, since I do not have image editor in this computer. I would like to suggest you that it is always a better idea to skecth the diagram or flowchart of the problem in order to get some insight of what are you facing and what are you going to do next.

We now try to calculate the concentration of A as presented in part 2 in liver. We already know the equilibrium concentration of A in digestion organs, which is 0.5 mg. Let us make the formula, similar with have been mentioned in previous post.

Q_total = C_blood x M_blood + C_kidneys x M_kidneys + C_liver x M_liver

Lets identify each of them.

Q_total is the equilibrium concentration of A in digestion tract, we already know this, which 0.5 mg

C is a term of concentration with the unit of mg of A/kg mass of specific organs. So C_blood is concentration of A inside the blood, mg of A/kg blood. The analogue for kidneys (C_kidneys) and liver (C_liver).

C_liver = 10 x C_blood
C_kidneys = 4 x C_blood

M is a mass of related organs. M_liver means the mass of liver, let us assume 5 gram. M_kidneys is the mass of rats kidneys, which we already know is 8 mg. M_blood, we also have known this, 500 mg (see previous post, physiologically based pharmacokinetics part 2)

Oke, so we have identified each of them, let us figure out the final formula.

Q_total = C_blood x M_blood + 4 x C_blood x M_kidneys + 10 x C_blood x M_liver

0.5 mg of A = C_blood x 0.5 kg blood + C_blood x 4 x 0.008 kg x 2 kidneys + C_blood x 10 x 0.005 kg liver

0.5 mg of A = C_blood x (0.5 kg + 0.064 kg + 0.05 kg)

C_blood = 0.5 mg of A / 0.614 kg_blood = 0.81 mg A/kg_blood

So next stage is to compuet C_kidneys and C_liver.

C_kidneys = 4 x 0.81 mg A/kg = 3.2 mg A/kg_kidneys
C_liver = 10 x 0.81 mg A/kg = 8.1 mg A/kg_liver

Thats it, I hope you get the point.

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This entry was posted on Saturday, June 9th, 2007 at 6:00 pm and is filed under Modelling. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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