Physiologically based pharmacokinetics example part 2
After simple calculation on previous post physiologicaly based pharmacokinetics part 1, we now try to compute the concentration of a chemical substance A in blood and in the kidney. Assume that 0.5 mg A is at equillibrium and distributed between the blood and the kidneys. Let us assume to total blood volume in rats is equal 500 ml. Under assumption that blood and water have approximately the same density (1 g/ml), 500 ml of blood is the same with 50 mg blood.
So following formula applies:
Qtotal = Qblood + Qkidney
Qtotal = Cblood x Mblood + Ckidney x Mkidney
C is concentration and M is mass of tissue organ. Usually, the concentration a toxic chemical is larger in kidneys are larger than that in the blood. So we assume that A in kidneys is 4 times more than that in blood. That would make Ckidney = 4 x Cblood
Qtotal = Cblood x Mblood + 4 x Cblood x Mkidney
Final formula would be:
Cblood = Qtotal / (Mblood + 4 x Mkidney)
By inputing the number (assuming that kidney mass of rat is 8 mg):
Cblood = 0.5 mg / (0.5 kg + 4 x 0.008 kg x 2 kidneys) = 0.88 mg of A/kgblood
Ckidney = 0.88 mg A/kgblood x 4 = 3.54 mg A/kgkidney
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