Question

A particular medicine once in the stomach is absorbed intothe blood stream at a rate proportional to the amount of medicine remainingin the stomach. The stomach absorbs 90% of the medicine in an hour. Oncein the blood stream the kidneys remove the medicine at a rate proportionalto the amount of medicine in the blood stream. For a given amount in theblood, the kidneys remove 75% of the medicine in 24 hours. A patient (whohas never taken the medicine) receives a pill with 10 mg of the medicine.The volume of the blood in a typical patient is 5 liters.Just set upthe differential equations that model this situation. LetS(t)denote the amount of medicine in the stomach, letB(t) denote the amountof medicine in the blood. Give the equations that relate the quantitiesSandB, indicate what assumptions you are making.

Answer 1

The drugs are generally given in varius routes.The drugs which are potentially need to be bio-transformed are given by oral routes.Then the drugs are metabolized in the stomach and absorbed in the blood stream.When the drugs gets absorbed it is not fully absorbed a little amount remains in the stomach and eliminated through the feaces.Finally when the drurs metaboliseed in the liver it is then eexcreated out through urine by the kidney.

Now here the 10mg of drur which is taken orally it's 90% is absorbed in the stomach.Lets assume that it is the maximum absorbing capacity of the drug in the stomach then-

• S(t)=10*90/100 mg=9 mg. So the absorbed amount of total drug in the stomach is 9 mg.
• Now the absorbed drug is fully in the blood stream.So B(t)= 9 mg

Now the 9mg of the drug is present in the person's blood which is then metabolized and then eliminated by the kidney. If we assume that the person's kidney is functioning normally then 75% of the drug is eliminated in 24 hour. Then the excreated amount of the drug is-

• Eliminated amount of drug=9*75/100 mg= 6.75 mg
• So the remaining amount of drug in blood after excreation SandB= (9-6.75) mg = 2.25 mg.