SIMPLE PBPK Model (Based on Problem 2-3)

A rat is fed 0.05 mg/day of chemical x for a long period of time. After several weeks, the amount of X in the rat's body reaches equilibrium, with 10% going through the digestive system without being absorbed, and the rest being absorbed by the blood. Half of the X in the blood is removed by the kidneys and excreted in urine. The remaining half is broken down into daughter chemicals by the liver. The total amount of X in the rat's body (exclusive of the digestive system) at equilibrium is 0.60 mg. The concentration of X in the kidneys is four times that in the blood; the concentration in the liver is 10 times that in the blood. Assume that a rat has 500 ml of blood, each rat kidney weights 5 g, and the liver also weighs 5 g.

a. Find the equilibrium concentrations of X in the blood, kidneys, and liver.

b. The kidney weight was actually estimated to be between 1 and 10 g. Do a sensitivity analysis to determine whether using the estimate 5 g. substantially affects the answer.

c. Find the Biotransfer Factors (BTF) for X in the blood, kidneys, and liver. How would the concentrations change if the administered dose were 0.01 per day?

d. Suppose the liver reaches a "saturation" concentration of 1.5 mg of x per kg and can only metabolize a maximum of 0.7 mg of X per day. What will the equilibrium concentrations in blood, kidneys, and liver be at a dose of 0.20 mg/day? What assumptions are made to arrive at this answer?