Applying the one-compartment model to a real world scenario When donating blood, one often is required to wait for several days after receiving a dose of certain medications. To see why this is a critical step, we can use our model to predict would happen if someone taking a prescribed drug regimen ignored this rule. Deliverable 3: In this deliverable, we will use mass balances to analyze what would happen if someone on an active drug regimen were to donate blood. To simplify the math, we will assume that the patient receiving the drug regimen is simultaneously donating blood via transfusion to a second patient at a rate of m = 0.25L/hr for four hours (two units of blood). As before, the first patient is receiving a drug regimen of Min(t). We will assume that the two patients have identical volumes (50L) and masses (50kg). (a) Draw a picture of the process using the stirred-tank model, keeping in mind that both patients will be metabolizing and excreting the drug. (b) Using mass balances on the appropriate control volume(s), show that the transfer function relating the drug concentration in the second patient to the drug received by the first patient is given by, C2(8) G(8) (5) Min (8) (s + ke)(8 + mi/V + ke) where C2(8) is the concentration of drug in the second patient in the Laplace domain), and as before ke = ker + km (c) Using Simulink, plot the four hour drug concentration profile in the second patient, assuming the first patient receives the same drug regimens as in parts (a)-(e) of Deliverable 2. You can again assume a drug half-life of 60 minutes. (d) What would the drug profile look like after the transfusion finishes? (e) Is this system underdamped, critically damped, or overdamped? Make sure you show your work and watch your units. mi/V2 Applying the one-compartment model to a real world scenario When donating blood, one often is required to wait for several days after receiving a dose of certain medications. To see why this is a critical step, we can use our model to predict would happen if someone taking a prescribed drug regimen ignored this rule. Deliverable 3: In this deliverable, we will use mass balances to analyze what would happen if someone on an active drug regimen were to donate blood. To simplify the math, we will assume that the patient receiving the drug regimen is simultaneously donating blood via transfusion to a second patient at a rate of m = 0.25L/hr for four hours (two units of blood). As before, the first patient is receiving a drug regimen of Min(t). We will assume that the two patients have identical volumes (50L) and masses (50kg). (a) Draw a picture of the process using the stirred-tank model, keeping in mind that both patients will be metabolizing and excreting the drug. (b) Using mass balances on the appropriate control volume(s), show that the transfer function relating the drug concentration in the second patient to the drug received by the first patient is given by, C2(8) G(8) (5) Min (8) (s + ke)(8 + mi/V + ke) where C2(8) is the concentration of drug in the second patient in the Laplace domain), and as before ke = ker + km (c) Using Simulink, plot the four hour drug concentration profile in the second patient, assuming the first patient receives the same drug regimens as in parts (a)-(e) of Deliverable 2. You can again assume a drug half-life of 60 minutes. (d) What would the drug profile look like after the transfusion finishes? (e) Is this system underdamped, critically damped, or overdamped? Make sure you show your work and watch your units. mi/V2
