Case Studies and Project Ideas: Pharmacokinetics - Multiple Dose

Drug and Metabolite Absorption and Disposition

Goal:

To build and use a complex pharmacokinetic model to determine a threapeutic regime for a patient

Scenario:

A seriously-ill patient has been hospitalized for an infection that the doctors wish to treat with a powerful antibotic. The doctors need the pharmacologists to help them develop a therapeutic regime for this patient. The patient can receive the antibotic orally, as an intravenous injection, and as an infusion through an intravenous drip. Your task is to build the model and then use the model to figure out what combination of administration routes: oral, IV, and infusion -- enable the patient to reach a therapeutic threshold of 25 mg/mL for the concentration of drug in the plasma. The patient should reach this threshold by at least Day 3 of the treatment and be able to maintain this threshold for 10 days.

Some specifics:

ADMINISTRATION OF THE DRUG:
Oral dosings and intravenous dosings are both PULSED in, since they are not continuously delivered. Infusion dosing is continuously delivered, and will be described later.

Oral dosing depends on three factors:

The oral dose in units of milligrams (mg): Set the dosage initially to 500 mg
The fraction of the dosage absorbed: Antibotics are absorbed well, so the fraction absorbed value should be set at 95% (0.95)
The interval that the drug is administered: Set the interval initally at 72 hours

The algorithm for the amount of oral dosing is:

oral dose * fraction absorbed * DT (where DT is a built-in function)

The patient should receive an oral dose immediately when the model begins to run, and every dosing interval after that time. The oral dose goes FIRST to the stomach before being absorbed into the plasma.

Intravenous dosing (IV) is also pulsed in. Typically, IV administration is absorbed 100%, and goes directly into the plasma. The factors that determine the amount of drug received intravenously are:

The IV dose in units of milligrams (mg). Set the dosage initially to 10 mg
The interval that the drug is administered. Set the interval initally at 5 hours

The algorithm for IV dosing is:

IV dose * DT (where DT is a built-in function)

Infusion dosing: since infusion dosing is continuous, we have a more complicated algorithm. We have to use a built-in function called MOD and an IF-THEN statement. The factors we need are:

The infusion dose in units of milligrams (mg). Set the dosage initially to 0 mg
The infusion time. Set the infusion time initially at 32 hours.
The interval that the drug is administered. Set the interval initally at 72 hours

Once you have these parameters, the algorithm for infusion dosing is: if (mod(time, infusion interval) infusion time) then (infusion dose/infusion time) else 0

Like IV administration, the infusion goes directly into the plasma.

Fate of the Drug:

The first part to consider is the absorption of the drug that has been administered orally from the stomach to the plasma. To calculate the amount of drug absorbed, we need an absorption coefficient, or ka. The value of the absorption coefficient for this drug is 1.0.

The other two administration routes put drug directly into the bloodstream (i.e. the plasma). Once in the plasma, the drug has two possible exit routes:

Elimination through the urine. You can keep track of the amount of drug that exits through the urine, or you can ignore it. The half-life of this drug is 8 hours. The elimination constant ke is calculated with the formula ke= 0.693/half-life.
Binding of the drug to proteins. Some of this drug gets "attached" or bound to proteins in the plasma. This process is bi-directional, meaning it can go two ways. You should keep track of the amount of plasma proteins in this model. To calculate the binding of drug to protein, you need three factors:
1. The amount of drug in the plasma
2. The amount of drug already attached or bound to the proteins
3. The plasma protein binding factor (PPB), a constant that is specific for this drug. Set the PPB at 25% (0.25)
The algorithm for this process is:

binding of drug to protein = (drug in plasma -(drug bound to protein*(1-PPB)))*PPB

Other Variables:

You need to calculate the concentration of the drug in the plasma and show that on your graph. The volume of distribution for this drug is 30 liters, and the threshold dosage is 25 mg/L.

You should run your simulation in hours for 10 days. Once your model is built, prepare an authoring page with sliders that allow you to change all of the parameters that are controllable -- dosage, intervals, times, etc.

Your goal again is to help the patient reach a therapeutic dosage by at least Day 3.

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