Case Study:Drug Dosage

CS 170:Computing for the Sciences

and Mathematics

Administrivia

Last time (in P265) Constrained Growth

Today Case Study: Drug Dosage HW3 Due HW4 Assigned

Pharmacokinetics

Scenario:Your company is developing a drug to help with something. You’ve been tasked with determining what the dosage instructions are going to be.

What you know: A little biology Minimum effective (and Minimum toxic) drug

concentrations Half-life of the drug

One-Compartment Model of Single Dose

Concentration of drug in system = amount of

drug/volume of blood

MEC = minimum effective concentration

MTC = maximum therapeutic concentration

or minimum toxic concentration

Example: Aspirin

Blood in an adult's body ≈ 5 litersAmount of plasma ≈ 3 litersTwo 325 mg tablets: 2(325)1000 µg

Plasma half-life (t1/2) of dose ~ 3.1 to 3.2 hr

Q = aspirin_in_plasma

dQ/dt = -KQ with K = -ln(0.5)/t1/2

Therapeutic range 150-300 µg/ml

Consider only a single dose

Example: Dilantin

Amount of plasma ≈ 3 litersOne 100 mg tablet: 100,000 µg

Plasma half-life (t1/2) of dose ~ 22 hrs

Q = dilantin_in_plasma

dQ/dt = -KQ with K = -ln(0.5)/t1/2

Therapeutic range 10-20 µg/ml Toxicity only occurs at > 20,000 µg/ml

Consider repeated doses. What is a good range?

Mathematics of Repeated Doses

Absorption level ≈ 0.12

Elimination rate of –ln(0.5)/22 ≈ 0.0315

Amount of drug in the system after 8 hr is Q

= Q0e-0.0315(8) ≈ (12)(0.7772) = 9.3264 mg

HOMEWORK!

READ Module 3.5 in the textbook

Homework 4 READ Module 7.4 in the textbook COMPLETE Projects 1 and 2 (page 276) Due next Monday, October 4th