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CS 170: Computing for the Sciences and Mathematics

CS 170: Computing for the Sciences and Mathematics. Case Study: Drug Dosage. Administrivia. Last time (in P265) Constrained Growth Today Case Study: Drug Dosage HW3 Due HW4 Assigned. Pharmacokinetics. Scenario:

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CS 170: Computing for the Sciences and Mathematics

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  1. CS 170:Computing for the Sciences and Mathematics Case Study: Drug Dosage

  2. Administrivia • Last time (in P265) • Constrained Growth • Today • Case Study: Drug Dosage • HW3 Due • HW4 Assigned

  3. 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

  4. 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

  5. Example: Aspirin • Blood in an adult's body ≈ 5 liters • Amount of plasma ≈ 3 liters • Two 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

  6. Example: Dilantin • Amount of plasma ≈ 3 liters • One 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?

  7. 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

  8. 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

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