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Pharmacokinetics Case Study: Determining Drug Dosage Instructions and Therapeutic Ranges

In this case study from CS 170, we explore the pharmacokinetics involved in developing drug dosage instructions. Focused on minimum effective and toxic concentrations, we analyze a one-compartment model for single doses, such as aspirin and Dilantin. Understanding pharmacokinetic principles like half-life and therapeutic ranges allows for informed decision-making on drug dosages. This study includes calculations for plasma concentration over time and principles of repeated dosage administration. Homework will reinforce these concepts, aiding in your grasp of pharmacologic calculations.

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Pharmacokinetics Case Study: Determining Drug Dosage Instructions and Therapeutic Ranges

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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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