Module 2 5 Drug Dosage Angela B Shiflet

Introduction • Errors in the dispensing and administration of medications occur frequently. • To determine what the correct/effective dosage is for each medication, we consider the following factors. • Drug absorption, distribution, metabolism, and elimination.

One-Compartment Model of Single Dose • Metabolism of a drug in the human body is a complex system to represent in a model. Thus, simplifying the assumptions about the drug and the body is necessary. • In this model, the body is assumed to be one homogeneous compartment, the distribution of the drug is instantaneous, the concentration of the drug is proportional to the drug dosage. The rate of elimination is proportional to the amount of drug in the system.

One-Compartment Model of Single Dose • Concentration of drug in system = amount of drug/volume of blood (its value should between MEC and MTC, i. e. therapeutic range) • MEC = minimum effective concentration • MTC = maximum therapeutic concentration or minimum toxic concentration • A drug’s half-life is the amount of time for half the drug to be eliminated from the system (useful for modeling as well as patient treatment).

One-Compartment Model of Single Dose • Blood in an adult's body ≈ 5 liters • Amount of plasma (fluid contains blood cells) ≈ 3 liters • Amount of serum (clear fluid that separates from blood when it clots) ≈ 3 liters • Two 325 mg (1000 µg) aspirin tablets: 2(325)1000 µg • Plasma half-life (t 1/2) of a dose from 300 mg to 650 mg is 3. 1 to 3. 2 hr • Q = aspirin_in_plasma (elimination) • d. Q/dt = -KQ with K = -ln(0. 5)/t 1/2 The rate of the drug leaving the system is proportional to the quantity of the drug in the system. From 2. 2, Q = Q 0*e-Kt

One-Compartment Model of Single Dose

$One-Compartment Model of Repeated Doses ingested = absorption_fraction * (pulse of dosage over each$

One-Compartment Model of Repeated Doses ingested = absorption_fraction * (pulse of dosage over each interval)

Mathematics of Repeated Doses • Assume instantaneous absorption and elimination is proportional to the amount in the system. Half-life = 22 hrs; interval = 8 hrs; MEC = 10 ug/m. L; MTC = 20 ug/m. L; volume = 3000 m. L (blood serum) • Adult dosage: one 100 -mg capsule three times a day • Absorption level (the fraction that enters the system) ≈ 0. 12 • Elimination rate of K = -ln(0. 5)/t 1/2 = -ln(0. 5)/22 ≈ 0. 0315 • Amount of drug in the system after 8 hr is Q = Q 0 e-0. 0315(8) ≈ (12)(0. 7772) = 9. 3264 mg; about 77. 72% of the drug remains in the system after 8 hours.

Qn - amount of drug in system immediately after dose n •

Repeated Doese

Multi-Compartment Model • One compartment model is more appropriate for an injection of a drug. • For a pill, which takes time to dissolve, be absorbed, and be distriuted within the system, a two-compartment model is more appropriate, where the first represents the digestive system and the second represents the blood, plasma, serum or a particular organ that the drug targets.

Multi-Compartment Model