Touqeer Ahmed Ph.D. Atta-ur-Rahman School of Applied Bioscience, National University of Sciences and Technology 21 st October, 2013

Introduction to Compartment Models A model is a hypothesis, using mathematical terms to describe quantitative relationships concisely. Pharmacokinetic models are relatively simple mathematical schemes that represent complex physiologic spaces or processes. Accurate modeling is important for precise determination of elimination rate Uses 1. Predict plasma, tissues and urine levels with dosage regimen 2. Calculation of the optimum dosage regimen for the patients 3. Estimate the possible accumulation of the drug and its metabolites 4. Correlate the drug concentration with the pharmacologic/toxicologic response 5. Evaluate differences between the rate and availability of the drugs 6. Describe the changes in the absorption during the disease state 7. Explain drug interactions

Calculations and Considerations X and Y axis Variables (independent and dependent) Standard way is to plot independent variable on the X axis and dependent variable on the Y axis Graphs (why straight line is important?) (because it helps us predict values for which there is no experimental observations are present) Slope Slope = y2 – y1 /x2 –x1 Rate of the reactions Zero order and first order reactions Half life t1/2

Units in Pharmacokinetics

Types of Pharmacokinetic Compartment Models 1. Mammillary models (most commonly used) Important characteristic is that the elimination of the drug is from the central compartment 2. Catenary model (since, like a train of the compartments, thats why rarely used) 3. Physiologic models (Flow model) Based on the known anatomic and physiologic data No curve data fitting is required The tissue size, blood flow to the tissues may vary in the pathophysiologic conditions Can be applied to the several species as the organs and their blood flow may not vary as much

Compartment Models One compartment Model Two compartment Model

One Compartment Model Compartment Model Elimination rate constant Equation Example Page number Apparent Volume of distribution Equation Its significance Clearance If dose is 100 mg dissolved in 10 ml and the 10 mg eliminated per min then Amount per unit time (10mg/min) –for the zero order Volume per unit time (1 ml/min) – for the first order Fraction per unit time (1/10 per min) – PKs take it as first order

Two Compartment Models K10 K12 K21 Central compartment Peripheral compartment Central compartment (highly perfused tissues): Heart, brain, hepatic portal system, kidney, skin muscles Peripheral compartment (slowly perfused tissues): Bone, ligament, tendons, cartilage and teeth e.g. Isotretinoin and colchicine studied in two compartment models Aminophylline (IV) follows this model Characteristic bi-exponential curve Reason for the bi-exponential curve-Figure number 4.3 Method of residual-Figure number 4.4 -Table number 4.3 Distribution and elimination