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Compartment Models. 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.
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Compartment Models Touqeer Ahmed Ph.D. Atta-ur-Rahman School of Applied Bioscience, National University of Sciences and Technology 21st 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 • Predict plasma, tissues and urine levels with dosage regimen • Calculation of the optimum dosage regimen for the patients • Estimate the possible accumulation of the drug and its metabolites • Correlate the drug concentration with the pharmacologic/toxicologic response • Evaluate differences between the rate and availability of the drugs • Describe the changes in the absorption during the disease state • 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
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 46-47 • 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 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 K12 Central compartment Peripheral compartment K21 Characteristic bi-exponential curve K10 Distribution and elimination • Reason for the bi-exponential curve-Figure number 4.3 • Method of residual-Figure number 4.4 • -Table number 4.3