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VM 8314 Pharmacokinetic Modeling (describing what happens) Dr. Jeff Wilcke VM 8314 Volume of distribution AKA “Apparent volume of distribution” The volume of fluid that appears to contain the amount of drug in the body May not be actual physiologic space(s) Relates amount to plasma concentration The volume that must be processed by organs of elimination Dr. Jeff Wilcke VM 8314 Volume of distribution Equations Experimentally: Vz = Dose / Cp0 Intellectually: Vz = Amount in the body / Cpt Units Liters or milliliters (whole animal or human beings) Liters/kg or milliliters/kg (typical vet med) Dr. Jeff Wilcke VM 8314 Volume of distribution 1) 2) 3) 4) Give IV Bolus Take samples over time Cp0 is Y axis interecept You know the dose Vz = Dose / Cp0 Dr. Jeff Wilcke VM 8314 Volume of Distribution Scenario Physiologic Space Drug distributed only to plasma water Blood volume = 7% of body weight Plasma water = 55% of blood volume Drug distributed evenly in ECF only Extracellular fluid volume = 25% of body weight Vz 0.0385 liters/kg 0.25 liters/kg Drug distributed evenly ECF and Intracellular fluid volume = 40% of body weight ICF only. 0.65 liters/kg ICF concentration = 3 x’s ECF 1.45 liters/kg Extracellular fluid volume + 3x intracellular fluid volume Dr. Jeff Wilcke VM 8314 Volume of distribution Much like row 2 or 3 of table Much like row 4 of table Dr. Jeff Wilcke VM 8314 Clearance The volume of plasma water cleared of drug during a specified period of time Dr. Jeff Wilcke VM 8314 Clearance Organ clearance is: Efficiency X Flow (fraction of drug removed X organ flow) Clearance = Q x E Total clearance is: The sum of all organ clearances Cl total=Cl hepatic + Cl renal + Cl pulmonary Experimentally: Clearance = Vz x λz Dr. Jeff Wilcke VM 8314 Clearance I know it’s weird but: At a particular concentration, extracting ½ the drug from ALL the flow is the same thing as extracting ALL the drug from ½ the flow (We “clearance” not “amount removed” because it works int with the samples we take and the math we can do). Dr. Jeff Wilcke VM 8314 So in one minute… 0% cleared from 0.5 ml. 200 µg/ml (1 ml) Passes through liver in 1 minute 100 % cleared from 0.5 ml. 100 µg/ml (1 ml) Clearance is 0.5 ml/min Dr. Jeff Wilcke VM 8314 Clearance Units Volume / unit time (l/hr, l/min, ml/min, etc.) Whole animals or human beings Volume / kilogram / unit time Animals Dr. Jeff Wilcke VM 8314 Rate constant of elimination (λz) The fraction of the volume of distribution cleared per unit time. The slope of the natural log plot of drug concentration verus time profile. Dr. Jeff Wilcke VM 8314 Clearing the tank… Dr. Jeff Wilcke VM 8314 Clearing the tank Concentration vs time points represent concentrations determined for samples taken from the tank. Dr. Jeff Wilcke VM 8314 Elimination half-life The time for elimination of one half of the total amount in the body Equation: T1/2 = 0.693/λz (elimination rate constant) Units: Time (hours, minutes, seconds…) Dr. Jeff Wilcke VM 8314 Elimination half life Utility Tissue Residues At 5 x T1/2 (after you stop dosing) 97% has been eliminated. Make sure you use the longest half-life Metabolites MAY be more important than the drug Absorption may have the longest half-life. Dr. Jeff Wilcke VM 8314 Elimination half-life Utility Approach to “Steady state” Drugs with long half-lifes “accumulate” during repeated administration A 5 x T1/2 concentrations reach 97% of steady state Digoxin – maximum effects 8 days after therapy starts Need for loading dose A loading dose is an initial dose given to shorten the time it takes to reach steady state (“load” the body to steady state amounts and concentrations). Dr. Jeff Wilcke VM 8314 Steady state Dr. Jeff Wilcke VM 8314 Absorption rate constant (ka) Fractional rate at which drug moves from the place the dose was put INTO the circulatory system. Units Time (hours, minutes, seconds…) Application Combined with elimination rate, determines time to reach peak concentration (C max) Dr. Jeff Wilcke VM 8314 Fraction of dose absorbed Other than IV, it is rare that the ENTIRE dose is actually absorbed Oral Destroyed, eliminated unchanged IM Hydrolyzed in tissue, bound to tissues, stuck in abscess Units Percentage or decimal (80% = 0.8) Dr. Jeff Wilcke VM 8314 Fraction of dose absorbed Bioavailability 60 50 40 µg/ml Two oral dose forms of the same drug. F of the “open triangle” dose form is ½ the “filled triangle” dose form. 30 20 10 0 0 1 2 3 4 5 6 Hours Dr. Jeff Wilcke 7 8 VM 8314 Fraction of dose aborbed Bioavailability and Bioequivalence Equal bioavailability (same F) and Bioequivalent Equal bioavailability (same F) and not Bioequivalent Dr. Jeff Wilcke