Pharmacokinetic Calculations - Dr Ritesh Raju + Prof Gerald Muench | 2021 | PDF

Pharmacokinetic calculations MD Year 1 2021 Prof Gerald Muench and Dr. Ritesh Raju School of Medicine University of Western Sydney LEARNING OBJECTIVES Explain bioavailability and bioequivalence Understand clearance and volume of distribution Compare the first order kinetics and zero order kinetics E...

Pharmacokinetic calculations MD Year 1 2021 Prof Gerald Muench and Dr. Ritesh Raju School of Medicine University of Western Sydney LEARNING OBJECTIVES Explain bioavailability and bioequivalence Understand clearance and volume of distribution Compare the first order kinetics and zero order kinetics Explain the one-compartment model and the twocompartment model Discuss the pharmacokinetic behavior of multipledosing Embrace the breathtaking calculations and the master equation Pharmacokinetic definitions and calculations Plasma concentrations after oral drug application Bioavailability Bioavailability is the fraction (percentage) of a given dose of a drug that gains access to the systemic circulation where it dissolves and can produce therapeutic effects Bioavailability is 100% following intravenous injection – there are no losses For orally given drugs bioavailability depends on: § absorption from the gastrointestinal system § first pass metabolism in the liver Examples of low bioavailability for orally given drugs are nitroglycerine (rapid first pass metabolism) and osteoporosis drug Fosamaxâ (very poor absorption) Bioavailability and Bioequivalence Absolute bioavailability is measured by: – comparing intravenous administration (iv) and oral administration (oral) – F = AUC oral /AUCiv D: dose; AUC: area under the plasma vs time curve Relative bioavailability - comparing different dosage forms, different routes or different conditions Bioequivalence: – a new product is allowed to market if it shows bioequivalence to the conventional drug(s) – Important parameters: AUC, Cmax (maximum plasma concentration) and Tmax (time required to achieve the maximum plasma concentration) An important Definition – The “apparent” Volume of Distribution (1) § Volume of distribution – measure of the apparent space in the body available to contain the drug. § Apparent volume of distribution (Vd): volume of fluid required to contain the total amount, Q, of drug in the body at the same concentration as the drug is present in the plasma, Cp: Vd = Q/Cp Volume of Distribution (2) Drugs confined to the plasma compartment (0.051 L/Kg) – strongly plasma protein-bound or very large molecules (e.g., dye, heparin) – Vd < 5L Drugs distributed in the extracellular compartment (0.21 L/kg) – water-soluble molecules (e.g., gentamicin) - cannot enter cells or cross barriers because of their low lipid solubility – 5L < Vd < 20 L Drugs distributed throughout the total body water (0.55 L/kg) – Drugs relatively lipid soluble and can cross cell membrane – 20L < Vd < 40 L Drugs distributed to (and concentrated in ) peripheral tissue – Partitioning into body fat (e.g., thiopentone, 0.2-0.35 L/kg), and bone (e.g., Ca2+ ions) can further increase volume of distribution – Vd > 40 L – exceed total body volume Volume of distribution can be larger then the body volume Multiple Oral Dosing and Blood Concentrations steady-state concentration (Css): rate of input is equivalent to the rate of output it normally takes 4-5 t1/2 to reach steady state. Ideally in drug treatment, a steady-state plasma concentration is required within the minimum effective concentration (mec) and the maximum safe concentration (msc) loading dose or priming dose for drugs that have a longer half-life Galbraith et al., 2000. Fundamental of Pharmacology (3th edition). Fig 10.1. Blood concentration Toxicity Optimal range (therapeutic window) No effect msc mec The body (a beaker with an defined apparent volume of distribution) is a well stirred compartment Single-Compartment Model Single-compartment model – For many drugs, Vd appears to be a single entity in terms of drug concentrations vs. time profiles – These drugs are consistent with the onecompartment model where the whole body is considered as a single well-stirred compartment – Linear relationship in semilogarithmic plot of Cp vs. time Dale and Haylett. 2004. Pharmacology Condensed. Figure 8.2, Pg 25 Two-Compartment Model Two Compartment model – For some drugs, they equilibrate with different tissues at different rates – These drugs are consistent with two compartment model where the whole body is considered to consist of a central and a peripheral compartment – Two-compartment model comprises a fast (a phase) and a slow (b phase) phase – Fast phase: redistribution of drug between the central and peripheral compartments Rang et al., 2003. Pharmacology, Figure 8.11, Pg 117. Rate of Reaction can be First or Zero Order Kinetics (rare) First order kinetics – Rate of the drug metabolism is proportional to the drug’s plasma concentration – Most drugs at therapeutic dosages tend to follow this pattern – Drugs following the first order kinetics have a fixed t1/2 Zero order (saturated) kinetics – Rate of the drug metabolism is constant and is independent of the drug’s plasma concentration – Increasing dose produces a disproportionate increase in plasma concentration – E.g., ethanol if consumed - £ 8 g/hr, it follows first-order kinetics - > 8 g/hr, it will follow zero-order kinetics as the limited amount of enzymes for metabolic processes become saturated by excess quantities of ethanol. Now the calculations PK Movie First order kinetics – terms to understand Ct is concentration after time t C0 is the initial concentration (t=0) k is the elimination rate constant t is the time Blood concentration (1) t1/2 t1/2 Time The relationship between a) the elimination rate constant and b) the half-life (time for the drug to reach 50% of concentration) is given by the following equation: (2) How transform formula 1 to formula 2 Ct / C0 = e-kt (at t1/2, Ct = 0.5 x Co) 0.5 = e -kt½ ln (0.5) = ln (e -kt½) - 0.693 = -kt½ 0.693 = kt1/2 kel = 0.693 t1/2 ? Also to note: kel = ln (C0/Ct) Dt ln (8/4) = 1 hr = ln (2) = 0.693 1 hr 1 hr Another term: Clearance The overall clearance of a drug (CL) is the theoretical volume of blood / plasma (a percentage of the total volume of distribution) which is totally cleared of drug per unit time Unit is volume per time unit (e.g. liter per hour) Because clearance is a first-order process, the amount of drug removed depends on the concentration (Amount = volume x concentration) Another term: The rate elimination constant (kel or ke) The fraction (percentage) of the drug in the body eliminated per unit time is determined by the rate elimination constant (kel). (CL=clearance, Vd =volume of distribution) (unit: hour -1) And remember this equation ? Half-life of a drug (t1/2): the time taken for concentration of drug in blood to fall to half of its original value t1/2 may also be calculated as THE MASTER equation Blood concentration All together: Half life, clearance, and elimiation rate constant t1/2 t1/2 Time Dale and Haylett. 2004. Pharmacology Condensed. Figure 8.2, Pg 25 Summary of Definitions The Volume of Distribution (Vd) is the amount of drug in the body divided by the concentration in the blood. Drugs that are highly lipid soluble have a very high volume of distribution (500 litres) – more than the actual body volume. Drugs which are lipid insoluble remain in the blood, and have a low Vd. (Unit: liter) The Clearance (Cl) of a drug is the volume of plasma from which the drug is completely removed per unit time. (The amount eliminated is proportional to the concentration of the drug in the blood) (Unit: liter/ hour) or (ml/min) The fraction of the drug in the body eliminated per unit time is determined by the elimination constant (kel). (unit: hour -1) Half-life of a drug (t1/2): the time taken for concentration of drug in blood to fall to half of its original value These parameters can all be linked by the master equation Calculation – Groupwork Drug distribution: You have a 10ml container of concentrated orange squash (= drug). You put this into a litre (ok 990ml!) of water. The volume of distribution (Vd) of the diluted orange squash is 1000ml. Drug elimination: If, each minute, you empty 10ml of the diluted orange liquid into the 10ml container, discard this, and replace it with 10ml of water, then the clearance is 10 ml per minute. Calculate the Elimination rate constant Drug half life A few more formula’s s ´ Loading Dose: May be used to achieve therapeutic levels of the drug (i.e levels at the desired steady state concentration) : Sometimes use to compensate for drug distribution in tissues F S = Salt Factor (usually 1) L/hr * mg/L = mg/hr Calculate dosage for 24hr F= Bioavailability References Rang, H.P., Dale, M.M., Ritter, J.M. and Moore, P.K. (Ed). (2003). Pharmacology (5th ed. or later). Edinburgh: Churchill Livingstone, chapters 7 and 8 http://medgadget.com/2009/09/_rxcalc_for_pharmacokin etic_calculations_on_the_iphone_1.html (the iPhone App) - http://www.thebody.com/content/art875.html