Quantitative Pharmacokinetics Pharmacokinetics involves the kinetics of drug absorption, distribution, and elimination. Disposition=Distribution+Elimination

Compartment model The body is viewed as a system with a number of compartments through which the drug is distributed at certain rates. This pharmacokinetic model has no physiologic meaning, but can be described schematically or mathematically according to constant rates in the cases of absorption and elimination.

One-compartment model The drug is instantaneously and uniformly distributed. Compartment ka ke Elimination Absorption

Two-compartment model Drugs are absorbed into the central compartment , distributed from the central compartment to the peripheral compartment, and eliminated from the central compartment.

Drug Plasma Concentration Curves In practice it is usually the drug concentration in plasma (Cp) that is measured. The drug concentration in plasma (Cp) is not equal to the drug concentration in the tissues. Changes in the plasma concentration quantitatively reflect changes in the tissues.

Onset: The time it takes for the drug to elicit a therapeutic response Minimum effective concentration (MEC): a minimum plasma concentration that will produce an effect. Drug Plasma Concentration Curves Time-action curve Onset: The time it takes for the drug to elicit a therapeutic response Minimum toxic concentration (MTC):a minimum concentration above which toxic effects may be experienced. Termination Onset

Therapeutic Range: the plasma concentrations between the MTC and the MEC Drug Plasma Concentration Curves Time-action curve Duration of action: The time between the onset of action and the time when the minimum effective concentration is reached by the declining blood concentrations Termination Onset

Cmax: maximum concentration Drug Plasma Concentration Curves The extent of absorption determines the height of the peak concentration Time-action curve toxic concentration Tmax :the time needed to reach the maximum Rate of absorption determines the time to the peak concentration Onset Termination

Area Under the Curve (AUC) The area under the curve (AUC) refers to the area under a concentration versus time curve for a drug A measure of the total amount of drug during the time course . The area is conveniently determined by the “trapezoidal rule”.

- quantifies ABSORPTION Bioavailability The fraction (F) of the administered dose of a drug that reaches the systemic circulation in an active form. - quantifies ABSORPTION Bioavailability is highly dependent on both the route of administration and the drug formulation.

Absolute Bioavailability the amount of drug that is absorbed by route X X 100 % F= the amount of drug that is absorbed after intravenous administration X 100 %

Relative Bioavailability Used to compare different formulations of the same medication AUCtest AUCreference Relative Bioavailability F’ = The same active compound in the same amount just from different manufactures or different batches from the same manufacture will result in equivalent concentrations in plasma and tissues when given to the same patient?

Relative Bioavailability Differences in bioavailability may arise due to variations in disintegration and dissolution rates. Relative bioavailability is one of the measures used to assess bioequivalence (BE) between two drug products.

the same active compound in the same amount Relative Bioavailability Chemical equivalence Bioequivalence the same active compound in the same amount the same patient in the same dosage regimen, result in equivalent concentrations of drug in plasma and tissues

Rate of Absorption (Rate of Bioavailability) Bioavailability is sometimes used to indicate both the extent and the rate at which an administered dose reaches the general circulation. Both the rate of absorption and the extent of absorption can influence the clinical effectiveness of a drug.

Bioequivalence: Extent & Rate of Absorption (Extent of absorption) AUCtest AUCref Relative bioavailability F’ = (Extent of absorption) Relative bioavailability Cmaxtest F’’ = Cmaxref (Rate of Absorption) 80%<F’ & F”<125% Two preparations of a drug are considered bioequivalent only when the rate and extent of bioavailability of the drug from them is not significantly different under suitable test conditions.

Apparent Volume of Distribution (Vd) The volume of fluid in which a drug would need to be dissolved to have the same concentration as it does in plasma. An apparent volume that represents the relationship between the dose of a drug and the resulting plasma concentration of the drug.

Vd = Dose (mg)/Cp0 (mg/L)= Litres Apparent Volume of Distribution The volume of distribution is normalized to body weight and will then be expressed as units of liters per kilogram. Cp0 Vd = Dose (mg)/Cp0 (mg/L)= Litres

Practice calculation A dose of analgesic (50mg) is administered i.v. and a blood sample is taken shortly afterwards. The initial concentration of analgesic in the blood sample is 0.85 µg.ml-1. Calculate the volume of distribution of the analgesic (in Litres).

Model solution V = D/C0 = 50 mg / 0.85 µg.ml-1 Mixed units! V = D/C0 = 50 mg / 0.85 µg.ml-1 = 50,000 µg / 0.85 µg.ml-1 = 58,824 ml = 59 Litres

Drug distribution and Body water Total body water plasma volume extracellular plasma 3 liters 5% interstitial volume interstitial volume 15 liters 25% intracellular volume intracellular 12 liters 20% 42 liters 70% Water composition in 60 Kg Body Weight 27 liters 45%

(The numbers are only rough approximation) Table 1. Relationship Between the Extent of Distribution and Vd in a 70 kg normal person (The numbers are only rough approximation) Vd, L % Body Weight Extent of Distribution 5 7 Only in plasma 5-20 7-28 In extracellular fluids 20-40 28-6 In total body fluids. >40 >56 In deep tissues; bound to peripheral tissues

Drug Clearance The volume of a biological fluid (generally plasma) from which that drug is removed ("cleared") in the unit of time (min). Units are in L/hr or L/hr/kg The clearance of a particular drug is constant in first order kinetics

Be not an indicator of how much drug is being removed Clearance Rate of elimination plasma concentration CL = Be not an indicator of how much drug is being removed Represents the theoretical volume of blood which is totally cleared of drug per unit time A descriptive term used to evaluate efficiency of drug removal from the body

Total body clearance is the sum of the individual organ clearances Clearance is the rate of elimination of a drug by all routes, relative to the concentration of that drug in any biological fluid. Total body clearance is the sum of the individual organ clearances CL = CLren + CLhep + CLother

Creatinine clearance is 100 ml/min Drug Clearance Renal Clearance The volume of plasma that is totally cleared of a drug in 1 min during passage through the kidneys. CLrenal= Renal excretion rate = ml/min Plasma concentration Creatinine clearance is 100 ml/min if the CLrenal is 100ml/min, it is filtered only if the CLrenal is <100ml/min, it is reabsorbed if the CLrenal is >100ml/min, it is secreted

Drug Clearance Hepatic Clearance The volume of plasma that is totally cleared of drug in 1 min during passage through the liver. Most drugs are cleared from the plasma mainly by biotransformation in the liver. Biliary excretion can also contribute to the hepatic clearance of a drug.

Hepatic Clearance Be more difficult to determine than renal clearance. Drug Clearance Hepatic Clearance Be more difficult to determine than renal clearance. Usually determined by multiplying hepatic blood flow by the arteriovenous drug concentration difference.