General Principles of Pharmacology and Toxicology Parisa Gazerani, Pharm D, PhD Assistant Professor Center for Sensory-Motor Interaction (SMI) Department of Health Science and Technology Aalborg University
2 Definitions and units symbols Symbol Units Definition A mg Amount of drug in body AUC mg*hour/l Total area under the plasma drug concentration-time curve AUC 0- mg*hour/l area under the plasma drug concentration-time curve from zero to infinite time AUC iv mg*hour/l area under the plasma drug concentration-time curve after an IV dose AUC oral mg*hour/l area under the plasma drug concentration-time curve after an oral dose C mg/ml Concentration of drug in plasma C 0 mg/ml Concentration of drug in plasma after a single dose extrapolated back to zero time C b mg/ml Concentration of drug in blood CL Total clearance of drug from plasma CL CR Creatinine clearance
3 Symbol Units Definition CL GF CL H Renal drug clearance by glumerular filtration Hepatic clearnce of drug from plasma CL int CL R Intrinsic clearance of drug in an organ of elimination Renal clearance of drug CL S Renal drug clearance by tubular secretion C max mg/l Maximum plasma drug concentration during a dosing interval C min mg/l Minimum plasma drug concentration during a dosing interval C ss mg/l Concentration of drug in plasma at steady state during a constant-rate intravenous infusion C uss mg/l Unbound concentration of drug in plasma at steady state during a constant-rate intravenous infusion C u mg/l Unbound drug concentration in plasma
4 Symbol Units Definition DR mg/hour Dosing rate E ratio Extraction ratio for an organ E H ratio Hepatic extraction ratio EC 50 mg/l Concentration giving one-half the maximum effect E max varies Maximum effect DR mg/hour Dosing rate E ratio Extraction ratio for an organ E H ratio Hepatic extraction ratio EC 50 mg/l Concentration giving one-half the maximum effect E max varies Maximum effect
5 Symbol Units Definition F ratio Bioavailability of drug f e ratio Fraction of drug systematically available that is excreted unchanged in urine f g ratio Fraction of an oral dosethat is absorbed intact into the portal circulation f H ratio Fraction of drug entering the liver that escapes extraction f m ratio Fraction of drug systematically available that is converted to a metabolite FR ratio Fraction of drug reaching the renal tubular fluid that is reabsorbed f u ratio Fraction of drug unbound in plasma f ut ratio Fraction of drug unbound in plasma GFR Glomerular filtration rate k /hour Elimination rate constant
6 Symbol Units Definition k a mm Association constant for the binding of drug to protein k m mg/l Michaelis-Menten constant Λ (lambda) ratio Ratio of concentrationof drug in whole blood to that in plasma P u mm Concentration of drug that does not bind drug Q H Hepatic blood flow (portal vein plus hepatic artery) V L Volume of distribution v mg/hour Velocity of enzyme reaction (conversion of drug to metabolite) V max mg/hour Maximal rate of enzyme reaction of saturating substrate concentration V p L Plasma volume V T L Physiologic volume outside plasma into which drug distributes Τ (tau) hour Dosing interval
7 Equations Elimination rate: CLxC Elimination rate = clearance (CL)xplasma drug concentration(c) mg/hour mg/l DR = CLxC ss Maintenance dose rate (DR) = clearance (CL)xsteady state drug concentration (C ss ) mg/hour mg/l C b = Cxλ and then λ = C b/ C Plasma concentration ratio = drug concentration in whole blood drug concentration in plasma
8 V = A/C Volume of distribution = total amount of drug in the body /plasma drug concentration V = V p + f u /f ut x V T Volume of distribution = plasma volume + fraction unbound in plasma fraction unbound in tissue x tissue volume Loading dose = V x C Loading dose = volume of distribution x target plasma concentration C t = C 0 x e kt Concentration at various time after the dose = Concentration at time zero x e kt K is elimination rate constant and t is time.
9 T 1/2 = 0.693/k Half-life (a reciprocal function of elimination rate constant). 0.693 is the natural logarithm of 2. 0.693xV T 1/2 =, K = CL/V CL CL H = Q H xe H Hepatic clearance = hepatic blood flow x hepatic extraction ratio E H = f u xcl int Q H + f u x CL int Unbound fraction x intrinsic clearance Extraction ratio = Blood flow + Unbound fraction x intrinsic clearance
10 CL int = V max /K m V max is the maximal velocity of the reaction at saturating substrate concentration or the maximal rate at which the enzyme can convert the drug to a metabolite. Km is the Michaelis constant and expresses how tightly the enzyme binds the drug substrate, the lower the Km, the tighter the binding! C LH = QH x f u xcl int Q H + f u x CL int F = f g x f H Bioavailability = fraction absorbed x fraction escaping first pass clearance F = AUC oral / AUC iv f H= 1 E H (the max oral bioavailability if the drug was totally absorbed from the gut into the portal circulation, fg = 1)
11 CL = CL R + CL H Total clearance = renal clearance + hepatic clearance f e = CL R /CL Fraction excreted unchanged = renal clearance/total clearance CL R = f u (GFR + CLs) (1- FR) Rnal clearance is the sum of glomerular filtration clearance (f u xgfr) and secretion clearance (f u x CL s ) multiplied by the fraction of drug that escapes reabsoption from the renal tubule (1- FR). F u = C u /C Fraction unbound = unbound drug concentration/total drug concentration Css = (FxDR)/CL Css is the steady state blood concentration and is a function of the dose rate, the bioavailability and the clearance of the drug.
12 CL () = dose (mg) AUC 0- (mgxhour/l) The AUC from zero time to the last plasma sample is determined as a number of trapezoids, and the area from the last data point (C last ) to infinite time is calculated as C last /k, where k is the elimination rate constant of the lowest elimination phase. V (L) = CL = t 1/2 (hour) xcl () 0.693 F xdose (mg) AUC 0-