Clinical Pharmacokinetics Lecture 3 PDF

Lecture 3 Dr.Sahar Badr Associate prof. of Clinical Pharmacy 17/09/2017 Clinical Pharmacokinetics_sems9_2017 1 Objectives: Describe the differences between linear pharmacokinetics and nonlinear pharmacokinetics. Discuss some potential risks in dosing drugs that follow non...

Lecture 3 Dr.Sahar Badr Associate prof. of Clinical Pharmacy 17/09/2017 Clinical Pharmacokinetics_sems9_2017 1 Objectives: Describe the differences between linear pharmacokinetics and nonlinear pharmacokinetics. Discuss some potential risks in dosing drugs that follow nonlinear kinetics. Explain how to detect nonlinear kinetics using AUC versus doses plots. Apply the appropriate equation and graphical methods, to calculate the Vmax and KM parameters after multiple dosing in a patient. Describe the use of the Michaelis–Menten equation to simulate the elimination of a drug by a saturable enzymatic process. 2  Linear versus Non-linear pharmacokinetics ▪ Regardless of the mode of drug administration, ▪ When the rate of drug administration =the rate of drug removal, The amount of drug in the body reaches a constant value. ▪ This equilibrium condition is known as steady-state serum concentrations (Css) ▪ If a plot of steady state concentrations (Css) versus doses yields a straight line, in this condition the drug follows linear pharmacokinetics. 3 Linear versus Non-linear pharmacokinetics 4 ▪ linear pharmacokinetics means that steady-state serum concentrations increase or decrease proportionally with dose. ▪ If the dose rate is increased or decreased say two-fold, the plasma drug concentration will also increase or decrease two-fold. ▪ Therefore, if a patient has a Css drug concentration of 10 μg/ml at a dosage rate of 100 mg/h ▪ The Css will increase to 15 μg/ml if the dosage rate is increased to 150 mg/h (i.e., a 50% increase in dose yields a 50% increase in Css) Css,new/Dnew=Css,old/Dold or Dnew= Css,new/Css,old. Dold ▪ However, for some drugs, the plasma drug concentration changes either more or less than would be expected from a change in dose rate. This is known as non-linear pharmacokinetic behaviour and 5 can cause problems when adjusting doses. ▪ Non-linear pharmacokinetics occurs when steady-state concentrations change is not proportional to the dose change. (mean that a plot of steady-state concentration versus dose is not a straight line) ▪ When CSS increases more than expected after a dosage increase, one explanation is that the processes eliminating the drug from the body have become saturated. ▪ This phenomenon is known as saturable or Michaelis-Menten pharmacokinetics (e.g. phenytoin, salicylic acid, theophylline) Saturable Elimination 6  drug concentration 17/09/2017 Clinical Pharmacokinetics_sems9_2017 7 ▪ If Css increases less than expected after a dosage increase (lower dashed line), one explanation is saturable plasma protein binding sites (e.g. valproic acid and disopyramide) Saturable protein binding or reabsorption: ▪ Above a certain drug concentration, drug protein binding or drug reabsorption in kidney tubules tends to reach maximal capacity. This leads to a disproportionate increase in the rate of elimination with decreasing drug concentrations. 8  Other drugs, such as carbamazepine, increase their own rate of metabolism from the body as dose is increased so steady-state serum concentrations increase less than expected. ▪ This process is known as autoinduction of drug metabolism. ▪ Drugs that exhibit non-linear pharmacokinetics are oftentimes very difficult to dose correctly and Pharmacokinetics exhibit significant inter-subject variability. ▪ Steady-state serum concentrations/doses plots for medications are determined in humans early during the drug development process. Because of this, by the time a new drug is available for general use it is usually known if the drug follows linear or non-linear pharmacokinetics. 9 Note: Nonlinearity may be at different kinetic levels of absorption, distribution, and/or elimination. 10  Michaelis-Menten Or Saturable Pharmacokinetics Michaelis-Menten is the type of non-linear pharmacokinetics that occurs when the number of drug molecules saturates the enzyme’s ability to metabolize the drug (Capacity-Limited Metabolism). The classic Michaelis-Menten relationship that is used for all enzyme systems: Rate of metabolism (elimination) (V)=-dC/dt=(Vmax⋅ C)/(Km+C) where Vmax is the maximum rate of metabolism (elimination) The unit of Vmax is the unit of elimination rate and normally is expressed as amount/time (e.g., mg/day). However, in some instances, it may be expressed as concentration/time (e.g., mg/L per day). C is the substrate concentration (e.g., mg/L) Km is Michaelis constant expressed in units of concentration (e.g., mg/L) where the rate of metabolism = Vmax/2 (is equal to the drug concentration or amount of drug in the body at 0.5Vmax), Km reflects the capacity of the enzyme system. Compare with this equation: Effect = (Emax. C)/(EC50 + C) 11 Michaelis-Menten saturation curve of an enzyme reaction Zero-order elimination Rate of drug elimination First-order elimination Drug conc [C] 12  Michaelis-Menten saturation curve of an enzyme reaction ▪ According to the principles of Michaelis-Menten kinetics, the rate of drug metabolism (v) changes as a function of drug concentration as demonstrated in this figure. 13 Clearance ▪ Michaelis-Menten pharmacokinetics implies that the clearance of a drug is not a constant as it is with linear pharmacokinetics, but is concentration- or dose- dependent. Cl = Vmax/(Km + C) ▪ As concentration increases, the clearance rate (Cl) decreases as the enzyme approaches saturable conditions. ▪ Therefore the concentrations increases disproportionately after a dosage increase. 14  For example, phenytoin follows saturable pharmacokinetics with average Michaelis-Menten constants of Vmax = 500 mg/d and Km = 4 mg/L. The therapeutic range (Css) of phenytoin is 10–20 mg/L (µg/ml). As the Css of phenytoin increases from 10 to 20 mg/L, clearance decreases from 36 to 21 L/d Cl = Vmax/(Km + Css) Cl = (500 mg/d) / (4 mg/L +10 mg/L) = 36 L/d Cl = (500 mg/d)/(4 mg/L + 20 mg/L) = 21 L/d 15 ▪ Unfortunately, there is so much interpatient variability in Michaelis- Menten pharmacokinetic parameters for a drug. ▪ For example: typically Vmax = 100–1000 mg/d and Km = 1–10 mg/L for phenytoin ▪ Therefore; dosing of drugs which follow saturable metabolism is extremely difficult. Volume of distribution ▪ The volume of distribution (V) is unaffected by saturable metabolism and is still determined by the physiological volume of blood (VB) and tissues (VT) as well as the unbound (free) concentration of drug in the blood (fB) and tissues (fT): V = VB + (fB/fT)VT 16 Half-life ▪ The half-life (t1/2) is still related to clearance and volume of distribution using the same equation as for linear pharmacokinetics: t1/2 = 0.693/K t1/2 = (0.693 ⋅ V)/Cl. ▪ Since clearance is dose- or concentration-dependent, half-life also changes with dosage or concentration changes. ▪ As doses or concentrations increase, clearance decreases and half-life becomes longer for the drug. ↑t1/2 = (0.693 ⋅ V)/↓Cl. 17 18 19 ▪ Phenytoin is an example of a drug which commonly has a Km value within or below the therapeutic range, the average Km value is about 4 mg/L. – The normally effective plasma concentrations for phenytoin are between 10 and 20 mg/L. ▪ Therefore it is quite possible for patients to be overdosed due to drug accumulation. ▪ At low concentration the apparent half-life is about 12 hours, whereas at higher concentration it may well be much greater than 24 hours. ▪ Dosing every 12 hours, the normal half-life, can rapidly lead to dangerous accumulation. ▪ At concentrations above 20 mg/L elimination maybe very slow in some patients. Dropping for example from 25 to 23 mg/L in 24 hours, whereas normally you would expect it to drop from 25 to 12.5 to 6 mg/L in 24 hours. 20 ▪ For a drug that is only removed by metabolism via one enzyme system, The Michaelis-Menten equation can be used to compute the maintenance dose (MD) required to achieve a target steady- state serum concentration (Css), at steady sate, the rate of elimination is equal to the drug dosing rate (R) : MD (R) = Vmax. Css/ Km+ Css ▪ When the Css for a drug is far below the Km value for the enzymes that metabolize the drug Css (Km>>Css), saturation of the enzymes does not occur and the value for Css is negligible, so this equation simplifies to: MD = (Vmax/Km) Css Cl = Vmax/(Km + Css) ▪ or, since Vmax/Km is a constant, MD = Cl ⋅ Css ▪ Therefore, when Km >> Css, drugs that are metabolized follow linear pharmacokinetics. The rate of drug elimination follows first- order pharmacokinetics (the amount of drug eliminated per unit time directly increases with the plasma drug concentration) 21 ▪ When the therapeutic range for a drug is far above the Km value for the enzyme system that metabolizes the drug (Css >> Km), saturation of the enzymes occurs and the value for Km is negligible. ▪ Km may be deleted from the denominator MD (R) = Vmax. Css/ Km+ Css Therefore the rate of metabolism (R) becomes a constant equal to Vmax. ▪ This equation shows that when the drug concentration (Css) is much higher than Km the rate of metabolism is a constant (Vmax), regardless of drug concentration. ▪ Under these conditions only a fixed amount of drug is metabolized because the enzyme system is completely saturated and cannot increase its metabolic capacity. ▪ This situation is also known as zero-order pharmacokinetics (the fraction of drug eliminated remains constant). 22 ▪ Based on these facts, it can be seen that any drug that is metabolized by enzymes undergoes Michaelis-Menten pharmacokinetics. ▪ But, the therapeutic ranges of most drugs are far below the Km for the enzymes that metabolize the agent. Because of this, most medications that are metabolized follow linear pharmacokinetics. ▪ However, even in these cases saturable drug metabolism can occur in drug overdose cases where the drug concentration far exceeds the therapeutic range for the medication. 23 Clinical Correlate ▪ Many drugs exhibit mixed-order pharmacokinetics, displaying first- order pharmacokinetics at low drug concentrations and zero-order pharmacokinetics at high concentrations. ▪ It is important to know the drug concentration at which a drug "order" switches from first to zero. Phenytoin is an example of a drug that switches order at therapeutic concentrations, whereas theophylline does not switch until concentrations reach the toxic range. 24 17/09/2017 Clinical Pharmacokinetics_sems9_2017 25