Non-Linear Kinetics (Cut off for Exam 3)

Question 1

Non-Linear Kinetics

Answer 1

• Saturation of PK processes, (ADME processes) leads to non-linear pharmacokinetics or dose-dependent PK
• Process follows Michaelis-Menten kinetics
• Also called dose-dependent kinetics

Question 2

Theoretical

Answer 2

• Rate of metabolism (velocity): dX/dt or dC/dt
• dC/dt = rate of decline of drug concentration at time t
• Vmax (aka Vm) = maximum rate of reaction, units Concentration/time
• Km = Michaelis-Menten equation constant, units = concentration

-dC/dt = Vmax * C / Km + C

Question 3

Linear v.s. Non-Linear Kinetics

Answer 3

• dC/dt v.s. C gives linear, hyperbolic curve
• *Note: Therapeutic concentrations of most drugs in body are well below their Km values and therefore elimination follows 1st order kinetics

Question 4

Case 1: Km&raquo_space; C

Answer 4

• Km + C ==> Km
• dC/dt = KC
• Corresponds to first order elimination of drug after IV bolus into 1-compartment model

Question 5

Case 2: Km &laquo_space;C

Answer 5

• Km + C ==> C
• dC/dt = Vmax
• Rate is independent of drug concentration
• Process reaction occurs at constant rate, Vmax

Question 6

Graphs + C/Km values

Answer 6

• Be able to recognize which cases produce which graphs
• C &laquo_space;Km = linear
• C > Km or C&raquo_space; Km = non-linear

Question 7

Drug Elimination: 1st Order Kinetics

Answer 7

• Half life - independent of dose (0.693/K)
• Composition of excretion products (fp and fm) - independent of dose
• AUC - dependent and proportional to dose
• Absorption kinetic has no effect on the above 3 aspects

Question 8

Drug Elimination: Non-linear

Answer 8

• Decline of drug levels in body is not exponential
• Half-life: dependent on dose
• AUC: dependent on dose, not proportional
• Composition of excretion products (parent drugs and metabolites) is affected by the size of dose, route of administration, and dosage forms
• Dose-response curve may show unusually large increases in pharmacologic effects with increasing dose

Question 9

Clearance

Answer 9

• At low concentrations: Cl = VK (linear)
• At high concentration: Cl = Vmax * V / C

General equation: Cl = Vmax * V / Km + C

At low concentrations, Cl is independent of concentration; at high concentrations, Cl decreases as the dose increases

Question 10

Half-Life

Answer 10

• At low concentrations: t1/2 = 0.693/K (linear)
• At high concentrations: t1/2 = 0.693 * C / Vmax

General equation: t1/2 = 0.693 * (Km + C) / Vmax

Question 11

Determining Km and Vmax

Answer 11

1. Determine Css at 2 separate dosing regimens
   R1/2 = Vmax * Css1/2 / Km + Css1/2
2. Combining equations and solving for Km:
   Km = (R2 - R1) / [(R1/Css1) - (R2/Css2)]
3. Substitute Km into either of the first equations and solve for Vmax
   Vmax = R * (Km + Css) / Css

Question 12

Css in Non-Linear

Answer 12

Solve from R equation:

Css = R * Km / Vmax - R