Dependence of PK Parameters on Dose or Time – Non-Linear Pharmacokinetics (PHCT 4800)

30 question–and–answer flashcards covering the key principles, equations, limiting cases, clinical examples, and calculation methods for linear versus non-linear (saturation) pharmacokinetics, with emphasis on Michaelis–Menten kinetics and drugs such as phenytoin and carbamazepine.

What is meant by “non-linear (dose-dependent) pharmacokinetics”?

A situation where one or more PK parameters (F, Vd, Cl, t½, k, Css, AUC) change with dose or time, so plasma concentrations are not directly proportional to the dose administered.

Give three common characteristics of drugs that display saturation kinetics.

1) Elimination no longer follows simple first-order kinetics; 2) Elimination half-life changes with dose (usually increases); 3) Css or AUC are not proportional to dose.

Which two ADME processes most frequently become saturated and cause non-linear PK?

Metabolism (biotransformation) and active tubular secretion in the kidney.

List two synonyms for non-linear pharmacokinetics.

Dose-dependent kinetics and Michaelis–Menten (saturation) kinetics.

In linear PK, how does Css change when the maintenance dose is doubled?

Css doubles (it changes proportionately with dose).

In non-linear PK, what happens to Css when the dose is doubled?

Css may increase more than two-fold (if clearance decreases) or less than two-fold (if clearance increases due to auto-induction); it is not predictably proportional.

Write the Michaelis–Menten equation used to describe saturable drug elimination.

−dCp/dt = (Vmax · Cp) / (Km + Cp).

What does Vmax represent in enzyme-mediated drug elimination?

The theoretical maximal rate of the elimination process when the enzyme system is fully saturated.

What does Km represent in Michaelis–Menten pharmacokinetics?

The drug concentration at which the elimination rate equals 50 % of Vmax; it reflects the capacity or affinity of the enzyme system.

When Cp ≪ Km, what order of elimination predominates and why?

First-order elimination, because the Michaelis–Menten equation reduces to −dCp/dt ≈ k·Cp (enzyme is unsaturated).

When Cp ≫ Km, what order of elimination predominates and why?

Zero-order elimination, because the equation reduces to −dCp/dt ≈ Vmax (enzyme is saturated and the rate is constant).

Define ‘dose-dependent clearance’.

A situation where total body clearance (ClT) changes with dose because intrinsic clearance (Cl’int), hepatic clearance (Clh), or overall ClT become saturated and are no longer constant.

How does auto-induction (e.g., carbamazepine) affect half-life over time?

It increases clearance, so the elimination half-life shortens with continued therapy (time-dependent non-linearity).

Which drug is the classic example of dose-dependent (non-linear) pharmacokinetics in the therapeutic range?

Phenytoin.

According to a previous exam question, which phenytoin patient is more likely to show dose-dependent PK: Km = 30 mg/L or Km = 600 mg/L (same Vmax)?

The patient with Km = 30 mg/L, because therapeutic concentrations (≈10–20 mg/L) are closer to Km, leading to saturation.

State the basic steady-state input–output relationship for a drug obeying Michaelis–Menten elimination.

R = (Vmax · Css) / (Km + Css), where R is the dosing rate at steady state.

Describe Method B (graphical) for determining Km and Vmax from two steady-state points.

Cross-multiply R and Css in R = Vmax·Css/(Km + Css) → RCss = VmaxCss − KmR; plotting RCss versus R gives a straight line whose slope = −Km and intercept = Vmax.

If phenytoin is given at 150 mg/day (Css = 8.6 mg/L) and 300 mg/day (Css = 25.1 mg/L), what are the calculated Km and Vmax (approx.)?

Km ≈ 27–28 mg/L and Vmax ≈ 630 mg/day (using Method B or simultaneous equations).

Using those Km and Vmax values, what maintenance dose would achieve Css = 15 mg/L?

About 225 mg/day (calculated R = Vmax·Css / (Km + Css) = 630·15 / 42.5 ≈ 222 mg/day).

In linear kinetics, what happens to t½, ClT and Vd when dose changes within the approved range?

They remain constant (dose-independent).

List three PK parameters that may NOT remain constant in non-linear pharmacokinetics.

Any of: bioavailability (F), volume of distribution (Vd), total clearance (ClT), half-life (t½), rate constants (ka, ke).

Why is predicting plasma concentration from a single low dose difficult for drugs with saturation kinetics?

Because the elimination rate varies with concentration; once the elimination pathway saturates, concentrations can rise disproportionately compared with the initial low-dose behavior.

What is the clinical danger of zero-order elimination at high concentrations?

The drug accumulates rapidly because elimination cannot increase further, raising the risk of toxicity.

During an IV infusion with first-order elimination, if the infusion rate doubles, what happens to time to reach steady state?

It does not change; time to steady state depends on t½, not on infusion rate (linear PK assumption).

For a drug with first-order elimination, what is the formula for total clearance using infusion data?

ClT = R / Css (units must match).

Give the equation that relates t½, Vd, and ClT in linear PK.

t½ = (0.693 · Vd) / ClT.

In dose-dependent clearance, how is intrinsic hepatic clearance (Cl’int) affected by increasing Cp?

Cl’int decreases as Cp approaches or exceeds Km because hepatic enzymes become saturated.

Explain why the metabolite profile of a drug may change with higher doses in non-linear PK.

Saturation of one metabolic pathway diverts drug to alternate pathways, altering the composition and ratio of metabolites.

What is meant by the term “time-dependent non-linearity”?

PK parameters change over time during chronic therapy (e.g., enzyme induction or inhibition), independent of dose size.