Non-linear Pharmacokinetics

Arthur G. Roberts

Linear PharmacokineticsAU

C

doseK

dose

Cl

dose

[Dru

g]pl

asm

a

time

ln[D

rug]

plas

ma

time

Increasing Dose

Increasing Dose

Non-linear Pharmacokinetics

• A.K.A. Dose-dependent Pharmacokinetics• Saturation– enzymes– carrier-mediated systems (e.g. transporters)– plasma binding proteins

• Pathological changes to Absorption, Distribution and Elimination

Non-linear Pharmacokinetics

• Metabolism• Time-dependent pharmacokinetics• Bioavailability• Drug protein binding

Saturation or capacity-limited metabolism

• Not first order kinetics• Elimination half-life is dose-dependent• AUC not proportional to bioavailability• Competition effects (drug requires same

carrier system)• Metabolite profile dose-dependent

Linear versus Non-linear

Large dose

small dose

Expectation if the kinetics is linear

What kinetics does A remind you of?

Which one exhibits non-linear pharmacokinetics

Michaelis-Menten KineticsUnits

Example Non-Linear

• Vmax = 0.5 mg/L*h

• Km = 0.1 mg/L

• How long for the [Drug]plasma to go from 20 to 12 mg/L?

Dose Decrease Time

D0 = starting doseDt = dose after time

Half Time

Saturation vs Not

• Vmax = 50 mg/(L*h)• Km = 100 mg/L• Half times for 25 mg, 50 mg, 200 mg, 400 mg

dose mg

v (m

g/hr

)

Km

~Linear

~Nonlinear

Time-dependent Pharmacokinetics• a.k.a. Chronopharmacokinetics• Cyclical (24 hours)• Non-cyclical (>>24 hours)• Auto-induction

– carbamazepine induces enzymes that eliminate it• Auto-inhibition

– Biochemistry- Product inhibition• Circadian Rhythms

Examples

• antimetabolite drug fluorouracil (FU)– least toxic in the morning.

• aminoglycoside– nephrotoxicity during the night

Bioavailability

• non-linear difficult to estimate.• AUC increases disproportionally to the dose.– enzymes saturated– GI tract saturation limited

Drug-Protein Binding

plasma bound

not plasma bound

prolongs half-life

[Dru

g]pl

asm

a

Decrease in slope

End of Non-linear Pharmacokinetics