Dosing Regimen Design

Nonlinear Kinetics

Saturable metabolism

When elimination is “linear”, CL is independent of the amount of drug in the body and the steady-state plasma concentration is directly proportional to the dosing rate:

Css = Ko/CL

Css,av = F•Dose/CL

Michaelis Menten Kinetics

dtEDd

CKCV

vM

max

1

32

kkk

KM

Michaelis-Menten Kinetics and Dosing Rate

Rate In = Rate Out

ssM

sso CK

CVK

max

o

oMss KV

KKC

max 0

5

10

15

20

25

0 100 200 300 400 500

Dose Rate [mg/h]

Cp

,ss

[m

g/L

]

CL=Vmax/Km

CL=Vmax/(Km+Cp,ss)

Vmax = 500 mg/h

KM = 4 mg/L

Non-linear relationship

As dose rate increases, there is a more-than-proportional increase in Cp,ss.

FDM/

Ko

Cp,ss CL

“Amplifier” or “positive feedback loop”

Example: phenytoinTherapeutic Window: 10-20 mg/L

Patient values of KM and Vmax: 3 mg/L & 425 mg/day.

Patient is taking 200 mg po b.i.d.

F = 0.85; DR = (0.85)(400 mg) = 340 mg/day

Css = KMDR/(Vmax - DR)

= (3mg/L)(340 mg/day)/(425 – 340 mg/day)

= 12 mg/LIf F increased to 0.95 because of product change, DR would be 380 mg/day and Css would be:

Css = (3)(380)/(425 – 380) = 25.3 mg/L

Time to steady state

As metabolism becomes saturated by escalating body level, CL is reduced and half life is increased. Time to steady state is thereby increased:

Rowland and Tozer, Fig. 22.15, p. 410.

= t90%

Change in CL also gets amplified

FDM/

Ko

Cp,ss CL

Principal examples of single saturable metabolism pathway: phenytoin and ethanol.Another possibility is that the drug is eliminated by several pathways, only some of which are saturable. Examples include salicylate, propranolol, and theophylline.

0.01

0.1

1

10

100

1000

10000

1 10 100 1000 10000

Ko, mg/hr

Css

, m

g/L

Parallel linear and saturable pathways

Db

CLlin = 1L/h

CLsat

KM = 2.22 mg/L

Vmax = 100 mg/h

CL = CLlin + CLsat

When Css << KM, CL = 100/2.22 + 1 = 46 L/h

When Css >> KM, CL 1 L/h

Two Plateaus

With parallel linear and saturable pathways, the Css vs. Ko relationship has two plateaus, below and above the KM of the saturable pathway.

With the parallel pathways system, saturation of one pathway is clinically important only when the saturable pathway accounts for more than 50% of CL in the linear region.

Ko

ke

Vmax, KM

Ko, mg/h Css, mg/L

1 0.022

2 0.044

4 0.090

7 0.163

10 0.240

25 0.713

50 2.05

100 13.8

250 151

500 401

1000 900

2500 2400

5000 4900

10000 9900

Ko

ke

Vmax, KM

linear

nonlinear

linear

Mo

eMeo

Meo

ess K

V

KkKk

V

VKKk

V

VK

kC 4

2

12

maxmax

Autoinduction: carbamazepine

tk

k

NktK

K

NK

Ea

ap

a

a

atE

tE

tE

ee

ee

e

e

Kk

k

V

DoseFC

1

1

1

1

tKEEE

tE

IeKKKK 0

Rowland and Tozer, Fig. 23-6, p. 430.

t1/2,I = 3.5 days

KE, /KE,0 = 2

KE

t

Pitlick, Levy, et al., J. Pharm. Sci. 65:462,1976.