Dosing Regimen Design

Two-Compartment ModelInfusionMultiple Dosing

Assessment of PK parameters

CL:

CL/F = (DM/)/Css,av and Css,av = AUCss,/

Relative F:

B

M

A

M

Aavss

Bavss

A

B

D

D

C

C

F

F

,,

,,

CLR:

CLR = (Ae,ss/ x Css,av) where Ae,ss is the amount of drug excreted in the urine over one .

InfusionV1

V2

k10

k12

k21

dX1/dt = Ko + k21X2 – k10X1 – k12X1

dX2/dt = k12X1 – k21X2

Ko

01

23

45

67

89

0 50 100

Time [h]

C [

mg

/L]

Cp

C2X1,ss = Kok21/ = Ko/k10

X2,ss = Kok12/

X1,ss/X2,ss = k21/k12 = V1/V2Cp,ss = Ko/CL = C2,ss

Infusion rate calculation

Same as for the one-compartment case:

Ko = CL x Cp,ss,desired

Post-Infusion Profile

0.1

1.0

10.0

0 50 100 150

Time [h]

C [

mg

/L]

V1V2

k10

k12

k21

Short Infusion

0.1

1.0

10.0

0 10 20 30 40 50 60

Time [h]

C [

mg

/L]

V1V2

k10

k12

k21

Duration of infusion

0.0

0.1

1.0

10.0

0 5 10 15 20 25 30

Time [h]

Cp

[m

g/L

]

bolus

8 hr infusion

75 hr infusion

V1V2

k10

k12

k21

Getting model parameter values

0.1

1.0

10.0

100.0

0 10 20 30

Time [h]

Cp

[m

g/L

]

0.1

1.0

10.0

100.0

0 10 20 30

Time [h]

Cp

[m

g/L

]

1. Semilog graph of Cp,t values.

2. Add line to log linear phase.

3. Subtract line from the Cp,t values.

4. Use slopes and intercepts of the two lines to calculate PK parameter values.

Cp = A’e-t + B’e-t

Getting model parameter values

Use A’, B’, , and :

V1 = Xo/(A + B)

k21 = (A + B)/(A + B)

k10 = /k21

k12 = + - k21 - k10

V2 = V1(k12/k21)

Vss = V1 + V2

V = V1(k12 + k21 - )/(k21 - )

V = V1k10/

CL = k10V1 = V

t1/2, = ln 2/

t1/2, = ln 2/

A = A’ / (1 - e-)

B = B’ / (1 - e-)

Xo = Ko

= infusion time

Multiple Dosing: i.v. bolus

0.1

1.0

10.0

0 20 40 60 80 100 120

Time

0.01

0.10

1.00

10.00

0 20 40 60 80 100 120

Time

ee

Bee

ACNN

N 11

11

max,

e

ee

Beee

ACNN

N 11

11

min,

e

B

e

ACss 11max,

e

e

Be

e

ACss 11min,

EE K

Np

Kss e

C

eVDoseF

C

11

10

max,One-Compartment

Gentamicin accumulation

Rowland and Tozer, Fig. 19-12, p. 330.

AUC and Css,av relationships

AUC0- = AUC0-,single dose = A/ + B/

FDose/ = CL Css,av

Css,av = FDose / CL

Loading Dose: lidocaine example

Rowland and Tozer, Fig. 19.10, p. 329.

V1V2

k10

k12

k21

Lidocaine LD: multiple bolus w/ 2.1, 3.0, 4.4 mg/min infusion

Applie

d P

harm

aco

kin

eti

cs,

2n

d E

d.,

p.

65

9,

Fig.

20

.2

Lidocaine LDA

pplie

d P

harm

aco

kin

eti

cs,

2n

d E

d.,

p.

66

0,

Fig.

20

.3