Download DOSE- AND TIME-DEPENDENT PHARMACOKINETICS

DOSE- AND TIMEDEPENDENT
PHARMACOKINETICS
CAUSES OF DOSE- OR TIME-DEPENDENT KINETICS
PROCESS
EXAMPLE
PARAMETER
Saturable gut wall transport
riboflavin
Saturable gut wall metabolism salicylamide
Poor solubility
griseofulvin
F
F
F
Saturable plasma protein
binding
disopyramide
fup
Active tubular secretion
Active tubular reabsorption
Alterations in urine pH
Alterations in urine flow
Nephrotoxicity
penicillin G
ascorbic acid
salicylic acid
theophylline
gentamicin
CLR
CLR
CLR
CLR
CLR
CAUSES OF DOSE- OR TIME-DEPENDENT KINETICS
PROCESS
EXAMPLE
PARAMETER
Capacity-limited metabolism
Autoinduction
Co-substrate depletion
Product (metabolite) inhibition
phenytoin
carbamazepine
acetaminophen
phenylbutazone
CLH
CLH
CLH
CLH
% of Dose Re cove re d in
Urine
I. ABSORPTION
Effect of dose on riboflavin urinary recovery when
given on an empty stomach. Date from: Levy G,
Jusko WJ. Factors affecting the absorption of riboflavin in
man. J Pharm Sci 55:285-289, 1966.
60
50
40
30
20
10
0
0
5
10 15 20 25 30 35
Dose (mg)
% of Dose Absorbe d
100
80
60
40
20
0
100
1000
10000
Daily Dose (mg)
Effect of dose on ascorbic acid absorption. Data from Blanchard J
et al. Am J Clin Nutr 66:1165-1171, 1997
Steady-state Vitamin C plasma concentration as a function of dose in 13
female subjects receiving doses from 30 to 2,500 mg. From: Levine M, et al.
A new recommended dietary allowance of vitamin C for healthy young
women. Proc Natl Acad Sci USA 98:9842-9846, 2001.
From: Levine M, et al. A new recommended dietary allowance of vitamin C for healthy
young women. Proc Natl Acad Sci USA 98:9842-9846, 2001.
Reproduced from: Rowland M, Tozet TN. Clinical Pharmacokinetics – Concepts and Applications, 3rd edition,
1995, p. 397.
Reproduced from: Rowland
M, Tozer TN. Ibid, p. 396.
II. ELIMINATION
A. CAPACITY-LIMITED ELIMINATION
1. MATHEMATICAL ANALYSIS
These processes can be described via the MichaelisMenten relationship:
k 1
k 2
[ E f ]  [S ] [ ES ] [ E ]  [ P]
k 1
k 1
k 2
[ E f ]  [S ] [ ES ] [ E ]  [ P]
k 1
[ ET ]  [ E f ]  [ ES ]
d [ ES ]
 k 1[ E f ][ S ]  k 1[ ES ]  k  2 [ ES ]
dt
d [ ES ]
 k 1[ E f ][ S ]  k 1[ ES ]  k  2 [ ES ]
dt
at steady state
d[ES]
0
dt
k 1[ E f ][ S ]  k 1[ ES ]  k  2 [ ES ]
k 1[ E f ][ S ]  (k 1  k  2 )[ ES ]
k 1  k  2

[ ES ]
k 1
[ E f ][ S ]
k-1 is a dissociation process, whereas k+2 requires the
breaking of bonds; thus, k-1>>k+2
[ E f ][ S ]
k1

 Km
[ ES ]
k1
Km 
[ E f ][ S ]
[ ES ]
Remember that [Ef] = [ET] – [ES]
[ ET  ES ][ S ]
Km 
[ ES ]
K m [ ES ]  [ ET ][ S ]  [ ES ][ S ]
K m [ ES ]  [ ES ][ S ]  [ ET ][ S ]
[ ES ]( K m  S )  [ ET ][ S ]
[ ET ][ S ]
[ ES ] 
(Km  S )
[ ET ][ S ]
[ ES ] 
(Km  S )
The rate of formation of the product is given as:
k  2 [ ES ]  v
or
v
[ ES ] 
k2
By implication, the maximum rate is given as
Vmax  [ ET ]k  2
Vmax
or [ ET ] 
k2
Vmax
[ S ]


k2 
v


k2
K m  [S ]
Vmax [ S ]
v
K m  [S ]
dC Vmax [C ]


dt K m  [C ]
For most drugs, Km >>C. Hence
dC Vmax [C ]


dt
Km
dC Vmax [C ]


dt
Km
Since Vmax and Km are constant for a given drug in a
given individual, this ratio will be constant. Elimination
will proceed in a first-order fashion.
Vmax

Km
where
dC

 C
dt
Drugs for which Km << C:
ethanol
salicylate
phenytoin
Numerous drugs after first-pass
2. Clinical Consequences
a. Relationship btwn dose and Cp
Reproduced from: Tozer TN, Winter ME. Phenytoin, In: Evans WE, Schentag JJ, Jusko WJ, Applied
Pharmacokinetics – Principles for Therapeutic Drug Monitoring. 3rd edition, 1992, p. 25-12
b. Relationship btwn dose and time to
steady-state
From: Ibid.
c. Relationship btwn dose and AUCo
(AUC (mcg-hr/mL)
3
2
Plasma AUC of
lorcainide in a subject
as a function of dose.
1
Data from: Janchen E et al.
Clin Pharmacol Ther 26:187,
1979.
0
0
100
200
300
400
Oral Dose (mg)
500
c. Relationship btwn dose and AUCo
0.006
AUC/Dose
0.005
0.004
Plasma AUC/Dose of
lorcainide in a subject
as a function of dose.
0.003
0.002
Data from: Janchen E et al.
Clin Pharmacol Ther 26:187,
1979.
0.001
0
0
100
200
300
400
Oral Dose (mg)
500
d. Relationship btwn dose and
bioavailability
% BIOVAILABLE
40
30
Bioavailability of
nicardipine after oral
administration. Data
20
10
from: Wagner JG et al.
Biopharm Drug Dispos 8:133148, 1987.
0
0
10
20
30
Oral Dose (mg)
40
e. Relationship btwn Cp and time
3. Determination of Michaelis-Menten
Parameters
a. Lineweaver-Burke Expression
Vmax  C
v
Km  C
1 Km  C

v Vmax  C
Km
1
1


v Vmax  C Vmax
1/v
1/Vmax
1/C
1/Km
Slope = Km/Vmax
b. In Vivo Determination
Vmax
Vmax  C ss
v
K m  C ss
If K 0  input rate
Vmax  C ss
K0 
K m  C ss
Km
K0
K 0 ( K m  C ss )  Vmax  C ss
K 0 K m  K 0C ss  Vmax  C ss
K 0C ss  (Vmax  C ss )  K 0 K m
K 0  Vmax
 K0 

 K m 
 C ss 
K0/Css
JB is an 18 yo male receiving phenytoin for prophylaxis
of post-traumatic head injury seizures. The following
steady state concentrations were obtained at the
indicated doses:
Dose (mg/d)
100
300
Css (mg/L)
3.7
47
From this data, determine this patient’s Km and Vmax
for phenytoin.
JB is an 18 yo male receiving phenytoin for prophylaxis
of post-traumatic head injury seizures. The following
steady state concentrations were obtained at the
indicated doses:
Dose (mg/d)
100
300
Css (mg/L)
3.7
47
Dose Rate/Css (L/d)
27
6.4
Vmax = 362 mg/d
K0 (mg/d)
Km = 9.7 mg/L
K0/Css (L/d)
What Css would be expected if a dose of 200 mg/d were
given to this patient?
Vmax  Css
K0 
K m  Css
(362 mg / d )Css
200 mg / d 
(9.7 mg / L)  Css
Css  12 mg / L
4. Application to Alcohol
Ethanol
Alcohol dehydrogenase
acetaldehyde
Avg Vmax = 10 g/hr
Km = 100 mg/L
Detectable pharmacologic effect: 250 mg/L
Lethal concentrations >7000 mg/L
Ethanol Clearance (L/hr)
Note: EtOH metabolism
becomes zero-order.
One jigger (45 mL) of 80
proof EtOH contains
~14 g of ethanol – which
exceeds the Vmax!
100
80
60
40
20
0
0
2000
4000
6000
8000
Ethanol Rate of
Metabolism (g/hr)
Ethanol conce ntration at site (mg/L)
10
8
6
4
2
0
0
2000
4000
6000
8000
Ethanol conce ntration at site (mg/L)
Data from: Rowland M, Tozer TN.
Ibid, p. 406.
Reproduced from: Ibid, p. 408.
Reproduced from: Ibid, p. 408.
B. Autoinduction
C. Saturable Renal Tubular Reabsorption
20
15
Plasma
Ascorbic
10
Acid
(mg/L)
5
0
Control
1 - 3 g/day 8 - 12 g/day
Steady-state plasma ascorbic acid concentration in healthy adults
receiving various regimens twice daily for 3 to 4 weeks. Control
subjects had no supplement. Estimated daily dietary intake of ascorbic acid was 5075 mg. From: Nutr Rep Intern 30:597-601, 1984.
Reproduced from: Rowland M, Tozer TN. Ibid, p. 404.
Plasma AUC (mcg/ml.hr)
III. SATURABLE PROTEIN BINDING
2000
1500
1000
AUCs
500
AUCm
0
0
250
500
750
1000
Dose (mg)
Dose vs AUC for naproxen after single (AUCs) and
multiple (AUCm) doses. From: Clin Pharmacol Ther 15:261-266, 1974.
F ree
P ercen t
3
2
1
0
0
100
200
300
400
500
N a p r o x e n P la s m a C o n c e n tr a tio n (m g /L )
In vitro binding of naproxen as a function of Cp.
free
concentration
ER
(mg/hr)
total
concentration
Naproxen Concentration
0.5
200
0.4
160
0.3
120
0.2
80
Unbound Drug
0.1
40
CL/F Unbound, L/hr
CL/F Total, L/hr
Total Drug
0.0
0.0
0.2
0.4
0.6
0.8
1.0
fu at 2 hr postdose
Relationship between oral clearance and fraction
unbound of oxaprozin. From: J Clin Pharmacol 36:985-997, 1996.