Transcript SERIOUS ADR - College of Science, Engineering and

COMPARTMENTAL ANALYSIS
OF DRUG DISTRIBUTION
Arthur J. Atkinson, Jr., M.D.
Senior Advisor in Clinical
Pharmacology
Clinical Center, NIH
DRUG DISTRIBUTION
THE POST-ABSORPTIVE TRANSFER
OF DRUG FROM ONE LOCATION IN
THE BODY TO ANOTHER
GOALS OF DRUG DISTRIBUTION
LECTURE
•
•
•
SIGNIFICANCE OF DRUG DISTRIBUTION
VOLUMES
PHYSIOLOGIC BASIS OF MULTICOMPARTMENT PHARMACOKINETIC
MODELS
CLINICAL IMPLICATIONS OF DRUG
DISTRIBUTION KINETICS
DIGOXIN DISTRIBUTION VOLUME
DOSE 750 μg
Vd 

 536 L
C0
1.4 μg/L
BODY FLUID SPACES
(CONVENTIONAL VIEW)
cell membranes
DRUGS WITH Vd CORRESPONDING TO
PHYSIOLOGICAL FLUID SPACES
INTRAVASCULAR SPACE:
NONE
EXTRACELLULAR FLUID SPACE:
INULIN
PROTEINS & OTHER MACROMOLECULES
NEUROMUSCULAR BLOCKING DRUGS (N+)
AMINOGLYCOSIDE ANTIBIOTICS (initially)
TOTAL BODY WATER:
UREA
CAFFEINE
ETHYL ALCOHOL
ANTIPYRINE (some protein binding)
DISTRIBUTION VOLUME OF
REPRESENTATIVE MACROMOLECULES
MW
V1
Vd(ss)
(kDa)
(mL/kg)
(mL/kg)
INULIN
5.2
55
164
FACTOR IX (FIX)
57
136
271
15.5
60
112
INTERLEUKIN-12 (IL-12)
53
52
59
GRANULOCYTE COLONY STIMULATING
FACTOR (G-CSF)
20
44
60
RECOMBINANT TISSUE PLASMINOGEN
ACTIVATOR (RT-PA)
65
59
106
MACROMOLECULE
INTERLEUKIN-2 (IL-2)
FACTORS AFFECTING Vd
ESTIMATES OF MOST DRUGS
BINDING TO PLASMA PROTEINS:
THYROXINE
THEOPHYLLINE
TISSUE BINDING (PARTITIONING):
DIGOXIN (Na+ - K+ ATPase)
LIPOPHILIC COMPOUNDS
PHYSIOLOGICAL SPACES FOR
DRUG DISTRIBUTION
CELL
MEMBRANES
ECF
ELIMINATION
ICF
EFFECT OF BINDING CHANGES ON
Vd OF THYROXINE & THEOPHYLLINE*
Vd  ECF  fu TBW - ECF 
fu is the “free fraction”, the fraction of drug in
plasma that is not bound to plasma proteins.
* Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.
IMPACT OF PROTEIN BINDING ON
THYROXINE DISTRIBUTION VOLUME*
fu = 0.03%
Vd = VECF
* From Larsen PR, Atkinson AJ Jr, et al. J Clin Invest 1970;49:1266-79.
IMPACT OF PROTEIN BINDING ON
THEOPHYLLINE DISTRIBUTION VOLUME*
fu = 60%
Vd = VECF + fuVICF
* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.
BASIS FOR INCREASED
THEOPHYLLINE Vd IN PREGNANCY
fU
(%)
FLUID SPACE
Vd(ss)
ESTIMATES
(L)
(L)
ECF
TBW
EST.
MEAS.
PREGNANT
24-26 WEEKS
88.9
13
34
32
30
36-38 WEEKS
87.0
21
40
38
37
77.4
12
33
28
28
71.9
12
33
27
31
POSTPARTUM
6-8 WEEKS
>6 MONTHS
* From Frederiksen MC, et al. Clin Pharmacol Ther 1986;40;321-8.
EFFECT OF BINDING CHANGES
ON Vd OF MOST DRUGS*
Vd  ECF  Φ fu TBW - ECF 
Ф is the ratio of tissue/plasma drug concentration.
* Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.
LIPID SOLUBILITY & 
VD (L/kg)
fU
Ф
OCTANOL/WATER PARTITION COEF. = 10 – 100*
PHENYTOIN
0.64
0.08
12
DIAZEPAM
1.10
0.013
185
OCTANOL/WATER PARTITION COEF. = 100 - >1000*
PROPRANOLOL
4.30
0.13
82
NORTRIPTYLINE 18.0
0.08
572
*measured at pH 7
APPARENT Vd OF DIGOXIN
Vd  ECF  Φ f u TBW - ECF 
ECF  11.2 L , TBW  34.3 L , f u  0.75 , Φ  20.4
Vd  11.2  20.4  0.75  34.3  L
Vd  536 L
Φ represents binding to Na+-K+ ATPase.
mµC/gm
TISSUE VS. PLASMA
DIGOXIN LEVELS
HOURS
GOALS OF DRUG DISTRIBUTION
LECTURE
•
•
•
SIGNIFICANCE OF DRUG DISTRIBUTION
VOLUMES
PHYSIOLOGIC BASIS OF MULTICOMPARTMENT PHARMACOKINETIC
MODELS
CLINICAL IMPLICATIONS OF DRUG
DISTRIBUTION KINETICS
BASIC PHARMACOKINETIC MODELS*
MODEL
NUMBER OF
COMPARTMENTS
MATHEMATICAL
CHARACTERISICS
NONCOMPARTMENTAL
0
CURVE FITTING TO DATA
COMPARTMENTAL
1–3
MODEL PARAMETERS
FIT TO DATA
“PHYSIOLOGICAL”
4 - 20
MODEL PARAMETERS
FIXED A PRIORI
* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.
MONES BERMAN
MATHEMATICAL VS.
PHYSICAL MODELS*
MATHEMATICAL MODEL:
FUNCTIONS OR DIFFERENTIAL EQUATIONS ARE
EMPLOYED WITHOUT REGARD TO ANY
MECHANISTIC ASPECTS OF THE SYSTEM
PHYSICAL MODEL:
IMPLIES CERTAIN MECHANISMS OR ENTITIES
THAT HAVE PHYSIOLOGICAL, BIOCHEMICAL OR
PHYSICAL SIGNIFICANCE
* Berman M: The formulation and testing of models.
Ann NY Acad Sci 1963;108:182-94
FIRST MULTICOMPARTMENTAL
ANALYSIS OF DRUG DISTRIBUTION*
* From Teorell T. Arch Intern Pharmacodyn 1937;57:205-25.
IS CENTRAL COMPARTMENT
INTRAVASCULAR SPACE?
•
•
USUALLY NOT IDENTIFIED AS SUCH
UNLESS DRUG GIVEN RAPIDLY IV
NEED TO CONSIDER:
- IF DISTRIBUTION LIMITED TO ECF,
COMPARE VC WITH PLASMA VOLUME.
- IF LARGER DISTRIBUTION VOLUME,
COMPARE VC WITH BLOOD VOLUME
ACCOUNTING FOR RBC/ PLASMA.
IF VC IS BASED ON PLASMA
CONCENTRATION MEASUREMENTS
VC(corr.)  VC(meas.)
 1  Hct  Hct RBC P  
RBC/P = red cell/plasma partition ratio
Hct = hematocrit
ANALYSIS OF PA & NAPA CENTRAL
COMPARTMENT VOLUMES*
INTRAVASCULAR SPACE
DRUG
VC
RBC/P
(L)
(L)
PREDICTED
OBSERVED
PA
6.7
1.52
5.6
5.5
NAPA
7.5
1.62
5.6
6.0
* From Stec GP, Atkinson AJ Jr. J Pharmacokinet Biopharm 1981;9:167-80.
ANALYSIS OF EXPERIMENTAL DATA
HOW MANY COMPARTMENTS?
DESPITE AVAILABILITY OF
COMPUTER PROGRAMS FOR
PK ANALYSIS, STILL NEED TO
MAKE INITIAL ESTIMATES.
TECHNIQUE OF CURVE PEELING
A’
β
α
COMPARTMENTAL ANALYSIS
DATA EQUATION:
C = A´e -αt + B´e -βt
Dose
Central
k21
V1
k01
Periph.
V2
k12
MODEL EQUATION:
dX1/dt = -(k0 + k12)X1 + k21X2
TWO-COMPARTMENT MODEL
Dose
Central
V1
Periph.
CLI
V2
CLE
Vd(ss) = V1 + V2
3 DISTRIBUTION VOLUMES
V
 DO S E C
V
t 1/2  C LE
d (extrap.)
0.693
 V  V  ..... V
d (area)
V
d (ss)

0
1
2
n
TWO-COMPARTMENT MODEL
Dose
Central
CLI
V1
CLE
Periph.
V2
k01
CLE = k01V1
INTERCOMPARTMENTAL CLEARANCE*
A VOLUME-INDEPENDENT PARAMETER
CHARACTERIZING THE RATE OF ANALYTE
TRANSFER BETWEEN COMPARTMENTS
OF A KINETIC MODEL
* From Saperstein et al. Am J Physiol 1955;181:330-6.
TWO-COMPARTMENT MODEL
Dose
k21
Central
V1
Periph.
CLI
V2
k12
CLE
CLI = k21 V1 = k12 V2
[PROCAINAMIDE]
(μg/mL)
3-COMPARTMENT MODEL OF PA
PHARMACOKINETICS
HOURS
CATENARY 3-COMPARTMENT
MODEL
cell membranes
[INULIN] (mg/dL)
ANALYSIS OF INULIN KINETICS WITH
A 2-COMPARTMENT MODEL*
AFTER INFUSION
AFTER BOLUS
MINUTES
* Gaudino M. Proc Soc Exper Biol Med 1949;70:672-4.
3-COMPARTMENT MODEL
OF INULIN KINETICS
EXTRACELLULAR FLUID
Dose
VF
VC
CLE
VS
CELL
MEMBRANES
BASIS FOR KINETIC HETEROGENETIY
EFFECTIVE
PORE SIZE
CAPILLARY
STRUCTURE
PRIMARY
LOCATION
LARGE
FENESTRATED
SPLANCHNIC BED
SMALL
CONTINUOUS
SOMATIC TISSUES
ENDOTHELIAL FENESTRAE IN
HEPATIC SINUSOIDS
INTERENDOTHELIAL CELL JUNCTION
IN CONTINUOUS CAPILLARY
PK-PD STUDY OF INSULIN ENHANCEMENT
OF SKELETAL MUSCLE GLUCOSE UPTAKE*
* From Sherwin RS, et al. J Clin Invest 1974;53:1481-92.
UREA-15N2 KINETICS IN
A NORMAL SUBJECT
MULTICOMPARTMENTAL MODEL
OF INULIN AND UREA KINETICS*
* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.
ROLE OF TRANSCAPILLARY EXCHANGE
THE CENTRAL COMPARTMENT FOR
BOTH UREA AND INULIN IS
INTRAVASCULAR SPACE.
THEREFORE, TRANSCAPILLARY
EXCHANGE IS THE RATE-LIMITING STEP
IN THE DISTRIBUTION OF BOTH
COMPOUNDS TO THE PERIPHERAL
COMPARTMENTS OF THE MAMMILLARY
3-COMPARTMENT MODEL.
RENKIN EQUATION*
Cl  Q (1 e
P/Q
)
Q = capillary blood flow
P = capillary permeability coefficient-surface
area product (sometimes denoted P•S).
* From Renkin EM. Am J Physiol 1953;183:125-36.
3-COMPARTMENT MODEL
Dose
VF
VC
CLE
VS
SIMULTANEOUS ANALYSIS OF INULIN
AND UREA-15N2 KINETICS
SUBJECT 1
INULIN
UREA
How does
QF + QS
compare
with C.O.?
FOR EACH COMPARTMENT
3 UNKNOWNS:
Q, PU , PI
3 EQUATIONS:
PU  Q ln Q Q - Cl U 
P I  Q ln Q Q - Cl I 
PU PI  DU D I
U = urea; I = inulin
D = free water diffusion coefficient
CARDIAC OUTPUT AND
COMPARTMENTAL BLOOD FLOWS*
QF
QS
L/min
3.05
3.42
4.41
4.54
3.93
3.87
0.64
L/min
2.10
1.48
1.00
1.65
1.37
1.52
0.40
QF + QS
SUBJECT NO.
1
2
3
4
5
MEAN
± S. D.
L/min
5.15
4.90
5.41
6.19
5.30
5.39
0.49
% C.O.
102
93
96
102
99
99
4
* From Odeh YK, et al. Clin Pharmacol Ther 1993;53;419-25.
MECHANISMS OF
TRANSCAPILLARY EXCHANGE
DIFFUSIVE TRANSFER:
M.W. < 6,000 DALTONS
CONVECTIVE TRANSFER:
M.W. > 50,000 DALTONS
CAPILLARY PERMEABILITY VS. M.W.*
* From Dedrick RL, Flessner MF. Immunity to Cancer 1989;II:429-38.
MECHANISMS OF
TRANSCAPILLARY EXCHANGE
TRANSFER OF SMALL MOLECULES (M.W. < 6,000 Da):
• TRANSFER PROPORTIONAL TO D
- POLAR, UNCHARGED (urea, inulin)
• TRANSFER RATE < PREDICTED FROM D
- HIGHLY CHARGED (quaternary compounds)
- INTERACT WITH PORES (procainamide)
• TRANSFER RATE > PREDICTED FROM D
- LIPID SOLUBLE COMPOUNDS (anesthetic gases)
- FACILITATED DIFFUSION (theophylline)
THEOPHYLLINE KINETICS
REFERENCED TO INULIN AND UREA
THEOPHYLLINE
UREA
INULIN
THEOPHYLLINE I.C. CLEARANCE AND
COMPARTMENTAL BLOOD FLOWS*
FAST
COMPARTMENT
L/min
SLOW
COMPARTMENT
L/min
I.C. CLEARANCE
4.50 ± 1.21
0.60 ± 0.14
BLOOD FLOW
4.00 ± 1.15
0.62 ± 0.21
* From Belknap SM, et al. J Pharmacol Exp Ther 1987;243:963-9.
UREA & THEOPHYLLINE DIFFUSION
COEFFICIENTS*
MOLECULAR
WEIGHT
(DALTONS)
CORRECTED
STOKESEINSTEIN
RADIUS
(Å)
Dm @ 37º C
(x 10-5 cm2/sec)
UREA
60
2.2
1.836
THEOPHYLLINE
180
3.4
1.098
* From Belknap SM, et al. J Pharmacol Exp Ther 1987;243;963-9.
PRESUMED CARRIER-MEDIATED
TRANSCAPILLARY EXCHANGE
O
O
N
H3C N
O
H
N
CH3
N
H N
N
THEOPHYLLINE
H
N
H N
N
HYPOXANTHINE
NH2 H
N
N
ADENINE
N
SIGNIFICANCE OF DRUG DISTRIBUTION RATE
• AFFECTS TOXICITY OF IV INJECTED DRUGS
THEOPHYLLINE
• DELAYS ONSET OF DRUG ACTION
DIGOXIN
INSULIN
• TERMINATES ACTION AFTER BOLUS DOSE
THIOPENTAL
LIDOCAINE
EARLY BENEFITS & LATER RISKS OF
INITIAL IV THEOPHYLLINE DOSES
1937 – THEOPHYLLINE 1st USED SUCCESSFULLY
TO TREAT “STATUS ASTHMATICUS”
Herrman G, Aynesworth MB. J Lab Clin Med 1937;23:135-48.
1943 – 3 CASES OF ARRHYTHMIC DEATH AFTER
“SLOW IV INJECTION” OF 200 mg THEOPHYLLINE
Merrill GA. JAMA 1943;123:1115.
1948 – 3 CASES OF CONVULSIVE CARDIORESPIRATORY
DEATH AFTER “SLOW BUT UNMEASURED
INJECTION” OF 88 - 300 mg THEOPHYLLINE
Bresnick E, et al. JAMA 1948;136:397-8.
1971 - IV INJECTION OF 250 – 750 mg THEOPHYLLINE
OVER 3 - 5 min RESULTS IN 60% OF DRUG-RELATED
CARDIAC ARRESTS IN LA COUNTY SHOCK WARD
Camarata, et al. Circulation 1971;44:688-95.
SAFETY LINKED TO RATE OF
THEOPHYLLINE ADMINISTRATION
• “THE TOTAL DOSE …..DOES NOT SEEM TO BE
IMPORTANT, WITHIN THERAPEUTIC LIMITS, THE
FATAL DOSE HAVING VARIED FROM 0.1 Gm TO
0.36 Gm. IT IS QUITE POSSIBLE THAT THE SPEED
OF INJECTION IS MORE IMPORTANT.”
Bresnick E, et al. JAMA 1948;136:397-8.
• CURRENT RECOMMENDATION:
IV THEOPHYLLINE LOADING DOSE SHOULD BE
5 mg/kg INFUSED OVER 20 – 40 min.
PK MODEL OF THEOPHYLLINE
DISTRIBUTION
IV
Dose
SPLANCHNIC
CNS
IVS
HEART
CLE
SOMATIC
CO = QF + QS
SIGNIFICANCE OF DRUG DISTRIBUTION RATE
• AFFECTS TOXICITY OF IV INJECTED DRUGS
THEOPHYLLINE
• DELAYS ONSET OF DRUG ACTION
DIGOXIN
INSULIN
• TERMINATES ACTION AFTER BOLUS DOSE
THIOPENTAL
LIDOCAINE
DIGOXIN IS NOT THE 1ST DRUG GIVEN TO
PATIENTS WITH ACUTE PULMONARY EDEMA
SV  HR
CO 
TPR
VASOCONSTRICTIVE EFFECTS
MYOCARDIAL EFFECTS
PLASMA VS. MYOCARDIAL DIGOXIN LEVELS
EFFECTS ON CNS VOMITING CENTER
SIGNIFICANCE OF DRUG DISTRIBUTION RATE
• AFFECTS TOXICITY OF IV INJECTED DRUGS
THEOPHYLLINE
• DELAYS ONSET OF DRUG ACTION
DIGOXIN
INSULIN
• TERMINATES ACTION AFTER BOLUS DOSE
THIOPENTAL
LIDOCAINE
DISTRIBUTION TERMINATES EFFECT
OF BOLUS LIDOCAINE DOSE*
THERAPEUTIC RANGE
* From Atkinson AJ Jr. In: Melmon KL, ed. Drug Therapeutics: Concepts for Physicians, 1981:17-33.
ANALYSIS OF LIDOCAINE
DISTRIBUTION KINETICS*
* From Benowitz N, et al. Clin Pharmacol Ther 1974;16:87-98.
CONSEQUENCES OF VERY
SLOW DRUG DISTRIBUTION
• “FLIP-FLOP” KINETICS
• EFFECTIVE HALF-LIFE
• PSEUDO DOSE DEPENDENCY
GENTAMICIN ELIMINATION PHASE
PRECEEDS ITS DISTRIBUTION PHASE*
* From Schentag JJ, et al. JAMA 1977;238:327-9.
GENTAMICIN ELIMINATION IN A
NEPHROTOXIC VS. NON-TOXIC PATIENT*
NEPHROTOXIC
NON-TOXIC
* From Coburn WA, et al. J Pharmacokinet Biopharm 1978;6:179-86.
CONSEQUENCES OF VERY
SLOW DRUG DISTRIBUTION
• “FLIP-FLOP” KINETICS
• EFFECTIVE HALF-LIFE
• PSEUDO DOSE DEPENDENCY
TOLRESTAT CUMULATION WITH
REPEATED DOSING*
*From Boxenbaum H, Battle M: J Clin Pharmacol 1995;35:763-6.
CUMULATION FACTOR
CF 
1
1 - e 
- kt
TOLRESTAT CUMULATION
OBSERVED C. F. (τ = 12 hr):
1.29
PREDICTED (T½ = 31.6 hr):
4.32
EFFECTIVE HALF- LIFE*
k
eff
t 1/2 eff
1  C Fobs 

ln
 CF 1
τ
 obs

ln 2

k
eff
* From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:763-66.
EFFECTIVE HALF-LIFE OF TOLRESTAT*
k eff
t 1/2 eff
1
 1.29 
1

ln 
  0.124 hr
12  1.29  1 
ln 2

 5.6 hr
0.124
* From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:763-66.
PSEUDO DOSE DEPENDENCY
DISTRIBUTION VOLUME OF
REPRESENTATIVE MACROMOLECULES
MW
V1
Vd(ss)
(kDa)
(mL/kg)
(mL/kg)
INULIN
5.2
55
164
FACTOR IX (FIX)
57
136
271
15.5
60
112
INTERLEUKIN-12 (IL-12)
53
52
59
GRANULOCYTE COLONY STIMULATING
FACTOR (G-CSF)
20
44
60
RECOMBINANT TISSUE PLASMINOGEN
ACTIVATOR (RT-PA)
65
59
106
MACROMOLECULE
INTERLEUKIN-2 (IL-2)
COMPARTMENTAL ANALYSIS OF
DRUG DISTRIBUTION
• PARAMETERS OF COMPARTMENTAL
MODELS
• THREE DIFFERENT DISTRIBUTION
VOLUMES
• TECHNIQUE OF CURVE PEELING
TWO-COMPARTMENT MODEL
Dose
k21
Central
V1
CLE
CLI
k12
k01
Periph.
V2
3 DISTRIBUTION VOLUMES
V
 DO S E C
V
t 1/2  C LE
d (extrap.)
0.693
 V  V  ..... V
d (area)
V
d (ss)

0
1
2
n
TECHNIQUE OF CURVE PEELING
A’
β
α