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Student Objectives for This - Boomer.org · Chapter 23 Pharmacodynamic Models and...
Transcript of Student Objectives for This - Boomer.org · Chapter 23 Pharmacodynamic Models and...
Chapter 23
Pharmacodynamic Models and Physiologically‐Based Pharmacokinetic Models
Spring 2012
PHAR 7633 Basic Pharmacokinetics
Student Objectives for This Chapter
• To understand the development and use of physiologically based pharmacokinetic (PBPK) models
• To understand the different types of concentration ‐effect relationships
• To understand the mathematical relationships involved with direct reversible pharmacological effect kinetics
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Goals of Modeling
• Codify current facts
• Testing competing hypotheses
• Predicting system response under new conditions
• Estimating inaccessible system variables
F. Eugene Yates (1973) 3
Pharmacokinetics (PK)
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Important are:F = BioavailabilityCL = ClearanceV = Volume of Distribution
IV
PO
Cp
t
Description of the time course and factors affecting the handling of drugs by the body.
Specific models are needed to make predictions of kinetic behavior of drugs at any dosages
• Compartmental Models (e.g., 1 CM, 2 CM) • Physiologic Models (e.g., PBPK)
Physiologically Based Pharmacokinetic Models (PBPK)
5Physiologically‐Based PK Model
PBPK model segregates the body into separate compartments representing organs interconnected by the blood circulation.
PBPK Model Requirements:• Experimental data
• Physiological Parameters(Tissue size, blood flow)
• Model construction
• Program for numerical solution of differential equations
QL
QHR
QM
QBM
QH
QG
QK
QO
IV
PO
Model of Simple Tissue Distribution
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Assumptions: Rapid equilibrium between tissue & venous blood
)C(CQdt
dAvTaT
T
AT = Amount in tissueQT = Tissue blood flowCa = Conc. arterial bloodCvT = Conc. tissue venous bloodKP = Tissue/plasma partition coefficient
Initial uptake (amount/time) = QT x Ca
CaCvT
VT
Capillary
QTQT
ArteryVein
CvT
CT
Tissue
vTPT CKC KP
Fick’s Law of Perfusion
)K
C(CQ
dt
dA
P
TaT
T
Drug Distribution within Tissue – Permeability Issues
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Capillary
Tissue cells
Artery
FiltrationReabsorption
Vein
Interstitial fluidOsmosis
Fick’s Law of Diffusion
)C(CPSdt
dA21
T
AT = Amount in tissue
PS = Permeability/Surfacearea constant
C1, C2 = Concentration
Initial uptake (amount/time) = PSxC1
Size, nature, permeability, binding and transporters can determine tissue uptake
Tissue Subcompartments
CaCv
Interstitial
Intracellular
Capillary
PS
PBPK Model Example: Thiopental
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Figure 23.3.4 Some Results for Thiopental Bischoff and Dedrick 1968(http://www.boomer.org/c/p4/c23/c2303.html )
PBPK Models: Pros vs. Cons
Advantages:– The prediction of plasma (blood) and tissue PK of drug candidates prior to in vivo experiments
– Support a better mechanistic understanding of PK properties from tissue kinetic data predicted, facilitating a more rational design during clinical candidate selection.
– Extrapolation across species, routes of administration, duration and timing of drug input and dose levels.
Limitations:– Considerable experimental and computational effort– Difficulty in obtaining realistic parameters
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Pharmacodynamics (PD)
Description of the time ‐course and factors controllingdrug effects on the body.
Important are:
Emax
EC50
keo, kin ,
= Capacity constant
= Sensitivity constant
= Various time constantsfor specific models
kin kin kin
S(t)C(t)
S(t-TP) S(t-TP-TR)
P R
Serum rHuEP
OConc., IU/L
Reticulocytes, %
10000
1000
100
100 5 10 15
765432
10 5 10 15 20
Time, day
SCDoses
EPO stimulatesproduction of RBC.10
Basic Tenets of Pharmacodynamics
Capacity-Limitation Turnover and HomeostasisE
ffec
t, %
Concentration
γγ50
γmax
CEC
CEE
Hill Function
The Law of Mass Action( D + R DR ) and smallquantity of targets leads to capacity-limitations in most responses.
Production LossBiologicalFactor
(R)
Rkkdt
dRlossproduction
Both diseases and therapeuticagents often interfere with thehomeostasis in the body resulting from the natural turnover of biological substances or functions.
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Biological Turnover Rates of Structures or Functions
Electrical Signals (msec)
Chemical Signals (min)
Mediators, Electrolytes (min)
Hormones (hr)
mRNA (hr)
Proteins / Enzymes (hr)
Cells (days)
Tissues (mo)
Organs (year)
Person ( .8 century)
Fast
Slow
BIOMARKERS
CLINICALEFFECTS
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Components of PK/PD Models
Jusko et al., JPB 23: 5, 1995
Review article:Mager DE, Wyska E, Jusko, WJ, Diversity of Mechanism‐Based Pharmacodynamic Models, Drug Met. Disp. 31: 510 (2003).
R
ResponseDisposition
KineticsBiophase
DistributionBiosensor
ProcessBiosignal
FluxTrans-
duction
Pharmacokinetics Pharmacodynamics
Drug
keoCP Ce
Biosignal
kin
kout
H
H
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Types of Drug Effects
Reversible• Direct
- Rapid- Slow
• Indirect- Synthesis, secretion- Cell trafficking- Enzyme induction
Irreversible• Chemotherapy• Enzyme inactivation
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Direct Reversible Effects
Clark’s Occupancy Theory: A. J. Clark (1933) proposed the first model to account for the quantitative behavior of a receptor-mediated process.
R + L RL Effectkon
koff
R = Receptor, L = Ligand, RTOT = Total ReceptorKD = Equilibrium Dissociation Constant (KD = kon/koff) 15
LK
LRRL
D
TOT
L
RLor
Effect
The “Law of Mass Action”
Hill Function:Emax = CapacityEC50 = Sensitivity
Hill AV , The possible effect of the aggregation of molecules of haemoglobinon its dissociation curve, J. Physiol. (London) 40: iv (1910).
= Hill Factorγγ
50
γmax
CEC
CEE
100
80
60
40
20
00 20 40 60 80
Eff
ect,
% 0.5
1
Concentration
= 2
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Properties of Hill Function
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γγ
γmax
CEC
CEE
50
When C << EC50
E = S · CS = Emax / EC50
When C = EC50
E = ½Emax
When C >> EC50
E = EmaxC
Eff
ect
Emax
EC50
Emax/2
LINEAR MODEL
CSEE 0
Relationship between change in QTc intervals and N - acetylprocainamide plasmaconcentrations in several patients. From Piergies et al, CPT 42: 107 (1987).
50max /ECES
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Red
ucti
on in
Pre
mat
ure
Ven
tric
ular
Con
trac
tion
Fre
quen
cy (
%)
Tocainide plasma concentration (g/ml)
Slopes of E vs. log C Plots are Often Linear
Intercept =
γ2
ECln 50
Slope = m =4
γEmax
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Simple Direct Effect: Inhibition of Cyclooxygenase Enzyme Activity in Blood by Dexamethasone
Zamacona et al, 2001
TIME, hr
0 8 16 24 32
COX A
CTIVITY (% of Baselin
e)
0
20
40
60
80
100
120
DEX
AMETHASO
NE CONC, n
M
0.1
1
10
100
DEXAMETHASONE CONC, nM
0
20
40
60
80
100
120
0 0.1 1 10 100 1000
IC50 = 1.42 nM
CIC
CIEE
50
max0 1
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PK/PD Expectations For Simple Direct Effects
tk0 eCC
CEC
CEE
50
max
Effect
Concentration
Time, hr
Profiles based on k = 0.4, Emax = 100, EC50 = 100. 21
PK PD
0
20
40
60
80
100
0.1 1 10 100 1000 10000
PK/PD Expectations For Simple Direct Effects, con’t
Effect
Concentration
Time, hr
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CEC
CEE
50
max
0
20
40
60
80
100
0.1 1 10 100 1000 10000
Time, hr
Effect
Concentration
PK PD
“No hysteresis”
Kinetics of Pharmacologic EffectsGerhard Levy, Clin. Pharmacol. Ther. 7:362 (1966)
tmkoEE logC
t
PK
2.3
k-
log C
E
Pharmacology
m
t
Eo
PD
mk
E
NB: Half‐life applies in PK but not PD!
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Slope = m =4
γEmax
Decline of Effect: Derivation
eAlogmE
meE
Alog
Kinetics:
2.3kt
AlogAlog
Combine:
2.3kt
meE
meE
t2.3km
EE
k = elimination constant
A = Amount of drug
m = Slope
e = Intercept
E° = Peak effect
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Pharmacodynamic Models Producing Delayed Responses
• Direct Effect: Active Metabolite
• Direct Effect: Biophase Distribution
• Direct Effect: Slow Receptor kon/koff
• Antibody‐Ligand Interaction
• Indirect Response: Inhibition of kin
• Indirect Response: Stimulation of kout
• Indirect Response: Inactivation
• Indirect Response: Cell Life‐Span Loss
• Irreversible Effect: Regeneration
• Transduction Process
PK
log C
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TimeResponse
Time
PDResponse
Conc.
“Counter clockwise Hysteresis”
Modeling a Biophase
Furchgott R (1955)Segre, Il Pharmaco (1968)Sheiner et. al., CPT (1979)
Pancuronium PK/PD – Muscle Relaxation
eC50ECeCmaxE
E
eCpCeokdt
edC
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Paralysis by Mechan
ical
Twitch Response, %
Pancuronium CP or CE (g/ml)
CPCe
keo = 0.1
0.3
0.5
2.0
keo = 0.1
2.0
EFFECT
CONCEN
TRATION
Role of keo in Determining Simple Drug Effects
PK/PD Model:CP Ce
keo
kele50
emax
CEC
CEE
TIME
Simulations of Plasma Drug Concentrations (Cp, dashed line) for monoexponential kinetics(Co = 1000, kel = 0.4), Effect Site Concentrations (Ce, solid lines) for the indicated values of keo, and Effect profiles for the Emax model with Emax = 100 and EC50 = 100.
TIME
0.3
Basic Indirect Response Models
(Dayneka et al., JPB 21: 457 1993).
Response(Mediator)
(R)
Production Removal
kin kout
Drugs can alter the production (kin) or dissipation (kout) process normally controlling endogenous levels of R. Drugs can inhibit ( ) or stimulate ( ) any of these processes.
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Irreversible Drug Effects: Antibiotics on Cell Killing
(Jusko, JPS 60: 892 1971)(Zhi et al, JPB 16: 1988)
RCkRkdtdR
s
Cell Growth
ks
k • C
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PK PD
Effects of Various Intraperitoneal Doses of Piperacillin on Killing and Growth Kinetics of Pseudomonas Aeruginosa in Neutropenic Mice
Cell Killing
Factors Affecting PK/PD: Covariates
Physiological
AGE: Young/Old
Sex
Pregnancy
Race
Genetics
Stress
Disease
Hepatic
Renal
Thyroid
Cystic Fibrosis
Obesity
Drug Interactions
Inhibitors
Inducers
Joint Mechanisms
Opposing Mechanisms
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Pharmacokinetics and Pharmacodynamics of d ‐ Tubocurarine in Infants, Children, and Adults
Fisher DM et al, Anesthesiology 57: 203 (1982).
Time (min)
ml∙min
‐1∙m
‐2
dTC Clearance (Cl)
0.6
0.3
0.0
EC50 g/ml
Neonates Infants Children Adults
Neonates Infants Children Adults
Infants show both reducedclearance (related to GFR)and greater sensitivity to dTC.
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Influence of extreme obesity on the body disposition and neuromuscular blocking effect of atracurium
Varin F, et al, CPT 48: 18 (1990).
ATR
ACURIUM, n
g/m
l, PLA
SMA
TIME (min)
NEU
ROMUSCULA
R BLO
CKADE (%
)
ATRACURIUM EFFECT COMPARTMENT CONCENTRATION (ng/ml)
PK Parameters:
Vss, L/kgTBW CL, ml/min/kgTBW
Normal 0.141 6.6Obese 0.067 3.5
PD Parameters: (Emax = 100)
t½keo, min EC50, ng/ml
8.3 3127.4 470 32
PK/PD and Pharmacogenetics
Albuterol Concentration (ng/m
l)
% Chan
ge in
FEV
1Time (h) Time (h)
The 2 ‐ adrenergic receptor gene polymorphism was assessedby PCR and found to be a major determinant of bronchodilatorresponse to albuterol. J.J. Lima et al, CPT 65: 519 (1999).
S(t)
2 phenotypes
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Pharmacodynamic Caveats
Measurements should be sensitive, gradual, reproducible, objective, and meaningful.
Studies should include baseline and span 2 or 3 dose levels with effects from 0 to Emax.
Measure major intermediary steps.
Models should recognize mechanism(s) of drug action.
Covariates are important!
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Modeling Dynamic Effects
PHARMACOKINETICS
BIOPHASE
MECHANISM
MODEL TYPE
TURNOVER
TRANSDUCTION
ADAPTATION
PATHOPHYSIOLOGY
DISEASE PROGRESSION
COMPLEXITIES
Requires Integration of Diverse Components35