M263 Clinical PharmacologyMar 30, 2011 (E. Landaw)
Pharmacokinetics & Pharmacodynamics
Basic Concepts Issues in Pharmacokinetics (PK)
Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability
Measures Compartmental Modeling
Pharmacodynamics (PD) Steady State Models Linking of PK & PD
Some Resources Texts
M Rowland & RN Tozer Clinical Pharmacokinetics 4th ed., Lippincott Williams & Wilkins 2011
AJ Atkinson et al. (eds). Principles of Clinical Pharmacology, Academic Press, 2nd Edition 2007
Web sites www.cc.nih.gov/training/training/principle
s.html
www.boomer.org/pkin/ (links to PK/PD resources)
Journals: Clinical Pharmacology & Therapeutics
(www.ascpt.org) J. Pharmacokinetics & Pharmacodynamics
Basic - Definitions Pharmacokinetics (PK) –
quantitative analysis of the kinetics (time course) and steady state (SS) relationships of drug “What the body does to the
drug”
Absorption Distribution Metabolism Excretion
Elimination
Basic - Definitions Pharmacodynamics (PD) –
quantitative analysis of relation of drug concentration at an effect site (Ce) to drug effect (E).
“What the drug does to the body”
Understand Dose-Effect relationships
SS: Ce measured plasma concentration
Non-SS: may need to use PK to infer Ce
Dosing Regimen
dose, frequency, route
Concentrations
Plasma, urine, tissue,…Parent and metabolites
EFFECTS
Rx, Toxic
Effect Site Concentrations
source: A. Atkinson
Steady State vs. Kinetic Studies
Steady state (SS) with constant IV infusion when conc. not changing with
time plasma conc. CSS reflects Ctissue
(usually) PK (+load) determine time until
~SS
SS from Repetitive dosing (oral, IM, etc.) eventually reach constant
“Profile SS” Cmax= peak ; Cmin= trough ;
average CSS
source: Rowland & Tozer
Repetitive Dosing and “Profile SS”
Cmax
Cmin
Steady State vs. Kinetic Studies
Many PK/PD concepts are for SSClearance; Volume of distribution
SS PD effect for given SS conc.
(time to PD SS may be longer than time to plasma SS)
But some studies are kinetice.g., single oral dose or I.V. bolus
Tracer kinetic studies; PETAim may be infer SS under rep. dosing
Linear vs Nonlinear System
“Linear Pharmacokinetics” double the dose concentration
doubles AUC proportional to dose Superposition principle (example): If {I.V. bolus} Civ(t) and {oral dose}
Coral(t) , then {both dosing together} C(t) Civ(t) + Coral(t)
holds for small enough doses (microdoses)
linearity for large doses if transport, binding, and elimination remain first order
“Nonlinear Kinetics” Example
Linear vs Nonlinear System single kinetic study + linearity can
predict response to any input, including getting to SS
but for NONlinear systems: CL, V, etc. not constant; depend on
CSS, Dose requires testing at different doses;
models time to SS not predicted by single
dose study Common nonlinearities
Saturation kinetics (Michaelis-Menten)
Saturable plasma protein, tissue binding
Threshold effects (e.g., glucose spilling)
Induction; Neuro./hormonal regulation
Importance of Experiment Design
Quality & interpretation of PK/PD data depend critically on design: Dose(s), route, and form (bolus vs
infusion) What to sample
Plasma, urine, tissue, PET, … Total vs. unbound concentrations Parent compound, metabolites PD Effect measures
What times to sample in a kinetic study
Train team: record what was done, not just asked
Pharmacokinetics & Pharmacodynamics
Basic Concepts Issues in Pharmacokinetics (PK)
Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability
Measures Compartmental Modeling
Pharmacodynamics (PD) Steady State Models Linking of PK & PD
Organ Clearance Physiology: organ clearance as SS
concept
“E” = Single pass extraction fraction: E = Elim. flux/ input flux = (Carterial –
Cvenous)/Carterial
Clearance Elim. flux/Cref (vol/time)
If use Carterial as Cref , Clearance = EQ
Carterial
Organ of eliminationQ blood flow
Cvenous
Elim. Flux = Q(Carterial – Cvenous) (mass/time)
Organ Clearance Clearance Elim. flux/Cref
Elimination (metabolism, transport) often function of unbound Cu (i.e., free fraction)
Cu = fuC (but fu not routine measurement)
Clearance = EQ high E (E>0.7), CL sensitive to Q,
not fu
low E (E<0.3) Q transit time E
CL sensitive to fu, CYP induction or inhibition
but SS “exposure” = fuAUC not sensitive to fu
Renal Clearance (CLR) Net Elim. flux = filtration + secretion
– reabsorb.
Net CLR = (urine exc. rate)/(mid-collection C)
(or use 24 hour urine collection and C(t) )
Renal Filtration flux = GFR fuC
GFR CLcreat= 120 ml plasma water/minute
CLR << GFR fu significant reabsorption
CLR >> GFR fu significant secretion
Total Clearance (CLT or just
CL) SS Clearances add:
CL = CLR + CLH + nonrenal/nonhepatic clearance
Estimating CL from single dose kinetic study i.v. Dose: CL = Dose/ ∫
C(t)dt =
Dose/AUC
Oral Dose: CL = FOral Dose/AUCwhere F = fraction of dose reaching
“central pool” (plasma + tissue in rapid equilibrium with
plasma)
CLoral CL/F = Oral Dose/AUC
0
Estimating AUC Trapezoidal rule:
Fit model of data to entire C(t). e.g.,
C(t) = A1exp(-1t) +… + Anexp(-nt)
AUC = A1/1 +… + An/n
.. . . . .
C(t)
t
May need to fit single exponential at end to estimate tail area to
source: Rowland & Tozer
Using Profile SS to estimate AUC
single dose AUC (from 0 to )
Profile SS after multiple repeated doses:
use area under one cycle to estimate single dose AUC
Predicting SS Concentration
Constant flux infusion I (mass/time)
SS plasma conc. CSS = C() total CL = (total Elim. Flux)/Cref
Here Cref is CSS
Since patient at steady state, Elim. Flux = I
Therefore, CSS = I / CL
Predicting SS Concentration
For i.v infusion flux I: CSS = I / CL
For repetitive oral dose D every T units of time, at Profile Steady State:
average CSS = (FD/T) / CL .
i.e. average CSS = (D/T) / CLoral
where CLoral estimated from kinetic study by
CLoral = Oral Dose/AUC =
CL/F
Half-lives and Residence Times 1-compartment approximation for body:
Drug distributes in single, well-mixed central pool
1st order elimination rate k (time-1); volume V
k = CL/V V = Dose/C(0) t1/2 = 0.693/k (half-life of drug in
whole body) MRT = 1/k (Mean Residence
Time in body) V = total drug distribution volume =
CL MRT
V C(t) = (Dose/V)exp(-kt)
t
logC(t)
k
0
. . . .
“Is this single exponential decay?”
0
10
20
30
40
0 4 8 12 16 20 24
time after IP injection (hours)
se
rum
co
nc
en
tra
tio
n (
nM
)
“What’s the half-life of this drug?”
conc. on LOG scale suggests “No!”
0.1
1
10
100
0 4 8 12 16 20 24
time after IP injection (hours)
se
rum
co
nc
en
tra
tio
n (
nM
)
initial t1/2 0.6 hours
terminal t1/2 14 hours
Half-lives and Residence Times
multi-compartment approximation for body: Drug distributes in central + peripheral
pool(s) C(t) exhibits elimination and
distribution kinetics
2 or more “half-lives,” but terminal half-life not always the main factor for dosing, accumulation, etc.
Relative importance each half-life depends on Ai/i
V1
t
logC(t)
0
. . . .C(t) = A1exp(-1t) + A2exp(-2t)
. . .
Schentag et al. JAMA 238:327-9, 1977
source: Rowland & Tozer
Caution: Interpreting Terminal t1/2
Terminal t1/2 often related to elimination
BUT NOT ALWAYS! counterexample:
gentamicin CLcr 6 – 107 ml/min terminal t1/2 in all
90 hrs renal impairment
affects mainly first half-life
avg CSS still (D/T)/CLoral
but dosing interval T to achieve desired Cmax/Cmin trickier to compute
Mean Residence Time (MRT)
MRT = mean time molecule of drug resides in body before being irreversibly eliminated
Assumes linear system May be useful summary
measure when there are multiple half-lives
Effective (overall) half-life = 0.693MRT
Mean Residence Time Estimating MRT from kinetic
studies: Measure plasma concentration C(t)
MRT AUMC/AUC ∫
tC(t)dt /AUC
Equality if elimination is exclusively from central pool and no traps. Need to use a model if there is peripheral elimination.
Measure total amount in body A(t) (e.g., total body scan)
MRT = ∫
A(t)dt/ A(0)
0
0
Mean Residence Time 1-compartment model
MRT = 1/k = V1/CL half-life = 0.693×MRT time to reach 90% SS following
constant flux infusion is 2.3 MRT’s = 3.3 half-lives
Multi-exponential model AUMC/AUC = w1(1/1) + … + wn(1/n)
where wi (Ai/i ) and w1 + … + wn = 1
2.3 MRT’s (i.e., 3.3 effective half-lives) is time to reach at least 84% SS
Distribution Volumes
Volume of Central Pool (V1) V1 = Dose/C(0) generally need several
recirculation times before well-mixed assumption holds
V1 often a little larger than plasma, even with multiexponential decay (includes tissues in rapid equilibrium with plasma by time of first sampling)
multi-compartment approximation for body: Drug distributes in central +
peripheral pool(s) C(t) exhibits elimination and
distribution kinetics
Back-extrapolated C(0) = A1 + A2
V1 = Dose/C(0)
V1
t
logC(t)
0
. . . .C(t) = A1exp(-1t) + A2exp(-2t)
. . .
SS Distribution Volume (VSS, VD or just V)
Assume body at SS (e.g., iv infusion)
A() is total amount (mass) of drug in body
Define V = A() / CSS
Hypothetical volume SS mass would have to occupy to yield same concentration as CSS
V = CL MRT Provides insights into
distribution, permeation, tissue binding, etc.
back-extrapolated C(0) from terminal decay (i.e., Vextrap) may overestimate V
source: Rowland & Tozer
t1/2 depends on CL and V
Absorption & Bioavailability
source: A. Atkinson
Bioavailability Measures of extent and rate of
absorption from admin. site to measurement site (latter usually central pool, i.e. plasma)
i .v. administration is “gold standard” for complete and instantaneous absorption
single oral dose: “informal” measures are:
tpeak
Cpeak
Bioavailability – formal measures
“F” estimates extent of absorption Separate i.v. and oral studies F = (Doseiv/Doseoral) AUCoral/AUCiv
fraction of administered dose reaching plasma
MAT (mean absorption time) AUMCoral/AUCoral - AUMCiv/AUCiv
Absorption rate constant (compart. model)
Absorption flux time course (deconvolution)
Example: Rifampicin pretreatment reduces oral
digoxin bioavailability
Example: Physiological PKPrediction, Scale-up , (Allometry)
Cho et al. Drug Metab. Dispos. 21:125-132.1993
Example: Compartmental Modeling
Metabolism Distribution phencyclidine analogs
Pharmacokinetics & Pharmacodynamics
Basic Concepts Issues in Pharmacokinetics (PK)
Clearance Half-lives and Residence Times Distribution Volumes Absorption & Bioavailability
Measures Compartmental Modeling
Pharmacodynamics (PD) Steady State Models Linking of PK & PD
Dose-Effect Relationships
Covariates age sex body size organ
function disease other drugs genes/
markers
Drug
Dose
Effect(s)
PK
C(t)PD
source: Frank M. Balis
Dose-Effect Endpoints
Graded
Quantal
• Continuous scale (dose ® effect)
• Measured in a single biologic unit
• Relates dose to intensity of effect
• All-or-none pharmacologic effect
• Population studies
• Relates dose to frequency of effect
source: Frank M. Balis
Simplest PD Model for Graded Effect
(Effect 10 Drug-Receptor complex)
k1
k2
Drug
Receptor
Effect
Drug-Receptor Complex
Effect =Maximal effect • [Drug]
KD + [Drug]
(KD = k2/k1)
Ligand-binding domain
Effector domain
source: Frank M. Balis
0
20
40
60
80
100
0 200 400 600 800
Graded Dose-Effect Curve
% of Maximal
Effect
[Drug]EC50
Maximal effect
source: Frank M. Balis
Dose-Effect Parameters
POTENCY:
EFFICACY:
The sensitivity of an organ or tissue to the drug
The maximum effect
source: Frank M. Balis
Comparing Dose-Effect Curves
0
20
40
60
80
100
1 10 100 1000
% of Maximal
Effect
[Drug]
Drug A
Drug C
Drug B
Effect =Maximal effect • [Drug]
KD + [Drug]
source: Frank M. Balis
Pharmacodynamic Models
Fixed effect model
Linear model
Log-linear model
Emax model
Sigmoid Emax model
Effect = E0 + S•[Drug]
Effect = I + S•Log([Drug])
Effect = EC50 + [Drug]H
Emax•[Drug]H
H
source: Frank M. Balis
Sigmoid Emax PD Model
0
20
40
60
80
100
0 20 40 60 80 100
0
20
40
60
80
100
1 10 100
[Drug]
Effect (%) Effect (%)
EC50EC50
H = 0.1
H = 5
H = 2H = 1
H = 0.5
source: Frank M. Balis
Concentration and Effect vs. Time
0
2
4
6
8
10
0
20
40
60
80
100
0 5 10 15 20 25
Conc./ Amount
Effect[% of EMAX]
Time
Central Compartment
Peripheral Compartment
Effect Compartment
Effect
Non-Steady State
source: Frank M. Balis
Hysteresis and Proteresis Loops
0
1
2
3
4
0 1 2 3 40
1
2
3
4
0 1 2 3 4
Plasma Drug Concentration
Intensity of Drug Effect
Intensity of Drug EffectHysteresis Loop
(Counterclockwise)Proteresis Loop
(Clockwise)
• Equilibration delay in plasma and effect site conc.
• Formation of active metabolite
• Receptor up-regulation
• Tolerance
• Receptor tachyphylaxis
PK/PD Applications Drug discovery/development
Scaling (cell culture animal human) Feasible dosing, drug delivery Predict and quantify inter- & intra-
patient variability Regulatory issues (FDA)
Basic and Clinical Sciences Understand in vivo mechanisms Quantify PK and PD study endpoints Design of clinical studies
Dosing regimens Timing of samples Identify important covariates
PK/PD Applications Therapy
Optimal treatment strategies Individualization of therapy Clinical monitoring (PD) or predicting
(PK/PD) efficacy and toxicity endpoints
Pharmacogenetics/pharmacogenomics Hereditary variations in response (PK or
PD) Identification of genes or loci Genome-based drug discovery Predict efficacy and potential adverse
effects