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The General Concepts of Pharmacokinetics and Pharmacodynamics
Hartmut Derendorf, PhDUniversity of Florida
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PHARMACOKINETICS
what the body does to the drug
PHARMACODYNAMICS
what the drug does to the body
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Pharmacokineticsconc. vs time
Co
nc
.
Time0 25
0.0
0.4
PK/PDeffect vs time
Time
Eff
ec
t
0
1
0 25
Pharmacodynamicsconc. vs effect
0
1
10-4 10-3Conc (log)
Eff
ec
t
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Pharmacokinetics
the time course of drug and metabolite concentrations in the body
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Pharmacokinetics helps
to optimize drug therapy:
dose
dosage regimen
dosage form
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What happens to a drug after its administration ?
("Fate of drug")
Liberation
Absorption
Distribution
Metabolism
Excretion
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Clearance
Volume of distribution
Half-life
Bioavailability
Protein Binding
Pharmacokinetic Parameters
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Clearance
quantifies ELIMINATION
is the volume of body fluid cleared per time unit (L/h, mL/min)
is usually constant
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Clearance
Eliminating Organ
CL = Q·E
Q Blood Flow
E Extraction Ratio
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Clearance
Parameters: Blood Flow, intrinsic clearance, protein bindingGood prediction of changes in clearance
Steady state
Q
Ci CoEliminating
Organ
int
int
CLfQ
CLfQCL
EQCL
C
CCE
u
u
i
oi
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High-extraction drugs
Low-extraction drugs
QCL
intCLfCL u
int
int
int
CLfQ
CLfQ
CLfQCL
u
u
u
int
int
int
CLfQ
CLfQ
CLfQCL
u
u
u
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Clearance
Clearance can be calculated from
Excretion rate / Concentratione.g. (mg/h) / (mg/L) = L/h
Dose / Area under the curve (AUC)e.g. mg / (mg·h/L) = L/h
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Clearance
Total body clearance is the sum of the individual organ clearances
CL = CLren + CLhep + CLother
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Volume of Distribution
- quantifies DISTRIBUTION
- relates drug concentration (Cp) to amount of drug in the body (X)
- gives information on the amount of drug distributed into the tissues
Vd = X / Cp
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Apparent Volume of DistributionX
V
C2 = X / Vd
Vd = X / C2
X
V
C1 = X / V
V = X / C1
C1 C2
C1 > C2
V < Vd
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Volume of Distribution
Dicloxacillin 0.1 L/kgGentamicin (ECF) 0.25 L/kgAntipyrine (TBW) 0.60 L/kgCiprofloxacin 1.8 L/kgAzithromycin 31 L/kg
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Half-Life
Half-life is the time it takes for the concentration to fall to half of its previous value
Half-life is a secondary pharmacokinetic parameter and depends on clearance and volume of distribution
CL
Vdt
693.02/1
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Half-Life
k elimination rate constantCL clearanceVd volume of distribution
kkt
693.02ln2/1
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Bioavailability
f is the fraction of the administered dose that reaches the systemic circulation
- quantifies ABSORPTION
iv
po
AUC
AUCF
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BioavailabilityRate and Extent of
Absorption
Cmax
0
10
20
30
40
50
60
70C
on
ce
ntr
atio
n (
ng
/ml)
Cmax
0 2 4 6 8 10 12
Time (hours) tmaxtmax
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Protein Binding
• reversibe vs. irreversible
• linear vs. nonlinear
• rapid equilibrium
The free (unbound) concentration
of the drug at the receptor site
should be used in PK/PD
correlations to make prediction for
pharmacological activity
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vascular space extravascular space
plasma protein binding
blood cell binding,
diffusion into blood cells,
binding to intracellular biological material
tissue cell binding,
diffusion into tissue cells,
binding to intracellular biological material
binding to extracellular biological material
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Interstitium
CapillaryCell
PerfusateDialysate
Microdialysis
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Microdialysis
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Pharmacokinetic profile of cefpodoxime (400 mg oral dose, n = 6)
0
1
2
3
4
5
6
0 2 4 6 8 10
Time (h)
Co
nc
en
tra
tio
n (
mg
/L)
plasma muscle free plasma
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Pharmacokinetic profile of cefixime (400 mg oral dose, n = 6)
0
1
2
3
4
5
6
0 2 4 6 8 10
Time (h)
Co
nc
en
trato
in (
mg
/L) plasma muscle free plasma
Mean ± SD
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Pharmacokinetics
Cefpodoxime Cefixime
AUCP [mg*h/L] 22.4 (8.7) 25.7 (8.4)
AUCT [mg*h/L] 15.4 (5.2) 7.4 (2.1)
Cmax, P [mg/L] 3.9 (1.2) 3.4 (1.1)
Cmax,T [mg/L] 2.1 (1.0) 0.9 (0.3)
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Two-compartment model
Xp
E
D
k12
Dose
Xc Drug in the central compartment
Xp Drug in the peripheral compartment
Drug eliminated
Xc
k10
k21
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Two-compartment model
0 1 2 3 4 5 6 7 8
Time (hours)
10-1
100
101
102
103
C (n
g/m
l)
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Short-term infusion
T
Cmax
C
18 19 20 21 22 23 24
t (h)
100
101
102
103
Cp (µ
g/m
l)
C* Cmin
*max
min
k
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Three-compartment model
Xp
E
D
k12
D Dose
E Drug eliminated
Xck
10
k21
k31
k13
Xps
d
Xc Drug in the central compartment
Xps Drug in the shallow peripheral compartment
Xpd Drug in the deep peripheral compartment
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XC
XPs
XPd
t [h]
0 48 96 144 192 240 288 336
X [m
g]
0
100
200
300
400
500
600
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Drug Delivery
Pharmacokinetics
Pharmacodynamics
Biopharmaceutics
PK-PD-Modeling
?
?
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Questions• What are the effects of protein binding on antibiotic
activity and interpretation of plasma levels?• What are the effects of a change in protein binding on
unbound concentrations?• Why do we monitor post-distribution peaks as indicators
of aminoglycoside activity?• Why do we monitor troughs as indicators of
aminoglycoside toxicity?• How do you interpret a high tissue level of a macrolide?
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Compartment Models
Parameters: Rate constants, interceptsLinear and nonlinear regression
Complete concentration-time-profilesSteady-state and non-steady-state
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Intravenous bolus
X E
D
k
D Dose
X Drug in the body
E Drug eliminated
One compartment model
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Intravenous bolusPlasma concentration (single dose)
tkeCC 0
Vd
DC 0
D DoseC0 Initial ConcentrationVd Volume of Distribution
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Normal Plot Semilogarithmic Plot
Intravenous bolus
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Intravenous bolusPlasma concentration (multiple dose, steady state)
CC e
e
k t
k
0
1
CC
e kmax
0
1 CC e
e
k
kmin
0
1
Peak Trough
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Intravenous bolusMultiple Dose
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First-order absorption
A E
D
k
Dose
Drug at absorption site
Drug in the body
Drug eliminated
Xka
f
One compartment model
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Oral administrationPlasma concentration (single dose)
CF D k
k k Vde ea
a
k t k ta
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Oral administration
t [h]
0 2 4 6 8 10 12
Cp
[ng/
mL]
0
100
200
300
400
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Oral administration
Average concentration (multiple dose, steady state)
CF D
CL
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Oral administrationMultiple Dose
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One compartment model
A E
D
k
Dose
Drug at absorption site
Drug in the body
Drug eliminated
XR0
f
Zero-order absorption
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Constant rate infusionPlasma concentration (during infusion)
CR
CLe k t 0 1
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Constant rate infusion
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Constant rate infusionPlasma concentration (steady state)
CR
CL 0
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Two-compartment modelPlasma concentration (single i.v. bolus dose)
C a e b et t
-phase: distribution phase
-phase: elimination phase
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t [h]
0 1 2 3 4 5 6 7 8
Cp
[g/
mL]
0.1
1
10
100
Two-compartment model
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Two-compartment model
Xp
Xc
Xp
Xc
Xp
Xc
initially steady state elimination phase
VD
Cc 0
Vdk
kVss c
1 12
21
VdCL
area
Volume of distribution
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Significance of Pharmacokinetic Parameters for Dosing
CLCDF
CLCR
desired
desired
0
VdCLD desired
)min(
)max(
desired
desired
C
CPTR
693.0
)ln( 2/1tPTR
Maintenance Dose
Loading Dose
Fluctuation
Dosing Interval