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The General Concepts of
Pharmacokinetics and
Pharmacodynamics
Prof. Hartmut Derendorf
University of Florida
PHARMACOKINETICS
what the body does to the drug
PHARMACODYNAMICS
what the drug does to the body
Pharmacokinetics
Pharmacodynamics
conc. vs time
0.4
conc. vs effect
Conc.
Effect
1
0.0
Time
0
25
10-4
PK/PD
effect vs time
1
Effect
0
0
0
Time
25
Conc (log)
10-3
Pharmacokinetics
the time course of drug and metabolite
concentrations in the body
Pharmacokinetics helps
to optimize drug therapy:
dose
dosage regimen
dosage form
What happens to a drug after its administration ?
("Fate of drug")
Liberation
Absorption
Distribution
Metabolism
Excretion
Pharmacokinetic Parameters
Clearance
Volume of distribution
Half-life
Bioavailability
Protein Binding
Clearance
quantifies ELIMINATION
is the volume of body fluid cleared per time
unit (L/h, mL/min)
is usually constant
Clearance
Eliminating
Organ
CL = Q·E
Q Blood Flow
E
Extraction Ratio
Clearance
Q
Ci
Eliminating
Organ
Co
Ci Co
E
Ci
CL Q E
Q f u CLint
CL
Q f u CLint
Parameters: Blood Flow, intrinsic clearance, protein binding
Good prediction of changes in clearance
Steady state
High-extraction drugs
Q fu CLint
CL
Q fu CLint
CL Q
Q fu CLint
Low-extraction drugs
Q fu CLint
CL
Q fu CLint
Q fu CLint
CL fu CLint
Clearance
Clearance can be calculated from
Excretion rate / Concentration
e.g. (mg/h) / (mg/L) = L/h
Dose / Area under the curve (AUC)
e.g. mg / (mg·h/L) = L/h
Clearance
Total body clearance is the sum of
the individual organ clearances
CL = CLren + CLhep + CLother
Volume of Distribution
Vd = X / Cp
- 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
Apparent Volume of Distribution
X
X
V
V
C1
C2
C1 > C2
C1 = X / V
V = X / C1
V < Vd
C2 = X / Vd
Vd = X / C2
Volume of Distribution
Dicloxacillin
Gentamicin (ECF)
Antipyrine (TBW)
Ciprofloxacin
Tigecycline
Azithromycin
0.1 L/kg
0.25 L/kg
0.60 L/kg
1.8 L/kg
8 L/kg
31 L/kg
Half-Life
t1/ 2
0.693 Vd
CL
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
Half-Life
t1/ 2
ln 2 0.693
k
k
CL k Vd
k
CL
Vd
elimination rate constant
clearance
volume of distribution
Bioavailability
F
AUCpo
AUCiv
- quantifies ABSORPTION
f is the fraction of the administered dose
that reaches the systemic circulation
Bioavailability
Rate and Extent of Absorption
70
Cmax
Concentration (ng/ml)
60
Cmax
50
40
30
20
10
0
0
2
tmax tmax
4
6
Time (hours)
8
10
12
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
vascular space
plasma
protein
binding
extravascular space
binding to
extracellular
biological
material
blood cell
binding,
tissue cell
binding,
diffusion into
blood cells,
diffusion into
tissue cells,
binding to
intracellular
biological
material
binding to
intracellular
biological
material
Microdialysis
Perfusate
Dialysate
Interstitium
Capillary
Cell
Microdialysis
Pharmacokinetic profile of cefpodoxime
(400 mg oral dose, n = 6)
plasm a
Concentration (mg/L)
6
m uscle
free plasm a
5
4
3
2
1
0
0
2
4
6
Time (h)
8
10
Pharmacokinetic profile of cefixime
(400 mg oral dose, n = 6)
Concentratoin (mg/L)
6
plasma
muscle
free plasma
Mean ± SD
5
4
3
2
1
0
0
2
4
6
Time (h)
8
10
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)
Two-compartment model
D
k 10
Xc
k 12
E
k 21
Xp
Dose
Xc Drug in the central compartment
Xp Drug in the peripheral compartment
Drug eliminated
Two-compartment model
103
C (ng/ml)
102
101
100
10-1
0
1
2
3
4
Time (hours)
5
6
7
8
Short-term infusion
Cp*max
Cp [µg/ml]
10
Cpmax
Cp*min
1
Cpmin
0.1
0
2
4
t [h]
6
8
Three-compartment model
d
Xp
k 31
k 13
D
Xc
k 12
k 10
E
k 21
s
Xp
D Dose
E Drug eliminated
Xc Drug in the central compartment
Xps Drug in the shallow peripheral compartment
Xpd Drug in the deep peripheral compartment
Three-compartment model
-phase:
distribution phase
-phase:
rapid elimination phase
-phase:
slow elimination phase
C ae
t
be
t
ce
t
600
XPd
500
X [mg]
400
XPs
300
200
XC
100
0
0
48
96
144
192
t [h]
240
288
336
Drug Delivery
?
Biopharmaceutics
Pharmacokinetics
?
PK-PD-Modeling
Pharmacodynamics
Biomarker vs. Surrogate Endpoint
Biomarker
Drug- or disease-induced measurable
physiological, pathophysiological or biochemical
change
Surrogate Endpoint
Biomarker that has predictive value for
therapeutic outcome
Sigmoid Emax - model
Emax C
E
n
n
EC50 C
n
E = intensity of effect
Emax = maximum effect
C = concentration
EC50 = concentration at 0.5 Emax
n = shape (slope) factor, Hill factor
Sigmoid Emax - model
normal plot
semilogarithmic plot
Pharmacodynamics of
Anti-infective Agents
•in vitro studies
steady state
dilution models
diffusion models
•animal studies
•clinical studies
Time above MIC
12
8
Cmax/MIC
16
Concentration (µg/mL)
Concentration (µg/mL)
16
MIC
4
0
Cmax
12
8
MIC
4
0
0
12
6
18
Time (hours)
24
0
6
12
24
18
Time (hours)
t > MIC
AUC24/MIC
Concentration (µg/mL)
16
12
8
PK
PD
Serum
MIC
MIC
4
0
0
6
12
24
18
Time (hours)
Kill Curves of Ceftriaxone
S. pneumoniae ATCC6303
MIC: 20 ng/mL
H. influenzae ATCC10211
MIC: 5 ng/mL
Kill Curves of Ceftriaxone
S. pneumoniae ATCC6303
MIC: 20 ng/mL
H. influenzae ATCC10211
MIC: 5 ng/mL
Pharmacodynamics
Pharmacokinetics
conc. vs effect
conc. vs time
Effect
Conc.
0.4
0
Time
25
Conc. (log)
PK/PD
effect vs time
Effect
0.0
1
0
0
Time
10-3
Concentration-dependent vs.
Time-dependent
Craig 1991
Kill Curves
flask
reservoir
tubing
connector
pump
waste
Auto-dilution system
PK-PD Model
k max C f
dN
k
dt
EC50 C f
N
Maximum Growth Rate Constant
k
Maximum Killing Rate Constant
k-kmax
Initially, bacteria are in log growth phase
PK-PD Model
In animals
Bacterial survival fraction of P. aeruginosa in a neutropenic mouse model at
different doses (mg/kg) of piperacillin (Zhi et al., 1988)
Single Dose
Piperacillin vs. E. coli
1014
control
1013
1012
1011
CFU/mL
1010
2g
109
108
4g
107
8g
106
105
104
103
102
101
100
0
2
4
6
Time (h)
8
10
Dosing Interval
Piperacillin (2g and 4g) vs. E. coli
q24h
q8h
50µg/mL q8h
0
5
10
15
20
25
0
5
Time (h)
10
15
Time (h)
15
20
25
0
5
20
25
CFU/mL
5
10
15
Time (h)
15
20
25
20
25
100µg/mL q4h
1011
1010
109
108
107
106
105
104
103
102
0
10
Time (h)
100µg/mL q8h
CFU/mL
CFU/mL
100µg/mL q24h
5
10
1011
1010
109
108
107
106
105
104
103
102
Time (h)
1011
1010
109
108
107
106
105
104
103
102
0
50µg/mL q4h
1011
1010
109
108
107
106
105
104
103
102
CFU/mL
1011
1010
109
108
107
106
105
104
103
102
CFU/mL
CFU/mL
50µg/mL q24h
q4h
20
25
1011
1010
109
108
107
106
105
104
103
102
0
5
10
15
Time (h)
FDA Draft-Guidance for Industry (1997)
Providing Clinical Evidence of Effectiveness for Human Drug and Biological Products
New Dosage Form of a Previously Studied Drug
In some cases, modified release dosage forms may be
approved on the basis of pharmacokinetic data linking
the new dosage form from a previously studied
immediate-release dosage form. Because the
pharmacokinetic patterns of controlled-release and
immediate release dosage forms are not identical, it is
generally important to have some understanding of the
relationship of blood concentration to response to
extrapolate to the new dosage form.
Plasma and free tissue levels
500mg
mg
500
IR IR
- Means
15
Cefaclor (m cg/m l)
12
9
6
3
0
0
1
2
3
4
Time (hours)
n = 12 (means +/- S.D.)
total plasma concentrations
free tissue concentrations
5
6
Plasma and free tissue levels
500 mg MR
750 mg MR
750 mg AF - Means
12
9
9
Ce fa clo r ( m cg /m l)
Cefaclor (mcg/ml)
500 mg AF - Means
12
6
3
0
6
3
0
0
1
2
3
4
5
6
0
Time ( hour s )
n = 12 (means +/- S.D.)
total plasma concentrations
free tissue concentrations
1
2
3
Time (hours )
4
5
6
750 mg MR bid vs 500 mg IR tid
Streptococcus pneumoniae
1013
1012
1011
1010
CFU/ml
109
108
107
106
105
104
103
102
101
0
6
12
time (h)
18
24
Summary
• A simple comparison of serum concentration and MIC is
usually not sufficient to evaluate the PK/PDrelationships af anti-infective agents.
• Protein binding and tissue distribution are important
pharmacokinetic parameters that need to be
considered. Microdialysis can provide information on
local exposure.
• PK-PD analysis based on MIC alone can be misleading.
• Microbiological kill curves provide more detailed
information about the PK/PD-relationships than simple
MIC values.
Conclusions
• PK/PD can help to streamline rational
clinical dose selection
• The final dose needs to be confirmed in
a clinical trial
PK/PD in Drug Development
Streamlining
Rational Approach
Cost Saving
Time Saving