GSK-Taiwan PK-PD workshop: Pharmacodynamics

Asian PK/PD Educational Workshop
The general concept of
pharmacodynamics
• modeling the antibacterial
effects
• relations PK / PD
This part uses material from presentations of H. Derendorf (Gainesville, Fla.)
made at the 2001 and 2001 ISAP Educational Workshops
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-1

What is pharmacodynamics
What the drug does to the body ...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-2

Pharmacokinetics
Pharmacodynamics
Concentration at
the site of
infection
Therapeutic
effects
Dosage
Serum concentration
varying
over time
Concentration in
non-target
tissues
Toxic
effects
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-3

Pharmacokinetics - Pharmacodynamics
0.4
Pharmacokinetics
conc. vs time
Pharmacodynamics
conc. vs effect
Conc.
Effect
0.0
0 25
Time
Conc. (log)
10-3
Effect
1
PK/PD
effect vs time
0
0
Time
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-4

Pharmacoynamics : what is the end-point
Effect
Pharmacodynamics
conc. vs effect
Conc. (log)
10-3
1. therapeutical result
• clinical ...
• laboratory ...
2. Biomarker
Drug- or disease-induced
measurable physiological,
pathophysiological or
biochemical change
3. Surrogate end-point
Biomarker that has predictive
value for therapeutic outcome
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-5

Pharmacodynamics : which are the models
The yes / no model
effect
concentration
• sharp threshold
• maximal effect immediately
observed
This is the model assumed by
• the sensitivity breakpoints
approach !!
• the cured / non-cured clinical
endpoint !!
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-6

Pharmacodynamics : which are the models
The linear model
effect
concentration
• continuouly increasing
effect
• effect matches dosing
This is the model assumed by
the "higher dosing in severe
infections" approach
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-7

Pharmacodynamics : which are the models
effect
The yes / no and the linear
models are almost never
observed in true phamacological
responses !!
concentration
Drugs (includig antibiotics) act
indeed by binding to their
targets,
effect
and this binding is saturable ...
concentration
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-8

The E-max model ...
• Drug concentration
increases at low initial
values seem more effective
than at large initial values
• There is a maximal effect
corresponding to maximal
receptor / target site
occupancy
EC 50
This is the classical model
used for non-antiinfective
drugs...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-9

The conventional E-max model is inadequate…
It ignores
• the threshold in effect seen
when passing across the MIC
• the fact that antibiotics may be
• bacteriostatic, or
• bactericidal
• the influence of time ...
EC 50
But, this model is useful to obtain a first description
of dose-response effects … if appropriate corrections
are introduced
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-10

Mathematical representations of the E-max model
ln EC 50 - 2
EC 50
Arithmetic abcissa
Logarithmic abcissa
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-11

Why a logarithmic abcissa ...
E max
MaximaI
intensity of
the response
E 50%
ln EC 50 - 2
E
E
EC
max
n
50
C
C
n
n
Logarithmic abcissa
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-12

The E-max model may be used to incorporate
the yes/no and the linear models within limits...
steep
The "shape factor"
describes the steepness
of the response ...
pseudolinear
E
E
EC
max
n
50
C
C
n
n
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-13

First points to consider in pharmacodynamic
modeling of antibiotic response
• Emax
• steepness
• point of initial
response
This is a description at a FIXED time only ...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-14

What means E-max (at a given time point)
absolute antibactrerial effect
(killing in arbitrary units)
Highly bactericidal
• fluoroquinolones
• aminoglycosides
Poorly bactericidal
• vancomycin
• macrolides
• tetracyclines
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-15

What does steepnes mean
relative antibacterial effect
(% of maximal)
Highly concentrationdependent
AB (as from MIC)
• fluoroquinolones
• aminoglycosides
• oritavancin
Poorly concentrationdependent
AB
once above threshold (=MIC)
• -lactams
• vancomycin
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-16

Pharmacodynamics : influence of time ...
All antibiotics are dependent on time...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-17

Pharmacodynamics : influence of time ...
But time is relatively unimportant for
highly concentration-dependent drugs
A 3 log reduction will be achieved in 4h, 2h or less
depending on concentration...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-18

Pharmacodynamics : influence of time ...
Whereas time becomes the CRITICAL
parameter for antibiotics with low
concentration dependency
1 log
2 logs
3 logs
You always need more than 8h to achive a 3 logs kill
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-19

Time-dependent antibiotics with shott half-lifes
are ineffective if not administered frequently
CFU/mL
10 14
10 13
10 12
10 11
10 10
10 9
10 8
10 7
10 6
10 5
10 4
10 3
10 2
10 1
10 0
0 2 4 6 8 10
Time (h)
control
2g
4g
8g
Piperacillin
modeling as
one single
injection
Limits of time during which
the AB concentr. remains
effective for the dose
considered (2 g, 4 g, 8 g)
...
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-20

Low doses of poorly-concentration dependent
antibiotics require frequent administration
Piperacillin modeled for a Cmax of 50 mg/L
CFU/mL
10 11
10 10
50µg/mL q24h
10 9
10 8
10 7
10 6
10 5
10 4
10 3
10 2
0 5 10 15 20 25
Time (h)
CFU/mL
10 11
10 10
50µg/mL q8h
10 9
10 8
10 7
10 6
10 5
10 4
10 3
10 2
0 5 10 15 20 25
Time (h)
CFU/mL
10 11
10 10
50µg/mL q4h
10 9
10 8
10 7
10 6
10 5
10 4
10 3
10 2
0 5 10 15 20 25
Time (h)
once-a-day q 8h q 4h
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-21

This where we are now ...
PK
PD
Therapeutic
effects
Dosing
• C max
• AUC
• half-life
• E max
• concentration
• time
Toxic
effects
GSK Asian PK/PD workshop -- Taipei, Taiwan, January 10th, | 5 - pharmacodynamics : general concepts
1-22