Kill Curve Analysis

Hartmut Derendorf, PhDUniversity of Florida

Drug Delivery

Pharmacokinetics

Pharmacodynamics

Biopharmaceutics

PK-PD-Modeling

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?

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

Emax - model

E = intensity of effect

Emax = maximum effect

C = concentration

EC50 = concentration at 0.5 Emax

CEC

CEE

50

max

EC50

Emax - model

Emax - model

ln EC50 - 2

Sigmoid Emax - model

E = intensity of effect

Emax = maximum effect

C = concentration

EC50 = concentration at 0.5 Emax

n = shape (slope) factor

nn50

nmax

CEC

CEE

Sigmoid Emax - model

normal plot semilogarithmic plot

Pharmacodynamics of Anti-infective Agents

•in vitro studiessteady state

dilution models

diffusion models

•animal studies

•clinical studies

NoncompartmentalPK-PD Models

•Time above MIC

•Cmax/MIC

•AUC24/MIC

•Area under the inhibitory curve (AUIC)

- based on reciprocal serum inhibitory titers

- calculated as AUC24/MIC for C>MIC

•AUC above MIC

0 6 18 2412

Con

cent

ratio

n (µ

g/m

L)

0

8

12

16

4

MIC

CmaxAUC > MIC

t > MIC

Time (hours)

•Time above MIC•Cmax/MIC•AUC24/MIC •AUIC •AUC above MIC

CeftazidimeK. pneumoniae in neutropenic mice

Craig 2002

TemafloxacinS. pneumoniae in neutropenic mice

Craig 2002

Pharmacokineticsconc. vs time

Co

nc.

Time0 250.0

0.4

PK/PDeffect vs time

Time

Eff

ect

0

1

0

Pharmacodynamicsconc. vs effect

10-3Conc. (log)

Eff

ect

Concentration-dependent vs. Time-dependent

Craig 1991

Auto-dilution system

flaskreservoir

tubingconnector

pump

waste

Kill Curves

NCEC

Ckk

dt

dN

f

f

50

max

Maximum Growth Rate Constant k

Maximum Killing Rate Constantk-kmax

PK-PD Model

Initially, bacteria are in log growth phase

PK-PD ModelIn animals

Bacterial survival fraction of P. aeruginosa in a neutropenic mouse model at different doses (mg/kg) of piperacillin (Zhi et al., 1988)

Single DosePiperacillin vs. E. coli

0 2 4 6 8 10

Time (h)

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

1014C

FU

/mL

control

2g

8g

4g

0 5 10 15 20 25102

103

104

105

107

108

109

1010

1011

CF

U/m

L

106

Time (h)

50µg/mL q24h

0 5 25102

103

104

105

106

107

108

109

1011

10 2015

CF

U/m

L

1010

100µg/mL q24h

Time (h)

0 5 10 15 20 25102

103

104

105

106

107

108

109

1011

1010

CF

U/m

L

50µg/mL q8h

Time (h)

0 5 10 15 20 25102

103

104

105

106

107

108

109

1010

1011

CF

U/m

L

100µg/mL q8h

Time (h)

0 5 10 15 20 25102

103

104

105

106

107

108

109

1010

1011

CF

U/m

L

50µg/mL q4h

Time (h)

0 5 10 15 20 25102

103

104

105

106

107

108

109

1010

1011

CF

U/m

L

100µg/mL q4h

Time (h)

Dosing IntervalPiperacillin (2g and 4g) vs. E. coli

q24h q8h q4h

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

n = 12 (means +/- S.D.) total plasma concentrations free tissue concentrations

500 mg IR

Plasma and free tissue levels

n = 12 (means +/- S.D.) total plasma concentrations free tissue concentrations

500 mg MR 750 mg MR

0 2 4 6 8

Time (hours)

102

103

104

105

106

107

108

109

CF

U/m

L

S. pneumo: 5 µg/mL

0 2 4 6 8

Time (hours)

102

103

104

105

106

107

108

109

CF

U/m

L

S. pneumo: 5 µg/mL, 2-dose

750 mg MR bid vs 500 mg IR tid

time (h)

0 6 12 18 24

Streptococcus pneumoniae

CF

U/m

l

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

500 mg MR bid vs 500 mg IR tid

time (h)

0 6 12 18 24

CF

U/m

l

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

Streptococcus pneumoniae

Conclusion

Microdialysis has opened the door to get better information about the drug concentrations at the site of action.

This, in combination with appropriate PK/PD-models, will allow for better dosing decisions than traditional approaches based on blood concentrations and MIC.

PK/PD in Drug Development

StreamliningRational Approach

Cost SavingTime Saving

Questions• What are some of the limitations of MICs?• What is the difference between AUC/MIC vs. AUIC?• Should one use total or unbound concentrations to

calculate PK/PD-indices?• Why do peak concentrations correlate with

aminoglycoside activity but not with beta-lactam activity?• Is AUC/MIC a reasonable PK/PD-index for a macrolide?