Pk/Pd modelling :Clinical Implications

JW MoutonDept Medical Microbiology

Canisius Wilhelmina Hospital

Nijmegen, The Netherlands

infections are treated with the same

dosing regimen irrespective of the absolute

susceptibility of the micro-organism

Susceptible

=

SusceptibleMIC = .016 mg/L

MIC = 2.0 mg/L

Pharmacokineticsconc. vs time

Con

c.

Time0 25

0.0

0.4

PK/PDeffect vs time

Time

Eff

ect

0

1

0 25

Pharmacodynamicsconc. vs effect

0

1

10-4 10-3Conc (log)

Eff

ect

Immunesystem Severity Infection

Forrest, 1993

Predictors of Clinical Response

AUIC =125 : a magical number??

• PK models : 125

• Animal studies granulocytopenic : 100

• Animal studies immunocompetent : 40

• Human studies: peak/MIC ratio: > 1:10, AUC/MIC

•There is a clear relation between pharmacodynamic index and effect.

•At some concentration there is a maximum effect

•Ideally, a dose should be chosen to obtain a maximum effect

Example Target Controlled DosingIxacin

• Patient 60 yr, pneumonia and suspected bacteraemia/sepsis

• Ixacin 400 mg IV q8h

• Gram negative rod, E-test MIC=0.01 mg/L

• Adjust dose to 100 mg/day

Mouton & Vinks, PW 134:816

Use of Pharmacodynamics in setting breakpoints

• Known concentration effect relationship– microbiology– clinical effect

• Standard dose used clinically– pharmacokinetic profile– patient/disease specifics

Breakpoints based on AUC/MIC =100

•Three studies have shown AUC/MIC predictive for outcome

•One prospective study Peak/MIC more predictive

Quinolones : dose optimalization

To peak or not to Peak?

•For most quinolones, because of the relatively long half-life, there is a strong correlation between AUC/MIC and Peak/MIC

Pharmacodynamics of fluoroquinolones against Pseudomonas infection in neutropenic rats

Drusano et.al., AAC, 1993, 37: 483-90.

• Survival linked to Peak/MIC when

ratio > 10/1

• Survival linked to AUC/MIC when

ratio < 10/1

! ! !

• Proteinbinding in animals/humans

• Duration of treatment

• Extended dosing interval

• Immune system

• Severity of infection

• Bacteriological vs Clinical cure

T>MIC: how long??breakpoints

• Free fractions of the drug (Fu)?• The same for all micro-organisms?• The same for all beta-lactams?• Efficacy vs emergence of resistance• The same for all infections?• Value in combination therapy?• Variance pk in population?• Static dose vs maximum effect?

• If maximum effect, which max effect?

Same all beta-lactams?Same all m.o.?

Drug Enterobacteriaceae S. pneumoniae

Ceftriaxone (F) 38 (34-42) 39 (37-41)

Cefotaxime 38 (36-40) 38 (36-40)

Ceftazidime 36 (27-42) 39 (35-42)

Cefpirome 35 (29-40) 37 (33-39)

MK-0826 32 (20-39)

Meropenem 22 (18-28)

Imipenem 24 (17-28)

Linezolid 40 (33-59)

T> MIC for static effect

Predicted efficacy of ticarcillin and tobramycinpseudomonas

-6 -5 -4 -3 -2 -1 0 1 2 3 4-6

-4

-2

0

2

4

predicted : t > 0.25 * mic ticarcillin and log auc tobramycin

Slope

Y-intercept

X-intercept

1/slope

0.9285 ± 0.07826

-2.815 ± 0.1250

3.032

1.077

r² 0.7830

dcfu predicted

dcfu

measu

red

Mouton ea., aac 1999

Concentration-time profile of beta-lactamVd = 20 L, Ka = 1.2 h-1, Ke = 0.3 h-1

0.20

1.20

2.20

3.20

4.20

5.20

6.20

7.20

8.20

9.20

10.20

11.20

12.20

13.20

14.20

15.20

16.20

17.20

18.20

19.20

0.00

1.25

2.50

3.75

5.00

6.25

7.50

8.75

10.0

0

11.2

5

12.5

0

13.7

5

15.0

0

16.2

5

17.5

0

18.7

5

20.0

0

21.2

5

22.5

0

23.7

5

0.95-1.00

0.90-0.95

0.85-0.90

0.80-0.85

0.75-0.80

0.70-0.75

0.65-0.70

0.60-0.65

0.55-0.60

0.50-0.55

0.45-0.50

0.40-0.45

0.35-0.40

0.30-0.35

0.25-0.30

0.20-0.25

0.15-0.20

0.10-0.15

0.05-0.10

0.00-0.05

Conc

Time

Prob

Monte Carlo Simulation of beta-lactamVd = 20 L, Ka = 1.2 h-1, Ke = 0.3 h-1, VC=20%

4h

10h

Mouton, Int J Antimicrob Agents april 2002

Monte Carlo Simulations in pk/pd (1)

• Estimates of pk parameter values and a measures of dispersion (usually SD)

• Simulate pk curves based here-on

Target Attainment Rates

• Pharmacokinetics of piperacillin– Population pk using npem2– ‘validation’using classical pk analysis (winnonlin)

• Use parameter estimates for Monte Carlo Simulation– Using sd’s only– Using correlation matrix

• Obtain TARS at various T>MICs

0 25 50 75 1000

20

40

60

80

100

LoHi

Average

T>MIC %

PR

OB

Monte Carlo Simulations in pk/pd (2)

• Estimates of pk parameter values and a measures of dispersion (usually SD)

• Obtain covariance matrix or correlation matrix

• Simulate pk curves based here-on :• The result will be SMALLER 95% CI because of

correlation between parameter estimates

0 25 50 75 1000

20

40

60

80

100

LoHi

Average

T>MIC %

PR

OB

* 1

00

Needed for TAR

• Pharmacokinetic profile of the drug

• Variation of PK parameters– Estimates of VC

– Population analysis, correlation matrix

Cumulative Fraction of Response

• TAR at each MIC• Distribution of MICs• Multiply, determine fraction and cum fraction

• Beware !!!!! For prediction, a ‘true’ MIC distribution is needed, NOT a biased collection of strains!!!!!

0.0625 0.125 0.25 0.5 1 2 40.0

0.1

0.2

0.3

0.4

MIC mg/L

frac

tio

n

After Drusano et al

Pharmacodynamic properties of beta-lactams

• Efficacy dependent on time above mic

• Relatively concentration independent

Target for concentration profiles optimizing time > mic

Avoid high peak concentrations

Target Concentrationcontinuous infusion

• Maximum effect time-kill at 4 x MIC• Maximum effect in vitro model 4 x MIC

(Mouton et al 1994)• Effect in endocarditis model 4 x MIC

(Xiong et al 1994)• Effect in pneumonia model dependent on

severity of infection (Roosendaal et al 1985,86)

Efficacy in Relation to MICcontinuous infusion ceftazidime, K. pneumoniae rat pneumonia

Roosendaal et al. 1986, AAC 30:403; Roosendaal et al. 1985, JID 152:373

Continuous InfusionPharmacokinetic Considerations

• Protein binding

• Linear relationship between clearance and dose

• Linear relationship between protein binding and dose

• Third compartment effects (CNS)

Dose Calculationscontinuous infusion

• Total Clearance estimate

• Volume of Distribution

• Elimination rate constant

TBC = Ke x Vd

Normogram Continuous Infusion

0 20 40 60 80 100 120 140 160 180 2000

1000

2000

3000

4000

5000

6000

64

32

16

8

4

clearance mL/min

do

se m

g/d

ay

Mouton & Vinks, JAC 1996

Example Target Controlled Dosingcefticostix

• Patient 60 yr, UTI and suspected bacteraemia/sepsis

• Cefticostix 1 g IV q8h• Gram negative rod, E-test MIC=0.12 mg/L• Adjust dose to 30 mg/day CI based on

patient clearance

Mouton & Vinks, PW 134:816

Example Cost EfficiencyContinuous Infusion Beta-lactam

Therapeutic Drug Monitoringcontinuous infusion

• Clearance estimate

• Variable clearance (ICU)

• Non-linear clearance

Ceftazidime concentrationsICU patients

Piperacillin concentrationscontinuous vs intermittent