eccmid 2003

Aminoglycosiden bij neonaten

Canisius-Wilhelmina HospitalNijmegen, The Netherlands

Johan W Mouton

Relationship between bacterial killing, MIC and antibacterial

effect

eccmid 2003

• Killing by Beta-lactams are time-dependent. It is often assumed that concentrations need to be above the MIC, and if concentrations decline below the MIC regrowth occurs. There is no PAE. Is this true? And Why?

0 4 81

10

100

1000

ticarcfu

3

4

5

6

7

8

9

time (h)

con

c m

g/L lo

g cfu

eccmid 2003

• Aminoglycosides have a PAE in vivo: bacteria do not regrow immediately when concentrations decline below the MIC. Why?

0 4 8 12 16 20 240.1

1

10

100

3

4

5

6

7

8

9

concentrationtobramycin

cfu observed

fig. 5

time h

con

cen

trat

ion

m

g/L

10log cfu

In vivo time kill curve

eccmid 2003

Patterns of activity: Kill curves of P. aeruginosa

ceftazidime tobramycin

eccmid 2003Figure 5

tobramycin

-2 -1 0 1 2 3-2

3

8

13

18

10log (conc tobramycin) mg/lki

llrat

e h

-1

meropenem

-3 -2 -1 0 1 2-2

-1

0

1

2

3

4

5

10log (conc meropenem) mg/l

killr

ate

h-1

1a 1b

3.59 h-1 13.4 h-1

SteepShallow

eccmid 2003

•Antibiotics showing increasing effect (killing) over a wide range of concentrations are called ‘concentration dependent’. In vivo effects are usually AUC and/or Peak related.

•Those with a limited range of increasing effect are called (wrongly) ‘concentration-independent’. In vivo effects are usually Time >MIC related.

eccmid 2003

Pk/Pd models

50

.maxECC

CEE

Emax model

eccmid 2003

Effect of Hill coefficient

0.01 0.10 1.00 10.00 100.000.0

0.5

1.0

Concentration

Effe

ct

EC50

Emax

=10=1

50.max

ECCCEE

eccmid 2003Figure 9

tobramycin

-2 -1 0 1 2 3-2

3

8

13

18

10log (conc tobramycin) mg/lki

llrat

e h

-1

meropenem

-3 -2 -1 0 1 2-2

-1

0

1

2

3

4

5

10log (conc meropenem) mg/l

killr

ate

h-1

1a 1b

3.59 h-1 13.4 h-1

SteepShallow

high : steep slope

'concentration independent'

low: shallow slope

'concentration dependent'

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2log(Cmeropenem) mg/l

killr

ate

log(

CF

U/m

l))/

h growthcorrected

measured

Since results from killing curves are growth + kill the killing rate has to be corrected for growth

eccmid 2003

P.aeruginosa cfu over timesimulation

0 4 8 12 16 20 240.1

1.0

10.0

100.0 conc tob

cfu

3

4

5

6

7

8

9

time (h)

co

nc m

g/L log

cfu

eccmid 2003

Effect Modelling

The number of bacteria at a certain point of time is the result of the initial inoculum + growth + kill

Function of bacterial growth over timeFunction of bacterial kill over time

eccmid 2003

NNN

dtdN )1(

max

Function of bacterial growth

Function of bacterial growth with Nmax

NdtdN

0 4 8 12 16 20 240

1

2

3

time (h)

lo

g d

cfu

Growth rate

eccmid 2003

Function of Bacterial Kill

NECC

CdtdN

50

Function of bacterial kill over time

eccmid 2003

(1)

N}EC+C

C-)N

N-(1{=

dt

dN

50

max

Growth Kill

Mouton et al 1997

Growth rate Max kill rate

eccmid 2003

(2)

N}EC+C

C-{=dtdN

50

0 4 8 12 16 20 240

1

2

3

time (h)

lo

g d

cfu

eccmid 2003

• We are not so much interested in number of bacteria / the change of bacteria over time as a function of concentration

• We ARE interested in the CONCENTRATIONS at which certain events occur (static effects, max effects etc)

• The equations therefore have to be rewritten with C as the ‘dependent’ variable

Effects vs concentration :chickens and eggs

eccmid 2003

(4) t}EC+C

C-{=NtN50

exp)0(/)( ln (5)

EC+C

C-tNtN50

/)0(/)(

)0(exp)( Nt}EC+C

C-{=tN50

eccmid 2003

500)(1

0)(1

1

ln

lnECC

NtN

t

NtN

t

Static concentrations :N(t)=N(0)

eccmid 2003

Static Concentration (SC)= (7)

50.

1

ECSC

The static concentration

If concentrations are higher, bacteria are killed. If concentrations are lower, they grow

eccmid 2003

• The MIC is read after 18h incubation

• And thus is a result of growth and killing over time rather than a parameter for a specific moment in time (such as the SC is)

• The big question :

Now, what about the MIC ??

eccmid 2003

MIC = SC ??

eccmid 2003

(8)

50.29.0

29.01

ECMIC

500)(1

0)(1

1

ln

lnECC

NtN

t

NtN

t

N(0) is beginning inoculum = 5. 105

t = 18hN(t) = 0 - 108

eccmid 2003

50.

1

ECSC

50.29.0

29.01

ECMIC

=

eccmid 2003

• Thus, bacteria do NOT regrow when concentrations decline below the MIC but DO when below the SC

• What is the quantitative relationship between MIC and SC?

• Growthrate in vitro vs growth in vivo

• Max kill rate equal

• Hill slope equal

• Time t 18h vs 0 h

eccmid 2003Figure 26

Conc independent

Conc dependenttobramycin

meropenem

the MIC and SC : effect of highand low Hill coefficients

0 2 4 6 8 100.01

0.1

1

10

mic =3.5sc =3.5

mic =0.71sc =0.71

maximum kill rate ( h-1 )

con

cen

trat

ion

mg

/l(M

IC o

r S

C)

eccmid 2003Figure 27

MIC / SC ratio for 8 values ofthe Hill coefficient

2 4 6 8 10-1

0

1

2

3

4

5

6

7

8

90.250.50.75124816

maximum kill rate ( h-1 )

MIC

/ S

Cv

ivo

eccmid 2003

• If is high, the MIC more or less equals the SC

• Decreasing results is an increase of the MIC/SC ratio

Relationship MIC and SC

eccmid 2003

• For concentration independent drugs the MIC ~ SC. This explains why regrowth occurs when concentrations decline below the MIC

• For most concentration dependent drugs, the MIC = SC. The SC is lower. This may, in part, explain the PAE of some drugs and the relation with AUC rather than T>MIC

Conclusions