eccmid 2003 aminoglycosiden bij neonaten canisius-wilhelmina hospital nijmegen, the netherlands...
TRANSCRIPT
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