Modelling the inactivation of Bacillus
subtilis spores by ethylene oxide processing
Gisela Cristina Mendes
Teresa Ribeiro da Silva Brandão
Cristina Luisa Miranda Silva
CBQF - Centro de Biotecnologia e Química Fina
Escola Superior de Biotecnologia
Universidade Católica Portuguesa,
Rua Dr. António Bernardino de Almeida
4200-072 Porto, Portugal
This study was supported by Bastos Viegas, S.A.
ETHYLENE OXIDE IS CURRENTLY A
DOMINANT STERILIZATION AGENT USED
IN MEDICAL DEVICES INDUSTRY
EO sterilization consumption for
medical devices
0
20
40
60
80
100
70
's
80
's
90
's
No
wa
da
ys
Decade
%
Advantages / Disadvantages
Advantages
Effectiveness Diffusivity
Bactericidal, fungicidal and virucidal properties
Compatibility with most materials
Process flexibility
Low temperature sterilization
Disadvantages
Toxicity of the sterilizing agent
Process complexity
Process cost
Processing time
Advantages / Disadvantages
Objectives
Understanding the full dynamics of the sterilization allows
design optimization / efficient control of the process -
Parametric release
Screen the most significant
variables on B. subtilis
inactivation by EO sterilization
Model the inactivation kinetics
of B. subtilis, including
the variables’ effects
Provide a method of
integrating lethality
Modelling microorganisms inactivation
Experimental design
Bacillus subtilis, var. niger or Bacillus atrophaeus spores (ATCC
9372) inoculated in strips (biological indicators, BIs)
Matrix: Drapes
Temperature and humidity sensors
EO sensor (
Infrared analyser in the sterilizer chamber headspace
)
Sterilization cycles
Modelling microorganisms inactivation
- Conditions defined according to the 2
3
factorial design -
Sterilization cycles
- Target exposure conditions –
40 and 60 ºC 50 and 90 %RH
250 and 1000
mg(EO)/L
Modelling microorganisms inactivation
Survival curves construction
1
st
order kinetics
Gompertz model
Gompertz function has the ability of modelling
both linear and asymmetrical sigmoidal data
(
)
+
−
λ
−
−
⋅
=
1
t
A
e
k
exp
exp
A
N
N
log
max
0
0
N
log
t.
k
N
log
+
−
=
Inactivation of B. subtilis spores by EO sterilization
- Conditions defined according to the 2
3
factorial design -
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500
2000
2500
3000
U (s)
lo
g
(
N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
1000
2000 3000 4000 5000 6000 7000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
2000
4000
6000
8000
10000 12000 14000
U (s)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500 2000 2500 3000 3500
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500
2000
2500
3000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
1000
2000
3000
4000
5000
6000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
300
600
900
1200
1500
1800
U (s)
lo
g
(N
/N
0
)
Legend
⁰ Experimental data
___ Fitted Gompertz model
___
Predicted data
- - - Upper and lower limits of predicted data (considering the
maximum fluctuations of temperature and EO concentration)
T=60 °C; EO=233 mg/L;
RH=63 %
T=44 °C; EO=257 mg/L;
RH=86 %
T=34 °C; EO=222 mg/L;
RH=60 %
T=40 °C; EO=980 mg/L;
RH=90 %
T=59 °C; EO=266 mg/L;
RH=85 %
T=33 °C; EO=940 mg/L;
RH=61 %
T=59 °C; EO=1004 mg/L;
RH=98 %
Data analysis
The
non-linear regression analysis
was carried in
Statistica© 6.0 software (StatSoft, USA), using the Levenberg-
Marquardt algorithm to minimize the sum of the squares of the
differences between the predicted and experimental values.
Data analysis
The experimental inactivation data were successfully fitted with
the Gompertz model:
- High precision of k
max
and
λ
estimates, since low errors were
attained (SHW
95%
);
- Residuals randomness and normality;
- Coefficient of determination (R
2
>0.98);
Data analysis and planning future work
The analysis of variance (ANOVA) allowed to identify the most
significant parameters affecting B. subtilis inactivation -
temperature and EO concentration
Additional experiments considering intermediate conditions of
these parameters were defined in order to model their effects
and combined effects on the lethality (runs 9 to 15)
Inactivation of B. subtilis spores by EO sterilization at
the additional experimental conditions
-7
-6
-5
-4
-3
-2
-1
0
0
1000
2000
3000
4000
U (s)
lo
g
(
N
/N
0
)
Legend
⁰ Experimental data
___ Fitted Gompertz model
Run 9 to Run 15
Estimated k
max
and l parameters of B. subtilis inactivation at the
temperature, EO concentration and relative humidity conditions tested
EO concentration influence on k
max
and
λ
k
max
= 3.22x10
-6
[EO] + 2.74x10
-4
k
max
= 4.25x10
-6
[EO] + 2.18x10-3
k
max
= 4.46x10
-6
[EO] + 3.53x10
-3
0
1
2
3
4
5
6
7
8
0
500
1000
1500
[EO] (mg/L)
k
m
a
x
x
1
0
3
(s
-1
)
37.0 ºC
50.5 ºC
60.0 ºC
λ
= -88.076ln[EO] + 853.05
λ
= -229.66ln[EO] + 1733.7
λ
= -446.4ln[EO] + 3570.8
0
200
400
600
800
1000
1200
0
200
400
600
800
1000
1200
[EO] (mg/L)
λ
(s
)
38.0 ºC
50.5 ºC
60.0 ºC
Influence of EO concentration on k
max
at
37.0
,
50.5
e
60.0
°C
Influence of EO concentration on
λ
at
38.0
,
50.5
and
60.0
°C
T influence on parameters
a
k
/
b
k
and
a
λ
/
b
λ
a
k
= 1.42x10
-4
T - 4.96x10
-3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0
10
20
30
40
50
60
70
T (ºC)
a
k
x
1
0
3
(
s
-1
)
b
k
= 5.54x10
-8
T + 1.25x10
-6
3.0
3.5
4.0
4.5
5.0
0
10
20
30
40
50
60
70
T (ºC)
b
k
x
1
0
6
(
L
m
g
-1
s
-1
)
a
λ
= 16.34T - 1063.61
-500
-400
-300
-200
-100
0
0
20
40
60
80
T (ºC)
a
λ
(
s
)
b
λ
= -124.74T + 8227.00
0
500
1000
1500
2000
2500
3000
3500
4000
0
20
40
60
80
T (ºC)
b
λ
(
s)
Influence of T on
a
k
e
b
k
parameters
Influence of T on
a
k
e
b
k
parameters
Data analysis
T and EO concentration have a negative effect on
λ
and a
positive effect on k
max
:
- Higher temperatures and EO concentration imply narrow
shoulder times and higher inactivation rates;
- Lower inactivation rates and more evident shoulder phases
were observed at the lowest temperature and EO
concentration;
Mathematical model resulting from the integration
of the T and EO concentration parameters for
lethality calculation of the EO sterilization process
[ ]
×
−
×
+
−
×
+
−
×
−
−
×
−
−
−
=
7.5
-
e
EO
6
10
1.25
T
8
10
5.54
3
10
4.96
T
4
10
1.42
exp
7.5)exp
(
0
N
N
log
[ ]
+
−
×
+
×
−
+
×
−
×
×
1
U
3
10
8.23
T
2
10
1.25
)
EO
ln(
3
10
1.06
T
1
10
1.63
Inactivation of B. subtilis spores by EO sterilization
- Conditions defined according to the 2
3
factorial design -
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500
2000
2500
3000
U (s)
lo
g
(
N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
1000
2000 3000 4000 5000 6000 7000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
2000
4000
6000
8000
10000 12000 14000
U (s)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500 2000 2500 3000 3500
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
500
1000
1500
2000
2500
3000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
1000
2000
3000
4000
5000
6000
U (s)
lo
g
(N
/N
0
)
-8
-7
-6
-5
-4
-3
-2
-1
0
0
300
600
900
1200
1500
1800
U (s)
lo
g
(N
/N
0
)
Legend
⁰ Experimental data
___ Fitted Gompertz model
___
Predicted data
- - - Upper and lower limits of predicted data (considering the
maximum fluctuations of temperature and EO concentration)
T=60 °C; EO=233 mg/L;
RH=63 %
T=44 °C; EO=257 mg/L;
RH=86 %
T=34 °C; EO=222 mg/L;
RH=60 %
T=40 °C; EO=980 mg/L;
RH=90 %
T=59 °C; EO=266 mg/L;
RH=85 %
T=33 °C; EO=940 mg/L;
RH=61 %
T=59 °C; EO=1004 mg/L;
RH=98 %
In conclusion
[ ]
×
−
×
+
−
×
+
−
×
−
−
×
−
−
−
=
7.5
-
e
EO
6
10
1.25
T
8
10
5.54
3
10
4.96
T
4
10
1.42
exp
7.5)exp
(
0
N
N
log
A mathematical inactivation model expressed only in terms of the
relevant process variables (T and EO concentration) was
achieved.
The conventional design of EO sterilization cycles usually involves
a significant amount of experimental work, which is time
consuming and also expensive. The results of this work are
certainly a contribution for an efficient control, design and
optimization of the EO sterilization process.
[ ]
+
−
×
+
×
−
+
×
−
×
×
1
U
3
10
8.23
T
2
10
1.25
)
EO
ln(
3
10
1.06
T
1
10
1.63
Thanks’
