Models of microbial inactivation: aplication in foods

(1)

Teresa Brandão

Cristina Silva

7

th

_{December 2007}

Predictive Microbiology

A tool to support food safety decisions

UNIVERSIDADE CATÓLICA PORTUGUESA

Escola Superior de Biotecnologia

Models of microbial inactivation

-- aplication in foods

aplication in foods

(2)

Mathematical modelling

some concepts ...

observation

= mathematical function (

_y

_{= f (}

variables

_x

_,

_q

_{) + e}

+

parameters

) + experimental error

Parameters estimation

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1000 2000 3000 4000 5000

x

y

q

*

Precise

?

Accurate

?

y

_model

y

_exp

minimization of the residuals

between

experimental

values

and the ones predicted by the

model

(3)

precise

and

accurate

description of data

model adequacy

quality of the parameters

objective

Mathematical modelling

(4)



fundamental description of the processes involved



more complex



black boxe



more simple (or not!)



practical application

advantages and disadvantages should be considered

decision depending on the final goal

mechanistic models

empirical models

Mathematical modelling

(5)

mathematical

complexity

model adequacy

model

parameters

quality

Mathematical modelling

(6)

knowledge of the process

process effect in the product

control of the variables involved

advantages

Mathematical modelling

(7)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

(8)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

design

Criteria

(9)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

design

Criteria

validation

(10)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

design

Criteria

validation

control

(11)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

design

Criteria

validation

control

optimization

Objectives

(12)

Processes

Chemical

Physical

Food Processes

Transport Phenomena

• heat

• mass

• momentum

Reaction kinetics

Properties

Modelling

Mathematical function

variables

parameters

data

Regression schemes

experimental design

Mathematical modelling

design

Criteria

validation

control

optimization

Objectives

quality

safety

(13)

safety

Mathematical modelling

(14)

predictive

microbiology

Mathematical modelling

(15)

mathematics

microbiology

statistics

predictive

microbiology

Mathematical modelling

(16)

prediction / simulation

development of efficient

inactivation processes

contribution to

safety

aplication

Predictive microbiology

(17)

Sigmoidal behaviour

Reflects the presence of microbial sub-populations

more

temperature

resistent

(or other environmental

stressing factor

)

inactivation

0

1

2

3

4

5

6

7

8

9

0

500 1000

1500

2000

tempo (s)

lo

g

N

Predictive microbiology

time (s)

(18)

0

1

2

3

4

5

6

7

8

0

20

40

60

80

100

120

140

0

1

2

3

4

5

6

7

8

0

20

40

60

80

100

120

140 Example

Miller (2004)

52.5 ºC

Listeria innocua

liquid medium

55 ºC

57.5 ºC

60 ºC

62.5 ºC

65 ºC

log N

time (min)

(19)

0

1

2

3

4

5

6

7

8

0

20

40

60

80

100

120

140 Example

52.5 ºC

55 ºC

57.5 ºC

60 ºC

62.5 ºC

65 ºC

log N

time (min)

Miller (2004)

Listeria innocua

liquid medium

(20)



primary

0

1

2

3

4

5

6

7

8

0

0.5

1

1.5

2

2.5

Te mpo (min) L o g C F U /g

kinetics

parameters

time (s)

Mathematical models

(21)



primary



secundary

0

1

2

3

4

5

6

7

8

0

0.5

1

1.5

2

2.5 parameters

pH

_a

_w

temperature

time (s)

Mathematical models

(22)



primary



secundary



tertiary -

all models integration

-

software

0

1

2

3

4

5

6

7

8

0

0.5

1

1.5

2

2.5 parameters

pH

_a

_w

temperature

time (s)

Mathematical models

(23)



primary

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000

logN

_k

logN

0

logN

res

L

Tempo (s)

empirical

_fundamental

Models for inactivation

(24)



primary

1 st

_order



kt



exp

N



₀



D

t

N

log

logN



₀



D – decimal reduction time

0 1 2 3 4 5 6 7 8 0 2 4 6 8 Tim e (m in) L o g C F U /g

Models for inactivation

(25)



primary



kt



exp

N



₀



D

t

N

log

logN



₀





k

t

 

1 F



exp



k

t



exp

F

N

2

1

0 









Cerf

(1977)

Kamau et al.

(1990)















_

















t

k

exp

1 F

1

2 t

k

exp

1 F

2 log

N

log

2

1

0 F

₁

– fraction of inactivated microorganisms

k

₁

e k

₂

– kinetic constants

biphasic

0 1 2 3 4 5 6 7 8 0 2 4 6 8 Tim e (m in) L o g C F U /g 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 Time (min) L o g C F U /m l

Models for inactivation

1 st

_order

(26)



primary

0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 Tim e (m in) L o g C F U /g



































_































L

t

k

exp

1 L

k

exp

1 F

1 L

t

k

exp

1 L

k

exp

1 F

log

N

log

2

1

0 Whiting & Buchanan

(1992)

L – lag or shoulder

Models for inactivation

(27)



primary

Cole et al.

(1993)





_





















σ

w

t

log

λ

σ

4 exp

1 α

w

α

N

log

0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 Tim e (m in) L o g C F U /g



































_































L

t

k

exp

1 L

k

exp

1 F

1 L

t

k

exp

1 L

k

exp

1 F

log

N

log

2

1

0 Whiting & Buchanan

(1992)

Distribution of

microbial population

heat sensitiveness

Models for inactivation

(28)



primary

Baranyi et al.

(1993)

   



t

0 

N

₀

N

t

k

dt

dN











function ‘lag’

function ‘tail’

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) lo g N

Models for inactivation

(29)



primary

Baranyi et al.

(1993)

   



t

0 

N

₀

N

t

k

dt

dN











function ‘lag’

function ‘tail’

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) lo g N









 

0 exp



k

t



Q

1

0 Q

1 t

k

exp

log

N

log

max

0 





















Geeraerd et al.

(2000)

 

Q

k

dt

dQ

N

Q

k

dt

dN

max

Q

max









Q – variable related to the physiological state of microorganisms

Models for inactivation

(30)



primary

Gompertz

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) lo g N

Bhaduri et al (1991)

Linton et al. (1995, 1996)

Xiong et al. (1999)































































L

t

1 N

N

log

e

k

exp

N

log

logN

0 res

0 Reparameterization for inactivation based on Zwitering et al. (1990)

Listeria monocytogenes

Models for inactivation

(31)



primary

Gompertz

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) lo g N

Bhaduri et al (1991)

Linton et al. (1995, 1996)

Xiong et al. (1999)

Logistic

Listeria monocytogenes







k

t

-

L



exp

1 c

logN





c – constant

Models for inactivation

Reparameterization for inactivation based on Zwitering et al. (1990)































































L

t

1 N

N

log

e

k

exp

N

log

logN

0 res

0

(32)

 Gompertz

0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) lo g N

Models for inactivation































































L

t

1 N

N

log

e

k

exp

N

log

logN

0 res

0 or





























































L

t

1 N

N

log

e

k

exp

N

log

N

log

0 res

0

(33)

Examples

Gompertz

Data of

Data of L.monocytogenes

L.monocytogenes Scott A at 52,56,60,64,68ºC

Scott A at 52,56,60,64,68ºC

(24 hours incubation at 5ºC in half cream)

0

1

2

3

4

5

6

7

8

9

0 1000

2000

3000

4000

5000

6000

7000

time (s)

lo

g

N

T=52 ºC

T=56 ºC

T=60 ºC

Gil (2002)

Casadei et al. (1998)

Statistica 6.0

(34)

Gompertz

Data of

Data of L.monocytogenes

L.monocytogenes Scott A at 52,56,60,64,68ºC

Scott A at 52,56,60,64,68ºC

(24 hours incubation at 5ºC in half cream)

0

1

2

3

4

5

6

7

8

9

0

50

100

150

200

250 time (s)

lo

g

N

T=64 ºC

T=68 ºC

T=60 ºC

Gil (2002)

Casadei et al. (1998)

Statistica 6.0

Examples

(35)

Gompertz

Data of

Data of L.innocua

L.innocua at 52.5 and 60ºC

at 52.5 and 60ºC

Parsley (

Parsley (Petroselinum crispum

Petroselinum crispum)) artificially contaminated

artificially contaminated

Miller (2006)

Statistica 6.0

logN

0 N

N

log

Examples

52.5ºC -7 -6 -5 -4 -3 -2 -1 0 0 25 50 75 100 125 150 175 200 tim e (m in) log (N /N0 ) 60ºC -7 -6 -5 -4 -3 -2 -1 0 0 2 4 6 8 10 12 14 16 tim e (m in) lo g( N /N0 ) T52.5ºC 0 1 2 3 4 5 6 7 8 9 0 50 100 150 200 250 tim e (m in) lo g N T60ºC 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 12 14 16 18

time (min)

lo

g

N

T = 52.5 ºC

T = 60 ºC

(36)



primary



secundary

Mathematical models

0

1

2

3

4

5

6

7

8

0

0.5

1

1.5

2

2.5 parameters

pH

_a

_w

temperature

time (s)

(37)



secundary

Arrhenius

Davey /

Arrhenius modified

“Square-root type models”

Ratkowsky et al.

(1982)

McMeekin et al.

(1987)

Adams et al.

(1991)

McMeekin et al. (1992)

)

T

b(T

k





_min

)

a

(a

)

T

b(T

k





_min

_w



_w

_min

)

pH

(pH

)

T

b(T

k





_min



_min















RT

E

-exp

k

₀

a

lnk



lnk

₀



_RT

E

a

2 W

4 W

3

2

1

0 C

a

C

a

T

C

T

C

lnk





)

pH

(pH

)

a

(a

)

T

b(T

k





_min

_w



_w

_min



_min

min – minimal value for growth





























ref

a

ref

exp

-

E

_R

_T

1 _T

1 k

k

Mathematical models

(38)

Examples

Gompertz

**k=0.0216 exp(-203.3/R*(1/T-1/333.15))**

Logistic

**k=0.0337 exp(-206.6/R*(1/T-1/333.15))**

Data of

Data of L.monocytogenes

L.monocytogenes Scott A

Scott A

(24 hours incubation at 5ºC in half cream)

0,00

0,05

0,10

0,15

0,20

0,25

320

325

330

335

340

345 Temperature (K)

k

(

1 /s

)

D

Ea=28.85 kJ/mol

D

Ea=27.56 kJ/mol

D

K

ref

=4.58x10

-3

s

-1

D

K

ref

=7.31x10

-3

s

-1

Arrhenius

k = f(T)

Gil (2002)

_{Statistica 6.0}

(39)

Examples

0

500 1000

1500

2000

2500

3000

320

325

330

335

340

345 Temperature (K)

L

(

s

)

Data of

Data of L.monocytogenes

L.monocytogenes Scott A

Scott A

(24 hours incubation at 5ºC in half cream)

L=116.3exp(344.1/R*(1/T-1/333.15))

R

2

_=0.9998

lag = f(T)

D

Ea=7.485 kJ/mol

D

L

ref

=7.595 s

-1

Gompertz

Gil (2002)

_{Statistica 6.0}

(40)

Examples

0 1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

320

325

330

335

340

345 Temperature (K)

l

(s

)

l

= 194.5exp(429.7/R*(1/T-1/333.15))

R

2

_=1.000

Data of

Data of L.monocytogenes

L.monocytogenes Scott A

Scott A

(24 hours incubation at 5ºC in half cream)

D

Ea=3.591 kJ/mol

D

l

_ref

=6.154 s

-1

lag = f(T)

Logistic

Gil (2002)

_{Statistica 6.0}

(41)

Mathematical models

More complexity !!

time-varying conditions

pH

_a

_w

temperature





)

tempo

(

d

N

log

d

(42)

Gompertz





)

tempo

(

d

N

log

d







L

t'



1 dt

'

N

log

exp(1)

k

exp

1 t'

L

N

log

exp(1)

k

exp(1)exp

k

logN

t

0

0 res

0 

























































































time-varying temperature conditions





























ref

a

ref

exp

-

E

_R

_T

1 _T

1 k

k





























ref

T

1 T

1 b

exp

a

L

Mathematical models

(43)

Gompertz

time-varying temperature conditions

Mathematical models

-7,0 -6,0 -5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 0 5 10 15 20 25 30 35 40 45 Tim e (m in) L o g ( N /N 0 ) 0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 T e m pe ra tu re ( ºC ) Palcam Agar

Parsley (

Parsley (Petroselinum crispum

Petroselinum crispum)

) artificially contaminated with

artificially contaminated with L. innocua

L. innocua

Miller (2006)

(44)

Gompertz

time-varying temperature conditions

Mathematical models

-6,0

-5,0

-4,0

-3,0

-2,0

-1,0

0,0

1,0

0

2

4

6

8 Tim e (m in)

L

o

g

(

N

/N

0 )

-20,0

0,0

20,0

40,0

60,0

80,0

100,0

T

e

m

p

e

ra

tu

re

(

ºC

)

Meat pockets artificially contaminated with

Meat pockets artificially contaminated with L. innocua

L. innocua

frying process

Miller (2006)

-20,0 0,0 20,0 40,0 60,0 80,0 100,0 0 10 20 30 40 50 60 70 Time (min) T e m p e ra tu re ( ºC )

(45)



tertiary

Models for inactivation

softwares

Microbial growth

Shelf life prediction

Microbial inactivation



(46)

Drawbacks

• microbial interaction

• natural strains diversity

• complexity of food structure

• food/microorganism

• modelling ‘lag’

• modelling ‘tail’

• predictions in real time-varying environmental conditions

(47)

BUGDEATH

Participation of our research team in the project ...

Surface

pasteurization of

foods

www.frperc.bris.ac.uk/bugdeath.htm

Predictive

microbiology

2001-2004

(48)

(49)

Partners

Bugdeath

1. Food Refrigeration and Process Engineering Research Center (FRPERC)

University of Bristol

2. Escola Superior de Biotecnologia (ESB)

Universidade Católica Portuguesa

3. Department of Chemical Engineering

Katholieke Universiteit Leuven (KUL)

4. Teagask, The National Food Center (NFC)

5. Campden & Chorleywood Food Research Association (CCFRA)

6. Faculty of Applied Science

University of West England (UWE)

7. Laboratoire de Ginie des Procidis Alimentares (ENITIA)

Ecole Nationale d’Inginieurs des Techniques des Industries Agricoles et Alimentaires

(50)

Objectives

• microbial inactivation studies at food surfaces

• development of precise and accurate inactivation models

• development of an equipment for surface food pasteurization

‘rig apparatus’

• software development for prediction

Bugdeath

(51)

Foods under study

potato

chicken

meat

Bugdeath

microorganisms

Listeria monocytogenes

E. coli

Salmonella

Campylobacter

(52)

rig apparatus

(53)

Bugdeath

Thermal processes

• steam

• dry air

H e a ting up a nd c ooling d own of sa mple s a t 5 5 C

Exp 1 , 2 a nd 3

-10 0 10 20 30 40 50 60 0 0.005 0.01 0.015 0.02 0.025 0.03 T i m e ( h ) Sample 1 Sample 2 # REF!

Rapid process

Temperature histories

Different

temperature

histories

can

be tested

rig apparatus

(54)

Dissemination session

Chipping Campden,

Agosto 2004

Escola Superior de Biotecnologia, Universidade Católica Portuguesa

Development of a user-friendly

combined heat, mass transfer and

microbial death model

Team

Pedro Pereira

Maria Manuel Gil

Teresa Brandão

Cristina Silva

(55)

‘Bugdeath’ - funded by the European Commission under the EC Framework 5; Quality of Life and Management of Living Resources Programme

Objectives

• Create a software application

User-friendly tool

Simulation of inactivation kinetics of

microorganisms on the surface of

foods

during pasteurisation treatments

(56)

Introduction

• Need to obtain reliable data on relationship

between microbial death and the surface

temperature of real foods

Lead to the design,

construction and

commission of equipment

Software application to

simulate results obtained in the

rig apparatus

(57)

Modelling

Microbial inactivation under

constant and time-varying

temperature conditions

Integrates

Heat transfer

phenomena

Prediction/simulation

purposes

Global model

(58)

Modelling

Two modelling approaches

• Accurate modelling of heat transfer

-

Description of the phenomena induced to the food surface

by a thermal process

• Modelling microbial inactivation behaviour under

such temperature conditions

(59)

Heat transfer model

Two modelling approaches

• One dimensional heat transfer model

• Combination of different phenomena

–

Conduction

–

Convection

–

Evaporation/condensation of water or steam

–

Radiation (not considered)

(60)

Heat transfer model

• Simplified model

Conduction/convection - Fourier

Geometry – plane sheet

No mass transfer phenomena considered

• Limits

Air velocity ranged from 15 m/s to 25 m/s

Extrapolation locked outside of conditions that can be

verified in the test rig

(61)

Heat transfer model

2

2 x

)

t

,

x

(

T

t

)

t

,

x

(

T











air

or

steam

sur



eff

top

T

h

x

T























sup

inf



inf

bot

T

h

x

T





















Crank-Nicholson method

t – time

T – temperature

h – heat transfer coefficient

α – thermal diffusivity

λ – Thermal conductivity

x

1

2

3

(62)

Boundary conditions - bottom

Exchanges between the bottom of the product and the

support can be neglected – product thickness < 0.5 cm

(63)

Heat transfer model

2

2 x

)

t

,

x

(

T

t

)

t

,

x

(

T











air

or

steam

sur



eff

top

T

h

x

T























sup

inf



inf

bot

T

h

x

T





















Crank-Nicholson method

t – time

T – temperature

h – heat transfer coefficient

α – thermal diffusivity

λ – Thermal conductivity

x

1

2

3

(64)

Effective coefficient – dry conditions

sur

max

T

w

T

m

sur

max

sur

air

eff

T

P

a

P

H

K

T

h

sur











convection

evaporation

k

_m

– mass transfer coefficient

(65)

Effective coefficient – wet conditions (steam)

h

_eff

T

_sur

= T

_steam

– 3ºC

Due to complexity of mathematical

expressions to be incorporated in

the software

(66)

Microbial inactivation model

• To predict microbial content at the surface of

foods

• It has the advantage of dealing with

time-varying temperature conditions

(67)

Microbial inactivation model

)

exp(

)

0 (

1 )

0 (

1 )

log(exp(

log

max

0 Q

k

t

Q

t

k

N









 

Q

N

k

dt

dN

Q

max





Q

k

dt

dQ

max





N – microbial cell density

Q – variable related to the physiological state of the cells

(68)

Microbial inactivation model





exp

ln

10 

1 

1

10 ln

exp

10 ln

)

,

(

max

a

c

z

T

z

D

a

T

k

_w

a

ref

w

































T = Tsur

Calculated on the basis of all considerations

of heat transport

(69)

(70)

Software Program

• The programme was developed using Real Basic®

5.2 application

• Food/microorganism selection is allowed

(database of thermal properties and kinetic parameters)

• On the basis of the selection of a heating regime of

the medium, the programme allows prediction of

the food surface temperature and simulates the

microbial load content along the whole process

time

(71)

(72)

(73)

(74)

(75)

(76)

Conclusions / outputs

• Software application simulates the results obtained

in the rig apparatus

• Valuable for developing appropriate and safety

thermal processes

• Marketed and commercially available

(77)

Teresa Brandão

Cristina Silva

7

th

_{December 2007}

Predictive Microbiology

A tool to support food safety decisions

UNIVERSIDADE CATÓLICA PORTUGUESA

Escola Superior de Biotecnologia

Thank you