Obtention and data management in predictive microbiology models

OBTENTION  AND  DATA   MANAGEMENT  IN   PREDICTIVE   MICROBIOLOGY  MODELS     Cris6na  L.M.  Silva       5th  _{September  2012}  

CBQF  –  Centro  de  Biotecnologia  e  Química  Fina,   Escola  Superior  de  Biotecnologia,  

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

ObjecFves  of  food  industry  

› PredicFon  of  shelf  life  

› Control/monitor  the  growth  of  microorganisms  

6   Product Design Primary Production Industrial Production Product Transport Logistics Trade Home Storage Consumption Disposal › DistribuFon  chain  

7   Product Design Primary Production Industrial Production Product Transport Logistics Trade Home Storage Consumption Disposal › DistribuFon  chain  

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

The  challenge  

› Microorganisms  response  depends  on:  

  - Intrinsic  factors       -­‐  Extrinsic  factors   -­‐  System  dynamics   pH   a_w   others   T   pH   humidity     salt   gas  concentraFon   others  

•   microbial  interac6on  

•     natural  strains  diversity    

•     history  of  ini6al  popula6on  

•     complexity  of  food  structure  

•     interac6on  food/microorganism  

 

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

PredicFve  microbiology  

The use of mathematical models in the description of

›  Thermal  lethality  

         -­‐  D  and  z  values  –  Bigelow  model  

      F_c =

∫

tp10 Tc −Trefm zm dt 0 ( )/

The  idea  is  not  even  recent!

 

mathematics

microbiology

statistics

predictive

Model à mathematical expression

     

 

i=1,2,...,n (number of experimental runs/observations) j=1,2,...,v k=1,2,...,p  

y

_i

= f(x

_ij

,

_θ

_k

_{) + ε}

_i 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 y_model y_exp θ* Precise ? Accurate ? Minimize differences

precise and accurate description of observations

model adequacy

quality of model parameters

"   knowledge of the process

"   process effects on product

"   control of process variables

Processes Chemical Physical Food Processes Transport Phenomena •  heat •  mass •  momentum Reaction kinetics Properties Modelling mathematical function

 

variables parameters data regression schemes   experimental design design Criterium   validation control optimization Objectives   quality safety

"

prediction / simulation

"

development of efficient

processes

contribution to

safety

aplication

sigmoidal behaviour

presence of aggregated microorganisms or sub populations more heat (or other stress factor) resistent

inactivation

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

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 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)

0 1 2 3 4 5 6 7 8 0 20 40 60 80 100 120 140 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

v  primary 0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 Time (min) Log C FU /g kinetics parameters

v  primary v  secondary 0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 Time (min) Log C FU /g parameters pH _aw temperature

v  primary

v  secondary

v  terciary - integration of the previous models - software

0 1 2 3 4 5 6 7 8 0 0,5 1 1,5 2 2,5 Time (min) Log C FU /g parameters pH _aw temperature

v  primary 0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 logN _k logN0 logNres L Time (s) empirical _fundamental

N₀ number of initial viable spore cells N_res number of residual spore cells k maximum inactivation rate L lag or shoulder

v  primary First order ( kt) exp N N = ₀ − D t N log logN = ₀ − ( k t) (1 F )exp( k t) exp F N N 2 1 1 1 0 = − + − − Cerf (1977) Kamau et al. (1990) ( ) ( ) ( )⎟⎟_⎠ ⎞ ⎜⎜ ⎝ ⎛ + − + + = t k exp 1 F 1 2 t k exp 1 F 2 log N N log 2 1 1 1 0

D – decimal reduction time

F₁ – fraction of inactivated microorganisms k₁ e k₂– kinetic constants biphasic 0 1 2 3 4 5 6 7 8 0 2 4 6 8 Time (min) LogC FU /g 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 Time (min) Log C F U /m l

v  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 Time (min) Log C FU /g ( ) ( ) ( ) ( ) ( )( ( )) ( ) ( ) ⎟⎟_⎠ ⎞ ⎜⎜ ⎝ ⎛ − + − + − + − + − + = L t k exp 1 L k exp 1 F 1 L t k exp 1 L k exp 1 F log N N log 2 2 1 1 1 1 0 Whiting & Buchanan (1992) distribution of heat sensibility of microbial populations L – lag or shoulder

v  primary Baranyi et al. (1993) ( ) ( ) (t 0) N₀ N N t t k dt dN = = − = α β ‘lag’ function ‘tail’ function 0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) log N

v  primary Baranyi et al. (1993) ( ) ( ) (t 0) N₀ N N t t k dt dN = = − = α β ‘lag’ function ‘tail’ function 0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) log N ( ) ( ) ( ) ( )0 exp( k t) Q 1 0 Q 1 t k exp log N N log max max 0 + − + − = ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ Geeraerd et al. (2000) ( ) Q k dt dQ N Q k k dt dN max Q max − = − =

v  primary Gompertz 0 1 2 3 4 5 6 7 8 9 0 500 1000 1500 2000 tempo (s) log N Bhaduri et al (1991) Linton et al. (1995, 1996) Xiong et al. (1999) ( ) ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = L t 1 N N log e k exp exp N N log logN logN res 0 res 0 0 Logistic Listeria monocytogenes ( ) (k t - L ) exp 1 c logN + = _{c – constant}

reparameterized for inactivation based in Zwitering (1990)

v  secondary

 

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} − _wmin ) pH (pH ) T b(T k = − _min − _min ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = RT E -exp k k ₀ a lnk = lnk₀ − _RTEa 2 W 4 W 3 2 2 1 0 C_{T T}C C a C a C lnk = + + + + ) pH (pH ) a (a ) T b(T

k = − _{min w} − _wmin − _min

min – minimal value for growth

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ref a ref exp - E_{R T}1 _T1 k k

v  tertiary

softwares

Microbial growth Shelf life prediction    

Difficul6es  in  food  processes  modelling:  

 

"      Dynamic  processes  

"      Complexity  and  heterogeneity  of  products  

Gompertz   ( ) ) time ( d N log d ( ) (L t') 1 dt' N N log ) 1 exp( k exp exp 1 ' t L N N log ) 1 exp( k exp ) 1 exp( k N log N log t 0 res 0 res 0 0 _∫ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − =

dynamic situation of temperature

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ref a ref exp - E_{R T}1 _T1 k k ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ref T 1 T 1 b exp a L Gill (2011)

Linear ( ) ) time ( d N log d

dynamic situation of temperature

(T Tref) z 1 ref 10 D D = − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −

∫

=

− PT 0 Zref T T ref T dt 10 D 1 0

10

N

N

approach by Vieira et al. (2002) Cupuaçu nectar

Case  studies:

 

( ) ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = L t 1 N N log e k exp exp N N log logN logN res 0 max res 0 0 Square-root! ! " kmax = c (T − d) Arrhenius! ! " " " ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ref a ref max k exp - E_{R T}1 _T1 k Williams-Landel-Ferry! ! " " ( ) ( )⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = min min T -T b T -T a 10 L Arrhenius! " " " " ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ref T 1 T 1 b exp a L

c, d !constants! Kref !reaction rate at Tref! Ea !activation energy! a, b !constants! 1! 2! 4! 3! Gill (2011)

log N! time (s)! 0 1 2 3 4 5 6 7 8 9 0 1000 2000 3000 4000 5000 6000 7000 T=52ºC T=56ºC logN time (s) 0 1 2 3 4 5 6 7 8 9 0 100 200 T=60ºC T=64ºC T=68ºC 0 500 1000 1500 2000 2500 3000 320 325 330 335 340 345 T (K) L ( s ) 0 0,05 0,1 0,15 0,2 0,25 0,3 320 325 330 335 340 345 T (K) kma x ( s -1) 0 1 2 3 4 5 6 7 8 9 0 1000 2000 3000 4000 5000 6000 7000 time (s) log N T=52ºC T=56ºC 0 1 2 3 4 5 6 7 8 9 0 100 200 time (s) log N T=60ºC T=64ºC T=68ºC Gompertz" Two-step" L= f(T)! kmax= f(T)! One-step"

Equations 1 and 4 selected"

Tank with water + L. innocua 15 minutes Weibull model Inumeration OzonaFon  

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

How  to  obtain  the  data  

› Experiments  in  broth  at  various  condiFons  (pH,  T,  a_w,  

[growth  inhibitors],  etc.)  

› InoculaFon  studies  in  foods  under  various  condiFons  

"   Heuris6c  sampling  

"      Experimental  design                                     Minimize  variance  of:    

"      predicted  response   "      parameter  es.mates  

Sampling:

 

"   Regression schemes "   Analysis of residuals

(

)

[

]

2 n 1 i k ij i n 1 i 2 i y f x , e SSR

_∑

_∑

= = θ − = = Least-squares _method

Data  analysis:

 

Mathematical

complexity Adequate description

model parameters

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

Available  soMware  

à predicts  shelf-­‐life  as  well   as  growth  of  spoilage  and   pathogenic  bacteria  in   seafood  

     

à evaluates  the  effect  of   constant  or  fluctuaFng   temperature  storage   condiFons  (Dalgaard  et   al.  2002,  2003,  2008)    

à more  than  40  models  for  different  bacterial  pathogens  

à the  soMware  allows  growth  or  inacFvaFon  of  pathogens  to  be   predicted  for  different  combinaFons  of  constant  temperature,  pH,   NaCl/a_w  and,  in  some  cases,  other  condiFons  such  as  organic  acid   type  and  concentraFon,  atmosphere,  or  nitrate    

à includes  more  than  40.000  curves/data  on  growth,  survival  or   inacFvaFon  of  microorganism  in  foods.    

à data  has  been  obtained  from  the  literature  or  provided  by  supporFng   insFtuFons  

à the  modelling  toolbox  within  ComBase  includes  the  Combase  Predictor   (previously  Growth  Predictor  and  Food  MicroMoodel).    

à French  decision  support  system  that  includes  (i)  a  database  with  growth   and  inacFvaFon  responses  of  microorganisms  in  foods  and  (ii)  predicFve   models  for  growth  and  inacFvaFon  of  pathogenic  bacteria  and  some   spoilage  microorganisms    

à predicts  the  effect  of  organic  acids,  temperature,  pH  and   moisture  on  growth  of  Listeria  monocytogenes  in  products      

predict  the  growth  of  

Listeria  monocytogenes  

and  Staphylococcus  

aureus  on  Ready-­‐To-­‐Eat  

meat  products  as  a   funcFon  of  pH  and   water  acFvity    

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

ValidaFon  studies  

› Before  market  introducFon,  valida6on  has  to  be  

carried  out  for  new  or  altered  products  

› AMer  the  concept/prototype  

 à  acceptance  tests  à  refinement  of  models  à  final   formulaFon  à  validaFons  in  challenge  test    

 

       have  to  be  performed             Milkowski (2012)

› This  is  the  main  difference  between  free  and  paied  

soMware  

› A  complete  challenge  test  takes  aproximately  3  

months  +  evaluaFon  of  process  variaFons  +  

idenFficaFon  of  acceptable  limits  for  formulaFon   limits    à  establish  a  theoreFcal  shelf  life  

› Industry  saves  costs  and  Fme  when  using  reliable    

predicFve  micro  modelling  

          Milkowski (2012)

› Industry  has  to  perform  validaFon  studies,  for  final  

verificaFon  

› The  analyFcal  values  for  pH,  water  acFvity,  moisture,  

etc    are  crucial    

› However,  predicFve  microbiology  does  not  replace    

hygiene  measure  or  Good  Manufacturing  PracFces            à  models  can  not  be  the  only  hurdle  to  pathogens  

          Milkowski (2012)

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

Acknowledgement  by  regulaFon    

          Milkowski (2012) › United  States:                    -­‐  U.S.  9CFR  RegulaFons  

         -­‐  2008  USDA  Supplementary  Guidance  

› European  Union:  

         -­‐  2005  &  2010  EU  regulaFon  

         

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

The  complexity  of  dynamic  condiFons    

›  The   greatest   modeller’s   effort   has   been   given   to   data   obtained  

under  constant  (or  staFc)  environmental  condiFons  

›  From  a  realisFc  point  of  view  this  is  somehow  restricFve,  since  the  

majority   of   thermal   processes   occur   under   Fme-­‐varying   environmental  condiFons,  and  kineFc  parameters  obtained  under   such   circumstances   may   differ   from   the   ones   esFmated   at   staFc  

OUTLINE  

› ObjecFves  of  food  industry  

› The  challenge  

› PredicFve  microbiology  

› How  to  obtain  the  data  

› Available  soMware  

› ValidaFon  studies  

› Acknowledgement  by  regulaFon  

› The  complexity  of  dynamic  condiFons  

› Conclusions  

Conclusions  

› Great  progresses  in  the  past  20  years  

› There  are  many  models  available,  each  with  its  

benefits  and  limitaFons  

› Yet  much  work  has  sFll  to  be  developed,  parFcularly  

kineFc  studies  under  dynamic  condiFons  

› ValidaFon  studies  have  to  be  carried  out  for  new  or  

altered  products,  due  to  the  complexity  of  the  systems    

› PredicFve  microbiology  is  a  powerful  tool,  but  does  

not  replace    hygiene  measures  or  Good  Manufacturing   PracFces    

Thank  you!  

 

  Teresa  Brandão   Mª  Manuel  Gil   Mª  FáFma  Miller   Elisabeth  Alexandre