SIST EN ISO 23691:2026

SLOVENSKI STANDARD
01-april-2026
Mikrobiologija v prehranski verigi - Ugotavljanje in uporaba kardinalnih vrednosti
(ISO 23691:2026)
Microbiology of the food chain - Determination and use of cardinal values (ISO
23691:2026)
Mikrobiologie der Lebensmittelkette - Bestimmung und Verwendung von Kardinalwerten
(ISO 23691:2026)
Microbiologie de la chaîne alimentaire - Détermination et utilisation des valeurs
cardinales (ISO 23691:2026)
Ta slovenski standard je istoveten z: EN ISO 23691:2026
ICS:
07.100.30 Mikrobiologija živil Food microbiology
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 23691
EUROPEAN STANDARD
NORME EUROPÉENNE
February 2026
EUROPÄISCHE NORM
ICS 07.100.30
English Version
Microbiology of the food chain - Determination and use of
cardinal values (ISO 23691:2026)
Microbiologie de la chaîne alimentaire - Détermination Mikrobiologie der Lebensmittelkette - Bestimmung
et utilisation des valeurs cardinales (ISO 23691:2026) und Verwendung von Kardinalwerten (ISO
23691:2026)
This European Standard was approved by CEN on 21 November 2025.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

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United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 23691:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 23691:2026) has been prepared by Technical Committee ISO/TC 34 "Food
products" in collaboration with Technical Committee CEN/TC 463 “Microbiology of the food chain” the
secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by August 2026, and conflicting national standards shall
be withdrawn at the latest by August 2026.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 23691:2026 has been approved by CEN as EN ISO 23691:2026 without any modification.

International
Standard
ISO 23691
First edition
Microbiology of the food chain —
2026-02
Determination and use of cardinal
values
Microbiologie de la chaîne alimentaire — Détermination et
utilisation des valeurs cardinales
Reference number
ISO 23691:2026(en) © ISO 2026
ISO 23691:2026(en)
© ISO 2026
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
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Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 23691:2026(en)
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Principle . 6
4.1 General .6
4.2 Gamma functions .7
4.2.1 General .7
4.2.2 Describing effects of temperature .7
4.2.3 Describing effects of pH .8
4.2.4 Describing effects of a .8
w
4.2.5 Describing the effects of concentrations of inhibitors .9
4.3 Process of cardinal values and food correction factor determination .10
4.4 Determination of the maximum specific growth rate .10
4.4.1 General .10
4.4.2 Binary dilution OD-based method .11
4.4.3 Direct plating method .11
4.5 Cardinal values determination . 12
4.6 Correction factor determination . 13
4.7 Validation .14
4.8 Use of cardinal values and food correction factor in predictions . 15
5 Reagents and materials .15
6 Apparatus .15
7 Experimental design and data collection .16
7.1 General .16
7.2 Preparation of culture and medium .16
7.2.1 Choice and storage of studied strain .16
7.2.2 Preparation and inoculation of the microbial culture .17
7.2.3 Preparation of the modified nutrient broth .17
7.3 Levels per factor to estimate cardinal values .18
7.3.1 General .18
7.3.2 Temperature .18
7.3.3 pH .19
7.3.4 Water activity. 20
7.3.5 Inhibitory compounds .21
7.4 Experimental design to estimate the maximum specific growth rate from the binary
dilution OD-based method . 22
7.5 Experimental design to estimate the maximum specific growth rate from the direct
plating method . 23
7.6 Determination of the food correction factor based on a challenge test . 23
7.7 Validation .24
8 Expression of the results: Estimation of the growth parameters .24
8.1 General .24
8.2 Assessment of maximum specific growth rate at each level of intrinsic or extrinsic
factors (first step) .24
8.2.1 General .24
8.2.2 Assessment of maximum specific growth rates from direct plating data . 25
8.2.3 Assessment of maximum specific growth rates by binary dilution OD-based
method . 25

iii
ISO 23691:2026(en)

8.3 Assessment of cardinal values and optimum growth rate in broth, µ (second
Broth
step) .
8.4 Assessment of C (third step) . 26
f
8.5 Validation (fourth step) .27
9 Use of cardinal values to perform microbial growth predictions .28
9.1 General . 28
9.2 Prerequisites for growth predictions . 28
9.3 Using cardinal values to simulate growth . 29
9.3.1 Growth simulation at a static given temperature . 29
9.3.2 Growth prediction with dynamic time-temperature scenario . 30
9.3.3 Growth simulation at a static condition of temperature, pH and a .31
w
10 Test report .33
11 Quality assurance .33
Annex A (informative) Indicative list of tools for primary and secondary fittings and
simulations.34
Annex B (informative) Guidance to obtain different a values when using different humectants
w
in broth .37
Annex C (informative) Growth rate determination .38
Annex D (informative) Plate design .42
Annex E (informative) Example of the use of cardinal values for growth simulation and its
variation .43
Bibliography .46

iv
ISO 23691:2026(en)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO’s adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 34, Food products, Subcommittee SC 9,
Microbiology, in collaboration with the European Committee for Standardization (CEN) Technical Committee
CEN/TC 463, Microbiology of the food chain, in accordance with the Agreement on technical cooperation
between ISO and CEN (Vienna Agreement).
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

v
ISO 23691:2026(en)
Introduction
Under the general principles of the Codex Alimentarius on food hygiene, it is the responsibility of the food
business operators (FBOs) to control microbiological hazards in foods and to manage microbial risks.
Therefore, it is the responsibility of the FBO to implement validated control measures, within the hazard
analysis and critical control point (HACCP) system, and conduct studies in order to investigate compliance
with the food safety criteria throughout the food chain.
In the framework of microbial risk assessment (MRA), several complementary approaches are developed
to estimate risks posed by pathogens or spoilage microorganisms in the food chain. MRA is adopted by
regulators under the auspices of the international agency for setting food standards. Predictive microbiology
is one of the recognized scientific approaches used to validate control measures within the HACCP system,
as well as to assess microbiological safety and quality of food, food production processes, food storage
conditions and food preparation recommendations dedicated to consumers.
Therefore, this document provides technical rules, procedures and calculations to estimate the cardinal
values of a microorganism of concern and use them in combination with challenge test results to simulate
and predict its growth in raw materials, intermediate products or end products under reasonably foreseeable
food processes, storage and use conditions.
To do so, this document includes the following sections:
— to identify the environmental factor(s) in scope (e.g. temperature, pH, a , organic acids);
w
— to define the appropriate experimental design;
— to estimate the cardinal values of a microorganism in broth medium;
— to perform a challenge test in the matrix of interest and derive the food correction factor and the
maximum microbial population density;
— to use the cardinal values and the food correction factor to predict the growth of the studied
microorganism in different conditions of interest (e.g. changes in time and temperature throughout the
chill chain, changes in formulation with addition of organic acids or preservatives).
Regulatory authorities can have specific recommendations, and these differences have been included as
much as possible in this document. It is, however, possible that additional requirements are needed to get a
regulatory approval of the study.
The use of this document involves expertise from the organizing laboratories in relevant fields such as
food microbiology, predictive microbiology and statistics. This expertise encompasses an understanding
of sampling theory and design of experiments, statistical analysis of microbiological data, and overview of
scientifically recognized and available mathematical concepts used in predictive microbiology.

vi
International Standard ISO 23691:2026(en)
Microbiology of the food chain — Determination and use of
cardinal values
WARNING — In order to safeguard the health of laboratory personnel, it is essential that tests for
detecting target microorganism(s) are only undertaken in properly equipped laboratories, under
the control of a skilled microbiologist, and that great care is taken in the disposal of all incubated
materials. Persons using this document should be familiar with normal laboratory practice. This
document does not purport to address all of the safety aspects, if any, associated with its use. It is the
responsibility of the user to establish appropriate safety and health practices.
1 Scope
This document establishes basic principles and specifies requirements and methods to determine the
cardinal values of bacteria and yeast strains and use them to predict microbial growth.
The four main steps of the approach are:
a) determination of the cardinal values in culture medium;
b) determination of the correction factor in the target food;
c) validation of the model;
d) simulations.
Four environmental factors are considered: temperature, pH, a and inhibitors (e.g. organic acids).
w
NOTE 1 Microbial competition is not considered as an inhibitor in this document and can be addressed by proper
modelling approaches.
The determination of cardinal values is performed in a two-step approach:
— the determination of maximum specific growth rates of the studied strain grown in broth under a defined
range of values of the studied environmental factor(s);
— the use of recognized predictive microbiology secondary models to fit the obtained experimental data to
obtain the cardinal values.
The use of cardinal values in microbial growth simulation is based on predictive microbiology primary and
secondary models. The cardinal values are combined with challenge test data to consider the matrix effect.
Depending on the goal of the growth simulation, it is important to account for variation of cardinal values
between strains within a bacterial or yeast species.
Cardinal values are a good indicator of a strain growth ability for the studied environmental factors. They
are therefore used as criteria to select strains, in addition to their origin and virulence, when performing
growth challenge tests (see ISO 20976-1) or in methods validation (see ISO 16140 series).
NOTE 2 This document focuses on the determination of cardinal values for one strain. The same methodology can
be used to characterize multiple strains independently to cover biological strain variability and include these results
in the predictions.
ISO 23691:2026(en)
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 7218, Microbiology of the food chain — General requirements and guidance for microbiological examinations
ISO 11133, Microbiology of food, animal feed and water — Preparation, production, storage and performance
testing of culture media
ISO 18787, Foodstuffs — Determination of water activity
ISO 20976-1:2019, Microbiology of the food chain — Requirements and guidelines for conducting challenge tests
of food and feed products — Part 1: Challenge tests to study growth potential, lag time and maximum growth
rate
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/
3.1
batch
group or set of identifiable food obtained through a given process under practically identical circumstances
and produced in a given place within one defined production period
Note 1 to entry: The batch is determined by parameters established beforehand by the organization and can be
described by other terms (e.g. lot).
[33]
[SOURCE: Commission Regulation (EC) No 2073/2005 , Article 2 (e), modified — “food obtained through”
replaced “products obtained from”. Note 1 to entry added.]
3.2
binary dilution optical-density-based method
binary dilution OD-based method
method used to stepwise dilute a microbial suspension with a constant dilution factor of two in each step
3.3
independent biological replicate
experiment performed using a newly prepared culture and a newly prepared medium
3.4
cardinal value
cardinal parameter
estimated minimum, optimum or maximum values of extrinsic factors (3.10) and intrinsic factors (3.15) (e.g.
temperature, pH, a , inhibitors) that characterize the growth of a given microbial strain
w
3.5
challenge test
study of the growth (or inactivation) of microorganism(s) artificially inoculated in food
3.6
coefficient of variation
C
V
ratio of the standard deviation to the mean

ISO 23691:2026(en)
3.7
correction factor
C
f
dimensionless value used to link the broth and the food optimum growth rates (3.22)

Note 1 to entry: It is the ratio of the optimum growth rate estimated in the studied matrix (µ ) to the optimum
Food

growth rate value estimated in broth (µ ).
Broth
3.8
detection time
t
d
time at which the optical density (OD) reaches the pre-defined target during the exponential growth
3.9
exponential growth phase
phase during which the multiplication of the microbial population is the fastest and when the maximum
specific growth rate (3.18) is reached
3.10
extrinsic factor
factor in the surrounding environment of the food or the broth, such as temperature or packaging gaseous
composition, which affects the growth kinetics of the microorganism
3.11
gamma concept
γ
concept establishing that intrinsic factors (3.15) (e.g. pH, water activity (3.36), inhibitors) and extrinsic
factors (3.10) (e.g. temperature, packaging gaseous composition) affect the maximum specific growth rate
(3.18) independently
3.12
gamma function
γ (X)
nonlinear, dimensionless function, normalized between zero (no growth) and one (optimum condition for
growth) describing the relative effect of a studied factor (X) on the maximum specific growth rate (3.18) (e.g.
γ (T), γ (pH), γ (a ), γ (I))
w
Note 1 to entry: When combined, the effect of the factors is multiplicative.
3.13
growth curve
graphic representation of the increasing number of living cells of a microbial population in any given
intrinsic and extrinsic condition over a period of time
3.14
inoculum
microbial suspension used to contaminate the studied food or broth at a desired concentration
3.15
intrinsic factor
factor related to the food matrix itself or the broth, such as nutrients, water activity (3.36), organic acids or
pH, which affects the growth kinetics of the microorganism
3.16
lag phase
phase, directly after inoculation, during which the microbial population is adapting to the environment,
before it enters the exponential growth phase (3.9)

ISO 23691:2026(en)
3.17
lag time
λ
kinetic parameter to characterize the duration of the lag phase (3.16)
Note 1 to entry: Lag time is expressed in time unit (h).
3.18
maximum specific growth rate
µ
max
kinetic parameter to characterize the exponential growth phase (3.9), represented by the slope of the curve
showing the evolution of the natural logarithm of the population as a function of time, under constant
growth conditions
Note 1 to entry: When the maximum specific growth rate is estimated in food, this is given as µ .
max,Food
−1
Note 2 to entry: Maximum specific growth rate is expressed in h .
3.19
minimal inhibitory concentration
MIC
estimated parameter representing the lowest concentration of an inhibitor that gives a value of maximum
specific growth rate (3.18) of zero
3.20
modified broth
culture medium with specific composition (e.g. increased salt content) or characteristic (e.g. pH) to study
intrinsic factors (3.15)
3.21
Monte Carlo simulation
iterative random sampling method that propagates variability (3.35) about model parameters to approximate
the distribution of input variables
Note 1 to entry: Monte Carlo simulations are extensively used in quantitative risk assessment and decision-making.
3.22
optimum growth rate
µ
highest value among the maximum specific growth rates (3.18), estimated at the optimum conditions for
growth of the microorganism in a studied food or broth
3.23
optimum growth rate in broth

µ
Broth
highest value among the maximum specific growth rates (3.18) in broth, estimated at the optimum conditions
for growth of the microorganism
3.24
optimum growth rate in food

µ
Food
highest value among the maximum specific growth rates (3.18) in food, estimated at the optimum conditions
for growth of the microorganism

Note 1 to entry: µ is a statistical parameter and is not measured in the food.
Food

Note 2 to entry: µ is a mathematical result obtained when all studied factors X are at their optimum values and
Food
the respective γ (X) terms are equal to 1.

ISO 23691:2026(en)
3.25
organizing laboratory
laboratory with responsibility for determining the cardinal values (3.4) and performing the simulations
Note 1 to entry: Data collection and data analysis (including fitting and simulation) are performed in a single or in
multiple laboratories.
3.26
pH value
measure of acidity or alkalinity of a material in an aqueous solution
[SOURCE: ISO 5127:2017, 3.12.2.29, modified — Notes 1 and 2 to entry deleted.]
3.27
pKa
quantitative measure (negative base-10 logarithm) of the acid dissociation constant or Ka value, which
indicates the strength of an acid in solution (the lower the pKa value the stronger the acid)
3.28
primary model
mathematical model describing the changes of microbial concentration in log cfu/g or /ml as a function of
time under constant and known conditions of intrinsic factor(s) (3.15) and/or extrinsic factor(s) (3.10)
Note 1 to entry: In this document, log refers to the decimal base.
3.29
relative standard error
r
standard error (se) (3.31) divided by the parameter estimate
Note 1 to entry: It is expressed as a percentage.
3.30
secondary model
mathematical model describing the effects of the intrinsic factor(s) (3.15) and/or extrinsic factor(s) (3.10)
(e.g. temperature, pH, a ) on the parameters of the primary model (3.28) (e.g. maximum specific growth rate
w
(3.18))
3.31
standard error
se
measure of the uncertainty (3.34) associated with the estimated parameter or the overall model fit
3.32
stationary phase
phase in which the microbial population no longer increases, having reached and remaining at its maximum
concentration
3.33
strong acid
acid characterized by its negative pKa (3.27)
Note 1 to entry: It ionizes completely in an aqueous solution by losing one proton. Hydrochloric and sulfuric acids are
examples of strong acids.
3.34
uncertainty
variation originating from lack of or incomplete knowledge of some characteristics of a system
Note 1 to entry: It originates from parameter uncertainty and model uncertainty.
Note 2 to entry: Sources of parameter uncertainty include lack of data, measurement errors, sampling errors and
systematic errors.
ISO 23691:2026(en)
Note 3 to entry: Sources of model uncertainty include model structure, excluded variables, model resolution,
extrapolation. The standard error (3.31) represents the uncertainty associated with the parameter.
3.35
variability
variation inherent to a given system, typically as a result of true heterogeneity of the studied population and
is irreducible by additional measurement
Note 1 to entry: Three variation sources are distinguished: between strain variability (intraspecies variability),
within strain variability and analytical variability.
Note 2 to entry: The between strain variability is not included in this document as it is designed to study only one
strain at a time.
Note 3 to entry: The standard deviation represents the within strain biological variability associated with the
parameter.
3.36
water activity
a
w
ratio of the water-vapour pressure in the medium or foodstuff to the vapour pressure of pure water at the
same temperature
Note 1 to entry: It represents the water available for the microorganisms to use.
[SOURCE: ISO 18787:2017, 3.1, modified — “ratio of the water-vapour pressure in the medium or foodstuff to
the vapour pressure of” replaced “partial water-vapour pressure in equilibrium with the product analysed
to the water-vapour saturation pressure in equilibrium with”. Formula and Notes 1 and 2 to entry deleted.
New Note 1 to entry added.]
3.37
weak acid
acid characterized by its positive pKa (3.27) which does not dissociate completely in aqueous solution
Note 1 to entry: Acetic acid and citric acid are examples of weak acids.
4 Principle
4.1 General
The general formula used to describe the effect of different independent intrinsic and extrinsic factors on
the maximum specific growth rate of a microorganism is based on a modular approach called the “gamma
[23]
concept” and described in Formula (1):
µ = µ · γ (T) · γ (pH) · γ (a ) · γ (I) (1)
max w
where
−1
µ maximum specific growth rate (h ) of the studied strain in the matrix;
max
 −1
µ
optimum growth rate (h ) of the studied strain in the matrix;
γ (T) dimensionless function describing the relative effect of the temperature on microbial growth;
γ (pH) dimensionless function describing the relative effect of the pH on microbial growth;
γ (a ) dimensionless function describing the relative effect of the a on microbial growth;
w w
γ (I) dimensionless functions describing the relative effect of different measurable inhibitors like
the undissociated form of the weak (organic) acids (HA) or CO .
ISO 23691:2026(en)
The γ terms all vary between 0 and 1, γ = 0 when growth is fully inhibited by the studied factor, and γ = 1
when growth is not at all inhibited by the studied factor.
There are various secondary models available in the literature to describe the mathematical expression of
the gamma terms. In this document, the cardinal models are used and presented in 4.2.
For the adequate use of the models and interpretation of data, knowledge of and experience in using
predictive microbiology models is essential.
4.2 Gamma functions
4.2.1 General
Under the gamma concept, the different intrinsic and extrinsic factors (e.g. temperature, pH, water activity,
inhibitors) have separate and independent effects (gamma function) on the maximum specific growth
rate, which implies that the cardinal values associated with a factor are also estimated separately and
independently.
Various mathematical models have been developed in the literature.
4.2.2 Describing effects of temperature
For describing the effects of temperature, one of the two following models shall be used:
— the cardinal temperature model with inflection (CTMI, see Formula (2)) shall be used when optimal and
[20]
super-optimal temperatures are required;
[16]
— the restricted Ratkowsky (linear) model (see Formula (3)) shall be used when the temperature
ranges from the minimum supporting growth up to a reference temperature that is below the optimal
temperature:
0,if TT
 C
min


TT TT

C
max

min
γ (T) = , if TTT
 C
max
min
TT TT TT TT TT2T
  
CC C
opt opt opttopt maxopt
min min min

 0, if TT
max

(2)
where
T is the temperature (°C);
C
T is the estimated minimum temperature for growth for the cardinal gamma term;
min
T is the estimated optimum temperature for growth;
opt
T is the estimated maximum temperature for growth;
max
0, if TT

R
min


 T  (3)

 TT 
R
min
 
, if TT
R
min
 
TT

R
ref
 
min
where
ISO 23691:2026(en)
T is the temperature (°C);
R
T is the estimated minimum temperature for growth for the restricted Ratkowsky gamma
min
term;
T is the reference temperature.
ref
In cases where the restricted Ratkowsky model is used for the gamma term to describe the effects of the
temperature, it is important not to use the model outside the experimental range on which it was developed.
4.2.3 Describing effects of pH
For describing the effects of pH, one of the two following models shall be used:
[20]
— the cardinal model in cases where the regular delta shape is observed (see Formula (4));
[3]
— the Aryani model in cases where there is a plateau observed around the optimum, making it impossible
to estimate pH (see Formula (5)):
max

0, ifpHpH
min


pHpH pHpH
C
max

min
 pH  , ifpH pH pH (4)

minmax
 pHpH pHpH pH pH

 
C max opt
min


0, ifpHpH

max
where
C
pH is the estimated minimum pH for growth for the cardinal gamma term;
min
pH is the estimated optimum pH for growth;
opt
pH is the estimated maximum pH for growth;
max
0, if pH pH

A
min


pHpH
A
 pH  (5)


min

pH pH

A 12/
min

12, if pH pH
AA

min
where
A
pH is the estimated minimum pH for growth for the Aryani gamma term;
min
is the pH at which the maximum specific growth rate, μ , is half of the µ .
pH max
1/2
4.2.4 Describing effects of a
w
For describing the effects of the a , models based on a linear (see Formula (6)) or nonlinear relationship,
w
[21]
such as the cardinal a model shown in Formula (7), shall be used:
w
L

0, if aa
ww,min


L
 a  (6)
aa
w
ww,min
L
if aa

ww,min
L
1 a

 wm, in
ISO 23691:2026(en)
where
a is the water activity;
w
L
a is the estimated minimum water activity for growth for the linear gamma term.
w,min
When a linear relationship is used to describe the effects of the a , it is important not to use the model
w
outside the experimental range on which it was developed (e.g. if experiments were performed up to 0,996 it
is not possible to extrapolate at 0,998).
 a 

w
 0,

n

C
aaaa


ww,,maxw wmin

,

n1
 C C C
aa a  aaa  aa aa aan .
 
  
wo,,pt wmin wo, pt wm,,in ww optw,,optw maxw,,optw min w


0,

if aa
ww,min
if aa a (7)
wm,,in ww max
if aa
ww,max
where
a is the water activity;
w
n is a shape parameter;
C
a is the estimated minimum a for growth for the cardinal gamma term;
w,min w
a is the estimated optimum a for growth;
w,opt w
a is the estimated maximum a for growth.
w,max w
NOTE Generally, n = 1 and a is assumed to be 1,0.
w,max
4.2.5 Describing the effects of concentrations of inhibitors
For describing the effects of concentrations of inhibitors including undissociated organic acids, CO and
others, Formula (8) shall be used:


I

 
1 , if I MIC

 
 I  (8)
MIC
  
0, if I MIC

...