U. S. Food and Drug Administration
Center for Food Safety and Applied Nutrition
June 2, 2000

1.KINETIC PARAMETERS FOR INACTIVATON OF MICROBIAL POPULATIONS

1.1. Models and Parameters

Kinetic parameters and models are used for the development of food preservation processes to ensure safety. They also provide the tools to compare the impact of different process technologies on reduction of microbial populations. The parameters used to analyze and report the reduction of a microbial population as a function of process parameters include empirical coefficients experimentally determined from microbial reduction kinetics, as well as constants from expressions based on chemical reaction kinetics. The purpose of this section is to present the models and kinetic parameters used to present and compare microbial inactivation data from thermal, pressure and electromagnetic processes.

1.1.1. Rate constants

The traditional approach to describing changes in microbial populations as a function of time has used the survivor curve equation:

log [N / N₀] = -t / D     (1)

where:

N = microbial population at any time, t

N₀ = initial microbial population

D = decimal reduction time, or time required for a 1-log cycle reduction in the microbial population.

The corresponding model from chemical reaction kinetics is the first-order kinetic model:

dN / dt = -kN     (2)

where:

k = reaction rate constant (first-order), or the slope of the natural logarithm of survivors in contrast to time for the microbial population.

Equation (2) can be integrated to obtain a more familiar expression for the reduction of microbial populations:

ln [N / N₀] = - k t     (3)

By comparing Eq. (1) and (3), the relationship between the decimal reduction time and the first-order reaction rate constant is:

k = 2.303 / D     (4)

The primary parameters (D-value or k) would describe the microbial population reduction at a constant and defined temperature, pressure and/or electric field. The inherent assumption in the use of these models (and the corresponding parameters) is that the reduction in microbial population is described by the first-order reaction model. Alternative models are being developed to explain microbial inactivation kinetics when the linearity of the data is questionable (Peleg and Cole 1998; Anderson 1996). If there is evidence of a different reaction model, different parameters need to be identified and used for process development and prediction purposes.

Only a limited amount of the published data on microbial inactivation has been analyzed using the reaction rate model to quantify first-order rate constants (k). On the other hand, most published data on changes of food quality attributes have been presented as reaction rate constants (k). As indicated by the relationship between D-value and k, published data can be easily transformed.

1.1.2. Temperature coefficients

Traditionally, the influence of temperature on microbial population inactivation rates has been expressed in terms of the thermal resistance constant (z-value) using the following model:

log [D / D_R] = -(T - T_R) / z     (5)

The thermal resistance constant z(T) is the temperature increase needed to accomplish a 1-log cycle reduction in the Dvalue. The reference decimal reduction time (D_R) is the magnitude at a reference temperature (T_R) within the range of temperatures used to generate experimental data. Microbial populations with higher resistance to temperature change are described by larger z(T). The most evident examples are the larger z(T) for spores compared to the ones for vegetative cells.

An alternative model for describing the influence of temperature on microbial population reduction rates is the Arrhenius equation. The model illustrates the influence of temperature on the reaction rate constant (k), as follows:

k = k₀ exp [-E / R T_A]     (6)

where:

k₀ = Arrhenius Constant

E = Activation Energy Constant

T_A = Absolute Temperature

R = Universal Gas Constant

Based on the Arrhenius model (Eq. 6), the slope of ln (k) in contrast to 1/T_A plot determines the temperature coefficient E (activation energy constant) . The activation energy constant describes the influence of temperature on the magnitude of the first-order reaction rate constant (k).

When the thermal resistance model and the Arrhenius model are applied to microbial population reduction rate data over the same temperature range, a relationship between the 2 coefficients [z(T) and E] is evident. By comparison of Eq. (5) and (6), the following relationship can be obtained:

E = 2.303 R T_A² / z     (7)

The temperature used in Eq. (7) should be selected as a mid-point in the range of temperatures used to generate the original experimental data. Equation (7) does suggest that the relationship between the 2 temperature coefficients [E and z(T)] depends on temperature. The magnitudes of the 2 coefficients, however, are significantly different, and any influence of temperature is negligible as long as the temperature reference is within the range used for data collection. The use of the coefficients [z(T) or E] should be limited to the range of temperatures used to obtain experimental D-values. The z(T) should only be used with a defined reference temperature as emphasized by Datta (1992).

The use of the first-order models and the corresponding models for temperature influence must be applied within the limits of data used to generate the parameters within the expressions. The estimation of the kinetic parameters from the appropriate model requires careful attention to statistical limits created by the experimental data. Several authors, including Arabshahi and Lund (1985) and van Boekel (1996), have demonstrated the influence of statistical parameters on the use of the prediction models.

1.1.3. Pressure coefficients

There are only limited references to parameters used to describe the influence of pressure on the rate of microbial population reduction. Zook and others (1999) have used a parameter similar to the thermal resistance constant z(T), based on the following model:

log[D / D_R] =-(P - P_R) / z     (8)

where:

D_R = decimal reduction time at a reference pressure (P_R).

In this report, the pressure coefficient will be defined as:

z(P) = the pressure increase required to accomplish a 1-log cycle reduction in the decimal reduction time (D-value).

In order for pressure resistance constant z(P) to be meaningful, it is important to include a minimum of 3 D-values in the analysis of data. All D-values must be obtained at the same temperature and above the threshold pressure needed for the target microbial inactivation. The threshold pressure (or critical pressure) is the pressure below which microbial inactivation does not occur.

An alternate model to describe the influence of pressure on microbial inactivation rates is based on the Eyring equation, as proposed by Weemaes and others (1999). The model describes the reaction rate constants (k) as follows:

ln (k) = ln(k_R) - [V( P - P_R)/RT_A]     (9)

where:

k_R = reaction rate constant at reference pressure (P_R)

V = activation volume constant

P = pressure

T_A = absolute temperature

The activation volume constant (V) is the pressure coefficient obtained from the slope of the ln (k) in contrast to (P - P_R) plot. The magnitude of V increases as the slope of the plot increases. When the rate of microbial inactivation increases significantly with small changes in pressure, the magnitude of the V will be larger. Alternatively, smaller values of V describe microbial populations with inactivation rates that would change less when pressure changes. As suggested when describing z(P) values, it is important for all reaction rate constants (k) used in the analysis to be measured at the same temperature. For the activation volume constant (V) to be useful and meaningful, the k constant should be measured at pressures above the threshold pressure needed to inactivate the target microbial population.

1.1.4. Electric field coefficients

As in the case of pressure processes, when microbial populations are exposed to pulsed electric fields (PEF), the electric field intensity applied should be above the threshold electric field intensity, the critical electric field intensity for the target microorganism. A model similar to those for temperature and pressure can be used to describe the influence of electric field intensity on the rate of microbial population reduction. The proposed model would be:

log [D / D_R] = -(E - E_R) / z     (10)

where:

D_R = decimal reduction time at a reference electric field intensity (E_R).

The electric field coefficient in this model is defined as:

z(E) = the increase in electric field intensity (E) required to reduce the decimal reduction time (D) by 1-log cycle at a specific temperature and pressure.

All D-values used in this type of analysis should be acquired at the same temperature and pressure. A minimum of 3 D-values should be obtained for the data analysis.

An alternative model for describing the influence of electric field intensity on the survival of a microbial population was proposed by Peleg (1995). The model is based on the Fermi equation and can be expressed as:

N / N₀ = 1/{1 + exp[( E - E_d ) / K]}     (11)

where:

E_d = the electric field intensity when microbial population has been reduced by 50%.

K = a coefficient with magnitude based on the slope of the survivor curve obtained at several levels of electric field intensity.

This model has been applied to survivor data for several different microbial populations to generate typical magnitudes of the coefficient (K) (Peleg 1995). Larger magnitudes of the coefficient would suggest a higher resistance to changes in electric field intensity.

A similar model has been proposed and used by Hulsheger and others (1981) and applied by Jeyamkondan and others (1999). The model describes the survivor number as a function of electric-field strength and treatment time:

N / N_o = { t / t_c }^{[- ( E - Ec ) / K ]}      (12)

where:

t = treatment time

t_c = critical treatment time or treatment time below which no inactivation of microorganisms occurs

E_c = critical electric field strength or electric field strength below which no inactivation of target microorganism occurs

K = specific rate constant

The model proposed by Hulsheger and others (1981) is similar to Eq. (11), but accounts for exposure time at a given electric field intensity. The coefficient (K) has a similar relation to electric field intensity as in Eq. (11) and the relative magnitudes should be interpreted in the same manner.

1.2. Kinetic Parameters for Inactivation of Microbial Pathogens

The purpose of this section is to provide an overview and discussion on the kinetic data of microbial population inactivation. This section addresses the use of kinetic parameters for development of processes and the comparison of parameters obtained for various microorganisms, including a discussion on the limitations of the parameters. Finally, the research needs will be addressed, with specific attention to recommendations on experimental approaches to be considered in the future.

Kinetic parameters describing the inactivation of microbial pathogens are presented in Tables 1A, B and C and are a summary of parameters presented in other sections of this report. The intent of the summary is to provide an overview and a comparison of the kinetic parameter magnitudes for the various microorganisms for each process technology. The parameters defined in Section 1.1. (D-value and z(T), z(P), z(E), E, k, K and V) have been calculated from data previously reported and using the models in Section 1.1 for thermal, pressure and PEF technologies. The parameters for thermal treatment also apply to microwave energy and electrical resistance (ohmic) processes, as well as any other technology where temperature is the primary factor in reduction of the microbial population. Likewise, the parameters for pressure or PEF treatments should apply to any process where pressure or electricity is the primary critical factor in reducing microbial populations. It must be noted that, given the scarcity of data, these are estimated parameters and there is an imminent need for more research in this area. Although this report contains references to several other technologies, the quantity of data describing the influence of the treatment on reduction of microbial populations is insufficient at this time.

Like in most of the published literature, in this report data have been analyzed assuming that the reduction in microbial populations follows a linear first-order model, with the exception of the PEF parameters that will be discussed in Section 1.2.2.4. The potential of non-linear inactivation data or the use of alternative models cannot be ignored. Because there is currently insufficient information on alternative models to allow the type of comparisons being considered in this portion of the report, these issues will be discussed when describing the specific technologies.

The use of consistent parameters for all preservation technologies should improve the efficiency of future investigations and encourage uniformity in the methodologies for establishment of minimum process requirements.

1.2.1. Process development

The parameters presented in Tables 1A, 1B and 1C parallel the traditional parameters used for development of thermal preservation processes. The basic model for process development is based on the survivor curve Eq. (1) or (2):

F = - D log [ N₀ / N ] = D log [ N / N₀ ]     (13)

or:

F = - ln [ N₀ / N ] / k = ln [ N / N₀ ] / k     (14)

where F is the total time required to reduce the microbial population by a specified magnitude needed to ensure product safety, under the conditions defined by D-value or k. The basic model assumes a linear first-order relationship between microbial population and time. Currently, there is a lack of historical evidence to support alternative models; however, there is considerable discussion about the appropriateness of using a first-order model to describe the reduction in microbial population for all preservation technologies. For example, models for PEF technology as presented in Eq. (11) and (12) should continue to be evaluated, but at this time, input parameters for these models are limited.

1.2.2. Inactivation data and parameters

1.2.2.1. Limitations of the calculated parameters

A few limitations need to be considered when interpreting the parameters presented in Tables 1A, B and C. Care should be taken when they are intended to be used as tools to develop processes, to compare the resistance of different microbial populations, or to identify appropriate surrogate microorganisms.

As illustrated in this report, the kinetic parameters for microbial populations exposed to thermal treatments have been assembled over a significant period of time. Over time, the published literature has included kinetic parameters needed to respond to most process, product and microbial situations. The parameters provide a sound basis to develop processes for the microwave energy and electrical resistance (ohmic) technologies. In addition, the available parameters provide a sound basis to compare different microbial populations and the influence of different product environments on the parameter magnitudes. The key issue for these electrothermal treatments is the lack of conclusive evidence on the existence of non-thermal effects influencing the reduction in microbial populations. It is believed, however, that those effects would add an extra factor of safety to the preservation process (see Microwave and Ohmic and Inductive Heating chapters).

In general, the data used to determine the D-values (and k-values) for pressure processes appear to be adequate. The limitations to these data are primarily associated with temperature control during pressure treatments. In addition, when temperature changes have been reported, the influence on the kinetic parameters has not been analyzed. The evidence suggesting a synergistic impact of pressure and temperature is too limited for use in process evaluation.

The most serious deficiency in pressure process kinetics is that most of the parameters (D and k) have been measured at a single pressure. Only 4 studies (Rovere and others 1996; Kalchayanand and others 1998; Zook and others 1999; Reddy and others 1999) have used 3 to 5 pressure levels, while controlling all other factors influencing the parameters. The results from these studies are adequate to evaluate the pressure coefficient [z(P)] and/or activation volume [V]. With exception of the 4 publications cited above, the estimated parameters are limited by the number of pressure magnitudes used, the lack of temperature control and the lack of multiple data for the same microorganism and/or product/substrate. By overcoming these limitations, parameters from future investigations will meet the needs of process development and product/microorganism comparisons.

The data available on the influence of PEF on microbial populations have many limitations. As will be indicated during the discussion of parameters in Table 1C, the kinetic parameters (D-value or k) are based on 2 points on the survivor curve, the initial population and the final population. It should be recognized that the values of parameters in Table 1C were not based on linear regression analysis. In addition, temperature controls and collection of multiple data points at the same temperature level are lacking.

At this time, no single report has measured the inactivation of microbial populations at several levels of electric field strength, leading to the quantification of the PEF coefficient z(E) . Although 3 such coefficients are presented in Table 1C, these coefficients have been estimated based on kinetic parameters reported in separate investigations and must be used with these limitations in mind. There are no published reports that evaluate the potential for a synergistic influence of electric field strength and temperature. There are only 2 reports with kinetic parameters based on Eq. (11) and (12) and these reports provide limited parameters on microorganisms of food safety concern. They do not include any of the microorganisms of food safety concern.

1.2.2.2. Thermal processes

The literature provides an impressive array of kinetic parameters to be used in the development of thermal processes. In addition to data and parameters on inactivation of microbial populations, Table 1A includes additional information on the medium used and specific experimental conditions (that is, temperature) when available. The time parameters are the decimal reduction time (D-value) and the corresponding rate constant (k). The temperature coefficients include the thermal resistance constant [z(T)] and the activation energy constant (E).

The kinetic parameters calculated for the thermal inactivation of microbial pathogens in Tables 1A, B and C should be considered when using any process technology where temperature is the primary mode of microbial inactivation. The most promising alternative thermal processes to reduce pathogenic microbial populations are microwave energy and electrical resistance (ohmic), which are included in this report. As suggested in the chapters on microwave and ohmic and inductive heating, it is assumed that the direct influence of microwave energy or electrical resistance on microorganisms is negligible. Therefore, thermal kinetic parameters should be considered for the above-mentioned electrothermal processes (ohmic, inductive and microwave heating).

Kinetic parameters for vegetative cells of Salmonella serovars, pathogenic Escherichia coli, Yersinia enterocolitica, pathogenic Vibrio spp., Aeromonas hydrophila, Campylobacter jejuni, Listeria monocytogenes and Staphylococcus aureus are presented in Table 1A. In general, the D-values are relatively small and the k-values are relatively large for the vegetative microorganisms normally targeted in pasteurization or other mild thermal processes. Other than the abnormally high D-values (low k-values) for Salmonella pathogens in milk chocolate, Salmonella Typhimurium and L. monocyctogenes are the most thermally resistant vegetative microorganisms. The largest D-value for Salmonella Typhimurium is 18.3 min (k= 0.126/min) at 55C. For L. monocyctogenes, the largest D-value is 16.7 min (k = 0.14/min) at 60C. The largest D-values for E. coli are 6.6 min (55 °C) for O111:B4 and 6.4 min (57 °C) for O157:H7. Based on limited data for O157:H7 in ground beef, a z(T) of 5.3 °C has been estimated. Other significant magnitudes for D-values include 6.6 min for A. hydrophila at 48 °C and 16.7 min for L. monocytogenes in cured ground beef at 60 °C. A z(T) of 5.56 °C for L. monocytogenes in milk has been estimated, based on published data.

In general, the thermal resistance constants z(T) for the vegetative microorganisms fall in the range between 4 and 7.7 °C. This range includes a z(T) of 5.3 °C for E. coli O157:H7 in ground beef and of 5.56 °C for L. monocytogenes in milk, both estimated from limited data presented in the references cited. The larger z(T) presented include 12.4 to 25 °C for Vibrio species (in fish products) and 17.7 to 18.9 °C for Salmonella serovars (in milk chocolate). These abnormally high z(T) for vegetative microorganisms should be noted for these products and may be specifically associated with them.

S. aureus, a vegetative microorganism that produces a heat-stable toxin, has D-values similar to other vegetative populations. The z(T) of 9.5 °C is relatively high and must be considered when developing processes for situations where S. aureus could present a health hazard.

The largest D-value (smallest k-value) reported at 110 °C for toxin-producing, sporeforming microorganisms is 12.42 min (0.185/min) for Clostridium botulinum proteolytic Type B spores in pureed peas. Most other D-values are in the more typical range of 1 to 3 min for spore-forming microorganisms. Other values to be noted are the D-value of 36.2 min (k = 0.064/min) for Bacillus cereus spores at 95 °C and 100 min (k = 0.023/min) for C. botulinum non-proteolytic Type E spores at 70 °C. When expressed at 110 °C, these D-values become 1.18 min for the B. cereus spores and less than 1 sec for the Type E spores.

Data for Bacillus subtilis spores have been included in Table 1A to illustrate the influence of ohmic heating on inactivation kinetics. These data were reported by Cho and others (1999) and indicate that the reduction in D-value (higher k-value) and the increase in z(T) (lower E) when using ohmic heating are statistically significant. These results suggest an independent and additional inactivation mechanism due to the electric current during the ohmic heating. The overall influence of these non-thermal effects, however, is not sufficient to consider the use of alternate kinetic parameters for development of ohmic heating processes. These authors have demonstrated that a 2-stage process involving ohmic heating, interrupted by a 20-min incubation, resulted in enhanced inactivation of B. subtilis spores. This increase in inactivation has been attributed to the positive influence of electric treatment on spore germination.

Separate data for microwave heating are not included in this section. The non-thermal effects of microwave processes on microbial inactivation have not been confirmed and appear to be of insufficient magnitude to be considered during development of processes.

1.2.2.3. Pressure processes

For processes involving the use of pressure for reduction of microbial populations, the F-value is the time the product needs to be exposed to the specified pressure and other conditions (that is, temperature) to accomplish the recommended amount of inactivation. Since the application of most of the pressure technologies involves instantaneous adjustment to the process pressure, the use of the basic model is straightforward. The pressure coefficients [z(P) or V] provide users with the flexibility to select the most appropriate pressure for the specific application. For pulsed-pressure technologies, the model would need to incorporate the influence of time and incremental pressure. In this case, the estimation of kinetic parameters will require the measurement of other variables.

The kinetic parameters for inactivation of microbial populations due to pressure are presented in Table 1B. The time parameters, decimal reduction time (D-value) and first-order rate constant (k), were calculated based on the reduction in microbial population at a constant pressure. The pressure coefficients are z(P) and the activation volume constant (V), as defined in Section 1.1.3. and indicate influence of pressure on the rate of inactivation. In most references cited, there are insufficient data to estimate these coefficients. Special consideration needs to be given to the combined use of pressure and temperature. Based on the current available information, the z(P) and z(T) parameters should be adequate for process development. The combined influence of pressure and temperature on inactivation kinetics for microbial populations has been investigated, although not extensively. Published reports suggest a synergistic impact of pressure and temperature on inactivation rates, but additional investigations are needed. The independent influence of pressure on rates, as indicated by the z(P) or V parameters, needs to be clearly established. The influence of temperature can be quantified in several ways, but the optimum approach would be based on the dependence of z(P) or V on temperature. Although minimum pressure thresholds for microbial inactivation are not presented in this section, these parameters are discussed in the section on high pressure processing.

Several investigations on Salmonella indicate that decimal reduction times (D-value) range from 1.48 to 6 min (k = 0.348 to 1.556/min), with pressure having an obvious influence on the rate. Most of the studies have been conducted at ambient temperatures (20 to 25 °C). The D-values for E. coli are as high as 15 min (k = 0.154/min) at 300 MPa and 6 min (k = 0.384/min) at 600 MPa for O157:H7. There are insufficient data to establish the influence of pressure or temperature and therefore z(P) or z(T) were not estimated.

Pressure appears to have a significant influence on inactivation rates for populations of S. aureus, apparently one of the most pressure-resistant vegetative bacteria, as suggested by D-values of 7.14 min (k = 0.323/min) at 600 MPa compared to 150 min (k = 0.015) at 400 MPa. D-values reported for 500 MPa are lower than the ones for 400 MPa, but were measured in a different medium and may be influenced by temperature. However, in comparable experiments, inactivation rates of selected strains of various Listeria spp. with, for example, D-values ranging from 1.48 min (k = 1.556/min) at 350 MPa to 15 min (k = 0.154/min) at 400 MPa were lower than the ones for S. aureus. These data were measured at ambient temperatures (20 to 25 °C). Recently, D-values of over 5 min were also reported for L. monocytogenes at 345 MPa and 25 °C (Alpas and others 1999).

Comprehensive data on inactivation rates of Clostridium sporogenes spores were reported by Rovere and others (1996). These data indicate that D-values are 0.695 min (k = 3.314/min) at 800 MPa at 108 °C compared to 16.772 min (k = 0.136/min) at 600 MPa at 90 °C. The magnitudes of these D-values are similar to the D-value of 12 min at 680 MPa reported in a separate investigation (Crawford and others 1996), even though the latter was measured at ambient temperatures. From the Rovere and others (1996) data, the influence of pressure on inactivation rate, z(P), were estimated to be 725 MPa at 93 °C, 962 MPa at 100 °C and 752 MPa at 108 °C. The inconsistent influence of temperature on z(P) may be associated with the limited range of temperatures and pressures used in the experimental investigation, as well as adequacy of temperature control during data collection.

Recent inactivation data for C. botulinum Type E Alaska and Type E beluga (Reddy and others 1999) indicate that their D-values were in the same range as for C. sporogenes. The D-values for C. botulinum Type E Alaska were lower in crab meat than in a buffer. The D-values for C. botulium Type A 62-A are generally higher than the values for C. sporogenes, even when considering the influence of temperature and pressure. The pressure coefficient z(P) for the Type A 62-A data was 1524 MPa. Surprisingly, this value was much higher than the z(P) values reported for C. sporogenes, even though data from C. sporogenes were recorded at lower temperatures.

An in-depth investigation of pressure inactivation of Saccharomyces cerevisiae in orange and apple juice has been reported by Zook and others (1999). The calculated D-values were 10.81 min (k = 0.21/min) at 300 MPa, where temperatures have been maintained at levels between 34 and 43.4 °C. These D-values are slightly higher than the ones reported earlier by Parish and others (1998). For apple juice and orange juice z(P) were 115 MPa and 117 MPa, respectively. These values are much lower than those reported for C. sporogenes and C. botulinum. Since data for 5 different pressures have been reported by Zook and others (1999), the activation volumes (V) could be estimated to be 1.24 X 10^-4 for orange juice and 1.37 X 10^-4 m³/mole for apple juice.

In summary, the most pressure-resistant pathogenic vegetative cell populations appear to be those of E. coli O157:H8 with a D-value of 6 min (k= 0.384/min) at 600 MPa, and S. aureus with a D-value of 7.14 min (k = 0.323/min) at 600 MPa. The most pressure-resistant spores appear to be C. sporogenes with a D-value of 16.772 min (k = 0.138/min) at 600MPa (T = 90 °C) and C. botulinum Type A 62-A with a D-value of 6.7 min (k = 0.344/min) at 827 MPa (T = 75 °C). The pressure coefficient z(P) of 1524 MPa at 75 °C for C. botulinum Type A 62-A constitutes an additional indication of the pressure resistance of the spore populations. A recent report shows little if any inactivation after 30 min of C. botulinum 17B and Cap 9B exposure to 827 MPa at 75 °C (Larkin and Reddy 1999).

1.2.2.4. Pulsed electric field processes

Currently, the majority of the kinetic parameters for the PEF technologies are in a form that fits the basic model [Eq. (13) or (14)]. Even with the limitations mentioned above, the use of the parameters and model to establish process time (F) would seem appropriate in the short term. Models, such as Eq. (11) or (12), provide desirable alternatives, but a great effort would be needed to evaluate them. The use of z(E) values provides the users with flexibility to select the optimum electric field strength for a given product and to evaluate the influence of other factors such as synergistic effects of electric field strength and temperature. Adequate inactivation data for estimating the kinetic parameters for microbial populations exposed to PEF are scarce. The information presented in Table 1C compares decimal reduction times (D-value) and first-order rate constants (k), for experiments where electrical field strength (E) and initial temperature were mostly available. Three different PEF coefficients have been presented: the z(E), the specific rate constant (K) from the Hulsheger model (Hulsheger and others 1981) and a similar constant (K) based on the analysis by Peleg (1995).

It should be noted that the D-values (k-values) have been determined from measurements of microbial population reduction after 1 exposure time to a given electrical field strength. The parameters obtained should be considered with this limitation. Furthermore, there is no evidence that the survivor curve during exposure to a pulsed electric field is described by a first-order model. The parameters are presented in this report to allow for more direct comparisons of the effectiveness of PEF in reducing different microbial populations, as well as to note the influence of the media on microbial inactivation. In addition, the D-values (k) provide a more direct approach to evaluating the influence of electric field strength on the rate of microbial population reduction. As will be emphasized later in this section of the report, there is a great need to better understand survivor curve shapes for microbial populations exposed to pulsed electric fields.

The results in Table 1C clearly indicate that the D-values are several orders of magnitude smaller than the same parameters for thermal or pressure processes. Assuming first-order kinetics through 6-12Ds, this suggests a significant advantage for PEF, when compared to the other technologies. This assumption may not be valid because inactivation of 99.9% of a cell population is frequently difficult to achieve.

Several investigations have reported data on reduction of E. coli populations exposed to PEF. The highest D-values are 4500 µs (k = 0.051 X 10-2 /µs) at 16 kV/cm and 17.8 µs (k = 12.94 X 10-2 /µs) at 70 kV/cm. Using a limited number of D-values, a z(E) of 41 kV/cm has been estimated. Note that this magnitude is based on less than ideal data, collected at temperatures ranging from 15 to 37 °C. The D-value of 4500 µs, at 16 kV/cm and 37 °C for E. coli would suggest that this microorganism is one of the more PEF resistant vegetative cell populations.

The investigations on the influence of PEF on Salmonella Dublin, S. aureus and Zygosaccharomyces bailii provide only limited amounts of data. The D-values for S. aureus are very similar to the magnitudes for E. coli, with values of 4000 to 6000 µs at relatively low electric field strength (16 kV/cm) and temperatures of 30-37 °C.

The data for the Listeria spp. indicate that D-values are as low as 18.8 µs at 50 kV/cm for Listeria innocua and as high as 540 µs at 20 kV/cm for L. monocyctogenes. Since these data were measured at relatively low temperatures (10 to 50 °C), the parameters would indicate that Listeria is one the more resistant vegetative cell populations to a PEF treatment.

The D-values of 50-60 µs (k = 3.84 to 4.61 X 10-2 /µs) at 50 kV/cm for B. cereus spores are higher than for other microbial populations at the same field strength and temperature. Two D-values (17.5 to 26.3 µs) for B. subtilis spores at the same pressure and from 2 different investigations were considerably lower than the D-values for B. cereus spores. Using the D-values for B. subtilis spores at 3 different electrical field strengths and within an ambient temperature range, a z(E) of 15.5 kV/cm has been estimated. Unexpectedly, this magnitude is much lower than the one estimated for vegetative cell populations (that is, E. coli with a z[E] of 41 kV/cm). These observations need more comprehensive investigation before any conclusions are reached.

Several investigations have reported data on inactivation of S. cerevisiae when exposed to PEF. Overall, the D-values vary significantly depending on the electric field strength and temperature. In general, the magnitudes are larger than E. coli, lower than L. monocytogenes and much less than B. subtilis spores. An z(E) of 17 kV/cm has been estimated from data reported for PEF treatments of S. cerevisiae in apple juice, much lower than the value estimated for E. coli (41 kV/cm) and similar to the one of B. subtilis spores (15.5 kV/cm).

The influence of electrical field strength (E) on the rate of microbial population inactivation may also be estimated from the coefficient (K). These parameters have been reported for a limited number of microbial populations. Among them, the populations with greater resistance to PEF would include Escherichia spp., Listeria spp., Pseudomonas spp. and Klebsiella spp. The coefficient z(E) was highest for Escherichia spp., which was higher than the one for B. subtilis spores. Data are insufficient to make valid comparisons of the relative resistance for vegetative and spore populations to PEF.

In summary, the survivor data for microbial populations exposed to PEF are too limited to be used in reaching definite conclusions about the magnitude of the kinetic parameters. In addition, data are not adequate to calculate parameters to compare the relative resistance of various microbial populations to PEF. For instance, data based on the same field strength and temperature are lacking. In addition, only a few of the published reports provide information on the threshold field strengths needed to initiate inactivation.

1.3. Future Research Needs

This section focuses on the research needs associated with kinetic parameters to be used for development of food preservation processes to ensure safety. For several technologies discussed in this report, the data necessary to estimate kinetic parameters are lacking. If these technologies are to evolve to industrial applications, kinetic data must be collected in the future.

The following is a list of research areas that need further investigation:

• Evaluation of the adequacy of a linear first-order survivor curve. Although there is evidence of various types of deviation from the historical model, a universally accepted alternative has not evolved. Future research on an appropriate model would be beneficial to all preservation technologies.
• Investigation on the influence of pressure on reduction of microbial populations using the proper experimental design (statistically valid, collection of data at different pressures and control of temperature and product), so that z(P) and/or activation volumes (V) are quantified. These investigations should also evaluate synergistic effects between pressure and temperature.
• Research on developing an experimental protocol for obtaining statistically reliable kinetic parameters to describe survivor curves for microbial populations exposed to PEF. These studies should incorporate multiple levels of electric field intensity, as well as the potential for synergy with temperature.
• Further research on the PEF microbial inactivation models presented as Eq. (11) or (12). The investigations need to provide reliable kinetic parameters for these models and for the microbial population of interest in food safety.