A model of non‐isothermal degradation of nutrients,pigments and enzymes

Published isothermal degradation curves for chlorophyll A and thiamine in the range 100–150 °C and the inactivation curves of polyphenol oxidase (PPO) in the range 50–80 °C could be described by the model C(t)/C₀ = exp[?b(T)tⁿ] where C(t) and C₀ are the momentary and initial concentrations, respectively, b(T) a temperature dependent ‘rate parameter’ and n, a constant. This suggested that the temporal degradation/inactivation events of all three had a Weibull distribution with a practically constant shape factor. The temperature dependence of the ‘rate parameter’ could be described by the log logistic model, b(T) = log_e[1 + exp[k(T ? T_c)], where T_c is a marker of the temperature level where the degradation/inactivation occurs at a significant rate and k the steepness of the b(T) increase once this temperature range has been exceeded. These two models were combined to produce a non‐isothermal degradation/inactivation model, similar to one recently developed for microbial inactivation. It is based on the assumption that the local slope of the non‐isothermal decay curve, ie the momentary decay rate, is the slope of the isothermal curve at the momentary temperature at a time that corresponds to the momentary concentration of the still intact or active molecules. This model, in the form of a differential equation, was solved numerically to produce degradation/inactivation curves under temperature profiles that included heating and cooling and oscillating temperatures. Such simulations can be used to assess the impact of planned commercial heat processes on the stability of compounds of nutritional and quality concerns and the efficacy of methods to inactivate enzymes. Simulated decay curves on which a random noise was superimposed were used to demonstrate that the degradation/inactivation parameters, k and T_c, can be calculated directly from non‐isothermal decay curves, provided that the validity of the Weibullian and log logistic models and the constancy of the shape factor n could be assumed. Copyright © 2004 Society of Chemical Industry     

Theoretical comparison of a new and the traditional method to calculate Clostridium botulinum survival during thermal inactivation

When published isothermal survival data of Clostridium botulinum spores in the range 101–121 °C were plotted in the form of logS(t) vs t relationships, where S(t) is the momentary survival ratio, they were all non‐linear. They had a noticeable upward concavity, in violation of the assumption that sporal inactivation is a process that follows first‐order reaction order kinetics. They could be described by the power law model logS(t) = ? b(T)t ^n(T), where b(T) and n(T) are temperature‐dependent coefficients of the order of 0.1–6 and about 0.4 respectively. These coefficients were used to construct simulated survival curves under different heating regimes with a recently proposed model. The model is based on the assumption that the local slope of the non‐isothermal survival curve, or the momentary inactivation rate, is determined solely by the momentary temperature and survival ratio, which in turn are functions of the population thermal history. The survival curves calculated with this model differ considerably from those produced by the standard method based on the traditional D and Z values. The shortcomings of the standard model are that these values depend on the number of points taken for the regression, and that its predicted survival ratios depend on the selected reference temperature. The differential equation which is proposed to replace it can be solved numerically using a program such as Mathematica®. Its predictions solely depend on the observed survival patterns under isothermal conditions and not on any preconceived kinetic model. Nevertheless, the method still needs verification with experimental non‐isothermal survival data, as has already been done with Listeria and Salmonella cells. © 2001 Society of Chemical Industry     

Comparing predicting models for heat inactivation of Listeria monocytogenes and Pseudomonas aeruginosa at different pH

Under the same experimental conditions it has been demonstrated that whereas survival curves of Listeria monocytogenes in the range of temperatures from 54 to 62 °C followed a first-order kinetic, those of Pseudomonas aeruginosa in the range of temperatures from 50 to 56 °C were not linear showing a shoulder followed by a linear region. The first order kinetic model did not describe survival curves of P. aeruginosa. A model based on the Weibull distribution (Log₁₀(N_t/N₀)=(1/−2.303)*(t/b)ⁿ)) accurately described the inactivation kinetics of both microorganisms at the three pHs of 4, 5.5, 7.4 investigated. For both microorganisms, the b value depended on the treatment temperature and the pH of the treatment medium. Whereas for L. monocytogenes the n value was independent of the treatment conditions, for P. aeruginosa the n value depended on the pH of the treatment medium.The model based on the Weibull distribution was capable of accurately predicting the treatment time to inactivate five Log₁₀ cycles of both microorganisms at the three pHs investigated.     

Microbial Inactivation Kinetics during High‐Pressure Carbon Dioxide Treatment: Nonlinear Model for the Combined Effect of Temperature and Pressure in Apple Juice

ABSTRACT: Isobaric and isothermal semi‐logarithmic survival curves of natural microflora in apple juice treated with high‐pressure carbon dioxide at 7, 13, and 16 MPa pressures and 35, 50, and 60 °C temperatures were fitted with a nonlinear equation to find the values of the coefficient b(P ), b(T ), n(P ), and n(T ). Profiles of the model parameters were obtained as a function of pressure and temperature. The model fitted with good agreement (R² > 0.945), the survival curves. An empirical equation was proposed to describe the combined effects of pressure and temperature. The equation, derived from a power law model, was written in the form: . The proposed model fitted the experimental data well. At 7 MPa and 50 and 60 °C, 13 MPa and 35 and 60 °C, 16 MPa and 35 °C, the model provided log₁₀ reduction residual values (observed value – fitted value) lower than 0.284 showing a good agreement between the experimental and the predicted survival levels.     

Probability of growth and toxin production by nonproteolytic Clostridium botulinum in rockfish fillets stored under modified atmospheres

Whether toxin production by Clostridium botulinum precedes or follows spoilage of fish stored under modified atmospheres (MA), remains unclear. In this factorial design study we inoculated a pool of nonproteolytic C. botulinum spores (5 type E, 4 type B, and 4 type F strains) at 6 levels (10⁴ to 10⁻¹) between two rockfish fillets and then incubated the fillets at 4, 8, 12 and 30°C under vacuum, 100% CO₂ and 70% CO₂+30% air for 21 days. The probability of toxigenesis by one spore was significantly affected (P<0.005) by temperature (T) and storage time (S_t), and not (P>0.1) by MA, MA×T or MA×S_t. At the 10° spore/sample level, the earliest time to detect toxin production at 4,8,12 and 30°C under all MAs was >21, 15–21, 6–9 and 2 days, respectively. No toxin production was detected at 4°C. Only type B toxin was present in the toxic samples. At 30°C storage, spoilage of fillets followed toxigenesis. Using linear and logistic regression models, equations were derived that could estimate the lag phase and predict the probability of one spore initiating growth under a particular storage condition.     

Effect of temperature and starch concentration on the creep/recovery behaviour of the grape molasses: modelling with ANN, ANFIS and response surface methodology

In this study, the effect of starch concentration (5, 7.5 and 10 %) and temperature (60, 70 and 80 °C) on the creep and recovery behaviour of grape molasses was investigated. Adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) models were established for the prediction of the compliance values (J(t)) based on temperature, starch concentration and time of the creep or recovery phases. The root mean square error, mean absolute error and R ² values were used for the comparison of the models which showed that the ANFIS model performed better than the ANN model for the desired purpose. The Burger model fitted the J(t) versus time data with R ² values ranging from 0.987 to 0.999. Response surface methodology (RSM) was performed to investigate the dependency of the creep (G ₀ , G ₁ , n ₀ and n ₁ ) and recovery (J _KV , B, C, J _max , J _∞ and  % recovery) parameters to temperature and starch concentration. As a result of this study, it was observed that deformation of the grape molasses samples increased with decrease in starch concentration and increase in temperature. The gel strength (S) values of the samples were also calculated and modelled by RSM. As increase in starch concentration caused an increase in S value, there was an inverse proportion between the temperature and S value.     

Stickiness of skim milk powder using the particle gun technique

The particle gun method for investigating the initiation of stickiness of dairy powders was examined using skim milk powder (SMP). The point at which significant stickiness occurred was at a constant temperature above the glass transition temperature (T_g) of amorphous lactose regardless of the temperature and relative humidity (RH) conditions of the air in the particle gun. This point has been called (T–T_g)_critical. The initial water activity of SMP did not significantly affect (T–T_g)_critical, confirming that stickiness is a surface phenomenon. Changing the particle feed rate did not effect (T–T_g)_critical or the rate at which the powder accumulated on the target plate. The errors in measuring the value of (T–T_g)_critical and the rate of stickiness development [slope of the deposition line versus (T–T_g)] for SMP were found to be 33.6 ± 0.8 °C and 3.1 ± 0.7% deposition °C^?1, respectively, after standardisation of the ambient air conditions around the powder feeder and the initial water activity of the SMP.     

A comparison of native and acid thinned normal and waxy corn starches: Physicochemical, thermal, morphological and pasting properties

The starches isolated from normal and waxy corn varieties were hydrolyzed with hydrochloric acid (0.14 mol equivalent/L) and evaluated for physicochemical and functional properties. Acid thinning decreased the amylose content and swelling power but increased the solubility. The light transmittance of acid thinned (AT) starch pastes was higher than those of their native starches after similar storage intervals. The scanning electron microscopic observation demonstrated that the acid thinning did not cause any disruption of the granular crystalline structure. Native normal corn starches showed lower onset temperature (T_o) and peak temperature (T_p) as compared to their counterpart AT starches, whereas the reverse was observed for waxy corn starch. Enthalpy of gelatinization (ΔH_gel) was lower in AT normal and waxy starches as compared to their native starches. The percentage of retrogradation (%R) was significantly higher for native corn starches as compared to their AT starches. A significant reduction in peak—(P_V), trough—(T_V), breakdown—(B_V), final—(F_V), and setback viscosity (S_V) was observed by acid thinning, and the reduction was more pronounced in AT waxy starches. Among AT starches, AT waxy starch showed the lowest values of P_V, T_V, B_V, F_V and S_V.     

Artificial neural network model for prediction of cold spot temperature in retort sterilization of starch-based foods

An artificial neural network (ANN) model was developed for prediction of the cold spot temperature profile during retort processing using starch dispersion (STD) as a model food. STDs of different concentrations were prepared by mixing corn starch powder with distilled water at 90 °C for 30 min. Each of the partially gelatinized STDs thus prepared was filled in retort pouches and processed in a retort under various combinations of holding temperature, holding time, and rotational speed. Thermocouples were inserted into selected pouches one by one to monitor the cold spot temperature at regular intervals. The profiles of cold spot temperature together with retort temperature thus obtained were served to ANN modeling as training or validation data. Back-propagation network was chosen as the network model. Input variables for the model were current and past temperatures of the cold spot (T_n, T_n−1, and T_n−2) and current retort temperature θ_n and current time t_n. Output was the temperature of the cold spot at the next time step T_n+1. A model with 2 hidden layers, which contained 11 and 15 nodes, respectively, was the best among the models tested. Using the model developed, prediction of a whole profile of the cold spot temperature was tested, starting from temperature data of the first three time steps with a whole profile of retort temperature monitored. The results showed very good performance of the model, relative errors for F₀ value prediction being less than 2%.     

Reliability‐based estimation of the survival of Listeria monocytogenes in chorizos

Reliability analysis is especially important when critical decisions are to be made involving potentially severe adverse consequences such as foodborne illness. Owing to uncertainty associated with the parameters controlling survival of Listeria monocytogenes in chorizo (a Mexican‐style sausage), the time needed to reduce the count by a certain number (n) of logs (t_nD) is probabilistic. In this paper the first‐order second‐moment (FOSM) method based on Taylor series expansion is used to derive the expected value and standard deviation of t_nD as function of the operating conditions (random variables) affecting survival, namely initial water activity (a_w0) of the sausage batter, storage temperature (T) and airflow velocity (F), along with their uncertainties characterised by their means and coefficients of variation. For any given n the derived t_nD probability distribution enables one to determine an estimate of t_nD for any desired level of reliability or confidence level, such as 50% (median value), 95%, 99%, etc. Among the conclusions drawn were: (i) the variability associated with T and F has a minor effect on estimating uncertainty in t_nD, whereas the reliability of t_nD estimation is greatly influenced by the uncertainty in a_w0; and (ii) the uncertainty in a_w0 has the greatest impact when a_w0 of the sausage formulation exceeds 0.90. The approach used and discussed in this paper can be applied to any survival/inactivation study to incorporate the effect of uncertainty in the various extrinsic and intrinsic parameters on the survival kinetics of the pathogen in a food system under evaluation. Copyright © 2006 Society of Chemical Industry     

Modeling changes in rheological properties of potatoes during storage under constant and variable conditions

The changes in rheological properties of potatoes stored at 5, 15, 25 °C and variable (fluctuating) temperature for 16 or 26 weeks were evaluated in terms of elasticity and viscosity parameters using axial compression and creep tests. Cylindrical test specimens (15 mm diameter and 30 mm long) were used. A third-degree polynomial best fitted the force-deformation curves in axial compression test (R²=0.98-0.99) whereas a four-element (Burgers) mechanical model adequately described the creep response of potatoes (R²=0.95-0.99). The tangent modulus of elasticity in axial compression and elasticity and viscosity parameters in creep tests in general decreased significantly (P<0.05) with increase in storage time both under constant and variable storage conditions. The changes in rheological properties of potatoes stored under constant storage condition were sufficiently described by a modified exponential model (R²=0.89-0.96) except for the viscosity parameter of the Maxwell component of the four-element model. The logarithm of degradation rate constant, k, and the constant, n, were linearly related to storage temperature. For the variable storage condition, a bulk mean temperature (T_bm) was calculated to account for a series combination of storage time and temperature to which the potatoes were subjected. The changes in rheological properties due to variable storage temperature were then described as a function of T_bm and storage time, t_s, using stepwise multiple regression. The result indicated that except the viscosity parameter of the Maxwell component of the four-element model, it was possible to describe the changes in rheological properties as a function of T_bm and t_s (R²=0.84-0.99).     

When is simple good enough: a comparison of the Gompertz,Baranyi, and three-phase linear models for fitting bacterial growth curves

The use of primary mathematical models with curve fitting software is dramatically changing quantitative food microbiology. The two most widely used primary growth models are the Baranyi and Gompertz models. A three-phase linear model was developed to determine how well growth curves could be described using a simpler model. The model divides bacterial growth curves into three phases: the lag and stationary phases where the specific growth rate is zero (gm=0), and the exponential phase where the logarithm of the bacterial population increases linearly with time (gm=constant). The model has four parameters: N_o(Log₈of initial population density), NMAX(Log₈of final population density), tLAG(time when lag phase ends), and tMAX(time when exponential phase ends). A comparison of the linear model was made against the Baranyi and Gompertz models, using established growth data forEscherichia coli0157:H7. The growth curves predicted by the three models showed good agreement. The linear model was more ‘robust' than the others, especially when experimental data were minimal. The physiological assumptions underlying the linear model are discussed, with particular emphasis on assuring that the model is consistent with bacterial behavior both as individual cells and as populations. It is proposed that the transitional behavior of bacteria at the end of the lag phase can be explained on the basis of biological variability.     

A mathematical model for moisture movement during continous and intermittent drying of <Emphasis Type="Italic">Eucalyptus saligna</Emphasis>

A modified diffusion-based mathematical model is proposed to describe the moisture movement during continuous and intermittent drying of Eucalyptus saligna. This model includes the temperature change, the surface drying coefficient (β _n ) and 2 diffusion coefficients [from green to FSP (D _f ) and from FSP to dry condition (D _o )] as important parameters. The final model expression obtained was M?=?exp (??25 β _n ² D _t /l²) with the β _n used was 1.5807 kg m^?2 s^?1, the D _f was 2.26?×?10^?11 m² s^?1, and the D _o was 5.85?×?10^?12 m² s^?1. The range of temperature change between heating and non-heating phases in the intermittent drying regimes was from 24.9 to 31.8 °C. The R² values obtained when the model was fitted into the drying data of different intermittent regimes ranged from 71.5 to 85.9%. The R² value was 87.4% when the model was fitted into continuous trial data. The high values of R² indicate that the model can be used to understand the moisture reduction both in intermittent and continuous regimes.     

Non‐Arrhenius and non‐WLF kinetics in food systems

The classic Arrhenius and WLF equations are commonly used to describe rate–temperature relations in food and biological systems. However, they are not unique models and, because of their mathematical structure, give equal weight to rate deviations at the low‐ and high‐temperature regions. This makes them particularly useful for systems where what happens at low temperatures is of interest, as in spoilage of foods during storage, or where the effect is indeed exponential over a large temperature range, as in the case of viscosity. There are systems, however, whose activity is only noticeable above a certain temperature level. A notable example is microbial inactivation, for which these two classical models must be inadequate simply because cells and spores are not destroyed at ambient temperature. For such systems a model that identifies the temperature level at which the rate becomes significant is required. Such an alternative model is Y = ln{1 + exp[c(T ? T _c)]} ^m, where Y is the rate parameter in question (eg a reaction rate constant), T_c is the marker of the temperature range where the changes accelerate, and c and m are constants. (When m = 1, Y at T ? T_c is linear. When m ≠ 1, m is a measure of the curvature of Y at T ? T_c.) This model has at least a comparable fit to published rate–temperature relationships of browning and microbial inactivation as well as viscosity–temperature data previously described by the Arrhenius or WLF equation. This alternative log logistic model is not based on the assumption that there is a universal analogy between totally unrelated systems and simple chemical reactions, which is explicitly assumed when the Arrhenius equation is used, and it has no special reference temperature, as in the WLF equation, whose physical significance is not always clear. It is solely based on the actual behaviour of the examined system and not on any preconceived kinetics. © 2002 Society of Chemical Industry     

Impact of compression,physical aging,and freezing rate on the crystallization characteristics of an amorphous sugar matrix

Amorphous matrices made up of sugar molecules, are frequently used in food and pharmaceutical industries. A drawback to their use is that they are susceptible to collapse, as a result of water uptake and an increase in temperature and subsequently crystallize. Herein, the crystallization characteristics of amorphous sugar (sucrose and α-lactose) preparations were analyzed, with the purpose of obtaining knowledge that could lead to the prediction of how long the amorphous state is retained under various conditions. The impact of compression, physical aging and freezing rate on the induction period (t_ind) for crystallization were examined. Freeze-dried sugar samples were compressed at 74 or 443 MPa (5 min) and then rehumidified at specified RHs. Some freeze-dried sucrose samples were physically aged, and alternatively freeze-drying was conducted under different conditions. The isothermal crystallization of the prepared samples at different temperatures (T), the glass transition and the crystallization temperature (T_cry) were measured, using differential scanning calorimetry. The compression markedly decreased the t_ind, while significantly lowered the hygroscopicity. Physical aging and slower-freezing also shortened the t_ind. The t_ind was found to be correlated exclusively with (T_cry–T), regardless of rehumidification, compression, sugar type, physical aging and freezing rate in the freeze-drying process.     

Salmonella typhimurium resistance on pulsed electric fields associated with membrane fluidity and gene regulation

Effects of different growth temperatures on cytoplasmic membrane fluidity and phospholipids phase transition temperature (T_m) of Salmonella typhimurium and resistance to pulsed electric field (PEF) inactivation, as well as the expression of stress-related genes and fatty acid biosynthesis-associated genes were investigated. Results indicated that the PEF resistance of S. typhimurium increased as growth temperature increased. S. typhimurium cultivated at 10 °C exhibited the lowest PEF resistance with the reduction of 4.23 log₁₀ CFU/mL, while the reduction of 2.10 log₁₀ CFU/mL was found in S. typhimurium cultivated at 45 °C under the same PEF treatment, due to the up-regulation of the expression of fabA gene, which was characterized by the lowest T_m of membrane phospholipids and the greatest membrane fluidity. Although the expression of alternative sigma factors were altered by growth temperature, these genes were not essential for S. typhimurium to develop PEF resistance, suggesting that the PEF resistance modified by growth temperature could be caused by alterations in membrane fluidity.Industrial relevancePulsed electric fields (PEF) treatment has been widely applied in nonthermal pasteurization and increasingly focused on synergistic combinations with other techniques such as thermal treatment, sonication and antibacterial agents to improve the efficacy of PEF to inactivate micro-organisms. Our results indicated that S. typhimurium cultivated at relatively lower temperature was easily inactivated by PEF, due to the up-regulation of the expression of fabA gene, which was characterized by the lowest phase transition temperature of cytoplasmic membrane phospholipids and the greatest membrane fluidity. Therefore, the underlying mechanism of alterations in PEF resistance of S. typhimurium induced by growth temperature was explored to achieve better understanding of microbial inactivation by PEF.     

Theoretical analysis on pulsed microwave heating of pork meat supported on ceramic plate

Theoretical analysis has been carried out to study the role of ceramic plates (alumina and SiC) and pulsed microwave heating of pork meat (Pork Luncheon Roll (PLR) and White Pudding (WP)) samples. Spatial hot spots occur either at the center of the sample or at the outer face or at the face attached with alumina plate and application of pulsing minimizes formation of hot spots within meat samples. Pulsing of microwave is characterized by set point for temperature difference (ΔT_S) and on–off constraints for temperature (T′). It is found that alumina plate with higher ΔT_S and lower T′ may be recommended for thick meat samples (both WP and PLR) whereas for thin meat samples, lower ΔT_S with alumina plate/without plate may be preferred. It is also observed that SiC plate may be selectively used with ΔT_S = 20 K for both the pork meats. The distributed microwave incidence is found to be effective due to lesser degree of thermal runaway in absence of pulsing for both meat samples.     

Defining treatment conditions for pulsed electric field pasteurization of apple juice

The influence of temperature and the presence of N^α-lauroyl ethylester (ethyl lauroyl arginate, LAE) on the inactivation caused by continuous pulsed electric field treatments (PEF) in Escherichia coli O157:H7 suspended in apple juice have been investigated to define treatment conditions applicable at industrial scale that promote an equivalent safety level when compared with thermal processing. In the range of experimental conditions investigated (outlet temperature: 20-40 °C, electric field strength: 20-30 kV, treatment time: 5-125 μs) at outlet temperatures equal or lower than 55 ± 1 °C, the inactivation of E. coli O157:H7 treated in apple juice ranged from 0.4 to 3.6 Log₁₀ cycles reduction and treated in apple juice supplemented with LAE (50 ppm) ranged from 0.9 to 6.7 Log₁₀ cycles reduction.An empirical mathematical model was developed to estimate the treatment time and total specific energy input to obtain 5 Log₁₀ cycles reduction in the population of E. coli O157:H7 suspended in apple juice supplemented with 50 ppm of LAE at different electric field strengths and inlet temperatures. Treatment conditions established for E. coli O157:H7 were validated with other PEF resistant Gram-positive (Listeria monocytogenes, and Staphylococcus aureus) and Gram-negative (Salmonella enterica serovar Typhimurium) strains. When the treatment was applied to the apple juice, a treatment of 25 kV/cm for 63 μs corresponding with an outlet temperature of 65 °C and input energy of 125 kJ/kg was required to achieve more than 5 Log₁₀ cycles in the four strains investigated. The addition of LAE reduced the treatment time required to obtain an equivalent inactivation (> 5 Log₁₀ cycles) in the four microorganisms to 38.4 μs, the outlet temperature to 55 °C, and the input energy to 83.2 kJ/kg.     

Limitations of the Log-Logistic Model for the Analysis of Sigmoidal Microbial Inactivation Data for High-Pressure Processing (HPP)

This study identified limitations of the log-logistic model to evaluate microbial inactivation kinetics by high-pressure processing (HPP) including the need to assign a numerical value to “approximate” the undefined expression log₁₀ t?=?0 and the misinterpretation of its parameters due to a derivation flaw. Peer-reviewed HPP microbial inactivation data were adjusted to a sigmoidal equation (SIG), the original “vitalistic” log-logistic models (VIT-1, VIT-6), and two functions that did not follow the original derivation procedure (LOG-1, LOG-6). Their goodness of fit was determined utilizing the coefficient of determination (R ² ) and Akaike information criteria (AIC). The shape of the survival curve greatly influenced the performance of log-logistic models. VIT and LOG models performed equally when the kinetic curve showed a sigmoidal shape, and the numerical values of their parameter estimates were identical regardless of the log₁₀ (t?=?0) approximation. Conversely, most concave curves yielded inaccurate parameter estimates for all models. LOG-1 and VIT-1 performed best when log₁₀ t?=?0 was ?1 or ?2, whereas LOG-6 and VIT-6 yielded best results for values of ?3 to ?9. SIG ranked last for most datasets but occasionally performed best (Akaike weight factor w_AICi ?=?0.40–1.00) when microbial survival counts showed clear sigmoidal shapes. VIT models consistently displayed R ² ?≥?0.98, and their parameters can be interpreted within a “biological” context using the corrected derivation shown for LOG models. However, concave curves are more frequently observed for HPP microbial inactivation, and fitting the experimental data to log-logistic models deems unnecessary.