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     

Estimation of the survival curve of Listeria monocytogenes during non-isothermal heat treatments

Published survival curves of Listeria monocytogenes under several constant temperatures in the range of 50–65°C could be described by the model Log₁₀[S(t)]=−b(T)t^n(T), where S(t) is the momentary survival ratio, and b(T) and n(T) coefficients whose temperature dependence was expressed by empirical models. When the temperature history T(t) is also expressed algebraically, b(T) and n(T) are transformed into time dependent terms, b[T(t)] and n[T(t)] respectively. If there is no growth and damage repair during the heating process, and the momentary inactivation rate only depends on the momentary temperature and survival ratio, then the solution of the differential equation dLog₁₀[S(t)]/dt=−b[T(t)]*n[T(t)]*{−Log₁₀[S(t)]/b[T(t)]}^∧{(n[T(t)]−1)/n[T(t)]} provides the survival curve under the specified non-isothermal conditions. The validity of this model is demonstrated by the agreement of its predictions, calculated numerically using Mathematica®, to reported survival data of Listeria during heating at a constant and varying rates. Unlike in the traditional calculation methods of microbial survival, the one employed here does not require that microbial mortality be a process following a first or any other order kinetics model.     

Seven Factor Response Surface Optimization of a Double-Stage Lye (NaOH) Peeling Process for Pimiento Peppers

A double-stage lye (NaOH) peeling process involving pretreatment (concentration, c₁ temperature, T₁ time, t₁), holding time (t_h), and post-treatment (C₂, T₂, t₂) was introduced for pimiento peppers (Capsicum annum L. cv. ‘Truhart’). The effect of the seven factors on four responses (unpeeled skin, peeling loss, product yield, and texture) were studied using Response Surface Methodology. Processing times (t₁ and t₂) and lye concentrations (c₁ and c₂) were the most important factors, while processing temperatures (T₁ and T₂) and holding time (t_h) had no significant effect on the peeling operation. A mild pretreatment of c₁? 3.2% NaOH for t₁= 130 sec combined with a relatively strong post-treatment of c₂? 8% NaOH for t₂= 60 sec at T₁= T₂= 84°C and t_h= 45 sec was found to result in an optimum process. The double-stage process was more effective than the conventional single-stage operation.     

A model of temperature effects on microbial populations from growth to lethality

The propagation/destruction rate constant of microbial populations over the entire temperature range from growth (k(T) > 0) to lethality (k(T) < 0) can be described by a single mathematical model in the from: where b is a dimensionless constant related to the height of the growth peak, T_m and T_c temperatures characteristic of the growth and lethal regimes and a₁ and a₂ constants (temperature units) indicating the span of the growth region and the steepness of k(T) in the lethal temperature region respectively. The fit of the model is demonstrated with published data on the effect of heat on two bacteria. Since bacterial spores, unless germinated, do not multiply, a reduced version of the model is sufficient to describe their destruction rate at moderate (almost no effect) and high (lethal) temperatures ie . The fit of this equation is demonstrated with published data on the heat destruction kinetics of two bacilli spores. If the relationship between the model's constants and environmental conditions such as pH, a_w, salts concentration, etc can be expressed algebraically the model can be used to describe the combined effect of the various factors within the frame work of a single mathematical equation. Although the model's applicability is only demonstrated with a limited number of microorganisms the concept that a single model can describe both the propagation and lethal regimes can be useful in other types of biological populations, eg insects.     

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.     

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.     

Kinetics of Thermal Inactivation of Peroxidase and Color Degradation of African Cowpea (Vigna unguiculata) Leaves

Cowpea leaves form an important part of the diet for many Kenyans, and they are normally consumed after a lengthy cooking process leading to the inactivation of peroxidase (POD) that could be used as an indicator for the potential shelf life of the vegetables. However, color degradation can simultaneously occur, leading to poor consumer acceptance of the product. The kinetics of POD in situ thermal (for thermal treatments in the range of 75 to 100 °C/120 min) inactivation showed a biphasic first‐order model, with Arrhenius temperature dependence of the rate constant. The kinetic parameters using a reference temperature (T_ref) of 80 °C were determined for both the heat‐labile phase (k_ref = 11.52 ± 0.95 × 10^?2 min^?1 and E_a of 109.67 ± 6.20 kJ/mol) and the heat‐stable isoenzyme fraction (k_ref = 0.29 ± 0.07 × 10^?2 min^?1 and E_a of 256.93 ± 15.27 kJ/mol). Color degradation (L*, a*, and b* value) during thermal treatment was investigated, in particular as the “a*” value (the value of green color). Thermal degradation (thermal treatments between 55 and 80 °C per 90 min) of the green color of the leaves followed a fractional conversion model and the temperature dependence of the inactivation rate constant can be described using the Arrhenius law. The kinetic parameters using a reference temperature (T_refC = 70 °C) were determined as k_refC = 13.53 ± 0.01 × 10^?2 min^?1 and E_aC = 88.78 ± 3.21 kJ/mol. The results indicate that severe inactivation of POD (as an indicator for improved shelf life of the cooked vegetables) is accompanied by severe color degradation and that conventional cooking methods (typically 10 min/100 °C) lead to a high residual POD activity suggesting a limited shelf life of the cooked vegetables.     

Modeling rennet coagulation time and curd firmness of milk

Milk coagulation properties (MCP) are traditionally expressed using rennet coagulation time (RCT), time to curd firmness (CF) of 20 mm (k₂₀), and CF 30 min after enzyme addition (a₃₀) values, all of which are single-point measures taken from the output of computerized renneting meters, such as the Formagraph. Thus, traditional MCP use only some of the available information. Moreover, because of the worldwide spreading of breeds such as the Holstein-Friesian, characterized by late-coagulating milk, it happens often that some samples do not coagulate at all, that a₃₀ is strongly and negatively related to RCT, and that k₂₀ is not measurable. The aim of the present work was to model CF as a function of time (CF_t, mm) over a 30-min interval. The model tested was CFt=CFP×(1−e−kCF×(t−RCT)), where CF_P (mm) is the potential asymptotical CF at an infinite time, k_CF (min⁻¹) is the curd firming rate constant, and RCT is measured in minutes. The CF_t model was initially applied to data of milk of each of 105 Brown Swiss cows from 7 herds, each sampled once (trial 1). Four samples did not coagulate within 30 min. Eighty-seven of the 101 individual equations obtained fit the CF data of milk samples very well, even though the samples differed in composition, and were produced by cows of different ages and days in milk, reared on different farms (coefficient of determination >0.99; average residual standard deviation = 0.21 mm). Samples with a very late RCT (slowly coagulating samples) yielded so few observational data points that curve parameters could not be precisely estimated. The repeatability of CF_t equation parameters was estimated using data obtained from 5 replicates of each of 2 samples of bulk milk from 5 Holstein-Friesian cows analyzed every day for 5 consecutive days (trial 2). Repeatability of RCT was better than that of the other 2 parameters. Moreover, traditional MCP values (RCT, a₃₀, and k₂₀) can be obtained from the individual CF_t equations, using all available information. The MCP estimated from equations were very similar to the single-point measures yielded by the computerized renneting meter (coefficient of determination >0.97), but repeatability was slightly better. The model allowed the estimation of k₂₀ for samples with a very late coagulation or with very slow curd firming. Finally, the 3 novel parameters used to assess different milk samples were less interdependent than are the traditional measures, and their practical and scientific utility requires further study.     

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     

The relation between (bio-)chemical, morphological, and mechanical properties of thermally processed carrots as influenced by high-pressure pretreatment condition

Thermal texture evolution kinetics (90–110 °C) of nonpretreated and high-pressure pretreated (HP = 400 MPa, 60 °C, 15 min) carrots were determined using a multiparameter approach (cutting, compression). Alcohol Insoluble Residues (AIR) were extracted before and after thermal processing of the samples and the degree of methylation (DM) was estimated. The β-elimination kinetics of the water soluble pectin extract from the AIR was studied and related to the changes in material properties. Morphological changes and tissue-failure characteristics were monitored. The mechanical properties were strongly dependent on the processing temperature and the DM of the samples. Texture degradation rate constants were independent of the texture measurement method. Increasing temperature accelerated the β-elimination reaction (k _b) and the thermosoftening (k _x) rates, but pretreatment condition slowed down the rates. Interestingly, a strong correlation (r > 0.99) between k _b and k _x occurred. Thermal processing resulted in cell-wall thickening accompanied by a transition from cell rupture to cell separation, a process retarded by pretreatment condition.     

Modelling of cooking-cooling processes for meat and poultry products

Traditional cooking‐cooling of processed meat and poultry products is industrially carried out in smokehouses or autoclaves. A mathematical model was developed to simulate these operations. Equations, describing heat transfer and thermal destruction of micro‐organisms and quality characteristics, were solved numerically. The model was validated experimentally for heat transfer and energy consumption and was used to perform a sensitivity analysis. Input variables were: process time (PT), smokehouse temperature (T_SH), bologna size (diameter, D and height, H), surface heat transfer coefficients (h_heat and h_cool), product thermal diffusivity (α_heat and α_cool). Output variables were: product core temperature (T_c), core and volume‐average lethality (P_cm and P_vm) and cook (C_c and C_v) values as well as surface (Q_s) and volume‐average (Q_v) quality retention, total specific energy consumption (En) and energy efficiency (Ce). Multiple linear regression models were developed to predict C_c and C_v from five inputs and used to obtain acceptable deviation ranges.     

Thermal resistance of aerobic spore formers isolated from food products

The heat resistance of aerobic spore formers isolated from dairy products and cocoa powder was examined to give an overview of occurring highly heat‐resistant spores. Experiments were conducted in phosphate buffer at different temperatures for 30 min. Two Geobacillus pallidus strains survived the heat treatment at 125 °C with log reductions of 6.68 and 6.73. Furthermore, the inactivation kinetics of one of these strains (Bacillus amyloliquefaciens) were determined using a modified Arrhenius model. The inactivation followed a reaction order of 1 with a reaction rate constant (k_ref) of 0.085/s at 394 K and an activation energy (E_a) of 209 kJ/mol.     

Thermomechanical properties of biodegradable films based on blends of gelatin and poly(vinyl alcohol)

The aim of this work was to study the effect of the poly(vinyl alcohol) (PVA) concentration on the thermal and viscoelastic properties of films based on blends of gelatin and PVA using differential scanning calorimetry (DSC) and dynamic-mechanical analysis (DMA). One glass transition was observed between 43 and 49 °C on the DSC curves obtained in the first scanning of the blended films, followed by fusion of the crystalline portion between 116 and 134 °C. However, the DMA results showed that only the films with 10% PVA had a single peak in the tan δ spectrum. However, when the PVA concentration was increased the dynamic mechanical spectra showed two peaks on the tan δ curves, indicating two T_gs. Despite this phase separation behavior the Gordon and Taylor model was successfully applied to correlate T_g as a function of film composition, thus determining k=7.47. In the DMA frequency tests, the DMA spectra showed that the storage modulus values decreased with increasing temperature. The master curves for the PVA–gelatin films were obtained applying the TTS principle (T_r=100 °C). The WLF model was thus applied allowing for the determination of the constants C₁ and C₂. The values of these constants increased with increasing PVA concentrations in the blend: C₁=49–66 and C₂=463–480. These values were used to calculate the fractional free volume of the films at the T_g and the thermal expansion coefficient of the films above the T_g.     

MATHEMATICAL MODEL FOR THE SURVIVAL OF LISTERIA MONOCYTOGENES IN MEXICAN-STYLE SAUSAGE

Survival of Listeria monocytogenes in chorizos (Mexican‐style sausages) was modeled in relation to initial water activity (a_w0) and storage conditions using the Weibull cumulative distribution function. Twenty survival curves were generated from chorizos formulated at a_w0 = 0.85–0.97 then stored under four temperature (T) and air inflow velocity (F) conditions. The Weibull model parameters (α and β) were determined for every curve. Predicted survival curves agreed with experimental curves with R² = 0.945–0.992. Regression models (R² = 0.981–0.984) were developed to relate α and β to operating conditions. The times to one‐ and two‐log reduction in count (t_1D and t_2D) were derived from the Weibull model in terms of α and β. A parametric study revealed that L. monocytogenes survival was most sensitive to a_w0 between 0.90 and 0.95. The inactivation of L. monocytogenes could be maximized with higher T and lower a_w0; however, F did not significantly influence survival.     

Validation of the integrated upward–horizontal–downward wicking test for providing intensive properties of textile fabrics

Traditional wicking tests provide information that is specific to the test fluid, apparatus, and conditions. As a result, this information cannot be used to make predictions about wicking rates beyond the respective test parameters. In contrast, a new upward–horizontal–downward (UHD) wicking test has been presented that provides intensive properties of fabrics in the form of permeability (k) and effective capillary radius (R _c) as functions of saturation (S). The UHD test was developed using water as the test fluid. If the k–S–R _c relationships are truly intrinsic to a given fabric, then they should not depend on the test fluid. Here, we conducted the UHD test on a knit fabric using three different test fluids characterized by different surface tensions, densities, and viscosities: dodecane, tetradecane, and hexadecane. All fluids fall on the same k vs. S and k vs. R _c curves, proving that these curves are intrinsic characteristics of the fabric. We then used the k–S–R _c properties to successfully predict the in-plane horizontal and downward wicking rates of two different fluids, octanol and water, in the fabric. These results validate the UHD wicking test as a method for providing intensive properties of textile fabrics which can then be used for predicting wicking rates.     

Rates of degradation of plant cell walls measured with a commercial cellulase preparation

The relationship between the degradability, determined with a commercial cellulase preparation, of the cell walls of various plant parts of Italian ryegrass, maize and red clover can be expressed as Y = A - Be^?k₁^t-Cek₂^t, where Y = percentage of cell walls degraded, t = reaction time, k₁ and k₂ are rates of degradation, and A, B, and C are constants where A = B + C. Degradability of the cell walls of Italian ryegrass or maize could be predicted accurately from the absorbance of the filtrate at λ_max 282-288 or 310-324 nm. Treatment of cell walls of barley straw with 0.1 or 1M sodium hydroxide for 7 or 20 h degraded between 12 and 41% of the walls and led to the release of p-coumaric and ferulic acids, the amount increasing with concentration of alkali and treatment time; the less concentrated alkali released more ferulic than p-coumaric acid. Treatment with the cellulase preparation of the residues from alkali treatment showed that they were almost twice as degradable as the untreated walls.     

The contribution of high pressure carbon dioxide in the inactivation kinetics and structural alteration of myrosinase

High pressure carbon dioxide (HPCD) has been verified to be an efficient way of inactivating enzyme activity. This work investigates the influence of temperature (T), pressure (P), exposure times (t) on the activity of commercial myrosinase (MYR) submitted to HPCD. Results showed that only 1.00% of MYR activity retained at 22 MPa and 65 °C for 5 min. Moreover, the first‐order reaction kinetic data of MYR inactivation as influenced by pressure of HPCD were analysed. With the pressure rising from 8 to 22 MPa at 55 °C, the inactivation rate constant (k) increased from 0.015 to 0.024 min^?1, while the decimal reduction time (D) decreased from 157.2 to 96.1 min. Additionally, a series of exploratory experiments were conducted to investigate the contribution of the HPCD parameters (T, P and CO₂ dissolution), with analysing circular dichroism spectroscopy and tryptophan fluorescence spectra, illustrate that CO₂ dissolution plays a dominant role in MYR inactivation and structural alteration.     

A model of microbial survival after exposure to pulsed electric fields

Survival curves of microorganisms exposed to pulsed electric fields have a characteristic sigmoid shape when plotted in linear coordinates. They can be described by the phenomenological model S(V, n) - 100/(1 + exp(V - V_c(n)) /a((n))) where S(V, n) is the percent surviving organisms, V the field intensity, n the number of pulses, V_c(n) critical field intensity corresponding to 50% survival and a(n) a constant representing the curve's steepness (about 90% of the loss in number occurs within V_c ± 3a). Testing the model with published data showed an excellent fit. Moreover, both V_c(n) and a(n) could be described in terms of a single exponential decay term, indicative of the increased lethality of the field as the number of pulses increases. These enabled the creation of three dimensional plots of the survival-field intensity-number of pulses relationships, with linear or semi-logarithmic scales, from which similarity and differences in resistance can be revealed at a glance. The tabulated model's constants can also be used for quantitative comparison of the survival curves of different organisms. WhenV ? V_c the model is reduced to log[S(V, n)/100] = -V/a(n), that is it entails the same type of semi-logarithmic relationship between survival and field intensity, a relationship that is traditionally used to present survival curves.     

Physical aging of glassy normal and waxy rice starches: effect of aging time on glass transition and enthalpy relaxation

Physical aging and glass transition characteristics of amorphous normal and waxy rice starches (11 and 15% moisture contents) were investigated under differential scanning calorimetry as function of aging time. Normal rice starch showed higher T_g than waxy rice starch. The T_g and ΔC_p at glass transition gradually increased with aging time, whereas fictive temperature was slightly reduced regardless of moisture content and starch type. The relaxation enthalpy and relaxation peak temperature increased with aging time until structural equilibrium was reached. Enthalpy increase was more significant in the early stage of aging whereas temperature increase was constant during the aging period tested (120 h). Aging kinetic analysis using Cowie and Ferguson model revealed that the amorphous normal and waxy rice starches behaved in different modes for the physical aging. Relaxation distribution parameter (β) of both starches was in a range of 0.3<β<0.7, but higher at a lower moisture content, and for normal starch than for waxy starch. Maximum relaxation enthalpy for normal starch (1.10 and 2.69 J/g, respectively, at 11 and 15% moistures) was higher than those of waxy starch (0.77 and 2.48 J/g). Based on the characteristic time (t_c), normal starch has slower progression toward an equilibrium than waxy starch. Overall results proved that physical aging kinetics were highly dependent on starch structure and composition.