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.     

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     

Evaluation and Quantification of Heat Treatments Applied to Food Preserves

The quantitative study of heat treatments for sterilisation uses the Bigelow model to calculate the sterilising value (F). Calculation of F requires the previous determination of parameters D (decimal reduction time at experimental temperature) and Z (thermal-death time parameter), obtained from the thermal-death kinetics. Herein we compare two different methods, namely the Bigelow model and a predictive-type statistical method, to calculate the sterilisation effect against Bacillus coagulans spores when heat was applied to runner bean preserves (variety: Helda). Samples were subjected to various autoclave treatments at working temperatures (T _ai) of 105, 107, 110, and 115°C for periods from 3 to 35 min. The microorganism used was B. coagulans. Sterilisation achieved by these autoclave treatments was determined by using the equation based on the Bigelow model (n _probe = F ^z _Ti/D _Ti) where n is the fractional concentration of colony-forming units (or some quality factor), F ^z _Ti is F at temperature T _i, and D _Ti is D at temperature T _i. The Bigelow model can be used to obtain Z (thermal-death time parameter), which is needed to calculate the traditional sterilisation factor F, but not to determine the reduction factor n for the heat treatments, particularly when microbial indicators with low decimal reduction times (D) are studied. The thermokinetic parameters for B. coagulans in runner bean solution resulted to be Z = 10.64°C and D ₁₂₁ = 0.0264 min (Af = 1.04). Treatment at 115°C for 20 min resulted in the most efficient sterilisation effect for B. coagulans.     

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.     

Using Dielectric Relaxation Spectroscopy to Characterize the Glass Transition Time of Polydextrose

Dielectric relaxation spectroscopy was used to characterize the glass transition time, t_g, of polydextrose, where the glass transition temperature, T_g, and water activity, a_w (relative humidity), were held constant during polydextrose relaxation. The t_g was determined from a shift in the peak frequency of the imaginary capacitance spectrum with time. It was found that when the peak frequency reaches 30 mHz, polydextrose undergoes glass transition. Glass transition time, t_g, is the time for polydextrose to undergo glass transition at a specific T_g and a_w. Results lead to a modified state diagram, where T_g is depressed with increasing a_w. This curve forms a boundary: (a) below the boundary, polydextrose does not undergo glass transition and (b) above the boundary, polydextrose rapidly undergoes glass transition. As the boundary curve is specified by a t_g value, it can assist in the selection of storage conditions. An important point on the boundary curve is at a_w = 0, where T_g0 = 115 °C. The methodology can also be used to calculate the stress‐relaxation viscosity of polydextrose as a function of T_g and a_w, which is important when characterizing the flow properties of polydextrose initially in powder form.     

Effect of water activity on the inactivation kinetics of Escherichia coli O157:H7 by electron beam in ground beef, chicken breast meat, and trout fillets

Water activity (a_w) of ground beef, chicken breast meat, and trout fillets was modified to intermediate (a_w 0.98–0.99) and lowest (a_w 0.94–0.96) levels. The meat samples with modified and unaltered (native, a_w 1.00) a_w were inoculated with Escherichia coli O157:H7 and subjected to electron beam (e‐beam). Survivor curves were plotted and the D₁₀‐values were calculated. The D₁₀‐values ranged from 0.22 kGy for trout at native a_w to 0.33 kGy for beef at intermediate, and chicken and trout at lowest a_w. Regardless of the species, a_w reduction increased E. coli resistance to e‐beam, suggesting that even small depletion of unbound water from food increases survival. The difference of the D₁₀‐values between the samples at intermediate and lowest a_w was insignificant. E‐beam could be used before a_w‐reducing techniques are applied to food products. However, this would require stringent microbial control following e‐beam processing. The ‘tailing’ of survivors was observed for some samples with reduced a_w.     

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     

Expressing the equivalence of non‐isothermal and isothermal heat sterilization processes

Currently, the sterility of heat‐processed food and pharmaceuticals is assessed in terms of an F₀ value, based on the equivalence of the heat treatment to an isothermal process at a reference temperature. This F₀ value, however, has a meaning if, and only if, the inactivation kinetics of the targeted spores (or cells) follow a first‐order relationship and the temperature dependence of the D value, the reciprocal of the rate constant, is log‐linear. There is growing evidence that these conditions are not satisfied by many spores, including those of Clostridium botulinum and vegetative cells. Consequently, a replacement for the F₀ value is proposed in the form of a momentary equivalent time at the reference temperature based on the actual survival pattern of the spores, which need not be log‐linear. This equivalent time can be calculated together with the theoretical survival ratio in real time, thus enabling an operator to monitor the lethality of ongoing industrial heat processes. The concept is demonstrated with published survival data of C. botulinum, for which the Weibullian and log‐logistic models served as primary and secondary models, respectively. The safety factor according to the proposed method is in the number of added minutes of processing, beyond the theoretical time needed to reduce the survival ratio of the targeted spores or cells to a level that would produce practical (or commercial) sterility. Copyright © 2006 Society of Chemical Industry     

Effect of Octenylsuccinylation on Rheological Properties of Corn Starch Pastes

Rheological properties of corn starch octenylsuccinate (OSA starch) pastes (5%, w/w), at different 1‐octenylsuccinic anhydride (OSA) contents (0, 1.0, 1.5, 2.0 and 2.5%, w/w) were evaluated in steady and dynamic shear. The OSA starch pastes had high shear‐thinning behaviors and their flow behaviors were described by power law, Casson, and Herschel‐Bulkley models. Magnitudes of consistency index (K, K_h) and yield stress (σ_oc, σ_h) increased with the increase in OSA content and the decrease in temperature. Over the temperature range of 10–50°C, the effect of temperature on apparent viscosity (η_a,100) was described by the Arrhenius equation. The activation energy values (E_a = 10.7–13.9 kJ/mol) of OSA starches were lower than that (E_a = 15.9 kJ/mol) of native starch. Dynamic frequency sweep test showed that both storage modulus (G′) and loss modulus (G′′) of OSA starch pastes increased with the increase in OSA content. Dynamic (η^*) and steady shear (η_a) viscosities of OSA starch pastes at various OSA contents did not follow the Cox‐Merz superposition rule.     

Effect of heating–cooling cycle on the opto‐structural properties of low‐density polyethylene fibres using two‐beam interference microscopy

A hot stage attached with a two‐beam interference (Pluta) microscope was used to apply a heating–cooling cycle (HCC) on low‐density polyethylene fibres (LDPE). The variation of the refractive indices (n ^∥ and n ^⊥) with the temperature was carried out during the heating and cooling of the LDPE fibres. The activation energy (E _a) and thermooptic coefficient (dn/dT) were calculated for the investigated LDPE fibres. The spectral dispersion curves, percent crystallinity and orientation function were determined for the treated LDPE fibres. It was found that the HCC for LDPE fibre implies: a reversible behaviour of both optical and structural properties against temperature and an improvement in the fibre crystallinity.     

Original article: Characterisation of water species revealed in the drying operation of Todarodes pacificus Steenstrup using water proton NMR analysis

For the discrimination of water molecules during the squid‐drying process, the water distribution was characterised by water proton NMR and moisture diffusivity (De) analysis methods as a function of the water content (W₀). The proton NMR spectrum showed three peaks indicating three different species (species‐A, ‐B, and ‐C) distributed in the squid muscle, each of which had a characteristic behaviour of the relaxation time (T₂) as a function of the W₀. The 1/T₂ of species‐A was drastically varied at W₀ = 120%‐d.b., indicating two further categories, i.e., species‐A₁ and ‐A₂. Species‐A₁ is available at W₀ > 120%‐d.b. and was characterised as having De = 5.1 × 10^?10 m² s^?1, activation energy of moisture diffusivity (E_D) = 17 kJ mol^?1, and relaxation rate 1/T₂ = 74 s^?1, as evaluated by the proton NMR spectrum without depending on W₀. Species‐A₂ is available at W₀ < 120%‐d.b., indicating a distribution of De = 4.8 × 10^?10–1.7 × 10^?10 m² s^?1, E_D = 25–35 kJ mol^?1 and 1/T₂ = 1.8 × 10³–1.5 × 10² s^?1 with increasing W₀. Species‐A₁ and ‐A₂ were assigned as weakly restricted water and strongly restricted water, respectively.     

Estimation of the Intrinsic Birefringence of the A,B and V Crystalline Forms of Amylose

Optical birefringence (Δn) for A, B, V_a, V_h amylose crystals were calculated by vector summation of bond polarizabilities. Orientation of the O‐H bond vectors in these amylose crystals is not well understood so results were given for a range of O‐H conformers. For B amylose, Δn was calculated to be 0.043‐0.058 for the Wu and Sarko crystal structure, while Δn = 0.0‐0.01 for the now widely accepted crystal structure of Imberty and Perez. This latter estimate is somewhat lower than experimental values of 0.031‐0.037 determined previously for highly oriented amylose films. Reasons for the discrepancy may include uncertainty in empirical polarizability parameters or neglect of contributions from amorphous components and water. Predicted values of Δn for A amylose were similar to B amylose while Δn for V amyloses were smaller (‐0.04‐0.0). These estimates of the intrinsic birefringence of amylose crystals should be helpful in estimating the degree of orientation for starch films/fibers and in better understanding the molecular origins of birefringence of oriented starch.     

Gelatinization and Pasting Properties of Waxy and Non‐waxy Rice Starches

Gelatinization and pasting properties of diverse rice types grown in two locations were examined by differential scanning calorimetry (DSC) and rotational rheometry, respectively. The data were compared to previously reported molecular starch properties for these samples: specifically, amylose content, starch molecular weight (M_w), and amylopectin side‐chain‐length distributions. Significant correlations were observed between amylose content, starch M_w, and the weight degree of polymerization of the long side chains of amylopectin F₁(DP_w) and many of the gelatinization and pasting properties measured. Higher amylose content corresponded with increased gelatinization onset (T_o) and peak temperatures (T_p), pasting onset and peak temperatures, and decreased peak and trough viscosity. Starch M_w correlated negatively with T_o, T_p, pasting onset, and peak temperature and positively with peak, trough, final, and breakdown viscosity. Amylopectin with DP_w 59‐78 of F₁(DP_w) correlated with increased T_o, T_p, pasting onset and peak temperature, and decreased peak, trough, final and breakdown viscosity. Pasting properties were also somewhat related to DP_w 21 of shorter side chains of amylopectin (F₂(DP_w)). Significant correlations between F₂(DP_w) and peak, final, and breakdown viscosity were observed (r = −0.447*, −0.391*, −0.388*, peak, final, and breakdown viscosity, respectively).     

Crystallization kinetics of palm oil in blends with palm-based diacylglycerol

Crystallization kinetics of palm oil (PO) in the presence of different concentrations (2, 5, 10, 30 and, 50% w/w) of palm-based diacylglycerol (PB-DAG) were investigated over different ranges of crystallization temperatures. Addition of 30 and 50% (w/w) of PB-DAG (high concentrations) increased significantly (P < 0.05) the melting point and crystallization onset while addition of 2 and 5% PB-DAG did not have significant (P > 0.05) effect. PO and PO blends with 2 and 5% of PB-DAG showed crystal transformation at crystallization temperatures (T_Cr) of 26, 26, 26.5 °C, respectively as reflected in corresponding changes of the Avrami parameters at below and above these T_Cr. This was especially evident for the blends containing 2 and 5% of PB-DAG. Individual comparison of induction time (T_i), Avrami exponent (n), Avrami constant (k) and half-time of crystallization (t_1/2) of blends classified under various supercooling ranges based on the supercooling closeness (± 0.1 °C), showed that addition of 5% of PB-DAG in most of the supercooling ranges significantly (P < 0.05) reduced nucleation rate as well as crystal growth velocity of PO. This was reflected in the significantly (P < 0.05) higher T_i and t_1/2 and lower k. Although the presence of 2% of PB-DAG was found to have inhibitory effect on PO crystallization, this effect was not significant (P > 0.05). Mode of crystal growth attributed to n was changed significantly only in presence of 5% of PB-DAG. Furthermore, presence of 10% PB-DAG showed ??'-stabilizing effect on PO. On the other hand, high concentrations of PB-DAG were found to significantly (P < 0.05) reduce T_i as well as t_1/2 and also increase k suggesting their promoting effects on nucleation and crystallization rate of PO even with the close supercoolings. In addition, they changed crystal growth mode of PO. Amongst the different concentrations of PB-DAG investigated, blend containing 50% of PB-DAG as compared to PO, not only, have healthier benefits but also, may have greater potential applications in plastic fat products due to its unique physical properties.     

Steady and Dynamic Shear Rheology of Rice Starch‐Galactomannan Mixtures

Rheological properties of rice starch‐galactomannan mixtures (5%, w/w) at different concentrations (0, 0.2, 0.4, 0.6 and 0.8%, w/w) of guar gum and locust bean gum (LBG) were investigated in steady and dynamic shear. Rice starch‐galactomannan mixtures showed high shear‐thinning flow behaviors with high Casson yield stress. Consistency index (K), apparent viscosity (η_a,100) and yield stress (σ_oc) increased with the increase in gum concentration. Over the temperature range of 20–65°C, the effect of temperature on apparent viscosity (η_a,100) was described by the Arrhenius equation. The activation energy values (E_a = 4.82–9.48 kJ/mol) of rice starch‐galactomannan mixtures (0.2–0.8% gum concentration) were much lower than that (E_a = 12.8 kJ/mol) of rice starch dispersion with no added gum. E_a values of rice starch‐LBG mixtures were lower in comparison to rice starch‐guar gum mixtures. Storage (G′) and loss (G′′) moduli of rice starch‐galactomannan mixtures increased with the increase in frequency (ω), while complex viscosity (η*) decreased. The magnitudes of G′ and G′′ increased with the increase in gum concentration. Dynamic rheological data of ln (G′, G′′) versus ln frequency (ω) of rice starch‐galactomannan mixtures have positive slopes with G′ greater than G′′ over most of the frequency range, indicating that their dynamic rheological behavior seems to be a weak gel‐like behavior.     

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.     

Sensitivity Analysis for Hygrostress Crack Formation in Cylindrical Food During Drying

A parametric analysis was performed to examine the influence of several factors on stress crack formation in cylindrical food during drying using a previously developed, validated simulation method. They included initial food moisture (W_o), air humidity (R_h) and temperature (T_a), convective surface mass transfer coefficient (h_m), convective surface heat transfer coefficient (h_t), moisture diffusivity (D_w), and initial food diameter (d_o). R_h influenced most strongly drying time for crack formation (t_cf), followed by T_a and W_o. The other 4 parameters in descending order of influence were h_m, h_t, d_o and D_w. The influence of all parameters, except W_o, was due to their influence on mass transfer Biot number, Bi_m, that was closely related to moisture concentration gradient in food. The influence of W_o was due to increased critical stress for crack formation with a reduced moisture level.     

Rheology of Rice Starch‐Sucrose Composites

The effect of sucrose at different concentrations (0, 10, 20 and 30%) on rheological properties of rice starch pastes (5% w/w) was investigated in steady and dynamic shear. The steady shear properties of rice starch‐sucrose composites were determined from rheological parameters for power law and Casson flow models. At 25°C all the starch‐sucrose composites exhibited a shear‐thinning flow behavior (n=0.25–0.44). The presence of sucrose resulted in the decrease in consistency index (K), apparent viscosity (η_a,100) and yield stress (σ_oc). Dynamic frequency sweeps at 25°C indicated that starch‐sucrose composites exhibited weak gel‐like behavior with storage moduli (G′) higher than loss moduli (G′′). G′ and G′′ values decreased with the increase in sucrose concentration. The dynamic (η*) and steady‐shear (η_a) viscosities at various sucrose concentrations did not follow the Cox‐Merz superposition rule. G′ values as a function of aging time (10 h) at 4°C showed a pseudoplateau region at long aging times. In general, the values of G′ and G′′ in rice starch‐sucrose composites were reduced in the presence of sucrose and depended on sucrose concentration.     

True Density Prediction of Garlic Slices Dehydrated by Convection

Physiochemical parameters with constant values are employed for the mass‐heat transfer modeling of the air drying process. However, structural properties are not constant under drying conditions. Empirical, semi‐theoretical, and theoretical models have been proposed to describe true density (ρ_p). These models only consider the ideal behavior and assume a linear relationship between ρ_p and moisture content (X); nevertheless, some materials exhibit a nonlinear behavior of ρ_p as a function of X with a tendency toward being concave‐down. This comportment, which can be observed in garlic and carrots, has been difficult to model mathematically. This work proposes a semi‐theoretical model for predicting ρ_p values, taking into account the concave‐down comportment that occurs at the end of the drying process. The model includes the ρ_s dependency on external conditions (air drying temperature (T_a)), the inside temperature of the garlic slices (T_i), and the moisture content (X) obtained from experimental data on the drying process. Calculations show that the dry solid density (ρ_s) is not a linear function of T_a, X, and T_i. An empirical correlation for ρ_s is proposed as a function of T_i and X. The adjustment equation for T_i is proposed as a function of T_a and X. The proposed model for ρ_p was validated using experimental data on the sliced garlic and was compared with theoretical and empirical models that are available in the scientific literature. Deviation between the experimental and predicted data was determined. An explanation of the nonlinear behavior of ρ_s and ρ_p in the function of X, taking into account second‐order phase changes, are then presented.