DSpace at VNU: Estimation of Accumulated Lethality Under Pressure-Assisted Thermal Processing

Food Bioprocess Technol DOI 10.1007/s11947-013-1140-6 ORIGINAL PAPER Estimation of Accumulated Lethality Under Pressure-Assisted Thermal Processing Loc Thai Nguyen & V M Balasubramaniam & Wannasawat Ratphitagsanti Received: 16 October 2012 / Accepted: 27 May 2013 # Springer Science+Business Media New York 2013 Abstract A study was conducted to develop an integrated process lethality model for pressure-assisted thermal processing (PATP) taking into consideration the lethal contribution of both pressure and heat on spore inactivation Assuming that the momentary inactivation rate was dependent on the survival ratio and momentary pressure–thermal history, a differential equation was formulated and numerically solved using the Runge–Kutta method Published data on combined pressure– heat inactivation of Bacillus amyloliquefaciens spores were used to obtain model kinetic parameters that considered both pressure and thermal effects The model was experimentally validated under several process scenarios using a pilot-scale high-pressure food processor Using first-order kinetics in the model resulted in the overestimation of log reduction compared to the experimental values When the nth-order kinetics was used, the computed accumulated lethality and the log reduction values were found to be in reasonable agreement with the experimental data Within the experimental conditions L T Nguyen Department of Food Technology, International University, Vietnam National University-HCMC, Quarter 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh City, Vietnam V M Balasubramaniam Department of Food Science and Technology, The Ohio State University, 2015 Fyffe Road, Columbus, OH 43210-1007, USA V M Balasubramaniam (*) Department of Food Agricultural and Biological Engineering, The Ohio State University, 2015 Fyffe Road, Columbus, OH 43210-1007, USA e-mail: balasubramaniam.1@osu.edu W Ratphitagsanti Department of Product Development, Faculty of Agro-Industry, Kasetsart University, 50 Ngam Wong Wan Road, Lad Yao, Chatuchak, Bangkok 10900, Thailand studied, spatial variation in process temperature resulted up to 3.5 log variation in survivors between the top and bottom of the carrier basket The predicted log reduction of B amyloliquefaciens spores in deionized water and carrot purée had satisfactory accuracy (1.07–1.12) and regression coefficients (0.83–0.92) The model was also able to predict log reductions obtained during a double-pulse treatment conducted using a pilot-scale high-pressure processor The developed model can be a useful tool to examine the effect of combined pressure–thermal treatment on bacterial spore lethality and assess PATP microbial safety Keywords Pressure-assisted thermal processing Accumulated lethality Bacterial spores F value Temperature distribution Introduction Pressure treatment at ambient temperature has been proven to be a viable alternative pasteurization method for the inactivation of vegetative bacteria, viruses, and yeasts (Farkas and Hoover 2000; Smelt 1998) However, the bacterial spores cannot be inactivated by pressure alone at ambient temperature even up to 1,500 MPa (Maggi et al 1996; Sale et al 1970) Pressure in combination with heat is needed for bacterial spore inactivation Pressure-assisted thermal processing (PATP), also known as pressure-assisted thermal sterilization, employs combined pressure (500–900 MPa) and heat (90–120 °C) treatment for the inactivation of bacterial spores (Akhtar et al 2009; Ananta et al 2001; Black et al 2007; Bull et al 2009; Gola et al 1996; Heinz and Knorr 2001; Koutchma et al 2005; Patazca et al 2006; Rajan et al 2006a, b; Reddy et al 2003; Rovere et al 1998) In February 2009, the Food and Drug Administration has issued “no objection” to an industrial petition of pressure-assisted thermal processing for the production of low-acid foods (http://www.foodprocessing.com/vendornews/2009/019.html) The petition primarily considered the lethal effect of heat Food Bioprocess Technol without taking credit for pressure lethality Pressure was only used to increase the preheated product temperature to 121 °C For successful commercialization of the PATP, the lethal contribution of both pressure and temperature on PATP microbial efficacy needs to be taken into account Sterilization process equivalent time (F value) has been traditionally used to establish thermal processes (Pflug 1995) The F value is the time required to achieve the desired level of microbial population reduction at a specified temperature to achieve either product safety or shelf-life expectations (Heldman and Hartel 1998) A range of different temperature–time combinations can be used to achieve the same result Thermal process calculations normally assume that bacterial destruction follows first-order kinetics (Eq 1)   N t logS t ị ẳ log 1ị ẳ N0 D where S(t) is the momentary survival ratio, N represents the number of spore survivors after treatment time t (in minutes), while N0 is the initial spore population D is the decimal reduction time (in minutes) The D value can also serve as the indicator of the thermal resistance of the studied microorganism Bigelow’s (1921) general method has been used for calculating the lethal rate (LR) during the thermal process (Eq 2) LR ¼ 10 ðT−T Þ z reduction time (D) and process resistance constant (z) become a function of both pressure and temperature Various researchers (Ahn et al 2007; Ananta et al 2001; Margosch et al 2004a, 2006; Rajan et al 2006a) further observed that during PATP, bacterial spores not always follow the firstorder kinetics In addition, the F value had to include pressure come-up time when transient pressure and temperature were observed It has been further reported (Ahn et al 2007; Margosh et al 2004b; Ratphitagsanti et al 2009) that a measurable fraction of spores was inactivated during pressure come-up time Limited studies attempted to extend the conventional F value concept to compare the benefits of PATP in preserving the quality of foods against thermal processing (Leadley et al 2008) or the process efficacy of different PATP conditions (Bull et al 2009; Koutchma et al 2005) In the absence of target spore kinetic data as a function of pressure and temperature, the F value was often calculated based on the thermal history only and the lethal effect of pressure was ignored (Bull et al 2009; Leadley et al 2008) Development of a model taking both the pressure and temperature lethal contribution into account will facilitate evaluating the PATP microbial process safety under different processing scenarios The objective of this study was to develop a model for estimating the accumulated lethality during PATP, considering the combined effects of pressure and temperature on spore inactivation ð2Þ where T0 is the reference temperature (in degree Celsius), z is the thermal resistance constant (in degree Celsius), and T is the process temperature (in degree Celsius) at any time during the thermal process Integrating lethal rate over process time can be used to determine the sterilization process equivalent time (accumulated process lethality), FT Z T−T F T ¼ 10 z dt ð3Þ The sterilization process equivalent time calculated at 121.1 °C is termed as F0 (Pflug 1995) Corradini et al (2006) pointed out that the thermal death time calculated using Eq and relevant relations are only valid when both the isothermal survival curve and the temperature dependence of D are log linear The application of elevated pressure reduced the D values and accelerated the inactivation of Bacillus amyloliquefaciens at 95, 105, and 110 °C (Rajan et al 2006a), hence enabling the heat treatment to be conducted at a lower temperature and under reduced thermal load PATP can inactivate the vegetative cells and bacterial spores while producing foods of higher quality as compared to that from conventional thermal processing (Black et al 2007) During PATP, both pressure and temperature can contribute to spore lethality The decimal Materials and Methods Model Development In Fig 1, the various stages in the development of an accumulated PATP process lethality model are summarized It was assumed that the momentary inactivation rate, dðlog S ðt ÞÞ , dt depended only on the momentary surviving ratio, log S(t), process temperature, and pressure, where S(t)=N/N0; N0 and N are the initial number of spore population and the spore survivors at any given process time t, respectively The model considered both linear (Eq 1) and nonlinear (Eq 4) inactivation kinetics for calculating the accumulated process lethality The following additional assumptions were also used for model development: Inactivation curves followed respective linear or nonlinear kinetics within the range of temperature and/or pressure considered Process lethality occurred above a minimum threshold pressure (>500 MPa) and temperature (>90 °C) for the inactivation of B amyloliquefaciens spores This threshold level may be different for different bacterial spores Above certain lethal pressure and thermal threshold levels, there Food Bioprocess Technol Literature based inactivation kinetics data for iso-baric and iso-thermal condition Fit the data using primary nth order kinetic model (Eq 5) and the secondary empirical models for kinetic parameters as a function of pressure and temperature (Eq 8) Fit the data using primary linear kinetics model (Eq 1) and the secondary empirical models for decimal reduction time (Eq 10) as a function of pressure and temperature Formulate differential equations for nth-order (Eq 13) and linear kinetics (Eq 14) and solve using Runge-Kutta method P, T experimental data from pilot scale equipment Obtain log reduction and accumulated lethality nT ;P ẳ a20 ỵ a21 P ỵ a22 T ỵ a23 P2 ỵ a24 T ỵ a25 PT Fig Stages used in model development for the determination of accumulated lethality during pressure-assisted thermal processing was no recovery of injury, repair, or growth of bacterial spores Only the pressure and temperature contributed to process lethality The potential contribution of transient pH shift to lethality under pressure was not considered For nonlinear kinetics, a general nth-order kinetic model (Margosch et al 2006) was chosen and can be described by ð4Þ For n≠1, the analytical solution of Eq can be presented as log À Á1 N ¼ log þ k t N 0n−1 ðn−1Þ 1−n N0 ð5Þ where k is the rate constant and n is the reaction order The temperature (in Kelvin) and pressure (in joules per cubic centimeter) dependency of the reaction constant k was derived through the relationship with Gibb’s free energy (G, in joules per mole; Hawley 1971) G ẳ R T lnk 6ị and ẳ PP0 ị2 ỵ PP0 ị T −T Þ !   T −ΔC p T ln ỵ T ỵ V PP0 ịS T T ị ỵ G0 T0 G PP0 ị2 PP0 ịT T ị ỵ a12 ln k T;P ẳ a10 ỵ a11 T  T  T! 8ị T PP0 T T ỵa13 T ln ỵ T ỵ a14 ỵ a15 T T0 T T Similarly, the reaction order, nT,P, can be related to pressure (in megapascal) and temperature (in degree Celsius) Compare model results using the experimental log reduction obtained in a pilot plant scale high pressure food processor dN ¼ −k N n dt the thermal expansion coefficient (in cubic centimeters per mole Kelvin), Cp the is isobaric specific heat (in joules per mole Kelvin), V is the volume (in cubic centimeters per mole), and S is the entropy (in joules per mole Kelvin) The subscript “0” designates the standard state and Δ the difference between the products and reactants The kinetic parameter, kT,P, can be expressed as a function of the process temperature and pressure based on thermodynamic Eqs and ð7Þ where, for spores, ΔG denotes the change in free energy between the recoverable and non-recoverable states (Heinz and Knorr 2001), R is the universal gas constant (8.314 J/mol K), β is the isothermal compressibility (in cm6 per joule mole), α is ð9Þ For linear kinetics, Eq was selected The decimal reduction time (DT,P) in Eq was related to pressure (in megapascal) and temperature (in degree Celsius) by an empirical equation DT;P ¼ 10ða30 þa31 Pþa32 T þa33 P þa34 T þa35 PT Þ ð10Þ Isothermal and Isobaric Kinetic Data The published experimental data on PATP inactivation of B amyloliquefaciens spores as a function of pressure (0.1– 700 MPa) and temperature (95–121 °C; Rajan et al 2006a) were used for the estimation of the nth-order kinetics parameters (kT,P, nT,P) and linear kinetic parameter DT,P by nonlinear regression using the Matlab software The values of the regression coefficients of Eqs 8, 9, and 10 were given in Table The modeling approach can potentially be extended to other bacterial spores provided that spore-specific pressure–temperature kinetic data are available Computation of Accumulated Process Lethality Limited studies reported combined pressure–thermal inactivation kinetic data under isothermal and isobaric process conditions (Ahn et al 2007; Margosh et al 2006; Patazca et al 2006; Rajan et al 2006a) For any unknown arbitrary PATP process with dynamic or static pressure and temperature conditions, the corresponding accumulated lethality and inactivation curve can be constructed from several discrete isothermal and isobaric processes A similar approach has been used during thermal processing studies (Campanella et al 2001; Corradini et al 2006) The momentary inactivation rate, dðlogdt S ðtÞÞ, at a specified instant during any arbitrary pressure–temperature Food Bioprocess Technol Table Coefficients of regression equation for inactivation kinetic parameters (Eqs 8, 9, and 10) of B amyloliquefaciens spores based on nonlinear regression Coefficients lnkT,P Coefficients nT,P Coefficients DT,P a10 a11 a12 a13 a14 11467.4 0.642 0.26 −314.925 −183.615 a20 a21 a22 a23 a24 −2.062 0.0127 −0.017 −0.000008 0.000146 a30 a31 a32 a33 a34 17.63375 −0.035 −0.06628 1.55E-05 −0.00021 a15 R2 −19.822 0.993 a25 R2 −0.0000022 0.794 a35 R2 1.06E-04 0.998 history was assumed to be equal to that of an isothermal– isobaric process having the same pressure and temperature values F ¼ log S ðt Þ D121:1∘ C; 0:1MPa ð15Þ Experimental Validation of the Model à d log S ðt Þ d logS t ị ẳ dt dt ! ẳ T ;P 2:303 n1ị k N0 ỵ k t à N n−1 ðn−1Þ ð11Þ where t* is the treatment time of an isothermal–isobaric process at which the momentary surviving ratio S is equal to that of the arbitrary process The momentary surviving ratio for the arbitrary process and the isothermal–isobaric process can be related as     1−n1 À Á T ;P ðnT ;P 1ị log S tị ẳ log S t ị ẳ log ỵ k T ;P t N nT ;P −1 ð12Þ From Eq 12, the treatment time t* of the isothermal– isobaric process was extracted and substituted in Eq 11 Then, the momentary inactivation rate, dðlogdt S ðtÞÞ, can be described as a function of time (t) of the arbitrary process considered ðnT ;P −1ÞlogS ðtÞ ðnT;P −1Þ d log S ðt Þ k T ;P N 10 ẳ dt 2:303 13ị Similarly, the differential equation for linear kinetics (Eq 1) was expressed as below: d log S t ị ẳ dt DT ;P 14ị For any arbitrary process, knowing the pressure–temperature history, the corresponding inactivation curve was constructed by solving the differential equation (Eq 13) using the Runge–Kutta method (Matlab, version 7.1.0246, Matworks Inc., Natick, MA) Once the inactivation curve was constructed, the accumulated lethality can be calculated from a known surviving ratio The performance of the developed model described above was experimentally validated by conducting microbial inactivation studies using pilot-scale high-pressure sterilization equipment Inoculated Sample Preparation Spores of B amyloliquefaciens TMW 2.479 Fad 82 were used for validation experiment The spore suspension was prepared by adapting the procedures described elsewhere (Rajan et al 2006a) Decimal reduction time values, D105°C,0.1 MPa and D105°C,600 MPa, of the prepared spore crop in deionized water (DIW) were about 28.1 and 0.84 min, respectively It is worth noting that the D values of the current study are similar to those reported by Rajan et al (2006a) These authors reported D105°C,0.1 MPa and D105°C, 600 MPa values for the spore of 24 and 0.72 min, respectively Differences in the preparation of spore media, spore cultures, food composition, etc., might have contributed to the difference Spore samples were inoculated into DIW and carrot purée (CP) For spores inoculated in DIW sample, 0.2 mL of B amyloliquefaciens spore suspensions (∼109 spores per milliliter) was added to 1.8 mL DIW and the aliquot was aseptically transferred into a pouch (polyethylene bags, 5.0× 2.5 cm, no 01-002-57, Fisher Scientific) The final spore concentration was about 1.4×108 spores per milliliter The sample pouches were then sealed using an Impulse heat sealer (American International Electric, Whittier, CA) The sealed pouches were kept in an ice water bath until the experiment was conducted Inoculated CP samples were prepared as follows: shelfstable carrot purée (pH 5.2, aw =0.935, k=0.58 W/m K; 2nd Foods Vegetable, Gerber Products Co., Fremont, MI) was purchased from a local grocery store A sample of CP (1.8 g) and 0.2 mL of spore suspension were placed inside a pouch (polyethylene bags, 50×25 mm, no 01-002-57, Fisher Food Bioprocess Technol Scientific) and heat-sealed (Impulse heat sealer, American International Electric) The final spore concentration was about 1.1×108 spores per gram of CP The content was then mixed thoroughly and the samples were kept in an ice water bath before the experiment (a) (b) Top Deionized water Large external pouch Dummy sample pouch Pressure-Assisted Thermal Processing Experiments for Model Validation Sample pouch Middle Heat seal to fix the sample pouch and thermocouple Stuffing box Experiments were carried out using a pilot scale (Iso-lab high-pressure food processor S-IL-110-610-08-W, Stansted Fluid Power Ltd., Essex, UK) The cylindrical pressure chamber had an internal diameter of 110 mm and height of 610 mm Propylene glycol (Brenntag Mid-South Inc., St Louis, MO) was utilized as the pressure-transmitting medium The system had the ability to adjust the compression and decompression rates Pressurization and depressurization rates at ∼6.5 and ∼8.3 MPa/s, respectively, were used Inside the pressure chamber, preheated samples to a certain initial temperature were loaded into an insulated cylindrical stainless steel carrier basket (95-mm diameter, 590mm length; FPG 11650.110, Stansted Fluid Power Ltd.) The equipment had provisions for monitoring the temperature at three different spatial locations of the carrier basket using a T-type thermocouple Additional details of the experimental setup were reported previously (Nguyen et al 2010) The inoculated pouch sample as well as a dummy sample pouch for temperature monitoring were placed together inside a larger pouch (70×140 mm) filled with DIW The temperature inside the dummy pouch during the experiments was monitored using a calibrated T-type thermocouple (Omega Engineering, Stamford, CT) Thermocouple wire junctions were welded together using TC welder (Hotspot, DCC Corporation, Pennsauken, NJ) The thermocouple was fed through the pouch using a C-5.2 stuffing box (EcklundHarrison Technologies, Fort Myers, FL; Fig 2) Pressure– temperature data were collected every second using a data acquisition system (Scan1000 v4.4.67, Hexatec Solutions Ltd., Northumberland, UK) The large pouch containing the inoculated sample and the dummy sample pouch for temperature measurement were mounted within a carrier basket using a custom-made sample rack Prior to loading the sample pouches, the carrier basket was filled with a preheated (75 °C) pressure-transmitting fluid Subsequently, the test samples along with the carrier basket containing the pressure-transmitting fluid were continued to be heated at 75 °C for 15 using an external heating bath This ensures that all the contents of the carrier basket are at a certain initial temperature prior to loading inside the pressure vessel (Nguyen et al 2010) The pressure vessel was maintained at a desired target temperature (105 °C) During pressurization, the pressure vessel was filled with a pressure-transmitting medium, pre- Thermocouple Bottom Fig Schematic diagram of sample placement in the carrier basket within the pressure vessel for the validation study (a) and sample packaging showing thermocouple placement (b) conditioned at about 75 °C The fluid entered into the pressure vessel via an opening in the bottom closure The fluid subsequently flowed upward via an annular space between the carrier basket and an inner pressure vessel wall and entered into the carrier basket from the top The contents of the carrier basket including the test pouches and pressuretransmitting fluid reach a final process temperature (105 °C) due to heat of compression at the target pressure (Nguyen et al 2010; Patazca et al 2007) The following PATP experiments were conducted to evaluate the model performance for predicting accumulated lethality: Predicting the effects of sample spatial variation during PATP treatment Samples were mounted within the carrier basket at the geometric center in three different (top, middle, and bottom) positions, 286 mm apart, to evaluate the spatial variation effects Samples were processed at 600 MPa for at a target process temperature of 105 °C DIW and CP samples were used as model food substances Each of the PATP experiments was independently repeated three times Predicting the effects of pressure pulsing Additional experiments were carried out to compare the model performance in predicting the efficacy of single- and double-pulse treatments Single-pulse experiments were performed at 600 MPa, 105 °C for Double-pulse experiments utilized the same process conditions (600 MPa, 105 °C), but the holding time for each pulse was kept at 2.5 The pulse interval between two pulses was about 10 s To minimize the number of experiments, the middle loading position was used for loading samples for double-pulse experiments Three independent runs were conducted for each process condition Food Bioprocess Technol Enumeration of Surviving Spores from the Treated Samples Treated spore samples were immediately cooled in an ice– water mix and analyzed for spore survivors within h after processing For CP samples, the mL-treated sample was mixed with 18 mL of 0.1 % peptone water and homogenized for 2.5 in a stomacher at 230 rpm (Seward Lab Stomacher, Norfolk, UK) One milliliter of the sample contents (DIW sample) or aliquot (CP sample) was serially diluted in mL of 0.1 % peptone water and then pour-plated on trypticase soy agar After incubating at 32 °C for 48 h, the viable counts of the surviving spores were enumerated Colonies were counted with a dark-field Quebec colony counter (Leica Microsystems, Richmond Hill, Ontario, Canada) The detection limit for the enumeration procedure was 10 colony forming units (CFU) per gram or milliliter of food matrix Evaluating the Model Performance The developed model was used to predict log reduction using a specified pressure–temperature history of the experimental conditions Subsequently, knowing the corresponding experimentally observed log reduction values, the model performance was evaluated based on the mean square of error (MSE), R2, and accuracy factor (Af; Chen and Hoover 2003; Rajan et al 2006a) X ðpredicted−observedÞ2 ð16Þ MSE ¼ n  X   log predicted observed 17ị A f ẳ 10 n A model capable of yielding good prediction should have small MSE, small Af and high R2 values Results and Discussion Preliminary tests were conducted to evaluate the accuracy of the developed model in estimating PATP lethality using the published literature Figure 3a presents the estimated vs published data (Rajan et al 2006a) of the log reduction for various PATP conditions The model predictions utilized both linear and nth-order inactivation kinetics As evident from these figures, the nth-order kinetics better estimated the log reduction during PATP treatment, while the linear kinetics overestimated PATP log reductions especially with increasing pressure holding times Similarly, the estimated log reduction using the nth-order model was closer to the experimental values for the non-isothermal condition (Fig 3b) Therefore, the accumulated lethality presented in subsequent sections was only based on the nth-order inactivation kinetics Sample Pressure–Temperature History during PATP Treatment Tables and summarized the sample temperatures at various stages during PATP treatments After preheating the test samples (data not shown), the samples were loaded inside the pressure vessel at temperature T0 (Tables and 3) After closing the vessel, pressurization (t1–t2) started at T1 and reached T2 The process temperature (T2–T3) was the average temperature of the test samples during the pressure holding time The samples were held for a specified holding time (t2– t3) and depressurized (t3–t4) It is worth noting that, due to the pilot-scale nature of the equipment in the study, it was difficult to precisely replicate the pressure–temperature history among various test runs; thus, actual temperature–pressure history data for each run are presented (Tables and 3) Our primary aim was to compute the accumulated lethality values for specific process conditions rather than evaluate and minimize the process non-uniformity within the pressure chamber The studies utilized a low product-to-pressure-transmitting fluid volume ratio, and thus thermal variation in the fluid is likely a dominant factor over the sample temperature history In addition, variations in the initial product temperature, temperature of the pressure-transmitting fluid within the carrier basket, and the pressure chamber also influenced the sample temperature at various stages of processing (Tables and 3) For a given process run, samples placed in the top location experienced higher temperature than those placed in the bottom (Table 2) Varieties of machine, product, and process factors, including equipment design, insulating properties of the pressure vessel and packaging material, sample/pressuretransmitting fluid ratio, properties of the pressure-transmitting fluid, could influence the temperature distribution within a pressure vessel This is a topic of current research in various laboratories (Hartmann et al 2004; Hartmann and Delgado 2003, 2005; Rauh et al 2009; Khurana and Karwe 2009; Knoerzer et al 2010; Grauwet et al 2010) Accumulated Lethality During PATP The accumulated lethality (FP,T) for both single- and doublepulse treatments in general increased with an increase in pressure holding time (Fig 4) FP,T included the lethal effects of both pressure and temperature The calculated accumulated lethality during the preheating and come-up time was negligible Similarly, negligible lethality accumulation was also estimated during the time elapse between the two pulses (t1-4 −t2-1; Fig 4b) as the temperature and pressure dropped below lethal values (i.e., 110 °C), thermal effects dominated over the pressure effect The developed approach will be useful for food processors to evaluate the microbial efficacy of various pressure–heat treatments Acknowledgments Financial support for the research was provided in part through a grant from The Ohio Agricultural Research and Development Center (OARDC) and the Center for Advanced Processing and Packaging Studies (CAPPS) 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scenarios The objective of this study was to develop a model for estimating the accumulated lethality during PATP,... lower (Fig 4a, b) Effects of Sample Spatial Variation on Accumulated Lethality during PATP The developed accumulated lethality (FP,T) model based on combined a pressure–temperature lethal effect reasonably