Ultrasound assisted thermal inactivation of spores in foods: Pathogenic and spoilage bacteria, molds and yeasts

Background: Pasteurization aims to achieve the reduction of vegetative microorganisms and resistant spores which are of risk to public health. Power ultrasound has been identified as a potential technology for non-thermal food pasteurization. It relies on the propagation of pressure waves (frequency ranging from 20 to 100 kHz) of high intensity sound/acoustic energy (10 – 1000 W/cm 2 ) inside a liquid or semisolid food, causing inactivation of pathogenic and spoilage microorganisms. This technology can also be used in simultaneous combination with temperature > 80 ◦ C (thermosonication, TS) to inactivate microbial spores. Scope and approach: The current knowledge on the effect of ultrasound alone (US), TS, and ultrasound followed by a thermal process (US → T) on different type of spores relevant for low-and high-acidic foods was reviewed, including the kinetic models describing their inactivation in specific foods. Key findings and conclusions: US at room temperature (without heat) has no effect on microbial spores. In terms of microbial spore inactivation efficiency, TS was the best method, followed by US → T (non-simultaneous application) and finally heat treatment without US (T). TS employing temperatures between 90 ◦ C and < 100 ◦ C is required for spore inactivation, as at the boiling point of water ultrasound intensity is reduced. There is a need to design efficient ultrasound probes which can withstand higher temperatures or incorporate pressure to improve gas bubble implosion, thus more results can be produced at higher temperatures and with different type of microorganisms. When reporting results from TS experiments, standardized ultrasound processing conditions including the actual power delivered to the food and expressed in acoustic power density (power/volume of liquid food, W/mL) or specific acoustic power (W/g food) should be used to allow the comparison of results from different studies. TS inactivation kinetics of some spores of bacteria and molds exhibited non-linear trends, thus TS should be examined in detail for reliable food processing.


Ultrasound fundamentals
Ultrasound (US) technology can be utilized in important food processing operations such as microbial inactivation, enzyme inactivation, drying, extraction, crystallization, filtration, freezing, emulsification, degassing, tenderization of meat, defoaming and oxidation processes (Awad, Moharram, Shaltout, Asker, & Youssef, 2012;Silva & Sulaiman, 2017;Sulaiman, Soo, Farid, & Silva, 2015). Ultrasound is of great interest for food pasteurization, as it requires lower temperatures than thermal pasteurization alone, it has less impact on food quality, such as nutritional and sensorial characteristics (Charoux, O'Donnell, & Tiwari, 2017;Tiwari & Mason, 2012). The main goal of ultrasound pasteurization of foods is to obtain 5 log reductions in target microorganisms (FDA, 2004). As any other pasteurization method, including thermal pasteurization, refrigerated distribution and management is required after the pasteurization process (Silva & Evelyn, 2018. High-power ultrasound also known by power ultrasound is characterized by acoustic waves of low frequency (20-100 kHz) with a typical sound intensity of 10-1000 W/cm 2 . It is a known technology used for cell disruptive purposes. According to Gao, Lewis, and Hemar (2016), the extent of microbial inactivation in ultrasonic treatments is mainly influenced by three factors: cavitation thresholds (intensity, amplitude, frequency, temperature, and external pressure), media (viscosity, volume, pH, and initial microbial number), and type of microorganism (cell wall, size and shape, spores or vegetative cells, and growth phases). The intensity of the ultrasound process is usually expressed as acoustic power density -APD (W/mL or W/cm 3 ) in which the actual power (W) is obtained from a calorimetric experiment or calculated from the ultrasound intensity (W/cm 2 ) dissipated from the probe with a known diameter (Tiwari & Mason, 2012). When information is limited to the maximum power, the APD may be estimated from the sample volume (assuming no heat loss in the system) and should be stated "less than" since the actual power is lower. The decrease in the power is inversely proportional to the equipment efficiency, which is around 50%. Generally, the ultrasound equipment used in research have a fixed frequency (a value between 20 and 40 kHz) and the intensity/energy/power of the treatment can be varied by changing the amplitude. Some units can be programmed to be switched on/off for short periods (e.g. 3 s on/3 s off) to minimize the thermal impact, lengthen the overall life-time, and save 50% energy compared to continuous treatments (Tiwari, 2015). With respect to temperature control during US processing, most authors circulated cold water through a jacketed vessel containing the sample to maintain a constant temperature during ultrasound processing. An external pressure can be applied to improve microbial inactivation by ultrasound, manosonication process (Gao et al., 2016). Power ultrasound may also be combined with other treatments such as natural antimicrobials and other preservation technologies such as high hydrostatic pressure and pulsed electric fields to enhance the ultrasound lethal effects and extend a food's shelf life.

Mechanism of microbial inactivation
Cavitation is the phenomenon that occurs during an ultrasound process which refers to the creation, growth, and violent collapse of micro gas bubbles, resulting in turbulence and high-shear forces (Chen, 2012;Feng & Yang, 2011;Piyasena, Mohareb, & McKellar, 2004). The collapse of gas bubbles also causes rapid temperature changes, in excess of 5000 K, and >199 MPa pressure at a micro scale. Cavitation can also cause dissociation of water vapor, producing free radicals as H + and OH − which may recombine to form hydrogen peroxide (H 2 O 2 ) (Riesz & Kondo, 1992). These mechanical, thermal, and chemical effects of cavitation have been suggested to induce stress to microbes, cause destruction of microbial cell structure, and inactivate key enzymes (Butz & Tauscher, 2002;Chemat, Zill-e-Huma, & Khan, 2011;Dolas, Saravanan, & Kaur, 2019). The inactivation of enzymes is related to the depolymerization effect (i.e. degradation of the biological polymers), which causes loss of enzyme activity (Dolas et al., 2019). The main mechanisms of microbial inactivation by ultrasound have been described by Dolas et al. (2019) (Fig. 1). Briefly, the shock waves created by collapsing bubbles shear and break the cell wall and membrane structures, leading to the disruption of the microbial cell components by the micromechanical shocks. Also, free radicals form which react and break the microbe DNA. In addition, the hydrogen peroxide (H 2 O 2 ) formed during the cavitation process is bactericidal and bacteriostatic. Fig. 2 shows physical alterations in the cellular structure of 2 microbial spores by ultrasound, including disturbed outer layer of spore, cell debris, and disturbed exosporium layer by ultrasound (Palanisamy, Seale, Turner, & Hemar, 2019). With respect to spore inactivation mechanisms by the simultaneous application of ultrasound and heat (thermosonication, TS), the following has been proposed: (i) release of calcium-dipicolinic acid (DPA), fatty acids, acyl glycerol and glycolipids due to great damage to the spore's exosporium on ultrasonication treatment, further causing a loss of spore resistance, and (ii) a subsequent inactivation by heat (Ansari, Ismail, & Farid, 2017;Lv, Zou, Chantapakul, et al., 2019;Palacios, Burgos, Hoz, Sanz, & Ordóñez, 1991).

Microbial spore-formers as pasteurization targets in foods
The classical objective of thermal pasteurization to achieve the inactivation of vegetative forms of microorganisms has been evolving with time. The current definition of pasteurization includes non-thermal pasteurization processes such as power ultrasound and is concerned with the reduction of resistant pathogenic microorganisms of public health risk (NACMCF, 2006;Bermúdez-Aguirre, 2017). Therefore, spore-formers have also become targets in the design of new processes, with recommendations of 5-6 log reductions in the spores, in particular for low-acid foods (Silva & Gibbs, 2009). Several classes of bacteria and fungi (mold and yeast) are able to produce spores. Bacterial spores are Fig. 1. Mechanism of microbial inactivation by ultrasound (Dolas et al., 2019). Reprinted with permission from Elsevier. Evelyn and F.V.M. Silva resistant and dormant microbial structures which are formed in response to extreme environmental conditions (e.g. nutrients depletion, shortage of water). The spores help in the survival of these microorganisms for prolonged periods in adverse environments due to its specific morphology, physiology, and chemical composition (Keynan, 1969). Bacterial spores are able to return to vegetative cells through germination induced by sub-lethal heating or nutrients/non-nutrients agents when favorable germination conditions are present. Unlike bacterial spores, fungal spores are part of their reproductive cycles which may be produced either sexually or asexually. Ascospores produced by sexual methods and belonging to ascomycetes sub-kingdom are often more resistant to heat than other forms of fungal spores such as conidiospores and yeast ascopores (Dijksterhuis, 2007;Pitt & Hocking, 2009). Heat or chemical treatment used alone or in combination can activate fungal spores to germinate into vegetative cells and grow (Sussman & Halvorson, 1966). The outgrowth of bacterial and fungal spore survivors in foods, can lead to food spoilage, or foodborne illnesses and outbreaks. Therefore, microbial spore-formers have also become targets in food pasteurization and preservation (Silva & Gibbs, 2001Evelyn & Silva, 2018a, 2018bSilva, Gibbs, Nunez, Almonacid, & Simpson, 2014;Silva & Evelyn, 2020). If spores are inactivated, one can assume all vegetative forms are also destroyed. The resistance of spores depends on the type of microbe (bacteria or fungi), the species and the strain.
In this study, the simultaneous application of ultrasound and heat (TS), or the sequential application of ultrasound followed by a thermal process (US→T) will be reviewed with respect to microbial spore inactivation, as they are considered more effective treatments for the inactivation of resistant spores.

Pathogenic bacterial spore-formers
Clostridium botulinum has been recognized as the most dangerous spore-former bacterium in low-acid foods (pH > 4.6) (Carlin, Girardin, et al., 2000;Gould, 1999;Lindström, Kiviniemi, & Korkeala, 2006), producing potent and fatal neuro-intoxication (Brown, 2000). Outbreaks of foodborne botulism in liquid foods such as milk and liquid herbal tea have been reported (Aureli, Fenica, & Franciosa, 1999;Kim et al., 2019;Therre, 1999;Weingart et al., 2010). Clostridium perfringens and Bacillus cereus are other pathogenic bacteria of concern in low-acid foods. The ability of some strains of B. cereus to thrive in temperatures at or below 8 • C (psychrotrophic) is the reason these strains are found in low-acid chilled foods (Carlin, Guinebretiere, et al., 2000;Dufrenne, Bijwaard, Te Giffel, Beumer, & Notermans, 1995;Silva et al., 2014). Milk is an example of liquid food which might often be contaminated by B. cereus and C. perfringens (Andersson, Ronner, & Granum, 1995;Chaturvedi & Shukla, 2015;Feligini et al., 2014). Bacillus licheniformis is another important foodborne disease bacterium. It has been frequently reported as the culprit in milk spoilage (Pavic et al., 2005). Heat and pressure resistance of this bacterium and other Bacillus species were also reported (Janstová & Lukásová, 2001;Nakayama, Yano, Kobayahi, Ishikawa, & Sakai, 1996). Other Clostridium and Bacillus bacteria have also become a concern in low-acid foods: Bacillus anthracis, Bacillus pumilus, Bacillus thuringiensis, Clostridium baratii, Clostridium butyricum, and Clostridium difficile (Aureli et al., 1986;Barash, Tang, & Arnon, 2005 Table 1 Inactivation of pathogenic Clostridium and Bacillus spores in low-acid foods and non-food liquids by thermosonication (TS) and ultrasound (US). nr ̶ not reported. a The acoustic power density is the ratio of the actual power dissipated to a given food volume (W/mL). When this power was not determined by the authors, we used the power of the machine (presented in parenthesis) for the calculation and presented the power density with < sign. The paste/semi-solid foods in Silva (2015a, 2015b) were weighed and energy is expressed as a specific acoustic power (W/g). b T was the average temperature during the ultrasound treatment. Silva (2015a, 2015b) and Lv et al. (2020) used a thermostatic water bath to keep the desired temperature during processing. Goodenough and Solberg (1972) and Khanal et al. (2014) used the sample immersed in a crushed ice/ice bath to control the temperatures (0-3 • C). Lv, Zou, Chantapakul, et al. (2019) controlled the temperature of the sample by circulating water through a water jacket. Temperature increase to ≤30 • C during 5 min ultrasound treatment (Sagong et al., 2013). Burgos et al. (1972) and  also used an ultrasound-controlled temperature.
1995; Rupnik & Songer, 2010;Salkinoja-Salonen et al., 1999). Table 1 shows the spore log reductions obtained for pathogenic Clostridium and Bacillus spores in low-acid beverages, other liquids and semisolid foods after ultrasound alone (0.33 to <20 W/mL or W/g) or combined with thermal treatments in the range of 70-80 • C. A few authors did not present APD and express the power output in different ways, causing difficult comparison among published literature (Table 1). To overcome this problem, the APD was estimated based on data provided by the authors, assuming 100% efficient (no heat loss) and a "<" sign was added before APD value estimated.

Effect of US and TS on pathogenic Clostridium and Bacillus spores
The analysis of Table 1 shows ultrasound alone (continuous or pulse mode supply of power, and using a probe or bath) was not sufficient to cause significant inactivation of Clostridium and Bacillus spores (≤0.9 log) due to the weak lethal effect of ultrasound alone on the spores , 2019aBurgos, Ordonez, & Sala, 1972;Evelyn & Silva, 2015a;Goodenough & Solberg, 1972;Khanal, Anand, & Muthukumarappan, 2014;Malyshev & Baillie, 2020). Higher log reductions were achieved (up to 1.9) with a cocktail of B. cereus in uncontrolled-room T and indirect ultrasound treatment, in which increases in the temperature up to 30 • C during 5 min treatments were reported (Sagong et al., 2013), confirming the important role of heat. Owusu-Ansah et al. (2020) also obtained 0.5-0.8 log for B. cereus in distilled water and blended pork after <3 W/mL-70 • C for 13.6 min. Other authors also reported difficulty in inactivating (0.4 log) mesophilic B. cereus ATCC 14579 in distilled water using TS (<20 W/mL-80 • C for 30 min) (Lv, Zou, Chantapakul, et al., 2019), similar resistance to US alone (Lv et al., 2020). On the other hand, psychrotrophic B. cereus NZRM 984 seemed less resistant than the other strains of B. cereus, as much higher inactivation (3.2-4.2 log) was achieved in several low-acid foods (cheese slurry, rice porridge, beef slurry) after a TS treatment of 0.33 W/g-70 • C for 1.5 min (Evelyn & Silva, 2015a) as opposed to the higher inactivation of NZRM 984 B. cereus spores could be due to higher heat susceptibility of this psychrotrophic strain, thus demonstrating the strain effect on the inactivation. In addition, the TS inactivation of B. cereus spores was also affected by the type of medium, a higher soluble solids content was observed to result in lower spore inactivation (Evelyn & Silva, 2015a). Thermosonication (TS) of two strains of C. perfringens at 0.33 W/g-75 • C for 20 min only achieved 0.90 log in beef slurry (Evelyn & Silva, 2015b), indicating even higher resistance to the TS treatments. Overall, bacterial spores have high degree of resistance to 75-80 • C thermosonication. Bacillus spores seemed less resistant to TS treatments and this is in agreement with the previous studies with several Bacillus species (Chandler et al., 2001;Gao et al., 2016;Gao, Lewis, Ashokkumar, & Hemar, 2014;Ordonez & Burgos, 1976), especially psychrotrophic group of Bacillus. Experiments testing more US and temperature combinations and T ≥ 75-80 • C for inactivating pathogenic Clostridium and Bacillus spores are needed to optimize inactivation and meet the recommended 5D reductions. Previous studies claim the TS intensity decreases as the temperature approaches the water boiling point, due to the high-water vapor tension (Garcia, Burgos, Sanz, & Ordonez, 1989), which limits the application of TS at high temperatures.

Effect of US and TS on spoilage bacterial spores
Thermosonication at higher temperatures appeared to produce better results. For example, Tremarin et al. (2017) obtained 5.0-5.5 log reduction of (10 days and 6-month old) spores of A. acidoterrestris in commercial apple juice (11 • Brix) when using a TS temperature of 95 • C for 20 min. Garcia et al. (1989) could achieve 5.5-6.3 log reductions of two B. subtilis strains in whole milk after a TS treatment at 100 • C for 10 min, indicating the important role of temperature in spore inactivation during TS treatments. These authors also observed a large increase in the microbial resistance to TS when using glycerol (~only 1 log reduction), as this compound caused a protective effect in the spores. The increase of TS temperature (>90 • C) resulted in a higher inactivation of bacterial Table 2 Inactivation of spoilage bacterial spores in low-and high-acid foods and non-food liquids by thermosonication (TS) and ultrasound (US). Nr ̶ not reported. a The acoustic power density is the ratio of the actual power dissipated to a given food volume (W/mL). When this power was not determined by the authors, we used the power of the machine (presented in parenthesis) For the calculation and presented the power density with < sign. b T was the average temperature during the ultrasound treatment. Broda (2007) and Khanal et al. (2014) used the sample immersed in an ice bath to control the temperatures. Garcia et al. (1989)

Table 3
Comparison of ultrasound (US) followed by heat treatment with ultrasound alone or thermal processing alone for the inactivation of pathogenic and spoilage bacterial spores in low-acid foods and non-food liquids. nr ̶ not reported. a The acoustic power density is the ratio of the actual power dissipated to a given food volume (W/mL). When this power was not determined by the authors, the power of the machine was used (presented in parenthesis) for the calculation and presented the power density with < sign. b US→T, TS, US and T represent ultrasound followed by heat treatment, simultaneous ultrasound and heat treatment or thermosonication, ultrasound alone and thermal treatment alone, respectively.

Table 4
Mold and yeast spore inactivation and modelling in high-acid foods and non-food liquids by thermosonication (TS).  (2015c)  spores. To date, there are a limited number of studies on TS inactivation of pathogenic and spoilage bacteria in various foods and with different ultrasound intensities. Recently, other authors studied the impact of ultrasonication combined with heat (80 • C for 10 min) or preservatives (e.g. 0.5-1.0% nisin) on the germination and growth of spoilage/pathogenic bacterial spores in milk Kakagianni, Chatzitzik, Koutsoumanis, & Valdramidis, 2020), in which the inhibitory effect on growth was observed for the heat stress as opposed to the nisin preservative. Table 3 shows a summary of Clostridium and Bacillus spores' inactivation (in terms of log reductions) in which a sequential treatment of ultrasound followed by thermal treatment (US→T) was attempted to enhance the lethality of the treatment. The authors compared the log reductions achieved with US→T treatment with the thermal treatment without US (T). Several authors also compared US→T with US, and Garcia et al. (1989) also compared the sequential US→T treatment with TS and T. Ultrasound conditions with power density of 1.1-3.7 W/mL during 5-15 min were applied to liquid or semisolid samples, followed by heating at temperatures in the range of 63-110 • C for 1-30 min. Khanal et al. (2014) obtained almost no inactivation and no difference (0.2-0.3) between US→T (3.7 W/mL-10 min followed by 63 • C for 30 min) or US and T alone at the same conditions for B. licheniformis and B. coagulans in non-fat milk. The same authors reported 0.6 log for G. stearothermophilus after US→T (3.7 W/mL-10 min followed by 80 • C for 1 min) vs 0.3 for US alone. Conclusively, these results show there are no major differences in the efficacy of these treatments (US→T, US and T).

Ultrasonication followed by heat treatment: effectiveness on bacterial spore inactivation
On the contrary, Burgos et al. (1972) showed that US→T instead of thermal processing alone increased the log reductions of B. cereus from <2.0 to 5.0 (12 min US → 110 • C-15 min), although the difference was lower for B. licheniformis in diluted Ringer solution. Garcia et al. (1989) also compared US→T (31 • C-15 min →100 • C-10 min) and T effect on B. subtilis spores in whole milk and obtained a small increase (from 0.9 to 1.5) in the log reduction for var niger-40 strain, while the other strain ATCC 6051 showed no benefit from the sequential treatment. Although there was no difference in B. subtilis inactivation after US→T (10 min US → 105 • C-10 min) and T treatment alone in diluted Ringer solution, Ordonez and Burgos (1976) observed 0.5-1.0 log higher reductions of this bacteria at higher temperatures (110 • C for 10 min), indicating a benefit from employing higher temperatures. Garcia et al. (1989) compared TS to US→T and T alone in which T and TS treatments were both conducted at 100 • C, and registered much higher reductions of two strains of B. subtilis (5.5 and 6.3 log) with TS than US→T (1.5 and 3.6 log) or exclusive thermal treatment T (0.9 and 3.9 log). In general, it seemed that simultaneous application of ultrasound and heat or TS was better than the sequential application of treatments (US→T), as it was able to sensitize more the bacterial spores causing the decrease of their resistance (>5.0 log) (Table 3). Higher inactivation for TS than for sequential ultrasound and heat indicates a synergistic bactericidal effect on spores of simultaneous application of both treatments. One possible explanation is the nonlethal intracellular injuries with ultrasound process, causing an increase of spores' sensitivity to heat treatment with subsequent disruption (Wordon, Mortimer, & Mcmaster, 2012).
Depending on the bacteria or food the sequential treatment can present advantages when compared to thermal treatment alone (T). Single T was the least effective method for spore inactivation in foods. More studies conducted with different microbial species/strains, foods, ultrasound intensities and higher TS temperatures (between 90 and 100 • C) are needed to compare the three ultrasound methods and draw more robust conclusions.
Saccharomyces (Saccharomyces cerevisiae, Saccharomyces bisporus), Zygosaccharomyces (Zygosaccharomyces bailii, Zygosaccharomyces rouxii) (Pitt & Hocking, 2009;Silva & Evelyn, 2018), Pichia (Pichia membranaefaciens, Pichia anomala) (Deák & Beuchat, 1993;Pitt & Hocking, 2009) and Rhodotorula (Rhodotorula mucilaginosa, Rhodotorula rubra) (Deák & Beuchat, 1993) are among the most common heat-resistant yeast species in high-acid and acidified foods. S. cerevisiae and Pichia membranefaciens were found in contaminated cheese and milk (Fleet, 1990). Table 4 presents the ultrasound and TS (0.33 and 16.2 W/mL, 55-75 • C) inactivation of mold and yeast spores in high-acid foods and non-food liquids. Yeast spores were able to resist the US in 0% alc/vol beer, with 1.2 log reductions after 16.2 W/mL US process for 15 min (Milani & Silva, 2017). TS at 75 • C-0.33 W/mL promoted a slow process of ascospore activation of 4-week old N. fischeri mold suspended in apple juice during the first 10 min, followed by inactivation, thus only 0.5 log reduction registered after 25 min TS process (Evelyn, Kim, & Silva, 2016). The same activation issues were also observed with 4-week old B. nivea, another heat resistant mold which was tested in strawberry puree during the first 5 min (Evelyn & Silva, 2015c). These activation of ascospores were followed by inactivation (0.5 log for N. fischeri after 25 min and 1.8 log for B. nivea after 15 min) Evelyn & Silva, 2015c). Increasing the age of these ascospores to 12 weeks, also increased the time needed to inactivate the spores (0.5 log for N. fischeri after 65 min and 1.8 log for B. nivea after 60 min) Evelyn & Silva, 2015c). The increase in resistance of older ascospores has been correlated with a more robust structure of the spore cell wall (Evelyn & Silva, 2017;Sussman & Halvorson, 1966;Wyatt et al., 2015). Other investigators concluded TS at 52.5 • C for 10 min with A. flavus and P. digitatum, resulted in lower inactivation levels (1.6-1.7 log) than TS at 60 • C in Sabouraud broth (López-Malo, Palou, Jiménez-Fernández, Alzamora, & Guerrero, 2005). S. cerevisiae yeast spores seemed to be the least resistant presenting 3.1 and 3.3 log reductions in 4.8% alc/vol and alcohol-free beers, respectively, after 16.2 W/mL-55 • C-10 min (Milani & Silva, 2017). Larger cells (e.g. yeast) have been considered more susceptible to ultrasound treatment than small cells, such as bacteria (Chemat et al., 2011). Nonetheless, each microbe has its specific structure which might respond differently to ultrasound processing (Gao et al., 2016).

Effect of US and TS on molds and yeasts spores
Among all the molds and yeasts studied N. fischeri was the most TS resistant with a resistance comparable to bacteria. Older spores (12week old) of N. fischeri and B. nivea demonstrated higher resistance to TS, thus posing a concern due to spores' activation and very long treatment times (>60 min) required for only 1-1.5 log reduction (Evelyn Table 5 Modelling the pathogenic and spoilage bacterial spore inactivation in foods and non-food liquids after thermosonication (TS) and ultrasound (US). nr ̶ not reported. a The acoustic power density is the ratio of the actual power dissipated to a given food volume (W/mL). When this power was not determined by the authors, the power of the machine was used (presented in parenthesis) for the calculation and presented the result with < sign. The paste/semi-solid foods in Silva (2015a, 2015b) were weighed and energy is expressed as specific acoustic power (W/g). b T was the average temperature during the ultrasound treatment. Silva (2015a, 2015b), Ganesan et al. (2015), and Beatty and Walsh (2016) used a thermostatic water bath to maintain the desired temperature during processing. Garcia et al. (1989) kept a constant by circulating glycerol from a thermostated bath. Tremarin et al. (2017Tremarin et al. ( , 2019 did not mention about the temperature control of ultrasound. c D T -value and z-values are the first-order kinetic parameters (Eqs. (2) and (3)  . Temperature also plays a significant role in the inactivation by TS. To date, no data was found on the effect of TS or US on mold spores in low-acid foods, although contamination and spoilage with molds is also possible (Evelyn & Silva, 2019).

Inactivation kinetics and equations
The inactivation behavior of microorganisms in foods under traditional thermal treatment or other non-thermal technologies such as TS is often considered as a first order, thus the simple first-order kinetics is the most common approach. The model has the following form (Eq. (1)): with N is the number of survivors after exposure to US or TS treatment for a specific time t (min), N 0 is the initial or untreated cell population in the food (cfu/g or cfu/mL), and k is the first-order or inactivation rate constant (min − 1 ). This equation is commonly expressed by microbiologists as follows (Eq. (2)): from which D T values are estimated from Equation (2) (min) or calculated from k (D = 2.303/k). D T -value which is the time in min at a certain temperature T necessary to cause one decimal reduction in the microbial population, 10 n to 10 n− 1 in the microbial concentration in food (Bigelow, 1921). The logarithm of D-values (obtained from the primary model) can be plotted against TS temperature (or US intensity), in which the reciprocal of the slope is equal to z T -value ( • C) and defined as the temperature increase that results in a 10-fold decrease in the D-value (Eq. (3)).
where D Tref is the D-value at a reference temperature T ref ( • C), and T is the temperature of the isothermal treatment ( • C). Weibull model is a good approach when the microbial log survivors at a specific TS temperature or intensity show a concavity or a tail. The two main parameters obtained are b (the scale factor) and n (the survival curve shape factor). This model is based on a vitalistic approach i.e. heterogeneity in the resistance distributed among individual cells within a population (Van Boekel, 2002) (Eq. (4)): The scale factor is a rate parameter related to the velocity of inactivation of the microorganism, whereas the shape factor describes the degree of curvilinearity. n < 1, n >1 and n = 1 correspond to survival curves with concave-upwards (tailings) and convex or concavedownwards (shoulders), and the Weibull model becomes the same as a simple first-order kinetic model, respectively.
Lorentzian is a non-linear model which has been used to describe the log survivors of resistant molds with thermosonication (TS) treatment, showing an initial activation shoulder followed by approximately linear inactivation (Evelyn & Silva, 2015c;. The four parameter Lorentzian curve peak functions (a, b, c, d) in Eq. (4) are obtained, where an illustrates the log N/N 0 intercept; b acts an amplitude of curve that is the height at the center of the distribution in log N/N 0 units; c is the center that is the time (t) value at the center of the distribution, and d is the width, a measure of the width of the distribution in the same units as t (Lorentz, 1875;Peng & Lu, 2006): Another possible approach is the polynomial model or response surface model (RSM), which is primarily an empirical model developed to predict the effect of multiple environmental factors (variables) on the microbial spore inactivation (Silva, Gibbs, Vieira, & Silva, 1999). A second-order polynomial equation involving first-order, second-order (quadratic), and interaction terms is generally used (Eq. (6)): where Y is the microbial spore logarithmic reduction (log N/N 0 ); B 0 , B i , B ii , and B ij are the estimated regression coefficients; X i and X j are the environmental factors such as temperature and amplitude; and ε is the error term. The RSM can be used to find the variables conditions resulting in maximum response (Y) (Beatty & Walsh, 2016;Ganesan et al., 2015).
To summarize, first-order and Weibull models (Equations (1), (2), (4) and (5)) can be used to characterize microbial spore inactivation for a single variable (fixed US/TS intensity or TS temperature). The Weibull model is often a more flexible model than the former one, as it is also applicable to non-linear survival curves, frequently showing downward and upward concavities (Van Boekel, 2002). As opposed to the first-order and Weibull models, the RSM model is able to include the effects of US/TS intensity, TS temperature and time in one single equation and predict conditions for maximum spore inactivation. Table 5 shows the model parameters estimated for describing TS and US inactivation of bacterial spores. The survival curves of bacterial spores by US alone displayed linear inactivation, thus first-order kinetics (Eqs. (1)-(3)). For example, US (0.33 W/g or W/mL-23 • C) inactivation of psychrotrophic B. cereus spores resulted in D-values of 141 min and 119 min in beef slurry and skim milk, respectively (Evelyn & Silva, 2015a). US (<19.2 W/mL) inactivation of A. acidoterrestris at room T resulted in D-values of 70 min in apple juice (Tremarin et al., 2017). Similarly, TS inactivation of both species also demonstrated a linear trend, with the following D-values: TS at 0.33 W/g or W/mL, D 70 • C -values = 0.36 min for B. cereus in beef slurry and D 70 • C -values = 2.93 min for B. cereus in skim milk, with z T -values = 25.8-45.7 • C (Evelyn & Silva, 2015a); D 95 • C -value of 8.9 min for A. acidoterrestris in apple juice (APD <19.2 W/mL) and D 78 • C -value of 28 min for A. acidoterrestris in orange juice (APD 20.2 W/mL) Tremarin et al., 2017); D 100 • C -values of two strains of B. subtilis spores of 1.60-1.82 min in whole milk with z T -values within 6.3-9.4 • C for APD of <5 W/mL (Garcia et al., 1989).

Bacterial spores
As opposed to their past works, Tremarin et al. (2019) demonstrated that the Weibull model (Eq. (4)) fitted the downward concavity survival data better than the first-order kinetics in describing TS (<19.2 W/mL-95 • C) inactivation of 6-month old A. acidoterrestris in apple juice with n = 1.18. TS (0.33 W/g-75 • C) inactivation of C. perfringens in beef slurry exhibited an upward concavity (n between 0.23 and 0.61) and was also best described by the Weibull model (Evelyn & Silva, 2015b). These results suggest that the TS inactivation of Clostridium genera and older spores of A. acidoterrestris pose a challenge to ultrasound processors, thus harsher processing conditions (higher temperature and/or acoustic power density) might be more effective. Subsequently, there is a need to design ultrasound units withstanding high temperature as previously mentioned. Nonetheless, more experiments are still required to better elucidate the kinetics of bacterial spore inactivation by TS.
Response surface methodology has also been used by several authors to investigate the simultaneous effects of ultrasound frequency (f), time (t), and temperature (T) or time (t), temperature (T), and amplitude (A) or solid concentration (S), temperature (T), and treatment time (t) on spore inactivation, and if possible to predict the processing conditions to achieve a desired log reduction of spores (Eq. (6)). For example, the predicted optimum process conditions are 84.8 • C-216 μm-5.8 min for 2.0 log reduction of B. atrophaeus spores in UHT milk, 31.5% S-60 • C-0.3 min for 0.4 log reduction of stearothermophilus spores in skim milk, and 20 Hz-70 • C-13.56 min for 0.5 log reduction of B. cereus spores in pork (Beatty & Walsh, 2016;Ganesan et al., 2015;Owusu-Ansah eta al., 2020), still revealing insufficient TS inactivation. Table 4 shows the reports regarding TS inactivation kinetics of mold and yeast spores. Milani and Silva (2017) investigated the effect of US alone (16.2 W/mL-23 • C) on S. cerevisiae spore survival in 0-7.0% alc/vol beers, and the curves showed a concave upward trend with low inactivation levels (≤1.2 log after 15 min).

Mold and yeast spores
The first-order model has been used to describe the log survivors of spores of A. flavus and P. digitatum in Sabouraud broth after 120 μm TS: D 60 • C -values = 2.18 min, D 52.5 • C -values = 5.9 min and z T -values = 17.3 • C were estimated for A. flavus, and D 52.5 • C -values = 6.31 min and z T -values = 11.9 • C were obtained for P. digitatum (López-Malo et al., 2005). Milani and Silva (2017) reported Weibull model for TS (16.2 W/mL-55 • C) inactivation of S. cerevisiae in 0% and 4.8% alc/vol beer due to an upward concavity (n between 0.11 and 0.26) observed in the survival curves, revealing an undesirable increase in spore resistance with processing time. The Lorentzian model was another non-linear model also used to describe the inactivation of the most resistant (N. fischeri and B. nivea, 4 and 12-week old) mold spores, exhibiting survival curves with an activation shoulders followed by a linear inactivation of spores (Eq. (5)) Evelyn & Silva, 2015c). Similar to bacteria, these results also indicate that ultrasound TS inactivation of certain species of resistant mold/yeast spores could exhibit non-linearity (Weibull and Lorentzian models adjusted to spore log survival data).

Conclusions and final remarks
Some bacteria, molds and yeasts can produce spores, a more resistant form of the microorganism. Ultrasound (US) alone is unable to inactivate microbial spores. Thermosonication (TS) is a better method than US, followed by heat treatment or conventional thermal processing for the inactivation of spores in liquid or semisolid foods. TS at ≥95 • C is needed to obtain 5D reduction in spores, as TS temperature plays a significant role in spore inactivation. The magnitude of pathogenic and spoilage spore resistance to TS is similar. The TS inactivation of resistant mold spores, critical for high-acid fruit products, was difficult and demonstrated challenging behaviors. TS spore resistance is also affected by the type of cell (microbial species/strain) and the beverage, indicating the importance of testing the most resistant spores in a specific food to design successful TS pasteurization for that food. Linear and nonlinear trends were observed for bacterial, mold and yeast spore inactivation in foods and non-food liquids after TS treatments. Species and spore age affected the inactivation kinetics and the presence of a nonlinear inactivation pattern. The concave upward of the log survival curves of C. perfringens described by Weibull model can be translated in an increase of microbial spore resistance with TS processing time. Similarly, the activation shoulder exhibited by N. fischeri and B. nivea molds submitted to TS is a concern and should be interpreted with more care. Thus, TS at higher T should be attempted.
To summarize, uniformity in reporting the intensity of the TS/US process is needed, such as using the acoustic power density in W/mL, so that proper comparison of results from different research groups is possible. More experiments should be carried out using higher TS temperature or ultrasound acoustic power density, and a wider range of TS conditions. US probes withstanding temperatures close to 100 • C are required, as those will enable a more rapid pasteurization than a conventional thermal pasteurization process. However, this increase in TS temperature is limited by the increase in water vapor tension, which reduces the cavitation effect. The addition of an external pressure could increase the power of bubble implosion hence the microbial inactivation, thus manothermosonication technology could possibly improve pasteurization performance and subsequent food preservation.