###### Abstract  
In this work, the inactivation kinetics of _Alicyclobacillus acidoterrestris_ spores by temperature-assisted high hydrostatic pressure was assessed by means of the Weibull model. Spores from two _A. acidoterrestris_ strains (a wild-type strain and a reference strain) were inoculated in commercial orange juice and subjected to high pressure levels (500 and 600 MPa) combined with four temperature regimes (25, 45, 60 and 70 \({}^{\circ}\)C) for time up to 30 min. Results showed that for a given high-pressure level spore inactivation was higher as temperature progressively increased. Furthermore, the Weibull model consistently produced satisfactory fit to the inactivation data based on the values of the root mean squared error (RMSE \(<\) 0.54 log colony-forming units (CFU)/mL) and the coefficient of determination (R\({}^{2}\)\(>\) 0.90 in most cases). The shape of inactivation curves was concave upward (\(p\)\(<\) 1) for all temperature/high pressure levels tested, indicating rapid inactivation of the sensitive cells of the bacterium whereas the remaining ones adapted to high hydrostatic pressure (HHP) treatment. The values of the shape (\(p\)) and scale (\(\delta\)) parameters of the Weibull model were dependent on the applied temperature for a given high pressure level and they were further described in a secondary model using first-order fitting curves to provide predictions of the surviving spore population at 55 and 65 \({}^{\circ}\)C. Results revealed a systematic over-prediction for the wild-type strain regardless of temperature and high pressure applied, whereas for the reference strain under-prediction was evident after 3 log-cycles reduction of the surviving bacteria spores. Overall, the results obtained indicate that the effectiveness of high hydrostatic pressure against _A. acidoterrestris_ spores is strain-dependent and also underline the need for temperature-assisted HPP for effective spore inactivation during orange juice processing. Alicyclobacillus acidoterrestris; high pressure processing; spore inactivation; orange juice; Weibull model +
Footnote †: journal: Applied Soft  
endospore-forming and non-pathogenic spoilage microorganism [2,8]. It has the ability to grow in a wide pH range (2.0-7.0) with optimal pH values between 3.5-4.0 and at a temperature range of 25-60 \({}^{\circ}\)C with optimal between 40-45 \({}^{\circ}\)C [9, 10, 11]. _A. acidoterrestris_ spores have the ability to survive pasteurization procedures of fruit juice and because of their acidophilic nature they can germinate and result in spoilage after favourable conditions [4,12]. The maximum concentration of _Alicyclobacillus_ spores that is accepted in the raw material by the fruit industry is 100 colony-forming units (CFU)/mL [13]. Part of the spore resistance is due to the presence of an external protein coat with strong hydrophobic bonds that stabilizes and reduces membrane permeability in extreme acidic and high-temperature environments [14]. Acidothermophilic bacteria like _A. acidoterrestris_ are considered to be important target microorganisms in quality control of heat-processed acidic foods. Therefore, it has been suggested as a reference microorganism for designing pasteurization processes in acidic fruit products [15,16]. Results concerning thermal inactivation of _A. acidoterrestris_ spores in orange juice showed a D-value at 90 \({}^{\circ}\)C between 10 and 23 min and at 95 \({}^{\circ}\)C between 2.5 and 8.7 min, depending on bacterial strain and the conditions of the experiment [17,18]. Consequently, typical juice pasteurization processes employed by the fruit juice industry today (i.e., 86 to 96 \({}^{\circ}\)C for 2 min) cannot ensure spore inactivation especially for products with longer shelf life [19]. The inactivation of _A.