An optimization algorithm for estimation of microbial survival parameters during thermal processing Guibing Chen a, ⁎, Osvaldo H. Campanella b a Center for Excellence in Post-Harvest Technologies, North Carolina A&T State University, The North Carolina Research Campus, 500 Laureate Way, Kannapolis, NC 28081, USA b Department of Agricultural and Biological Engineering, Purdue University, 225 S. University Street, West Lafayette, IN 47907, USA abstract article info Article history: Received 31 May 2011 Received in revised form 6 December 2011 Accepted 11 December 2011 Available online 17 December 2011 Keywords: Optimization algorithm Microbial survival parameters Non-isothermal treatment Isothermal microbial survival curves are usually described by either linear or nonlinear time-dependent models, from which non-isothermal survival curves can be generated if the parameters describing the surviv- al kinetics of the microbial population are known. In order to estimate these parameters, an algorithm based on the steepest decent optimization method was developed. The algorithm searches the values of the survival parameters which minimize the sum of the squared differences between the experimental data and the cal- culated values provided by the model. The difference of the proposed algorithm with a typical optimization technique is that each data point used is not necessarily coming from the same thermal treatment; instead, data from different non-isothermal processes can be used. The developed algorithm was tested by using pub- lished non-isothermal survival data of Salmonella. The data showed that the survival curves can be described by the Weibull model, an already accepted and frequently used nonlinear model. Salmonella's survival pa- rameters were estimated from the end points and all data points, respectively, of three non-isothermal sur- vival curves. The results obtained showed that the number of survival data points must be sufficiently large to obtain true or statistically sound values of the survival parameters. A suitable way to achieve this is to imple- ment the algorithm using all data points of multiple non-isothermal survival curves or a large number of end points of non-isothermal treatments. Mathematically, the developed algorithm should be applicable to any microbial survival kinetics accurately describing the inactivation of the microorganisms because no specific survival kinetics has to be pre-assumed to run the algorithm. Published by Elsevier B.V. 1. Introduction Foods that provide suitable conditions for growth of microorgan- isms need to be sterilized or pasteurized in order to make them mi- crobiologically safe and to extend their shelf life. Microbial inactivation caused by thermal sterilization or pasteurization process- es is usually evaluated by accumulated lethality, which must be accu- rately estimated when establishing a valid thermal process and/or dealing with process deviations. Traditionally, microbial inactivation in thermal processes of foods is estimated by using the linear or first order kinetic model which is still used in some widely used com- mercial thermal process software such as CalSoft (Allpax, Covington, LA, USA) and NumeriCAL (JBT Food Tech, Madera, CA, USA). However, various nonlinear models have been proposed (e.g., Linton et al., 1995; Peleg and Cole, 1998) due to the frequently observed insuffi- ciency of linear models to describe these non-linear survival kinetics (Van Boekel, 2002). Usually, the selection of a suitable survival model is based on how well the model fits measured survival curves. In thermal processes, food product temperature varies with time due to the inherent unsteady state characteristic of the heat transfer process. Thus, the required time to achieve a prescribed lethality has to be estimated under non-isothermal conditions. The required time to achieve a prescribed lethality is even longer in batch retorts due to the extra come-up-time, which is the time required for the re- tort to reach its target temperature. Therefore, lethality achieved in thermally processed foods is the integration of momentary lethal ef- fects, the rate of which is a function of temperature. With realistic as- sumptions, the accumulated lethality in a thermal process can be estimated from an isothermal survival kinetic model (Chen et al., 2007) provided that the survival kinetic parameters are known. The conventional approach for calculating the microbial survival parame- ters is based on a series of isothermal survival curves determined at different temperatures. This approach is straightforward and contains two steps. First, the experimental isothermal survival curves are fitted by a suitable model and the model parameters corresponding to each temperature are obtained. Second, the obtained microbial model pa- rameters are plotted against temperature and suitable mathematical relationships between these parameters and temperature are International Journal of Food Microbiology 154 (2012) 52–58 ⁎ Corresponding author at: Center for Excellence in Post-Harvest Technologies, North Carolina A&T State University, The North Carolina Research Campus, 500 Laure- ate Way, Suite 4222, Kannapolis, NC 28081, USA. Tel.: +1 704 2505701; fax: +1 704 2505709. E-mail address: gchen@ncat.edu (G. Chen). 0168-1605/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.ijfoodmicro.2011.12.019 Contents lists available at SciVerse ScienceDirect International Journal of Food Microbiology journal homepage: www.elsevier.com/locate/ijfoodmicro