Radovan Gospavic

Mathematical modelling for predicting the growth of Pseudomonas spp. in poultry under variable temperature conditions.

A dynamic growth model under variable temperature conditions was implemented and calibrated using raw data for microbial growth of Pseudomonas spp. in poultry under aerobic conditions. The primary model was implemented using measurement data under a set of fixed temperatures. The two primary models used for predicting the growth under constant temperature conditions were: Baranyi and modified Gompertz. For the Baranyi model the maximum specific growth rate and the lag phase at constant environmental conditions are expressed in exact form and it has been shown that in limit case when maximal cells concentration is much higher than the initial concentration the maximum specific growth rate is approximately equal to the specific growth rate. The model parameters are determined in a temperature range of 2-20 degrees C. As a secondary model the square root model was used for maximum specific growth rate in both models. In both models the main assumption, that the initial physiological state of the inoculum is constant and independent of the environmental parameters, is used, and a free parameter was implemented which was determined by minimizing the mean square error (MSE) relative to the measurement data. Two temperature profiles were used for calibration of the models on the initial conditions of the cells.

Modelling of laser-material interaction using semi-analytical approach

In this paper different aspects of laser-material interaction were considered. Semi-analytical method was developed and applied to analysis of spatial and temporal distribution of temperature field inside bulk materials. In particular, cases with cylindrical geometry, finite diameter and infinite length as well as cylindrical geometry, finite diameter and finite length were considered. For solving the governing partial differential equations (PDEs) the Laplace transform and the Fourier method of variables separation were used. In this way instead of the original governing PDEs, ordinary differential equations were solved. Particular solutions of the ordinary differential equations were used for evaluating the general solution, which was expressed in terms of series of particular solutions. The unknown coefficients in the series of particular solutions were determined using the boundary and initial conditions. The laser-material interaction was represented using the thermal model. These interactions for the cases of the high power laser in pulse and continuous regime were analysed. The incident intensity of laser radiation was under critical intensity.Using these methods the temperature field distribution was obtained in the Laplace transform domain. The convolution integral and the Green function were used to determine the temperature field in time domain. General semi-analytical methods and numerical solutions of appropriate transcendent equations were considered and numerical results for Al specimens were presented. The influences of laser beam parameters to the temperature field distribution and isothermal curves inside the bulk material were evaluated.

3D modeling of material heating with the laser beam for cylindrical geometry

In this work an analytical approach for analyzing heating of material with a laser beam is presented. A thermal model of interaction for the case of cylindrical geometry of the material and asymmetric distribution of the laser beam intensity is used and an analytical procedure is developed to analyze the temporal and the spatial distribution of the temperature field inside the bulk of material. This kind of consideration is of practical interest in cases where the excitation by the laser beam is not symmetric in respect to its position or shape, e.g., multi-mode working regimes or asymmetrical distribution of the laser beam intensity. The heating effects were considered in the temperature range up to the melting point. The thermal and the optical parameters of the material were assumed to be independent of the temperature and were given constant values in the temperature range of interest. This approach makes use of the Laplace transform, in order to eliminate dependence on time. The Fourier method of variable separation was used to obtain the temperature field distribution in the Laplace transform domain. By using the pulse response and Duhamels principle the 3D temperature field distribution in time domain is obtained. By using an appropriate set of orthogonal functions in r directions, the numerical procedure is made more effective, saving this way the CPU time. The general solutions for the temporal as well as spatial temperature field distributions are evaluated in a closed form in terms of the particular solutions of the governing partial differential equation (PDE). Because of linearity of the governing PDE, the superposition principle was used in the case of complex distributions of the laser beam intensity. The influence of different kinds of laser beam parameters to the temperature field distributions was considered.

A Novel HACCP System Supported By QMRAFor Increased Food Safety

A novel approach based on integration of the existing Hazard Analysis and Critical Control Point (HACCP) approach with the Quantitative Microbial Risk Assessment (QMRA) is presented which is developed as part of the Chill-On EC FP6 research project. Though the paper deals with the main principles of operation of the system, some elements of practical implementation and operation of the HACCP system combined with QMRA as well as a Shelf Life Predictor (SLP) are presented. The novel HACCP system makes use of QMRA for estimating the risk to consumers due to consumption of food contaminated with Specific Foodborne Pathogens (SFP) or estimating the remaining shelf life of the product. The system is designed for help with increasing the quality and safety of products in food supply chains.

Physiologically Based Pharmacokinetic (PBPK) model for biodistribution of radiolabeled peptides in patients with neuroendocrine tumours

Objective(s): The objectives of this work was to assess the benefits of the application of Physiologically Based Pharmacokinetic (PBPK) models in patients with different neuroendocrine tumours (NET) who were treated with Lu-177 DOTATATE. The model utilises clinical data on biodistribution of radiolabeled peptides (RLPs) obtained by whole body scintigraphy (WBS) of the patients. Methods: The blood flow restricted (perfusion rate limited) type of the PBPK model for biodistribution of radiolabeled peptides (RLPs) in individual human organs is based on the multi-compartment approach, which takes into account the main physiological processes in the organism: absorption, distribution, metabolism and excretion (ADME). The approach calibrates the PBPK model for each patient in order to increase the accuracy of the dose estimation. Datasets obtained using WBS in four patients have been used to obtain the unknown model parameters. The scintigraphic data were acquired using a double head gamma camera in patients with different neuroendocrine tumours who were treated with Lu-177 DOTATATE. The activity administered to each patient was 7400 MBq. Results: Satisfactory agreement of the model predictions with the data obtained from the WBS for each patient has been achieved. Conclusion: The study indicates that the PBPK model can be used for more accurate calculation of biodistribution and absorbed doses in patients. This approach is the first attempt of utilizing scintigraphic data in PBPK models, which was obtained during Lu-177 peptide therapy of patients with NET.

Evaluation of QMRA performance for Listeria monocytogenes in cold smoked salmon

Food-borne listeriosis, caused by Listeria monocytogenes (Lm), is relatively rare but the relatively high rate of fatality (20–30%) compared to other food-borne microbial pathogens such as Salmonella makes it a serious disease. The foodstuff is recognised as the primary route of transmission for human exposure. A wide variety of food or raw material may become contaminated with Lm but the majority of listeriosis cases are related to ready-to-eat (RTE) food. The important factor related to food-borne listeriosis is that Lm can grow under low (refrigerated) temperatures when given sufficient time. Therefore, RTE products with long shelf life are under risk with respect to growth of Lm to critical concentrations. A stochastic model for the growth of Lm with the inhibiting effect of lactic acid bacteria (LAB) in cold smoked salmon (CSS) was developed. An existing deterministic model for the growth of Lm was adapted by adding the Winner stochastic process in order to simulate the growth of Lm. The Poisson distribution is used to represent the initial count (occurrence) of Lm. A deterministic model for growth of LAB is used and the inhibiting effects of Lm and LAB on each other are taken into account. The Beta-Poisson model is used for estimating the dose response. The model has been tested during field trials with CSS performed in August 2010. The salmon was slaughtered in Norway and transported to France where it was processed. The model, implemented within the QMRA module, indicated that growth of Lm would occur in the CSS samples investigated. However, the

Stochastic Risk Assessment OfListeria Monocytogenes

The availability of information on the population’s exposure to the biological agents is crucial for characterising the risks of associated food-borne pathogens. Unfortunately, the available exposure data are insufficient to assess the public health impact of pathogens. Effective dose-response models are required to evaluate the risks. The growth of the micro-organisms in the food is also important. The prediction of the microbial population in food plays important role in finding the risk of certain adverse effects on human population. This study combines the stochastic growth models with the dose-response models to find the risk of illness in consumers due to the consumption of contaminated food.

Microbial Growth Modelling Under VariableTemperature Conditions

The application of a Quantitative Microbial Risk Assessment (QMRA) in food supply chains requires accurate prediction of microbial growth under variable temperature conditions. A dynamical growth model under variable temperature conditions was developed using raw data for microbial growth of Pseudomonas spp. in poultry under aerobic conditions from a food supply chain in Germany. The primary model was developed using measurement data under a set of fixed temperatures and constant environmental conditions. The two primary models used for modelling the growth under constant temperature conditions were: Baranyi and modified Gompertz. As a secondary model the square root model was used for maximal growth rate in the Baranyi model and polynomial interpolation for the modified Gompertz model. In the case of the Baranyi model the main assumption, that the initial physiological state of the inoculum is constant and independent of the environmental parameters, is used. The generated dynamical models are validated by comparing the predictions obtained by both models with data measured under dynamical temperature conditions. Two temperature profiles were used for comparison and good agreement has been found between experimental data and model predictions.

Boundary element—dual reciprocity formulation for bound electron states in semiconductor quantum wires

Using the boundary element dual reciprocity method-multi-domain (DRM-MD) a bound electron states and corresponding wave functions in semiconductor quantum wires embedded in a matrix were considered. The single circular and rectangular as well as the two near circular quantum wires were analyzed. In the case of two coupled quantum wires the dependence of the resulting wave function and eigenenergies as a function of the distance between wires was calculated. The DRM-MD gave a linear electron state model and developed numerical approach accurately captured the symmetry breaking and splitting of the degenerated energy states due to presence of additional wire. According to the symmetry of the structures a suitable mesh reduction was employed and different modes were considered separately. For a case of hetero-structures domain decomposition was used.