Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

The cardiopulmonary reflexes of spontaneously hypertensive rats are normalized after regression of left ventricular hypertrophy and hypertension

Cardiopulmonary reflexes are activated via changes in cardiac filling pressure (volume-sensitive reflex) and chemical stimulation (chemosensitive reflex). The sensitivity of the cardiopulmonary reflexes to these stimuli is impaired in the spontaneously hypertensive rat (SHR) and other models of hypertension and is thought to be associated with cardiac hypertrophy. The present study investigated whether the sensitivity of the cardiopulmonary reflexes in SHR is restored when cardiac hypertrophy and hypertension are reduced by enalapril treatment. Untreated SHR and WKY rats were fed a normal diet. Another groups of rats were treated with enalapril (10 mg kg-1 day-1, mixed in the diet; SHRE or WKYE) for one month. After treatment, the volume-sensitive reflex was evaluated in each group by determining the decrease in magnitude of the efferent renal sympathetic nerve activity (RSNA) produced by acute isotonic saline volume expansion. Chemoreflex sensitivity was evaluated by examining the bradycardia response elicited by phenyldiguanide administration. Cardiac hypertrophy was determined from the left ventricular/body weight (LV/BW) ratio. Volume expansion produced an attenuated renal sympathoinhibitory response in SHR as compared to WKY rats. As compared to the levels observed in normotensive WKY rats, however, enalapril treatment restored the volume expansion-induced decrease in RSNA in SHRE. SHR with established hypertension had a higher LV/BW ratio (45%) as compared to normotensive WKY rats. With enalapril treatment, the LV/BW ratio was reduced to 19% in SHRE. Finally, the reflex-induced bradycardia response produced by phenyldiguanide was significantly attenuated in SHR compared to WKY rats. Unlike the effects on the volume reflex, the sensitivity of the cardiac chemosensitive reflex to phenyldiguanide was not restored by enalapril treatment in SHRE. Taken together, these results indicate that the impairment of the volume-sensitive, but not the chemosensitive, reflex can be restored by treatment of SHR with enalapril. It is possible that by augmenting the gain of the volume-sensitive reflex control of RSNA, enalapril contributed to the reversal of cardiac hypertrophy and normalization of arterial blood pressure in SHR.

A mathematical framework for group analysis of von Willebrand factor multimeric composition following luminography

The objective of the present study was to establish a method for quantitative analysis of von Willebrand factor (vWF) multimeric composition using a mathematical framework based on curve fitting. Plasma vWF multimers from 15 healthy subjects and 13 patients with advanced pulmonary vascular disease were analyzed by Western immunoblotting followed by luminography. Quantitative analysis of luminographs was carried out by calculating the relative densities of low, intermediate and high molecular weight fractions using laser densitometry. For each densitometric peak (representing a given fraction of vWF multimers) a mean area value was obtained using data from all group subjects (patients and normal individuals) and plotted against the distance between the peak and IgM (950 kDa). Curves were constructed for each group using nonlinear fitting. Results indicated that highly accurate curves could be obtained for healthy controls and patients, with respective coefficients of determination (r²) of 0.9898 and 0.9778. Differences were observed between patients and normal subjects regarding curve shape, coefficients and the region of highest protein concentration. We conclude that the method provides accurate quantitative information on the composition of vWF multimers and may be useful for comparisons between groups and possibly treatments.

Mathematical modeling of electro-rotation spectra of small particles in liquid solutions: Application to human erythrocyte aggregates

Electro-rotation can be used to determine the dielectric properties of cells, as well as to observe dynamic changes in both dielectric and morphological properties. Suspended biological cells and particles respond to alternating-field polarization by moving, deforming or rotating. While in linearly polarized alternating fields the particles are oriented along their axis of highest polarizability, in circularly polarized fields the axis of lowest polarizability aligns perpendicular to the plane of field rotation. Ellipsoidal models for cells are frequently applied, which include, beside sphere-shaped cells, also the limiting cases of rods and disks. Human erythrocyte cells, due to their particular shape, hardly resemble an ellipsoid. The additional effect of rouleaux formation with different numbers of aggregations suggests a model of circular cylinders of variable length. In the present study, the induced dipole moment of short cylinders was calculated and applied to rouleaux of human erythrocytes, which move freely in a suspending conductive medium under the effect of a rotating external field. Electro-rotation torque spectra are calculated for such aggregations of different length. Both the maximum rotation speeds and the peak frequencies of the torque are found to depend clearly on the size of the rouleaux. While the rotation speed grows with rouleaux length, the field frequency nup is lowest for the largest cell aggregations where the torque shows a maximum.

Mathematical modelling of the osmotic dehydration of cherry tomato (Lycopersicon esculentum var. cerasiforme)

Osmotic dehydration of cherry tomato as influenced by osmotic agent (sodium chloride and a mixed sodium chloride and sucrose solutions) and solution concentration (10 and 25% w/w) at room temperature (25°C) was studied. Kinetics of water loss and solids uptake were determined by a two parameter model, based on Fick's second law and applied to spherical geometry. The water apparent diffusivity coefficients obtained ranged from 2.17x10-10 to 11.69x10-10 m²/s.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.

Mathematical modeling of dehydration of 'Fuji' and 'Gala' apples slices using infrared

The objective of this work was to determine and model the infrared dehydration curves of apple slices - Fuji and Gala varieties. The slices were dehydrated until constant mass, in a prototype dryer with infrared heating source. The applied temperatures ranged from 50 to 100 °C. Due to the physical characteristics of the product, the dehydration curve was divided in two periods, constant and falling, separated by the critical moisture content. A linear model was used to describe the constant dehydration period. Empirical models traditionally used to model the drying behavior of agricultural products were fitted to the experimental data of the falling dehydration period. Critical moisture contents of 2.811 and 3.103 kgw kgs-1 were observed for the Fuji and Gala varieties, respectively. Based on the results, it was concluded that the constant dehydration rates presented a direct relationship with the temperature; thus, it was possible to fit a model that describes the moisture content variation in function of time and temperature. Among the tested models, which describe the falling dehydration period, the model proposed by Midilli presented the best fit for all studied conditions.

Mathematical modeling of microbial growth in milk

A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

Evaluation of a new mathematical model to describe Clostridium perfringens growth during the cooling of cooked ground beef

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.

Ordered probit regression analysis of the effect of brand name on beer acceptance by consumers

Ordered probit regression was used to analyze data of sensory acceptance tests designed to study the effect of brand name on the acceptability of beer samples. Eight different brands of Pilsen beer were evaluated by 101 consumers in two sessions of acceptance tests: blind evaluation and brand information test. Ordered probit regression, although a relatively sophisticated technique compared to others used to analyze sensory data, was chosen to enable the observation of consumers' behavior using graphical interpretations of estimated probabilities plotted against hedonic scales. It can be concluded that brands B, C, and D had a positive effect on the sensory acceptance of the product, whereas brands A, F, G, and H had a negative influence on consumers' evaluation of the samples. On the other hand, brand E had little influence on consumers' assessment.

Drying kinetics of potato pulp waste

Potato pulp waste (PPW) drying was investigated under different experimental conditions (temperatures from 50 to 70 °C and air flow from 0.06 to 0.092 m³ m- 2 s- 1) as a possible way to recover the waste generated by potato chip industries and to select the best-fit model to the experimental results of PPW drying. As a criterion to evaluate the fitting of mathematical models, a method based on the sum of the scores assigned to the four evaluated statistical parameters was used: regression coefficient (R²), relative mean error P (%), root mean square error (RMSE), and reduced chi-square (χ²). The results revealed that temperature and air velocity are important parameters to reduce PPW drying time. The models Midilli and Diffusion had the lowest sum values, i.e., with the best fit to the drying data, satisfactorily representing the drying kinetics of PPW.

Multivariate study and regression analysis of gluten-free granola

This study developed a gluten-free granola and evaluated it during storage with the application of multivariate and regression analysis of the sensory and instrumental parameters. The physicochemical, sensory, and nutritional characteristics of a product containing quinoa, amaranth and linseed were evaluated. The crude protein and lipid contents ranged from 97.49 and 122.72 g kg-1 of food, respectively. The polyunsaturated/saturated, and n-6:n-3 fatty acid ratios ranged from 2.82 and 2.59:1, respectively. Granola had the best alpha-linolenic acid content, nutritional indices in the lipid fraction, and mineral content. There were good hygienic and sanitary conditions during storage; probably due to the low water activity of the formulation, which contributed to inhibit microbial growth. The sensory attributes ranged from 'like very much' to 'like slightly', and the regression models were highly fitted and correlated during the storage period. A reduction in the sensory attribute levels and in the product physical stabilisation was verified by principal component analysis. The use of the affective test acceptance and instrumental analysis combined with statistical methods allowed us to obtain promising results about the characteristics of gluten-free granola.

Mathematical modeling of microwave dried celery leaves and determination of the effective moisture diffusivities and activation energy

Celery (Apium graveolens L. var. secalinum Alef) leaves with 50±0.07 g weight and 91.75±0.15% humidity (~11.21 db) were dried using 8 different microwave power densities ranging between 1.8-20 W g-1, until the humidity fell down to 8.95±0.23% (~0.1 db). Microwave drying processes were completed between 5.5 and 77 min depending on the microwave power densities. In this study, measured values were compared with predicted values obtained from twenty thin layer drying theoretical, semi-empirical and empirical equations with a new thin layer drying equation. Within applied microwave power density; models whose coefficient and correlation (R²) values are highest were chosen as the best models. Weibull distribution model gave the most suitable predictions at all power density. At increasing microwave power densities, the effective moisture diffusivity values ranged from 1.595 10-10 to 6.377 10-12 m2 s-1. The activation energy was calculated using an exponential expression based on Arrhenius equation. The linear relationship between the drying rate constant and effective moisture diffusivity gave the best fit.