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.

Mathematical simulation parameters for drying of cassava starch pellets

Based on experimental tests, it was obtained the equations for drying, equilibrium moisture content, latent heat of vaporization of water contained in the product and the equation of specific heat of cassava starch pellets, essential parameters for realizing modeling and mathematical simulation of mechanical drying of cassava starch for a new technique proposed, consisting of preformed by pelleting and subsequent artificial drying of starch pellets. Drying tests were conducted in an experimental chamber by varying the air temperature, relative humidity, air velocity and product load. The specific heat of starch was determined by differential scanning calorimetry. The generated equations were validated through regression analysis, finding an appropriate correlation of the data, which indicates that by using these equations, can accurately model and simulate the drying process of cassava starch pellets.

Uterine Doppler velocimetry of the uterine arteries in the second and third trimesters for the prediction of gestational outcome

PURPOSE: The aim of this longitudinal study was to investigate the value of uterine artery Doppler sonography during the second and third trimesters in the prediction of adverse pregnancy outcome in low-risk women. METHODS: From July 2011 to August 2012, a total of 205 singleton pregnant women presenting at our antenatal clinic were enrolled in this prospective study and were assessed for baseline demographic and obstetric data. They underwent ultrasound evaluation at the time of second and third trimesters, both included Doppler assessment of bilateral uterine arteries to determine the values of the pulsatility index (PI) and resistance index (RI) and presence of early diastolic notch. The endpoint of this study was assessing the sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of Doppler ultrasonography of the uterine artery, for the prediction of adverse pregnancy outcomes including preeclampsia, stillbirth, placental abruption and preterm labor. RESULTS: The mean age of cases was 26.4±5.11. The uterine artery PI and RI values for both second (PI: 1.1±0.42 versus 1.53±0.59, p=0.002; RI: 0.55±0.09 versus 0.72±0.13, p=0.000 respectively) and third-trimester (PI: 0.77±0.31 versus 1.09±0.46, p=0.000; RI: 0.46±0.10 versus 0.60±0.14, p=0.010 respectively) evaluations were significantly higher in patients with adverse pregnancy outcome than in normal women. Combination of PI and RI >95th percentile and presence of bilateral notch in second trimester get sensitivity and specificity of 36.1 and 97% respectively, while these measures were 57.5 and 98.2% in third trimester. CONCLUSIONS: According to our study, it seems that uterine artery Doppler may be a valuable tool for the prediction of a variety of adverse outcomes in second and third trimesters.

Criteria for prediction of metastatic axillary lymph nodes in early-stage breast cancer

PURPOSE: To estimate the likelihood of axillary lymph node involvement for patients with early-stage breast cancer, based on a variety of clinical and pathological factors. METHODS: A retrospective analysis was done in hospital databases from 1999 to 2007. Two hundred thirty-nine patients were diagnosed with early-stage breast cancer. Predictive factors, such as patient age, tumor size, lymphovascular invasion, histological grade and immunohistochemical subtype were analyzed to identify variables that may be associated with axillary lymph node metastasis. RESULTS: Patients with tumors that are negative for estrogen receptor, progesterone receptor, and HER2 had approximately a 90% lower chance of developing lymph node metastasis than those with luminal A tumors (e.g., ER+ and/or PR+ and HER2-) - Odds Ratio: 0.11; 95% confidence interval: 0.01-0.88; p=0.01. Furthermore, the risk for lymph node metastasis of luminal A tumors seemed to decrease as patient age increased, and it was directly correlated with tumor size. CONCLUSION: The molecular classification of early-stage breast cancer using immunohistochemistry may help predicting the probability of developing axillary lymph node metastasis. Further studies are needed to optimize predictions for nodal involvement, with the aim of aiding the decision-making process for breast cancer treatment.

A temperature predicting model for manufacturing processes requiring coiling

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model.

Fluid dynamic modelling and simulation of circulating fluidized bed reactors: importance of the interface turbulence transfer

The main objective of this work is to analyze the importance of the gas-solid interface transfer of the kinetic energy of the turbulent motion on the accuracy of prediction of the fluid dynamic of Circulating Fluidized Bed (CFB) reactors. CFB reactors are used in a variety of industrial applications related to combustion, incineration and catalytic cracking. In this work a two-dimensional fluid dynamic model for gas-particle flow has been used to compute the porosity, the pressure, and the velocity fields of both phases in 2-D axisymmetrical cylindrical co-ordinates. The fluid dynamic model is based on the two fluid model approach in which both phases are considered to be continuous and fully interpenetrating. CFB processes are essentially turbulent. The model of effective stress on each phase is that of a Newtonian fluid, where the effective gas viscosity was calculated from the standard k-epsilon turbulence model and the transport coefficients of the particulate phase were calculated from the kinetic theory of granular flow (KTGF). This work shows that the turbulence transfer between the phases is very important for a better representation of the fluid dynamics of CFB reactors, especially for systems with internal recirculation and high gradients of particle concentration. Two systems with different characteristics were analyzed. The results were compared with experimental data available in the literature. The results were obtained by using a computer code developed by the authors. The finite volume method with collocated grid, the hybrid interpolation scheme, the false time step strategy and SIMPLEC (Semi-Implicit Method for Pressure Linked Equations - Consistent) algorithm were used to obtain the numerical solution.

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.

Growth and Development of Purple Nutsedge Based on Days or Thermal Units

This work was carried out with the objective of elaborating mathematical models to predict growth and development of purple nutsedge (Cyperus rotundus) based on days or accumulated thermal units (growing degree days). Thus, two independent trials were developed, the first with a decreasing photoperiod (March to July) and the second with an increasing photoperiod (August to November). In each trial, ten assessments of plant growth and development were performed, quantifying total dry matter and the species phenology. After that, phenology was fit to first degree equations, considering individual trials or their grouping. In the same way, the total dry matter was fit to logistic-type models. In all regressions four temporal scales possibilities were assessed for the x axis: accumulated days or growing degree days (GDD) with base temperatures (Tb) of 10, 12 and 15 oC. For both photoperiod conditions, growth and development of purple nutsedge were adequately fit to prediction mathematical models based on accumulated thermal units, highlighting Tb = 12 oC. Considering GDD calculated with Tb = 12 oC, purple nutsedge phenology may be predicted by y = 0.113x, while species growth may be predicted by y = 37.678/(1+(x/509.353)-7.047).

Early prediction of poor outcome in patients with acute asthma in the emergency room

Early identification of patients who need hospitalization or patients who should be discharged would be helpful for the management of acute asthma in the emergency room. The objective of the present study was to examine the clinical and pulmonary functional measures used during the first hour of assessment of acute asthma in the emergency room in order to predict the outcome. We evaluated 88 patients. The inclusion criteria were age between 12 and 55 years, forced expiratory volume in the first second below 50% of predicted value, and no history of chronic disease or pregnancy. After baseline evaluation, all patients were treated with 2.5 mg albuterol delivered by nebulization every 20 min in the first hour and 60 mg of intravenous methylprednisolone. Patients were reevaluated after 60 min of treatment. Sixty-five patients (73.9%) were successfully treated and discharged from the emergency room (good responders), and 23 (26.1%) were hospitalized or were treated and discharged with relapse within 10 days (poor responders). A predictive index was developed: peak expiratory flow rates after 1 h <=0% of predicted values and accessory muscle use after 1 h. The index ranged from 0 to 2. An index of 1 or higher presented a sensitivity of 74.0, a specificity of 69.0, a positive predictive value of 46.0, and a negative predictive value of 88.0. It was possible to predict outcome in the first hour of management of acute asthma in the emergency room when the index score was 0 or 2.

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.

Prediction of exposed domains of envelope glycoprotein in Indian HIV-1 isolates and experimental confirmation of their immunogenicity in humans

We describe the impact of subtype differences on the seroreactivity of linear antigenic epitopes in envelope glycoprotein of HIV-1 isolates from different geographical locations. By computer analysis, we predicted potential antigenic sites of envelope glycoprotein (gp120 and gp4l) of this virus. For this purpose, after fetching sequences of proteins of interest from data banks, values of hydrophilicity, flexibility, accessibility, inverted hydrophobicity, and secondary structure were considered. We identified several potential antigenic epitopes in a B subtype strain of envelope glycoprotein of HIV-1 (IIIB). Solid- phase peptide synthesis methods of Merrifield and Fmoc chemistry were used for synthesizing peptides. These synthetic peptides corresponded mainly to the C2, V3 and CD4 binding sites of gp120 and some parts of the ectodomain of gp41. The reactivity of these peptides was tested by ELISA against different HIV-1-positive sera from different locations in India. For two of these predicted epitopes, the corresponding Indian consensus sequences (LAIERYLKQQLLGWG and DIIGDIRQAHCNISEDKWNET) (subtype C) were also synthesized and their reactivity was tested by ELISA. These peptides also distinguished HIV-1-positive sera of Indians with C subtype infections from sera from HIV-negative subjects.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Fuzzy expert system in the prediction of neonatal resuscitation

In view of the importance of anticipating the occurrence of critical situations in medicine, we propose the use of a fuzzy expert system to predict the need for advanced neonatal resuscitation efforts in the delivery room. This system relates the maternal medical, obstetric and neonatal characteristics to the clinical conditions of the newborn, providing a risk measurement of need of advanced neonatal resuscitation measures. It is structured as a fuzzy composition developed on the basis of the subjective perception of danger of nine neonatologists facing 61 antenatal and intrapartum clinical situations which provide a degree of association with the risk of occurrence of perinatal asphyxia. The resulting relational matrix describes the association between clinical factors and risk of perinatal asphyxia. Analyzing the inputs of the presence or absence of all 61 clinical factors, the system returns the rate of risk of perinatal asphyxia as output. A prospectively collected series of 304 cases of perinatal care was analyzed to ascertain system performance. The fuzzy expert system presented a sensitivity of 76.5% and specificity of 94.8% in the identification of the need for advanced neonatal resuscitation measures, considering a cut-off value of 5 on a scale ranging from 0 to 10. The area under the receiver operating characteristic curve was 0.93. The identification of risk situations plays an important role in the planning of health care. These preliminary results encourage us to develop further studies and to refine this model, which is intended to implement an auxiliary system able to help health care staff to make decisions in perinatal care.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.