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.

L-carnitine as an ergogenic aid for patients with chronic obstructive pulmonary disease submitted to whole-body and respiratory muscle training programs

The effects of adding L-carnitine to a whole-body and respiratory training program were determined in moderate-to-severe chronic obstructive pulmonary disease (COPD) patients. Sixteen COPD patients (66 ± 7 years) were randomly assigned to L-carnitine (CG) or placebo group (PG) that received either L-carnitine or saline solution (2 g/day, orally) for 6 weeks (forced expiratory volume on first second was 38 ± 16 and 36 ± 12%, respectively). Both groups participated in three weekly 30-min treadmill and threshold inspiratory muscle training sessions, with 3 sets of 10 loaded inspirations (40%) at maximal inspiratory pressure. Nutritional status, exercise tolerance on a treadmill and six-minute walking test, blood lactate, heart rate, blood pressure, and respiratory muscle strength were determined as baseline and on day 42. Maximal capacity in the incremental exercise test was significantly improved in both groups (P < 0.05). Blood lactate, blood pressure, oxygen saturation, and heart rate at identical exercise levels were lower in CG after training (P < 0.05). Inspiratory muscle strength and walking test tolerance were significantly improved in both groups, but the gains of CG were significantly higher than those of PG (40 ± 14 vs 14 ± 5 cmH2O, and 87 ± 30 vs 34 ± 29 m, respectively; P < 0.05). Blood lactate concentration was significantly lower in CG than in PG (1.6 ± 0.7 vs 2.3 ± 0.7 mM, P < 0.05). The present data suggest that carnitine can improve exercise tolerance and inspiratory muscle strength in COPD patients, as well as reduce lactate production.

Financial support of graduate programs in Brazil: quo vadis?

Graduate programs provide the highest level of formal education and thus are crucial for the development of any country. However, official Brazilian data clearly show a dramatic decrease in the number and values of scholarships available to graduate programs in Brazil over the last few years, despite the importance and growth of such programs. Between 1995 and 2004, investment by the Coordenadoria de Aperfeiçoamento de Pessoal do Ensino Superior (CAPES, subordinate to the Ministry of Education and Culture) in funding scholarships, corrected for inflation in the period, actually decreased by 51%. In addition, during the period between 1994 and 2004, there was a loss of about 60% in the purchasing power of the graduate scholarships provided by CAPES and the National Council for Science and Technology (CNPq). To reverse this trend, we propose the development of sectorial funding for Brazilian graduate programs to guarantee the availability and continuity of financial support for this strategic activity.

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.

Effect of three exercise programs on patients with chronic obstructive pulmonary disease

We compared the effect of three different exercise programs on patients with chronic obstructive pulmonary disease including strength training at 50_80% of one-repetition maximum (1-RM) (ST; N = 11), low-intensity general training (LGT; N = 13), or combined training groups (CT; N = 11). Body composition, muscle strength, treadmill endurance test (TEnd), 6-min walk test (6MWT), Saint George's Respiratory Questionnaire (SGRQ), and baseline dyspnea (BDI) were assessed prior to and after the training programs (12 weeks). The training modalities showed similar improvements (P > 0.05) in SGRQ-total (ST = 13 ± 14%; CT = 12 ± 14%; LGT = 11 ± 10%), BDI (ST = 1.8 ± 4; CT = 1.8 ± 3; LGT = 1 ± 2), 6MWT (ST = 43 ± 51 m; CT = 48 ± 50 m; LGT = 31 ± 75 m), and TEnd (ST = 11 ± 20 min; CT = 11 ± 11 min; LGT = 7 ± 5 min). In the ST and CT groups, an additional improvement in 1-RM values was shown (P < 0.05) compared to the LGT group (ST = 10 ± 6 to 57 ± 36 kg; CT = 6 ± 2 to 38 ± 16 kg; LGT = 1 ± 2 to 16 ± 12 kg). The addition of strength training to our current training program increased muscle strength; however, it produced no additional improvement in walking endurance, dyspnea or quality of life. A simple combined training program provides benefits without increasing the duration of the training sessions.

Exercise may cause myocardial ischemia at the anaerobic threshold in cardiac rehabilitation programs

Myocardial ischemia may occur during an exercise session in cardiac rehabilitation programs. However, it has not been established whether it is elicited when exercise prescription is based on heart rate corresponding to the anaerobic threshold as measured by cardiopulmonary exercise testing. Our objective was to determine the incidence of myocardial ischemia in cardiac rehabilitation programs according to myocardial perfusion SPECT in exercise programs based on the anaerobic threshold. Thirty-nine patients (35 men and 4 women) diagnosed with coronary artery disease by coronary angiography and stress technetium-99m-sestamibi gated SPECT associated with a baseline cardiopulmonary exercise test were assessed. Ages ranged from 45 to 75 years. A second cardiopulmonary exercise test determined training intensity at the anaerobic threshold. Repeat gated-SPECT was obtained after a third cardiopulmonary exercise test at the prescribed workload and heart rate. Myocardial perfusion images were analyzed using a score system of 6.4 at rest, 13.9 at peak stress, and 10.7 during the prescribed exercise (P < 0.05). The presence of myocardial ischemia during exercise was defined as a difference ≥2 between the summed stress score and summed rest score. Accordingly, 25 (64%) patients were classified as ischemic and 14 (36%) as nonischemic. MIBI-SPECT showed myocardial ischemia during exercise within the anaerobic threshold. The 64% prevalence of ischemia observed in the study should not be looked on as representative of the whole population of patients undergoing exercise programs. Changes in patient care and exercise programs were implemented as a result of our finding of ischemia during the prescribed exercise.

Citations to papers from Brazilian institutions: a more effective indicator to assess productivity and the impact of research in graduate programs

A recent assessment of 4400 postgraduate courses in Brazil by CAPES (a federal government agency dedicated to the improvement of the quality of and research at the postgraduate level) stimulated a large amount of manifestations in the press, scientific journals and scientific congresses. This gigantic effort to classify 16,400 scientific journals in order to provide indicators for assessment proved to be puzzling and methodologically erroneous in terms of gauging the institutions from a metric point of view. A simple algorithm is proposed here to weigh the scientometric indicators that should be considered in the assessment of a scientific institution. I conclude here that the simple gauge of the total number of citations accounts for both the productivity of scientists and the impact of articles. The effort spent in this exercise is relatively small, and the sources of information are fully accessible. As an exercise to estimate the value of the methodology, 12 institutions of physics (10 from Brazil, one from the USA and one from Italy) have been evaluated.

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.

Comparative analysis of vitamin A and iron content in food according to different food composition tables and nutritional evaluation software programs

The objective of this study was to analyze retinol equivalent and iron content in different food composition tables and nutritional evaluation software programs. A literature search was conduct to identify tables and software available in Brazil containing information about retinol equivalent and iron content that are currently used by nutritionists. Ten tables and five software programs were selected for this study. The methodology used to present the retinol equivalent and iron content was evaluated and no pattern to obtain such content was found in the tables and software programs analyzed. Only one of the tables had enough information for the calculation of retinol equivalents; this table is recommended to all Latin America As for the iron content, three of the tables analyzed stand out and therefore should be used; two of them are based on national foods and the other is recommended for use in all Latin America countries. None of the software programs evaluated use the conversion factors suggested by IVACG to assess the vitamin A content in foods. Special attention should be given to the content of iron provided in the software programs since they use tables as international sources and fortified foods.

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.