On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Solution of aerospace problems using structured and unstructured strategies

Products developed at industries, institutes and research centers are expected to have high level of quality and performance, having a minimum waste, which require efficient and robust tools to numerically simulate stringent project conditions with great reliability. In this context, Computational Fluid Dynamics (CFD) plays an important role and the present work shows two numerical algorithms that are used in the CFD community to solve the Euler and Navier-Stokes equations applied to typical aerospace and aeronautical problems. Particularly, unstructured discretization of the spatial domain has gained special attention by the international community due to its ease in discretizing complex spatial domains. This work has the main objective of illustrating some advantages and disadvantages of numerical algorithms using structured and unstructured spatial discretization of the flow governing equations. Numerical methods include a finite volume formulation and the Euler and Navier-Stokes equations are applied to solve a transonic nozzle problem, a low supersonic airfoil problem and a hypersonic inlet problem. In a structured context, these problems are solved using MacCormack’s implicit algorithm with Steger and Warming’s flux vector splitting technique, while, in an unstructured context, Jameson and Mavriplis’ explicit algorithm is used. Convergence acceleration is obtained using a spatially variable time stepping procedure.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Structure and function of the cystic fibrosis transmembrane conductance regulator

Cystic fibrosis (CF) is a lethal autosomal recessive genetic disease caused by mutations in the CF transmembrane conductance regulator (CFTR). Mutations in the CFTR gene may result in a defective processing of its protein and alter the function and regulation of this channel. Mutations are associated with different symptoms, including pancreatic insufficiency, bile duct obstruction, infertility in males, high sweat Cl-, intestinal obstruction, nasal polyp formation, chronic sinusitis, mucus dehydration, and chronic Pseudomonas aeruginosa and Staphylococcus aureus lung infection, responsible for 90% of the mortality of CF patients. The gene responsible for the cellular defect in CF was cloned in 1989 and its protein product CFTR is activated by an increase of intracellular cAMP. The CFTR contains two membrane domains, each with six transmembrane domain segments, two nucleotide-binding domains (NBDs), and a cytoplasmic domain. In this review we discuss the studies that have correlated the role of each CFTR domain in the protein function as a chloride channel and as a regulator of the outwardly rectifying Cl- channels (ORCCs).

Total and segmental colonic transit time in constipated patients with Chagas’ disease without megaesophagus or megacolon

Manometric and pharmacological tests have shown that motor abnormalities may occur in the non-dilated colons of chagasic patients. In order to investigate the presence of abnormalities of colonic function in constipated patients with Chagas’ disease (ChC) without megaesophagus or megacolon, studies of total and segmental colonic transit time with radiopaque markers were performed on 15 ChC patients, 27 healthy volunteers and 17 patients with idiopathic constipation (IC). The values obtained for the control group were similar to those reported in the literature (total colonic time: 34.1 ± 15.6 h; right colon: 9.9 ± 7.3 h; left colon: 10.8 ± 10 h, and rectosigmoid: 12.6 ± 9.9 h). Colonic transit time data permitted us to divide both IC and ChC patients into groups with normal transit and those with slow colonic transit. Colonic inertia was detected in 41% of IC patients and in 13% of ChC patients; left colon isolated stasis (hindgut dysfunction) was detected in 12% of IC patients and 7% of ChC patients, and outlet obstruction was detected in 6% of IC patients and 7% of ChC patients. There were no significant differences in total or segmental colonic transit times between slow transit IC and slow transit ChC patients. In conclusion, an impairment of colonic motility was detected in about 30% of constipated patients with Chagas’ disease without megaesophagus or megacolon. This subgroup of patients presented no distinctive clinical feature or pattern of colonic dysmotility when compared to patients with slow transit idiopathic constipation.

Scintigraphy and Doppler ultrasonography for the evaluation of obstructive urinary calculi

Forty-seven patients with unilateral obstructive calculi (12 males and 35 females) were submitted to 99mTc-diethylene triamine pentaacetic acid (DTPA) or 99mTc-dimercaptosuccinic acid (DMSA) scans for assessment of renal function. The scans revealed unilateral functional deficit in 68 and 66% of the patients, respectively. A calculus size of 1.1 to 2.0 cm was significantly associated with deficit detected by DTPA, but duration of obstruction and calculus localization were not. After relief of the obstruction, the mean percent renal function of the affected kidney was found to be significantly increased from 25 ± 12% to 29 ± 12% in DTPA and from 21 ± 15% to 24 ± 12% in DMSA. Initial Doppler ultrasonography performed in 35 patients detected an increased resistive index in 10 (29%). In the remaining patients with a normal resistive index, ureteral urinary jet was observed, indicating partial obstruction. The high frequency of renal function impairment detected by DTPA and of tubulointerstitial damage detected by DMSA as well as the slight amelioration of unilateral renal function after relief of obstruction suggest that scintigraphy assessment may help evaluate the unilateral percentage of renal function and monitor renal function recovery when it occurs. The presence of a urinary jet detected by Doppler ultrasonography further indicates the severity of obstruction and the recovery prognosis.

Effect of asthma severity on symptom perception in childhood asthma

Individual ability to perceive airway obstruction varies substantially. The factors influencing the perception of asthma are probably numerous and not well established in children. The present study was designed to examine the influence of asthma severity, use of preventive medication, age and gender on the association between respiratory symptoms (RS) and peak expiratory flow (PEF) rates in asthmatic children. We followed 92 asthmatic children, aged 6 to 16 years, for five months. Symptom scores were recorded daily and PEF was measured twice a day. The correlations among variables at the within-person level over time were analyzed for each child and for the pooled data by multivariate analysis. After pooling the data, there was a significant (P<0.05) correlation between each symptom and PEF; 60% of the children were accurate perceivers (defined by a statistically significant correlation between symptoms and PEF across time) for diurnal symptoms and 37% for nocturnal symptoms. The accuracy of perception was independent of asthma severity, age, gender or the use of preventive medication. Symptom perception is inaccurate in a substantial number of asthmatic children, independently of clinical severity, age, gender or use of preventive medication. It is not clear why some asthmatic patients are capable of accurately perceiving the severity of airway obstruction while others are not.

Patient and physician evaluation of the severity of acute asthma exacerbations

We studied the ability of patients not experienced in the use of peak expiratory flow meters to assess the severity of their asthma exacerbations and compared it to the assessment of experienced clinicians. We also evaluated which data of physical examination and medical history are used by physicians to subjectively evaluate the severity of asthma attacks. Fifty-seven adult patients (15 men and 42 women, with a mean (± SD) age of 37.3 ± 14.5 years and 24.0 ± 17.9 years of asthma symptoms) with asthma exacerbations were evaluated in a University Hospital Emergency Department. Patients and physicians independently evaluated the severity of the asthma attack using a linear scale. Patient score, physician score and forced expiratory volume at the first second (FEV1) were correlated with history and physical examination variables, and were also considered as dependent variables in multiple linear regression models. FEV1 correlated significantly with the physician score (rho = 0.42, P = 0.001), but not with patient score (rho = 0.03; P = 0.77). Use of neck accessory muscles, expiratory time and wheezing intensity were the explanatory variables in the FEV1 regression model and were also present in the physician score model. We conclude that physicians evaluate asthma exacerbation severity better than patients and that physician's scoring of asthma severity correlated significantly with objective measures of airway obstruction (FEV1). Some variables (the use of neck accessory muscles, expiratory time and wheezing intensity) persisted as explanatory variables in physician score and FEV1 regression models, and should be emphasized in medical schools and emergency settings.

Asthma: where is it going?

Asthma is characterized by reversible airway obstruction, airway hyperresponsiveness, and airway inflammation. Although our understanding of its pathophysiological mechanisms continues to evolve, the relative contributions of airway hyperresponsiveness and inflammation are still debated. The first mechanism identified as important for asthma was bronchial hyperresponsiveness. In a second step, asthma was recognized also as an inflammatory disease, with chronic inflammation inducing structural changes or remodeling. However, persistence of airway dysfunction despite inflammatory control is observed in chronic severe asthma of both adults and children. More recently, a potential role for epithelial-mesenchymal communication or transition is emerging, with epithelial injury often resulting in a self-sustaining phenotype of wound repair modulation by activation/reactivation of the epithelial-mesenchymal trophic unit, suggesting that chronic asthma can be more than an inflammatory disease. It is noteworthy that the gene-environmental interactions critical for the development of a full asthma phenotype involve processes similar to those occurring in branching morphogenesis. In addition, a central role for airway smooth muscle in the pathogenesis of the disease has been explored, highlighting its secretory function as well as different intrinsic properties compared to normal subjects. These new concepts can potentially shed light on the mechanisms underlying some asthma phenotypes and improve our understanding of the disease in terms of the therapeutic strategies to be applied. How we understand asthma and its mechanisms along time will be the focus of this overview.

Relationship between disease severity and quality of life in patients with chronic obstructive pulmonary disease

Few studies have evaluated the relationship between Airways Questionnaire 20 (AQ20), a measure of the quality of life, scores and physiological outcomes or with systemic markers of disease in patients with chronic obstructive pulmonary disease (COPD). The aim of the present study was to investigate the relationship of forced expiratory volume in 1 s (FEV1), body mass index, fat-free mass index, 6-min walk test (6MWT) results, dyspnea sensation and peripheral oxygen saturation (SpO2) with the quality of life of COPD patients. Ninety-nine patients with COPD (mean age: 64.2 ± 9.2 years; mean FEV1: 60.4 ± 25.2% of predicted) were evaluated using spirometry, body composition measurement and the 6MWT. The baseline dyspnea index (BDI) and the Modified Medical Research Council (MMRC) scale were used to quantify dyspnea. Quality of life was assessed using the AQ20 and the St. George's Respiratory Questionnaire (SGRQ). The Charlson index was used to determine comorbidity. The body mass index/airflow obstruction/dyspnea/exercise capacity (BODE) index was also calculated. AQ20 and SGRQ scores correlated significantly with FEV1, SpO2, 6MWT, MMRC and BDI values as did with BODE index. In the multivariate analyses, MMRC or BDI were identified as predictors of AQ20 and SGRQ scores (P < 0.001 in all cases). Thus, the relationship between AQ20 and disease severity is similar to that described for SGRQ. Therefore, the AQ20, a simple and brief instrument, can be very useful to evaluate the general impact of disease when the time allotted for measurement of the quality of life is limited.

Advances in biliary atresia: from patient care to research

Biliary atresia, the most common cause of liver transplantation in children, remains a challenge for clinicians and investigators. The development of new therapeutic options, besides the typical hepatoportoenterostomy, depends on a greater understanding of its pathogenesis and how it relates to the clinical phenotypes at diagnosis and the rate of disease progression. In this review, we present a perspective of how recent research has advanced the understanding of the disease and has improved clinical care protocols. Molecular and morphological analyses at diagnosis point to the potential contributions of polymorphism in the CFC1 and VEGF genes to the pathogenesis of the disease, and to an association between the degree of bile duct proliferation and long-term outcome. In experimental models, cholangiocytes do not appear to have antigen-presenting properties despite a substantial innate and adaptive immune response that targets the biliary epithelium and produces duct obstruction. Initial clinical trials assessing the efficacy of corticosteroids in decreasing the inflammation and improving outcome do not show a superior effect of corticosteroids as an adjuvant treatment following hepatoportoenterostomy. The best outcome still remains linked to an early diagnosis and surgical treatment. In this regard, the Yellow Alert campaign by the Sociedade Brasileira de Pediatria and the inclusion of the Stool Color Card in the health booklet given to every neonate in Brazil have the potential to decrease the age of diagnosis, shorten the time between diagnosis and surgical treatment, and improve the long-term outcome of children with this devastating disease.

Three-year follow-up study of respiratory and systemic manifestations of chronic obstructive pulmonary disease

Few studies show patient outcomes over time in chronic obstructive pulmonary disease (COPD). In the present study, we monitored forced expiratory volume in the first second (FEV1) and other manifestations of the disease over 3 years in 133 COPD patients (69% males, age = 65 ± 9 years, FEV1 = 59 ± 25%) evaluated at baseline. During follow-up, 15 patients (11%) died and 23 (17%) dropped out. Measurements for 95 (72%) COPD patients alive after 3 years were analyzed. FEV1, body mass index (BMI), 6-min walking distance (6MWD), Medical Research Council scale (MRC), Saint George’s Respiratory Questionnaire (SGRQ), Charlson Comorbidity index, and BODE index were obtained at baseline and after 3 years. At baseline, 17 patients (18%) presented mild, 39% moderate, 19% severe, and 24% very severe COPD. Predicted FEV1 % and BMI did not change over the period (P > 0.05). FEV1 in liters [1.25 (0.96-1.72) vs 1.26 (0.88-1.60) L; P < 0.001], 6MWD (438 ± 86 vs 412 ± 100 m; P < 0.001), MRC [1 (1-2) vs 2 (1-3); P = 0.002], Charlson index [3 (3-4) vs4 (3-5); P = 0.009], BODE index (2.2 ± 1.8 vs 2.6 ± 2.3; P = 0.008), and total SGRQ (42 ± 19 vs 44 ± 19%; P = 0.041) worsened after 3 years compared to baseline measurements. These data show that COPD patients deteriorated during the 3-year follow-up despite the fact that they had only minor modifications in airway obstruction and body composition. They support the need for comprehensive patient assessment to better identify disease progression.

Dynamic expression of desmin, α-SMA and TGF-β1 during hepatic fibrogenesis induced by selective bile duct ligation in young rats

We previously described a selective bile duct ligation model to elucidate the process of hepatic fibrogenesis in children with biliary atresia or intrahepatic biliary stenosis. Using this model, we identified changes in the expression of alpha smooth muscle actin (α-SMA) both in the obstructed parenchyma and in the hepatic parenchyma adjacent to the obstruction. However, the expression profiles of desmin and TGF-β1, molecules known to be involved in hepatic fibrogenesis, were unchanged when analyzed by semiquantitative polymerase chain reaction (RT-PCR). Thus, the molecular mechanisms involved in the modulation of liver fibrosis in this experimental model are not fully understood. This study aimed to evaluate the molecular changes in an experimental model of selective bile duct ligation and to compare the gene expression changes observed in RT-PCR and in real-time quantitative PCR (qRT‐PCR). Twenty-eight Wistar rats of both sexes and weaning age (21-23 days old) were used. The rats were separated into groups that were assessed 7 or 60 days after selective biliary duct ligation. The expression of desmin, α-SMA and TGF-β1 was examined in tissue from hepatic parenchyma with biliary obstruction (BO) and in hepatic parenchyma without biliary obstruction (WBO), using RT-PCR and qRT‐PCR. The results obtained in this study using these two methods were significantly different. The BO parenchyma had a more severe fibrogenic reaction, with increased α-SMA and TGF-β1 expression after 7 days. The WBO parenchyma presented a later, fibrotic response, with increased desmin expression 7 days after surgery and increased α-SMA 60 days after surgery. The qRT‐PCR technique was more sensitive to expression changes than the semiquantitative method.

Difusão do cloreto de sódio no processo de salga de queijos: modelagem matemática com o emprego do método de elementos finitos

A transferência de um soluto (cloreto de sódio), através de uma matriz sólida tridimensional (queijo) foi estudada aplicando-se o método de elementos finitos. A formulação variacional (Galerkin) do problema diferencial (modelo de difusão) teve como base teórica a 2ª lei de Fick. Os procedimentos para integração no tempo foram o de Crank-Nicolson e o de Euler-modificado, que foram escolhidos por apresentarem estabilidade incondicional. O programa computacional desenvolvido mostrou-se versátil para resolver situações de amostragem em condições mais realistas e pode ser aplicado para geometrias complexas. O modelo proposto permitiu uma boa estimativa do ganho de sal no queijo, usando um coeficiente de difusão cujo valor pode ser obtido por extrapolação de dados experimentais. A aplicação do método numérico (MEF), com o esquema de Crank-Nicolson, na simulação da difusão do cloreto de sódio na salga de queijos, mostrou boa aproximação quando os resultados foram comparados com os valores experimentais encontrados na literatura especializada.