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.

New auxiliary indicators for the differential diagnosis of functional cardiorespiratory limitation in patients with chronic obstructive pulmonary disease and congestive heart failure

OBJECTIVE: To differentiate the nature of functional cardiorespiratory limitations during exercise in individuals with chronic obstructive pulmonary disease (COPD) or congestive heart failure (CHF) and to determine indicators that may help their classifications. METHODS: The study comprised 40 patients: 23 with COPD and 17 with CHF. All individuals underwent maximal cardiopulmonary exercise testing on a treadmill. RESULTS: The values of peak gas exchange ratio (R peak), peak carbon dioxide production (VCO2 peak), and peak oxygen ventilatory equivalent (V E O2 peak) were higher in the patients with CHF than in those with COPD, and, therefore, those were the variables that characterized the differences between the groups. For group classification, the differentiating functions with the R peak, VCO2 peak (L/min), and V E O2 peak variables were used as follows: group COPD: - 44.886 + 78.832 x R peak + 5.442 x VCO2 peak + 0.336 x V E O2 peak; group CHF: - 69.251 + 89.740 x R peak + 8.461 x VCO2 peak + 0.574 x V E O2 peak. The differentiating function, whose result is greater, correctly classifies the patient's group as 90%. CONCLUSION: The R peak, VCO2 peak, and V E O2 peak values may be used to identify the cause of the functional cardiorespiratory limitations in patients with COPD and CHF.

Differential gene expression during Trypanosoma cruzi metacyclogenesis

The transformation of epimastigotes into metacyclic trypomastigotes involves changes in the pattern of expressed genes, resulting in important morphological and functional differences between these developmental forms of Trypanosoma cruzi. In order to identify and characterize genes involved in triggering the metacyclogenesis process and in conferring to metacyclic trypomastigotes their stage specific biological properties, we have developed a method allowing the isolation of genes specifically expressed when comparing two close related cell populations (representation of differential expression or RDE). The method is based on the PCR amplification of gene sequences selected by hybridizing and subtracting the populations in such a way that after some cycles of hybridization-amplification genes specific to a given population are highly enriched. The use of this method in the analysis of differential gene expression during T. cruzi metacyclogenesis (6 hr and 24 hr of differentiation and metacyclic trypomastigotes) resulted in the isolation of several clones from each time point. Northern blot analysis showed that some genes are transiently expressed (6 hr and 24 hr differentiating cells), while others are present in differentiating cells and in metacyclic trypomastigotes. Nucleotide sequencing of six clones characterized so far showed that they do not display any homology to gene sequences available in the GeneBank.

Experimental hepatic fibrosis due to Capillaria hepatica infection (differential features presented by rats and mice)

Rats and mice are among the most susceptible hosts for the helminth Capillaria hepatica. More information on the similarities and differences between the hepatic pathology presented by these two parasite hosts are needed, since they may represent good models for the study of hepatic fibrosis. Early changes are similar for both hosts and are represented by necro-inflammatory lesions around dead parasites and their eggs and diffuse and intense reactive hepatitis. Although worms remain alive longer in mice than in rats, hepatic changes are more rapidly and deeply modulated in the former, even leading to almost complete disappearance of fibrosis. As for the rats, the modulation of the focal lesions is followed by the formation of septal fibrosis, a process where fine and long fibrous septa appear connecting portal spaces and central veins in such a way as to form a final morphologic picture of cirrhosis. Hepatic functional changes usually present good correlations with the morphologic findings at the different phases of the infection evolution. Therefore C. hepatica infection in rats and mice represent two different models of hepatic fibrosis and these differences, if properly known and understood, can be explored to answer different questions regarding several aspects of hepatic fibrosis

Functional complementation of a yeast knockout strain by Schistosoma mansoni Rho1 GTPase in the presence of caffeine, an agent that affects mutants defective in the protein kinase C signal transduction pathway

In a previous study, the Schistosoma mansoni Rho1 protein was able to complement Rho1 null mutant Saccharomyces cerevisiae cells at restrictive temperatures and under osmotic stress (low calcium concentration) better than the human homologue (RhoA). It is known that under osmotic stress, the S. cerevisiae Rho1 triggers two distinct pathways: activation of the membrane 1,3-beta-glucan synthase enzymatic complex and activation of the protein kinase C1 signal transduction pathway, promoting the transcription of response genes. In the present work the SmRho1 protein and its mutants smrho1E97P, smrho1L101T, and smrho1E97P, L101T were used to try to clarify the basis for the differential complementation of Rho1 knockout yeast strain by the human and S. mansoni genes. Experiments of functional complementation in the presence of caffeine and in the presence of the osmotic regulator sorbitol were conducted. SmRho1 and its mutants showed a differential complementation of the yeast cells in the presence of caffeine, since smrho1E97P and smrho1E97P, L101T mutants showed a delay in the growth when compared to the yeast complemented with the wild type SmRho1. However, in the presence of sorbitol and caffeine the wild type SmRho1 and mutants showed a similar complementation phenotype, as they allowed yeast growth in all caffeine concentrations tested.

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

A brain microdialysis study on 5-HT release in freely moving rat lines selectively bred for differential 5-HT1A receptor function

Breeding for high and low hypothermic responses to systemic administration of a serotonin1A (5-HT1A) receptor agonist (8-hydroxy-2-(di-n-propylamino)tetralin, 8-OH-DPAT) has resulted in high DPAT-sensitive (HDS) and low DPAT-sensitive (LDS) lines of rats, respectively. These lines also differ in several behavioral measures associated with stress. In the present microdialysis study we observed that basal 5-HT concentrations in the prefrontal cortex and dorsal hippocampus did not differ significantly between HDS and LDS rats. Thus, behavioral differences between the HDS and LDS lines might not be attributed to differences in basal 5-HT release. However, both lines had lower basal levels of 5-HT release than their randomly bred control group (random DPAT-sensitive, RDS) in the prefrontal cortex (mean ± SEM, pg/20 µl, was 3.0 ± 0.4 for LDS, 3.8 ± 0.3 for HDS and 6.4 ± 0.6 for RDS; F(2,59) = 5.8, P<0.005). The administration of (±)-fenfluramine (10 mg/kg) induced a greater increase in hippocampal 5-HT levels in HDS rats (500%) as compared with LDS (248%) or RDS (243%) rats (P<0.0001). There were no significant differences in the prefrontal cortex among lines, with a fenfluramine-induced 5-HT increase of about 900% in the three groups. This differential response to fenfluramine may be due to functional alterations of hippocampal 5-HT reuptake sites in the HDS line.