Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs

We construct, for any given $\ell = \frac{1}{2} + {\mathbb N}_0,$ the second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. The generators are obtained by a coset construction and the PDEs are constructed by standard Lie symmetry technique. It is observed that the invariant PDEs have significant difference for $\ell > \frac{3}{2}.$Comment: 22pages, 3figure

Noninvasive assessment of left and right ventricular filling in myocardial infarction with a two-dimensional Doppler echocardiography method

Inflow characteristics of left and right ventricular filling were assessed in 40 patients with myocardial infarction and in 10 normal subjects by pulsed Doppler echocardiography. Patients with myocardial infarction were subdivided into four groups, focusing on the involvement of right ventricular and septal branches of the coronary arteries. Group I consisted of 11 patients with anterior infarction who showed an obstructive lesion of the proximal left anterior descending branch involving the first septal perforator with a patent right coronary artery. Group II consisted of 10 patients with inferior infarction who showed an obstructive lesion of the proximal right coronary artery involving the right ventricular branch. Group III consisted of 12 patients with both anterior and inferior infarction who showed obstructive lesions of both the proximal left anterior descending branch and the right coronary artery involving the right ventricular branch. Group IV consisted of seven patients with lateral infarction who showed an obstructive lesion of the diagonal branch or branches of the circumflex coronary artery with a patent left anterior descending branch and right coronary artery.Three measurements were performed from the trans-mitral and transtricuspidal inflow velocity patterns to assess the left and right ventricular diastolic behaviors. These measurements were: 1) acceleration half-time, 2) deceleration half-time of early diastolic rapid inflow, and 3) the ratio of the peak velocity of early diastolic rapid inflow to that of the late diastolic inflow due to the atrial contraction.Impaired diastolic filling of the left ventricle compensated by enhanced left atrial contraction was observed in patients with myocardial infarction from groups I, II, III and IV. Impaired diastolic filling of the right ventricle compensated by enhanced right atrial contraction was revealed in groups I, II and III. It is supposed that myocardial damage of the interventricular septum and a part of the right ventricular anterior wall perfused from the left anterior descending branch might be one of the causes for mildly impaired diastolic filling of the right ventricle in group I patients with a patent right coronary artery

Endothelial-mesenchymal transition in human atrial fibrillation

Background: Atrial fibrosis is a hallmark of atrial structural remodeling leading to the persistence of atrial fibrillation. Although fibroblasts play a major role in atrial fibrosis, their source in the adult atrium is unclear. We tested the hypothesis that endothelial cells contribute to fibroblast accumulation through an endothelial-mesenchymal transition in the atrium of patients with atrial fibrillation. Methods and results: The study group consisted of patients with atrial fibrillation and valvular disease or atrial septal defect who underwent left atrial appendectomy during cardiac surgery (n =38). The amount of fibrotic depositions in the left atrium positively correlated with left atrial dimension. Furthermore, snail and S100A4, indicative of endothelial-mesenchymal transition, were quantified in the left atrium using western blot analysis, which showed statistically significant correlations with left atrial dimension. Immunofluorescence assay of the left atrial tissue identified snail and S100A4 being expressed within the endocardium which is composed of CD31+ cells. The snail-positive endocardium also showed the expression of membrane type 1-matrix metalloproteinase. Immunofluorescence multi-labeling experiments identified that heat shock protein 47, prolyl-4-hydroxylase, and procollagen type 1 co-localized with snail and S100A4 within the endothelial cells of the left atrium, indicating the mesenchymal phenotype to produce collagen. Conclusions: In this study, we showed that the endothelial-mesenchymal transition occurs in the atrium of patients with atrial fibrillation. This observation should help in constructing a novel therapeutic approach for preventing atrial structural remodeling. © 2016 Japanese College of Cardiology