Stochastic equation for a jumping process with long-time correlations

A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by the power-law autocorrelation function. Therefore, it can serve as a model of the 1/f noise as well as a model of the stochastic force in the generalized Langevin equation. This equation is solved for the noise correlations 1/t; the resulting velocity distribution has sharply falling tails. The system preserves the memory about the initial condition for a very long time.Comment: 7 pages, 5 Postscript figure

Usefulness of three-dimensional echocardiography for the assessment of ventricular function in children: Comparison with cardiac magnetic resonance, with a focus on patients with arrhythmia

Background: Focusing on patients with arrhythmia, the aims of this study was to assess ventricular function in children using three-dimensional echocardiography (3D-ECHO) and to compare the results to those obtained with cardiac magnetic resonance (CMR).Methods: The study group consisted of 43 children in whom 3D-ECHO and CMR were performed. Twenty-five patients had a ventricular arrhythmia, 7 left ventricular cardiomyopathies, 9 proved to be healthy. In all children, 3D-ECHO (offline analysis) was used to assess ventricular ejection fraction (EF). The results were compared to CMR using the Bland-Altman analysis and linear regression. The Student paired T-test was used to compare of means between both modalities.Results: The relation between the results derived from both methods is linear (for left ventricle: estimated slope = 1.031, p < 0.0001, R-squared = 0.998; for right ventricle: estimated slope = 0.993, p < 0.0001, R-squared = 0.998). In spite of minimal mean differences between results for both ventricles and narrow 95% confidence intervals, the paired t-test proved those differences not to be significant (p > 0.05) for the right ventricle but statistically significant (p < 0.05) for the left ventricle, for which the left ventricular EF calculated in 3D-ECHO was systematically underestimated with a mean difference of –1.8% ± 2.6% (p < 0.0001).Conclusions: Three-dimensional echocardiography assessment of both left and right ventricular EF in children showed high significant correlation and agreement with CMR. 3D-ECHO could be a valuable tool in follow-up of children with arrhythmic disorders requiring regular assessment of ventricular function

Muscle pathology in myotonic dystrophy: light and electron microscopic investigation in eighteen patients

Myotonic dystrophy (DM) is the most common muscular dystrophy in adults. Two known genetic subtypes include DM1 (myotonic dystrophy type 1) and DM2 (myotonic dystrophy type 2). Genetic testing is considered as the only reliable diagnostic criterion in myotonic dystrophies. Relatively little is known about DM1 and DM2 myopathology. Thus, the aim of our study was to characterise light and electron microscopic features of DM1 and DM2 in patients with genetically proven types of the disease. We studied 3 DM1 cases and 15 DM2 cases from which muscle biopsies were taken for diagnostic purposes during the period from 1973 to 2006, before genetic testing became available at our hospital. The DM1 group included 3 males (age at biopsy 15–19). The DM2 group included 15 patients (5 men and 10 women, age at biopsy 26–60). The preferential type 1 fibre atrophy was seen in all three DM1 cases in light microscopy, and substantial central nucleation was present in two biopsies. Electron microscopy revealed central nuclei in all three examined muscle biopsies. No other structural or degenerative changes were detected, probably due to the young age of our patients. Central nucleation, prevalence of type 2 muscle fibres, and the presence of pyknotic nuclear clumps were observed in DM2 patients in light microscopy. Among the ultrastructural abnormalities observed in our DM2 group, the presence of internal nuclei, severely atrophied muscle fibres, and lipofuscin accumulation were consistent findings. In addition, a variety of ultrastructural abnormalities were identified by us in DM2. It appears that no single ultrastructural abnormality is characteristic for the DM2 muscle pathology. It seems, however, that certain constellations of morphological changes might be indicative of certain types of myotonic dystrophy. (Folia Morphol 2011; 70, 2: 121–129