On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Diagnostic reference levels for the most frequent radiological examinations carried out in Brazil

Objectives. A large-scale survey of doses to patients undergoing the most frequent radiological examinations was carried out in health services in Sao Paulo (347 radiological examinations per 1 000 inhabitants), the most populous Brazilian state. Methods. A postal dosimetric kit with thermoluminescence dosimeters was used to evaluate the entrance surface dose (ESD) to patients. A stratified sampling technique applied to the national health database furnished important data on the distribution of equipment and the annual number of examinations. Chest, head (skull and sinus), and spine (cervical, thoracic, and lumbar) examinations were included in the trial. A total of 83 rooms and 868 patients were included, and 1 415 values of ESD were measured. Results. The data show large coefficients of variation in tube charge, giving rise to large variations in ESD values. Also, a series of high ESD values associated with unnecessary localizing fluoroscopy were detected. Diagnostic reference levels were determined, based on the 75th percentile (third quartile) of the ESD distributions. For adult patients, the diagnostic reference levels achieved are very similar to those obtained in international surveys. However, the situation is different for pediatric patients: the ESD values found in this survey are twice as large as the international recommendations for chest radiographs of children. Conclusions. Despite the reduced number of ESD values and rooms for the pediatric patient group, it is recommended that practices in chest examinations be revised and that specific national reference doses and image quality be established after a broader survey is carried out.

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

Inside the `cavernous sinus` or `parasellar region` the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.