Probabilistic tractography provides estimates of the probability of a structural connection between points or regions in a brain volume, based on information from diffusion MRI. The ability to estimate the uncertainty associated with reconstructed pathways is valuable, but noise in the image data leads to premature termination or erroneous trajectories in sampled streamlines. In this work we de...

We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of flows. Percolating flows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-...

In this work has been proposed a numerical scheme with the aim of simulate the coalescence process between water drops immersed in a continuous phase (n-heptane). This numerical scheme is based in the Finite Volume method and two different values for the initial velocity of the drops were chosen. Depending of the initial velocity of collision some scenarios emerge, such as: permanent coalescenc...

Euler’s equation expresses the relationship between the velocity and the pressure fields in inviscid flow. Written in terms of streamline coordinates, this equation gives information about not only about the pressure-velocity relationship along a streamline (Bernoulli’s equation), but also about how these quantities are related as one moves in the direction transverse to the streamlines. The tr...

Qualitative visual analysis of flow patterns in cerebral aneurysms is important for assessing the risk of rupture. According to current research, the flow patterns close to the aneurysm surface (e.g. impingement zone) provide a good insight. Streamlines can be easily interpreted and are commonly used for visualizing and exploring blood flow. However, standard ways of seeding these streamlines, ...

In scientific visualization, we often handle vector or direction fields. An efficient way of visualizing such a vector or direction field is to cover the whole domain studied by a set of streamlines because they give good information about the flow and the topology of the underlying field. In this article, we propose to optimize already constructed streamlines by defining an optimization criter...

Diffusion tensor imaging (DTI) tractography provides noninvasive measures of structural cortico-cortical connectivity of the brain. However, the agreement between DTI-tractography-based measures and histological 'ground truth' has not been quantified. In this study, we reconstructed the 3D density distribution maps (DDM) of fibers labeled with an anatomical tracer, biotinylated dextran amine (B...

In present work, the time independent laminar flow of a viscous, incompressible fluid in two dimensions flow has been studied. The fluid had been allowed to flow in a channel with an obstruction which was a rectangular plate of definite dimensions. The flow of water had been considered to be steady with uniform incident velocity with various boundary conditions. The resulting NavierStokes equat...

We investigate the properties of an axisymmetric non-magnetized gas flow without angular momentum on a small compact object, in particular, on a Schwarzschild black hole in the supersonic region near the object; the velocity of the object itself is assumed to be low compared to the speed of sound at infinity. First of all, we see that the streamlines intersect (i.e., a caustic forms) on the sym...

We present an interactive system for computer aided generation of line art drawings to illustrate 3D models that are given as triangulated surfaces. In a preprocessing step an enhanced 2D view of the scene is computed by sampling for every pixel the shading, the normal vectors and the principal directions obtained from discrete curvature analysis. Then streamlines are traced in the 2D direction...