A Phase Field Model for Continuous Clustering on Vector Fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.

Vessel enhancing diffusion: a scale space representation of vessel

A method is proposed to enhance vascular structures within the framework of scale space theory. We combine a smooth vessel filter which is based on a geometrical analysis of the Hessian's eigensystem, with a non-linear anisotropic diffusion scheme. The amount and orientation of diffusion depend on the local vessel likeliness. Vessel enhancing diffusion (VED) is applied to patient and phantom data and compared to linear, regularized Perona-Malik, edge and coherence enhancing diffusion. The method performs better than most of the existing techniques in visualizing vessels with varying radii and in enhancing vessel appearance. A diameter study on phantom data shows that VED least affects the accuracy of diameter measurements. It is shown that using VED as a preprocessing step improves level set based segmentation of the cerebral vasculature, in particular segmentation of the smaller vessels of the vasculature

Vessel tractography using an intensity based tensor model

In this paper, we propose a novel tubular structure segmen- tation method, which is based on an intensity-based tensor that fits to a vessel. Our model is initialized with a single seed point and it is ca- pable of capturing whole vessel tree by an automatic branch detection algorithm. The centerline of the vessel as well as its thickness is extracted. We demonstrated the performance of our algorithm on 3 complex contrast varying tubular structured synthetic datasets for quantitative validation. Additionally, extracted arteries from 10 CTA (Computed Tomography An- giography) volumes are qualitatively evaluated by a cardiologist expert’s visual scores

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour