Gap Filling of 3-D Microvascular Networks by Tensor Voting

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated

Spatial development of transport structures in apple (Malus x domestica Borkh.) fruit

The void network and vascular system are important pathways for the transport of gases, water and solutes in apple fruit (Malus x domestica Borkh). Here we used X-ray micro-tomography at various spatial resolutions to investigate the growth of these transport structures in 3D during fruit development of ‘Jonagold’ apple. The size of the void space and porosity in the cortex tissue increased considerably. In the core tissue, the porosity was consistently lower, and seemed to decrease towards the end of the maturation period. The voids in the core were more narrow and fragmented than the voids in the cortex. Both the void network in the core and in the cortex changed significantly in terms of void morphology. An automated segmentation protocol underestimated the total vasculature length by 9 to 12% in comparison to manually processed images. Vascular networks increased in length from a total of 5 meter at 9 weeks after full bloom, to more than 20 meter corresponding to 5 cm of vascular tissue per cubic centimeter of apple tissue. A high degree of branching in both the void network and vascular system and a complex three-dimensional pattern was observed across the whole fruit. The 3D visualisations of the transport structures may be useful for numerical modeling of organ growth and transport processes in fruit

A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available