X-ray micro-tomography and pore network modeling of single-phase fixed-bed reactors.

A three-dimensional (3D) irregular and unstructured pore network was built using local topological and geometrical properties of an isometric bead pack imaged by means of a high-resolution X-ray computed micro-tomography technique. A pore network model was developed to analyze the 3D laminar/inertial(non-Darcy) flows at the mesoscopic (pore level) and macroscopic (after ensemble-averaging) levels. The non-linear laminar flow signatures were captured at the mesoscale on the basis of analogies with contraction and expansion friction losses. The model provided remarkably good predictions of macroscopic frictional loss gradient in Darcy and non-Darcy regimes with clear-cut demarcation using channel-based Reynolds number statistics. It was also able to differentiate contributions due to pore and channel linear losses, and contraction/expansion quadratic losses. Macroscopic mechanical dispersion was analyzed in terms of retroflow channels, and transverse and longitudinal Péclet numbers. The model qualitatively retrieved the Péclet-Reynolds scaling law expected for heterogeneous networks with predominance of mechanical dispersion. Advocated in watermark is the potential of pore network modeling to build a posteriori constitutive relations for the closures of the more conventional macroscopic Euler approaches to capture more realistically single-phase flow phenomena in fixed-bed reactor applications in chemical engineering

PLoS One

Quantitative analysis of the vascular network anatomy is critical for the understanding of the vasculature structure and function. In this study, we have combined microcomputed tomography (microCT) and computational analysis to provide quantitative three-dimensional geometrical and topological characterization of the normal kidney vasculature, and to investigate how 2 core genes of the Wnt/planar cell polarity, Frizzled4 and Frizzled6, affect vascular network morphogenesis. Experiments were performed on frizzled4 (Fzd4-/-) and frizzled6 (Fzd6-/-) deleted mice and littermate controls (WT) perfused with a contrast medium after euthanasia and exsanguination. The kidneys were scanned with a high-resolution (16 μm) microCT imaging system, followed by 3D reconstruction of the arterial vasculature. Computational treatment includes decomposition of 3D networks based on Diameter-Defined Strahler Order (DDSO). We have calculated quantitative (i) Global scale parameters, such as the volume of the vasculature and its fractal dimension (ii) Structural parameters depending on the DDSO hierarchical levels such as hierarchical ordering, diameter, length and branching angles of the vessel segments, and (iii) Functional parameters such as estimated resistance to blood flow alongside the vascular tree and average density of terminal arterioles. In normal kidneys, fractal dimension was 2.07±0.11 (n = 7), and was significantly lower in Fzd4-/- (1.71±0.04; n = 4), and Fzd6-/- (1.54±0.09; n = 3) kidneys. The DDSO number was 5 in WT and Fzd4-/-, and only 4 in Fzd6-/-. Scaling characteristics such as diameter and length of vessel segments were altered in mutants, whereas bifurcation angles were not different from WT. Fzd4 and Fzd6 deletion increased vessel resistance, calculated using the Hagen-Poiseuille equation, for each DDSO, and decreased the density and the homogeneity of the distal vessel segments. Our results show that our methodology is suitable for 3D quantitative characterization of vascular networks, and that Fzd4 and Fzd6 genes have a deep patterning effect on arterial vessel morphogenesis that may determine its functional efficiency

An Effective Fractal-Tree Closure Model for Simulating Blood Flow in Large Arterial Networks

The aim of the present work is to address the closure problem for hemodynamic simulations by developing a exible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure out flow boundary condition. To achieve this goal, we model blood flow in the sub-pixel vasculature by using a non-linear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime (radii 500 μm – 10 μm). We introduce a variable vessel length-to-radius ratio for small arteries and arterioles, while also addressing non-Newtonian blood rheology and arterial wall viscoelasticity effects in small arteries and arterioles. This methodology aims to overcome substantial cut-off radius sensitivities, typically arising in structured tree and linearized impedance models. The proposed model is not sensitive to out flow boundary conditions applied at the end points of the fractal network, and thus does not require calibration of resistance/capacitance parameters typically required for out flow conditions. The proposed model convergences to a periodic state in two cardiac cycles even when started from zero-flow initial conditions. The resulting fractal-trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have scaled up a Discontinuous Galerkin solver that utilizes the MPI/OpenMP hybrid programming paradigm to thousands of computer cores, and can simulate blood flow in networks of millions of arterial segments at the rate of one cycle per 5 minutes. The proposed model has been extensively tested on a large and complex cranial network with 50 parent, patient-specific arteries and 21 outlets to which fractal trees where attached, resulting to a network of up to 4,392,484 vessels in total, and a detailed network of the arm with 276 parent arteries and 103 outlets (a total of 702,188 vessels after attaching the fractal trees), returning physiological flow and pressure wave predictions without requiring any parameter estimation or calibration procedures. We present a novel methodology to overcome substantial cut-off radius sensitivitie