A mathematical characterization of anatomically consistent blood capillary networks

Abstract Blood microcirculation is the site of control tissue perfusion, blood-tissue exchange, and blood volume. Despite many irregularities, almost ubiquitously, one can recognize in vessels a hierarchy arterioles venules, organized tree-like structures, capillary plexi, net-like structures. Whilst for venules it may be envisageable to obtain geometries needed numerical simulations from imaging techniques, size numerosity capillaries makes this task much more cumbersome. For reason, interesting study approaches generate silico -derived artifacts networks, even view machine-learning based which require large amount samples training. Artificial networks must correctly reflect proper metrics topology, turn, will ensure with boundary conditions physiological flux net sufficient nutrient distribution surrounding tissues. In paper, we introduce sequence curves whose limit space filling Hilbert curve discuss its inherent properties backbone artificial network suitable element sequence. The represents significant synthesis basic metric features and, context, studied analytically. framework, malleable entity allows shape according physical indicators. particular, two factors are shown topology scaling: iteration step generation characteristic length REV, respectively. Based on points certain step, then via spline interpolation smoothed version curve, fine–tunes tortuosity. A volumetric construction obtained building tubular neighborhood backbone, computed tuned as well. Numerical flow geometry show fields occurring network.