相关论文: Branching exponents of synthetic vascular trees un…
In 1926, Murray proposed the first law for the optimal design of blood vessels. He minimized the power dissipation arising from the trade-off between fluid circulation and blood maintenance. The law, based on a constant fluid viscosity,…
The understanding of the mechanisms driving vascular development is still limited. Techniques to generate vascular trees synthetically have been developed to tackle this problem. However, most algorithms are limited to single trees inside…
Murray's cubic branching law ($\alpha=3$) predicts a universal diameter scaling exponent for all hierarchical transport networks, yet arterial trees yield $\alpha \sim 2.7-2.9$. We show that this discrepancy has a structural origin:…
The equivalence of two optimality principles leading to Murray's law has been discussed. The first approach is based on minimization of biological work needed for maintaining the blood flow through the vessels at required level. The second…
Does the complex processes of angiogenesis during organism development ultimately lead to a near optimal coronary vasculature in the organs of adult mammals? We examine this hypothesis using a powerful and universal method, built on…
We examine the role of complexity on arterial tree structures, determining globally optimal vessel arrangements using the Simulated AnneaLing Vascular Optimization (SALVO) algorithm, which we have previously used to reproduce features of…
In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a…
Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality…
We build an evolutionary scenario that explains how some crucial physiological constraints in the arterial network of mammals - i.e. hematocrit, vessels diameters and arterial pressure drops - could have been selected by evolution. We…
Murray's theory of constrained minimum-power branchings is critically reviewed in a generalised framework for a range of cases: channels with arbitrary cross-section shape, laminar flows of Newtonian and non-Newtonian fluids, and low and…
Understanding of vascular organization is a long-standing problem in quantitative biology and biophysics and is essential for the growth of large cultured tissues. Approaches are needed that (1) make predictions of optimal arteriovenous…
We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with…
Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to…
We hereby present a full synthetic model, able to mimic the various constituents of the cerebral vascular tree, including the cerebral arteries, bifurcations and intracranial aneurysms. This model intends to provide a substantial dataset of…
We are interested in the local limits of families of random trees that satisfy the Markov branching property, which is fulfilled by a wide range of models. Loosely, this property entails that given the sizes of the sub-trees above the root,…
Full strong-branching is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an…
The branching geometry of biological transport networks is characterized by a diameter scaling exponent $\alpha$. Two structural attractors compete: impedance matching ($\alpha \sim 2$) for pulsatile flow and viscous-metabolic minimization…
Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi, and animals. By combining machine-learning techniques with new theory that relates vascular form to…
The vascular network of leaves, comprising xylem and phloem, is a highly optimized system for the delivery of water, nutrients, and sugars. The design rules for these naturally occurring networks have been studied since the time of Leonardo…
The prevailing theory for metabolic scaling is based on area-preserved, space-filling fractal vascular networks. However, it's known both theoretically and experimentally that animals' vascular systems obey Murray's cubic branching law.…