Related papers: Analysis of the optimality principles responsible …
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 branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria. Our synthetic tree model does not incorporate…
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…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…
As nutrients travel through microcirculation and are absorbed, their availability continuously decreases. However, a uniform nutrient distribution is critical, as it prevents tissue death in poorly supplied areas. How, then, do vascular…
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:…
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…
Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the…
Microcirculation of blood and oxygen transport play important roles in biological function of optic nerve and are directly affected by damages or pathologies. This work develops a multi-domain model for optic nerve, that includes important…
Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced…
Vascular networks are used across the kingdoms of life to transport fluids, nutrients and cellular material. A popular unifying idea for understanding the diversity and constraints of these networks is that the conduits making up the…
Flux of rigid or soft particles (such as drops, vesicles, red blood cells, etc.) in a channel is a complex function of particle concentration, which depends on the details of induced dissipation and suspension structure due to hydrodynamic…
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…
Within animals, oxygen exchange occurs within networks containing potentially billions of microvessels that are distributed throughout the animal's body. Innovative imaging methods now allow for mapping of the architecture and blood flows…
The analysis of biological networks encompasses a wide variety of fields from genomic research of protein-protein interaction networks, to the physiological study of biologically optimized tree-like vascular networks. It is certain that…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
Self-regulation of living tissue as an example of self-organization phenomena in active fractal systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
Transport networks are crucial for the functioning of natural and technological systems. We study a mathematical model of vascular network adaptation, where the network structure dynamically adjusts to changes in blood flow and pressure.…
Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals, or…
We analyse mathematical models in order to understand how microstructural features of vascular networks may affect blood-flow dynamics, and to identify particular characteristics that promote the onset of self-sustained oscillations. By…