Tradeoffs between energy efficiency and mechanical response in fluid flow networks

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 hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example ...

Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related to the study of incompressible flow through compliant thin-walled tubes. The mechanical interaction between blood flow and vessel wall must be properly described by the model. Recent works show the benefits of characterizing the rheology of...

The separation of measured arterial pressure into a reservoir pressure and an excess pressure was introduced nearly 20 years ago as an heuristic hypothesis. We demonstrate that a two-time asymptotic analysis of the 1-D conservation equations in each artery coupled with the separation of the smaller arteries into inviscid and resistance arteries, based on their resistance coefficients, results, for the first time, in a formal derivation of the reservoir pressure. The key to th...

We derive the main properties of adaptive Hagen-Poiseuille flows in elastic microchannel networks akin to biological veins in organisms. We show that adaptive Hagen-Poiseuille flows successfully simulate key features of \textit{Physarum polycephalum} networks, replicating physiological out-of-equilibrium phenomena like peristalsis and shuttle streaming, associated with the mechanism of nutrient transport in \textit{Physarum}. A new topological steady state has been identified...

In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the wa...

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles...

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 different biological networks have different optimization criteria and we are interested in those networks optimized for fluid transport within the circulatory system. Many theories currently exist. For instance, distributive vascular geometry...

In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.

Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that lead to constraints on their topological organization. In this study, we compare and contrast two types of biological distribution networks: mycelial fungi and the vasculature system on the surface of rodent brains. Both systems are alike in ...

Using analytical expressions for the pressure and velocity waveforms in tapered vessels, we construct a linear 1D model for wave propagation in stenotic vessels in the frequency domain. We demonstrate that using only two parameters to approximate the exact geometry of the constriction (length and degree of stenosis), we can construct a model that can be solved analytically and can approximate with excellent accuracy the response of the original vessel for a wide range of phys...