Physical and geometric determinants of transport in feto-placental microvascular networks

Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations unde...

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 da Vinci, who constructed a local rule for comparing the widths of in- and outgoing veins at branch points. Recently, physical models have been developed that seek to explain the full morphogenesis of leaf venial networks in which veins gr...

The flow of fluids at branching junctions plays important kinematic and dynamic roles in most biological and industrial flow systems. The present paper highlights some key issues related to the flow of fluids at these junctions with special emphasis on the biological flow networks particularly blood transportation vasculature.

Transport networks are typically optimized, either by evolutionary pressures in biological systems or by human design in engineered structures. In the case of systems such as the animal vasculature, the transport of fluids is hindered by the inherent viscous resistance to flow while being kept in a dynamic state by the pulsatile nature of the heart and elastic properties of the vessel walls. While this imparted pulsatility necessarily increases the dissipation of energy cause...

We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a theoretical {one-dimensional advection} model for blood flow in microvascular networks{ that relies on the widely used laws for rheology and phase separation}. We discuss the ramifications for microfluidic experiments and measurements using ...

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive clinical tool that is commonly used in the clinical settings to measure blood velocity waveform at several locations on brain's vasculature. This amount of data is grossly insufficient for training machine learning surrogate models, such as deep ...

The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these micro-clots affect the large scale blood flow or to what extent they decrease functionality. Motivated by this, we investigate how flow is rerouted after the occlusion of a single edge in networks with a hierarchy in edge cond...

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 function of single vessel resistances and mutual vessel interactions. In this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry is com...

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. The model is based on local feedback mechanisms that occur on different time scales in the mammalian vasculature. The cost exponent $\gamma$ tunes the vessel growth in the adaptation rule, and we test the hypothesis that the cost exponent is ...

In this article, we review the mathematical modeling for the vascular system.