Robust Increase in Supply by Vessel Dilation in Globally Coupled Microvasculature

Abstract

Neuronal activity induces changes in blood flow by locally dilating vessels in the brain microvasculature. How can the local dilation of a single vessel increase flow-based metabolite supply, given that flows are globally coupled within microvasculature? Solving the supply dynamics for rat brain microvasculature, we find one parameter regime to dominate physiologically. This regime allows for robust increase in supply independent of the position in the network, which we explain analytically. We show that local coupling of vessels promotes spatially correlated increased supply by dilation.Vascular networks pervade all organs of animals and are the paradigm of adaptive transport networks. Their self-organized architecture continuously inspires the search for their underlying physical principles [1][2][3][4] and at the same time serves as a template for designing efficient networks in engineering [5]. The blood flowing through vessels transports nutrients, hormones, and metabolites to adjacent tissues. Metabolite exchange primarily occurs within the fine vessel meshwork formed by microvasculature. In the brain, local metabolite demand can abruptly rise due to an increase in neural activity [6], altering blood flow [7,8] in the same brain region, observable in fMRI [9]. During the process of increased neuronal activity, neurons signal their increased demand to adjacent astrocyte cells, which in turn trigger small ring muscles surrounding blood vessels to relax [10]. Thus, neural activity drives local dilation of a vessel [11,12], and hence regulates metabolite supply [7,13]. However, from a fluid dynamics perspective there is a mystery: blood vessels form a highly interconnected network in the microvasculature [8], resulting in a global coupling of blood flow. A single dilating vessel can potentially change the metabolite supply in a broad region of the networkand thus the local increase due to dilation is a function of specific network topology. Quantitatively, how much control over changes in blood-based supply resides in a single dilating vessel?Models considering metabolite spread in tissue date back more than a hundred years to A. Krogh [14]. Krogh's model estimates the supply pattern in a tissue enclosed by vessels assuming that supply is constant on all vessel walls. Yet, on a larger tissue scale, supply spatially varies along the vasculature since resources supplied upstream are not available downstream. Alternative models consider vessel-based transport [15], yet only diffusive transport is taken into account. The combined importance of advection and diffusion for transporting solutes in a single tube was discovered by G.I. Taylor [16,17], with subsequent work outlining modifications due to solute absorption at the tube boundary [18][19][20]. Yet, there has been much less work capturing the coupling of advection and diffusion in tubular network struc-tures [21,22], including solute absorption [23]. The impact of a dilating vessel is hard to estimate since not only the absorption dynamics on the level of sing...

Resilience of three-dimensional sinusoidal networks in liver tissue

“…We speculate that adaptive mechanisms, like shear-dependent regulation of sinusoid diameter [ 30 – 32 ], or sinusoid contraction dependent on local concentration of solutes [ 54 ], may facilitate a more homogeneous distribution. Moreover, the diameter of red blood cells is only slightly smaller than the diameter of the sinusoids, which can result in transient clogging of sinusoids, especially where flow is high [ 33 , 34 , 55 ] or where the diameter of sinusoids is reduced by adaptive mechanisms.…”

“…This renders these networks highly vulnerable to the removal of high-current edges, despite their resilience against random removal of edges. In the discussion, we speculate on mechanisms such as shear-dependent adaptation of the diameter of sinusoids [ 30 – 32 ], or transient clogging by erythrocytes [ 33 , 34 ], which would both affect especially high-current edges, and could homogenize the time-averaged distribution of currents in the network, thereby reducing the vulnerability of sinusoidal networks to the removal of high-current edges.…”

On biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions

“…Here, the cross section average c (z) would have to be considered in conjunction with a radial disturbance δc (z, r), corresponding to the case of classic Taylor dispersion [43]. Combining this framework with the absorption of metabolite was discussed in great detail by Meigel et al [2,3]. As we here consider the small capillary regime, however, we assume that the effects of lateral concentration perturbations are negligible and refrain from considering them.…”

“…November 2021 2/20 transport to be a non-trivial interplay between the flow pattern and diffusion while incorporating a concentration dependent solute uptake along the vessel surfaces. This dispersion model was initiated as an appropriate metabolite transport model during slime mold morphogenesis [36,37], but has since been utilized to account for the adaptation phenomena found in plants and vertebrate capillaries [2,3]. On the other hand, Garvrilchenko et al [4] suggested an adaptation model on the grounds of the Krogh model to account for the explicit supply of discrete service elements in the tissue.…”

Revealing structure-function relationships in functional flow networks via persistent homology

“…The impairment of this ability has been linked to various neurological diseases [12], including Alzheimer's disease in particular [13]. More generally, the ability to tune the conductances of edges or locally restructure connectivity enables animals [14,15], plants [16,17], fungi [18], and slime molds [19] to control the spatial distribution of water, nutrients, oxygen, or metabolic byproducts.…”