Robust Increase in Supply by Vessel Dilation in Globally Coupled Microvasculature

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.

Figure 1

Supply, $\varphi$, by a single vessel can be partitioned into three distinctive regimes as a function of dimensionless parameters characterizing flow and absorption, $\mathrm{Pe}=\overline{U}L/\kappa$ and $S=\kappa \gamma L/R\overline{U}$. Dotted lines indicate separation of regimes. The remaining nondimensional parameter is fixed at $\alpha =0.001$. Error ellipsoids contain the annotated percentage of vessels of the here-considered rat brain microvasculature [8] with physiological parameters for $\gamma$ and $\kappa$; see the main text.

Figure 2

The advective regime is robust in increasing supply by dilation. Histogram of change in supply $\mathrm{\Delta }\varphi$ due to a single vessel dilating by 10%. Lines indicate a range covering 69% with a percentage of 15.5% in both directions showing a lower or higher supply outside the indicated range. Big dots indicate the median, with values of 0.17, 0.10, and 0.11 for the all-absorbing, advective, and diffusive regimes, respectively. For each histogram, 120 vessels of the respective regime were randomly chosen and dilated.

Figure 3

The advective and diffusive regimes robustly increase supply downstream of a dilating vessel at the cost of decreasing supply in parallel vessels. (a) Enlargement of microvasculature excerpt exemplifying the neighborhood change in supply due to a single vessel dilation of 10% (advective regime, black arrow). Inlet marked by yellow star. Blue denotes a decrease, while red denotes an increase in supply in the individual vessels. The total change in supply is $\mathrm{\Delta }{\varphi }_{\text{tot}}=6.4\%$ in the downstream vessels and ${\varphi }_{\text{tot}}=0.8\%$ in the parallel vessels. The change in $C_0$ for the dilating vessel is below $\mathrm{\Delta }{C}_0<3\times {10}^{-4}$. (b) Neighborhood statistics of supply increase “$+$” or decrease “$-$” due to a dilating vessel in the respective regime. Evaluated is the overall change in supply in up to four vessels downstream or parallel to the dilated vessel chosen at the main inlet of a loop. The dilated vessel itself is excluded from the statistics here.