Insights into cerebral haemodynamics and oxygenation utilising in vivo mural cell imaging and mathematical modelling

Abstract

The neurovascular mechanisms underpinning the local regulation of cerebral blood flow (CBF) and oxygen transport remain elusive. In this study we have combined novel in vivo imaging of cortical microvascular and mural cell architecture with mathematical modelling of blood flow and oxygen transport, to provide new insights into CBF regulation that would be inaccessible in a conventional experimental context. Our study indicates that vasoconstriction of smooth muscle actin-covered vessels, rather than pericyte-covered capillaries, induces stable reductions in downstream intravascular capillary and tissue oxygenation. We also propose that seemingly paradoxical observations in the literature around reduced blood velocity in response to arteriolar constrictions might be caused by a propagation of constrictions to upstream penetrating arterioles. We provide support for pericytes acting as signalling conduits for upstream smooth muscle activation, and erythrocyte deformation as a complementary regulatory mechanism. Finally, we caution against the use of blood velocity as a proxy measurement for flow. Our combined imaging-modelling platform complements conventional experimentation allowing cerebrovascular physiology to be probed in unprecedented detail.

Figure 1

Mathematical modelling of blood flow in the cortical microvasculature, using 3D confocal imaging data from transgenic mice. (a) A view of the cortical vascular network showing smooth muscle actin-covered vessels (SMA, green), from transgenic expression of m-Cherry, and blood vessel lumen (orange), from exogeneous administration of fluorescent dextran. (b) An enhanced view showing the location of SMA-expressing vessels. (c) The vascular network, following image segmentation, with vessels colour-coded based on classification (red: SMA-expressing arterioles; blue: veins; green: capillaries). (d) Simulated cortical blood pressures within the cortical network. (e) A scatter plot of vessel diameter against simulated, blood vessel haematocrit from our baseline simulation. (f) A scatter plot of volumetric blood flow (nL/min) against intravascular PO₂ (mmHg). Data points in (e) and (f) are colour-coded according to vessel classification, as per (c).

Figure 2

Sites of simulated blood vessel constrictions in SMA-expressing vessels (purple). (a) The location of single branching-order precapillary arteriole constriction (circled); the black line indicates the site of a single-cell constriction. (b) Constriction of a precapillary arteriole, with bi-directional constriction cascade to the entire adjoining penetrating arteriole. (c) Constriction of a precapillary arteriole and uni-directional propagation to upstream sections of the penetrating arteriole. The dashed line indicates the point at which the penetrating arteriole bifurcates to the precapillary arteriole.

Figure 3

Box plots showing simulated blood velocity and flow changes in response to vasoconstriction. The top row of graphs shows blood velocity changes as a percentage of the baseline solution, and the bottom row shows blood flow changes. From left to right, plots show the responses to constrictions in penetrating arterioles (left), precapillary arterioles (middle) and capillaries (right). Results are presented for each constriction scenario (1) single-cell constriction, (2) constriction of the entire vessel, (3) bi-directional and (4) uni-directional constriction of the local penetrating arteriole. Note, cases (2) and (3) are equivalent for penetrating arterioles and the mean values for each are indicated with circles. Case 4 for penetrating arterioles provides the velocity change for the neighbouring downstream vessel from the site of constriction. Mean values are indicated in blue. See Supplementary Fig. S2 for outliers.

Figure 4

Simulated single vessel constrictions and the subsequent change in vessel and tissue PO₂. Box plots indicated the percentage change in vessel PO₂ in constricted (a) penetrating arterioles, (b) precapillary arterioles and (c) capillaries, when compared to baseline PO₂ in said vessel. Noting, for (a,b) constriction cascade is induce by constriction of SMA-covered vessels. (d) The percentage change in local tissue PO₂ as a consequence of constrictions in (c). Mean values are indicated in blue and outliers (data larger than q₃ + 3(q₃ − q₁)/2 or smaller than q₁ − 3(q₃ − q₁)/2, where q₁ and q₃ are the 25^th and 75^th percentiles, respectively) by red crosses.

Figure 5

Simulated single vessel constrictions (a total of 25, with constriction cascade induced by constriction of SMA-covered vessels) and the subsequent changes in global tissue PO₂. Box plots indicated the percentage change in tissue PO₂, when compared to baseline tissue PO₂, as a consequence of singular constrictions of (a) penetrating arterioles, (b) precapillary arterioles and (c) capillaries. (d,e,f) 3-dimensional visualisations of spatial changes in tissue PO₂ as a result of constrictions in (d) a penetrating arteriole, (e) a precapillary arteriole and (f) a capillary. (g) 3-dimensional visualisation of the cortical network, in which black lines indicate the initial site of constriction for (d) and (e), and where the capillary constriction in (f) occurred downstream of (e). Note, absolute percentage changes < 20% for (d) and absolute values < 5% for (e) and (f) are not shown, for clarity.

Figure 6

Simulating SMA constriction cascade following pericyte constriction. Percentage changes in: 1) unconstricted and 2) constricted capillaries with uni-directional SMA propagation for (a) pressure, (b) flow, (c) velocity, (d) haematocrit (H_D) and (e) vessel PO₂. (f) A plot of mean change in capillary PO₂ against capillary order, as a result of local SMA constriction. Error bars represent standard deviation and, consequently, the redistribution of O2 through the cortical network.

Figure 7

Capillary PO₂ changes initiated by erythrocyte deformation. Box plots show the percentage change in PO₂ for capillaries initially below 25 mmHg, for erythrocyte deformation occuring in isolation, and when coupled to arteriolar (SMA) dilation.