Table 1.
Overview of literature data on capillary diameters in rodents.
Fig 1.
Pre-processing of the microvascular networks and the approach to assign boundary conditions.
(A) Histogram-based upscaling approach for microvascular network 1. The grey and the black histogram show the original and the final diameter distribution, respectively. The mean, the standard deviation (std), the maximum value (max) and the minimum value (min) of all capillary diameters are stated in grey and black for the original and the final capillary diameter distribution, respectively. The red curve is the goal beta distribution. (B) Summary of the pressure measurements in the pial vasculature available in literature and the fit we used to assign the pressure boundary conditions at the pial arterioles. At the pial venules we uniformly prescribed a pressure of 10 mmHg. Data from: Harper [7], Werber [8], Hudetz [44], Shapiro [9]. (C) Schematic illustration of the steps of the hierarchical boundary condition approach. On the left the three different components of the full compound network are shown. The red and green spheres in the realistic implant represent the pial and capillary in- and outflows, respectively.
Table 2.
Characteristic parameters of the analyzed microvascular networks (MVNs).
Table 3.
Validation of the simulation results with literature data.
Fig 2.
Pathway characteristics of red blood cells (RBCs) through cortical microvascular networks (MVNs).
(A) MVN 1 with five 200 μm thick analysis layers (ALs). (B) Five exemplary RBC paths through MVN 1. The five paths enter the capillary bed in the 5 different ALs (yellow: AL 1, light green: AL 2, dark green: AL 3, light blue: AL 4, dark blue: AL 5). The spheres illustrate the start and the end points of the capillary bed along the underlying path. The flow direction in the DAs and the AVs are shown by the adjacent arrows. (C) Cortical depth of the capillary start point over the cortical depth of the capillary end point. The scatter plot shows all available end points for every start point. The color code represents the relative frequency of occurrence of the end point. The red line is a linear fit to the data points (underlying equation given in Eq (5)). The Pearson’s correlation coefficient is r = 0.86. (D) & (E) Pressure and diameter over the path length for two exemplary trajectories of two RBCs from MVN 1 with their capillary start point lying in AL 2 (light green RBC trajectory in (B)) and in AL 4 (light blue RBC trajectory in (B)), respectively. PA: pial artery, DA: descending arteriole, A: arteriole, C: capillary, V: venule, AV: ascending venule, PV: pial vein
Table 4.
Number of available unique paths from DA+A to V+AV for the five ALs averaged over the RBC trajectories from 3 MVNs.
Table 5.
Pearson’s correlation coefficient for the relative end point frequencies and five trajectory characteristics averaged over 3 MVNs.
Fig 3.
Pressure drop along the pathway of red blood cells (RBCs) and layer-specific flow characteristics.
(A) Averaged pressure curves for the five analysis layers (ALs) (thick lines). The average locations of the capillaries are marked by green circles for each AL. The thin curves in the background represent the raw data and the thin green shading highlights the location of the capillaries for the raw data. (B) Capillary transit time ttC, transit path length tsC and RBC velocity vRBC for the five ALs (green symbols and error-bars, mean ± standard deviation). The scatter plot in the background shows the raw data for all MVNs studied. (C) Feeding properties for the five ALs. From top to bottom: (i) Number of feeding branches for the capillary bed, (ii) sum of blood flow rate through the feeding branches and (iii) sum of RBC flow rate through the feeding branches. (D),(E) & (F) Averaged pressure drop and averaged path length for different vessel types. The color coding facilitates the differentiation between arterioles (red), capillaries (green) and venules (blue). The standard deviation for the averaged pressure at the start of the different vessel types is given by the vertical error bars. The horizontal error bars represent the standard deviation for the averaged path length for the different vessel types. Fig (D),(E) and (F) show the averaged results for all RBCs with a capillary start point in AL 1, AL 3 and AL 5, respectively. PA: pial atery, DA: descending arteriole, A: arteriole, C: capillary, V: venule, AV: ascending venule, PV: pial vein