Fig 1.
The relative velocity difference is smaller at divergent than at convergent capillary bifurcations.
(A-B) Examples of an in vivo divergent (A) and convergent (B) capillary bifurcation. (C) Line scans for the divergent bifurcation in (A). (D) RBC velocity in the daughter vessels of a divergent bifurcation in vivo. Dotted lines: median of each velocity. The velocity measurements have been performed consecutively (Methods). Further examples: S5 Fig. (E) Upper plot: Bulk flow velocity
in the daughter vessels of a divergent bifurcation for the simulation with red blood cells (RBCs, Methods). The time course has been smoothed by a moving average (Methods). Lower plot: Instantaneous relative velocity difference
. Dotted lines: median of each variable. Blue box:
, well-balanced flow situation. Further examples: S6 Fig. (F-J) Histogram: Distribution of the relative velocity difference at divergent
(F, H, J) and convergent
(G, I) capillary bifurcations for the simulation with RBCs (H, I) with passive particles, pPs (J) and in vivo (superscript: RBC; F, G). The histograms are normalized, i.e., the density of the underlying empirical distributions is displayed. Lower plot: Raw data for histograms. Blue bars: Well-balanced bifurcations (
). DoWB: Degree of well-balanced bifurcations: ratio of the number of well-balanced bifurcations to the total number of bifurcations (n). A detailed analysis of the distributions is provided in the Methods. (K) Cumulative density of |Δrv| for the simulation with RBCs and the in vivo measurements. Filling indicates regions where the cumulative density of divergent bifurcations is larger than that of convergent ones. For all in vivo measurements (D, F-G, K) the RBC velocity is displayed instead of the bulk flow velocity (superscript: RBC). Mouse icon: in vivo measurements. Computer icon: simulation results.
Fig 2.
The impact of red blood cells balances outflow velocities at divergent capillary bifurcations and increases hematocrit heterogeneity in the capillary bed.
(A-B) Absolute velocity difference at well-balanced and unbalanced divergent bifurcations for the simulation with red blood cells (RBCs) and with passive particles (pPs). : bulk flow velocity in each daughter vessel of the bifurcation.
: mean velocity in the daughter vessels. n: total number of bifurcations. The bifurcations are grouped into well-balanced and unbalanced based on the results from the simulation with RBCs. The same sets of bifurcations are compared for both simulations. We only depict velocities up to 14 mm/s (represents > 99.9% of all bifurcations). (C) Microvascular network 1 (MVN 1). The colouring highlights capillaries and outflow vessels of capillary divergent bifurcations. (D) Hematocrit distribution for the simulation with RBCs and with pPs (n = 13,988, Q1: lower quartile, Q3: upper quartile, Definition boxplot: Methods). (E-F) Hematocrit distribution in MVN 1 for the simulation with RBCs (E) and with pPs (F). In all plots only the daughter vessels of divergent bifurcation are considered (‘outflow vessels’, 53% of all capillaries, Methods, S8 Fig). In (A), (B) and (D) the data from MVN 1 and 2 is combined.
Fig 3.
Capillary dilation locally increases the flow rate and the number of red blood cells.
(A-D) Simulated relative change in flow rate (A) and in the number of red blood cells, nRBC (B-D) in response to a capillary dilation of 10% along a 100 μm capillary segment. (A-B): with red blood cells (RBCs), dilation at well-balanced bifurcation, (C): with RBCs, dilation at unbalanced bifurcation, (D): without phase separation, dilation at well-balanced bifurcation. Colour legend in (E). A sensitivity analysis on the threshold values for well-balanced and unbalanced bifurcations is provided in S12 and S13 Figs. (E) Schematic of divergent capillary bifurcation. (F) Quotient awith pPs of flow ratios for the simulation, with passive particles (pPs) as a function of the quotient awith RBCs of flow ratios for the simulation with RBCs for well-balanced bifurcations. Turquoise: awith pPs > awith RBCs, grey: awith RBCs > awith pPs. (A-B), (D), (F): Results from 50 capillary dilations. (C): Results from 70 capillary dilations. Statistical significance: Wilcoxon signed-rank test, ***: p<0.001, ns: non-significant (Methods). Definition boxplot: Methods.
Fig 4.
The simulated relative changes in response to capillary dilation are very local.
(A-B) Vessels three generations up- and downstream of the site of dilation. (A) Schematic example. Roman numbers: generation up- and downstream of the site of dilation (one exemplary branch). (B) Realistic example from microvascular network 1 (MVN 1). (C-D) Simulated relative change in flow rate (C) and in the number of RBCs (nRBC) (D) for the dilated vessel and the vessels up to three generations up- and downstream of the site of dilation. Colour legend in (A). (C-D): Results from 50 capillary dilations at well-balanced divergent bifurcations. Statistical significance: Mann-Whitney U Test, ***: p<0.001, ns: non-significant (Methods). Definition boxplot: Methods.
Fig 5.
Well-balanced bifurcations are on average only 38 μm apart from any point in tissue.
(A) Microvascular network 1 (MVN 1) and the five analysis layers (ALs) each 200 μm thick (Fig from [12]). (B) Minimum path length between well-balanced bifurcation (wb-bif.) and descending arterioles (DA)/ ascending venules (AV) for MVN 1 (left) and MVN 2 (right). The error bars show the standard error of the mean. The results of the statistical analysis are presented in S7 and S8 Tables. (C) Distribution of the distance from all tissue points to the closest outflow vessel of a well-balanced bifurcation. Upper plot: MVN 1, raw data in (D), Lower plot: MVN 2. (D) Distance for all tissue points to the closest outflow vessel of a well-balanced bifurcation in MVN 1. Distances >100 μm are mostly located at the border. The details to compute the variables shown in (B-D) are presented in the Methods.