The severity of microstrokes depends on local vascular topology and baseline perfusion
- Institute of Pharmacology and Toxicology, University of Zurich, Switzerland
- Institute of Fluid Dynamics, ETH Zurich, Switzerland
- Neuroscience Center Zurich, University and ETH Zurich, Switzerland
Figures
Figure 1 with 2 supplements
Impact of the local vascular topology on the severity of a microstroke.
(a-d) Illustration of the four possible topological configurations at a microstroke capillary (MSC). For each topological configuration, a schematic (upper left) and a realistic example (lower …
Figure 1—figure supplement 1
Absolute flow changes in response to occlusions of different MSC types and frequency of flow decreases.
(a–d) Average relative absolute change in flow rate for capillaries up- and downstream of the MSC. For each topological configuration the flow field for ≥20 microstrokes has been computed (n: …
Figure 1—figure supplement 2
Flow direction changes for the four MSC types.
(a) Percentage of flow direction changes for the four possible topological configurations at a MSC (Figure 1a–d). Only percentage values > 2% are annotated. For each topological configuration, ≥20 …
Figure 2 with 5 supplements
Flow reduction in analysis boxes around the microstroke capillary (MSC).
(a) Schematic introducing how the volume factor is defined (Materials and methods). The MSC is highlighted in dark red. Inflow and outflow vessels of the analysis box are annotated with arrows. Vinit…
Figure 2—figure supplement 1
Occurrences of different vessels categories within the analysis box around the MSC.
(a–d) Percentage of vessels within the analysis box, which are positioned differently with respect to the 2-in-2-out MSC. (a) Percentage of vessels upstream and downstream of the MSC for an …
Figure 2—figure supplement 2
Differences between the relative change in flow rate and in red blood cell (RBC) flux at a 2-in-2-out MSC.
(a–b) Average relative decrease in flow rate (a) and in RBC flux (b) for capillaries upstream and downstream of the MSC (only capillaries with a flow decrease are displayed). Only at …
Figure 2—figure supplement 3
Impact of the baseline flow rate on the severity of a microstroke in a 2-in-2-out microstroke capillary (MSC).
(a–b) Average relative change in flow rate for capillaries upstream and downstream of the MSC. The red line indicates the median relative change if only capillaries with flow decrease are …
Figure 2—figure supplement 4
Impact of the cortical depth on the severity of a microstroke in a 2-in-2-out microstroke capillary (MSC).
(a–d) Upper: Schematic of a 2-in-2-out and the realistic microvascular network, which has been divided into five analysis layers (AL) each 200 µm thick. The arrow indicates the AL for which the …
Figure 2—figure supplement 5
Impact of the distance of the microstroke capillary (MSC) to the penetrating vessels on the severity of a microstroke in a 2-in-2-out.
(a, b) Average relative change in flow rate for capillaries upstream and downstream of the MSC. The red line indicates the median relative change if only capillaries with flow decrease are …
Figure 3
Flow reduction in analysis boxes around the microstroke capillary (MSC) for multi-capillary occlusions.
(a) Capillaries in an analysis box of 1.6 nl (volume factor = 8). The occluded capillaries are highlighted in dark red (left: one occluded capillary, right: nine occluded capillaries). Two distinct …
Figure 4 with 1 supplement
Distribution of arterial- and venule-sided capillaries within the microvascular networks (MVNs).
(a) Schematic to introduce the concept of the AV-factor (Materials and methods). The unique flow paths from capillary ij to the descending arteriole (DA)/ascending venule (AV) main branch are …
Figure 4—figure supplement 1
Average AV-factor in analysis cubes of varying size for microvascular network 1 (MVN1, a) and MVN2 (b).
To compute the average AV-factor the MVNs are discretized by analysis cube of varying size (Materials and methods). Neighboring analysis cubes overlap by half their side length. This results in 7336 …
Figure 5 with 2 supplements
Characteristics of the four topological configurations at a microstroke capillary (MSC) for both microvascular networks (MVNs).
(a) Schematic of the four topological configurations at a MSC. The MSC is color coded in accordance with subfigures (b–k). (b) Grid representation of the tissue in which realistic MVN1 is embedded. …
Figure 5—figure supplement 1
Length and distance to penetrating vessels of microstroke capillaries (MSC) of different types.
(a) Schematic of the four topological configurations at the MSC. The MSC is color coded in accordance with subfigures (b–k). (b, c) Median vessel length of the four MSC types (b: MVN1, c: MVN2). (d–g…
Figure 5—figure supplement 2
Median flow rate, median, and total relative supplied tissue volume for the four microstroke capillary (MSC) types over cortical depth.
(a–c) Schematic of a realistic microvascular network, which has been divided into five analysis layers (AL) each 200 µm thick. The arrow indicates for which AL the results are depicted in the …
Figure 6 with 1 supplement
Changes in flow paths in response to single and multiple microstrokes in MVN1.
(a) Schematic of the four topological configurations at the microstroke capillary (MSC). The MSC is color coded in accordance with subfigures (b) and (d). (b) Total number of flow paths connecting a …
Figure 6—figure supplement 1
Changes in the number of flow paths and the number of DA-AV-endpoint-pairs in response to a microstroke.
(a) Schematic of the four topological configurations at the microstroke capillary (MSC). The MSC is color coded in accordance with subfigures (b–d). (b) Difference (Diff.) in the total number of …
Tables
Author response table 1
Validation of the simulation results with literature data.
Table from: [15].
| DA: qRBCin[nl s-1] | DA+A: vRBC [mm s-1] | C: vRBC[mm s-1] | C: qRBC [RBCs s-1] | |
|---|---|---|---|---|
| Literature | 0.1 - 10.0[50] | 2.0 – 30.0[50] | mean: 0.4 – 2.0 [4, 10, 11, 13, 14, 51, 52] | mean: 38.6 – 62.0 [13, 14, 53] |
| MVN 1 | 0.88 ± 1.87 | 2.44 ± 4.56 | 0.82 ± 1.31 | 59.1 ± 237.6 |
| MVN 2 | 5.15 ± 8.57 | 5.28 ± 7.61 | 1.38 ± 1.96 | 88.4 ± 574.0 |
| MVN 3 | 0.96 ± 1.00 | 2.73 ± 4.97 | 0.59 ± 0.93 | 29.8 ± 219.0 |
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qRBCin: RBC flow rate in the first segments of the DA, vRBC: RBC velocity in the DA+A, qRBC: RBC flux. The values of the simulation results are given as mean ± standard deviation. For the RBC flux qRBC the median ± standard deviation are given. DA: descending arteriole, A: arteriole, C: capillary, MVN: microvascular network.
Additional files
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Supplementary file 1
Selection criteria, MSC types over depth and statistics.
(a) Overview of the eight selection criteria used to analyze the impact of structural and functional characteristics on the severity of a microstroke. The different microstroke capillary (MSC) types are depicted in Figure 1a–d. For cases 1–7, the cortical depth selection criterion requires that only the source of the MSC be within the given range. For cases 8–12, at least one of the vertices should be within the given range, while the second one may be ±50 µm outside the given range. The mean and standard deviation (std) are calculated from the results of the baseline simulation for the eight chosen MSC per case. For the mean and std of the cortical depth the values of the source and the target vertex are both considered. The definition of the main branch is provided in the methods. DA: descending arteriole. AV: ascending venule. n: simulated number of MSCs per case. (b) Distribution of microstroke capillary (MSC) types over cortical depth for microvascular network (MVN) 1 and 2. AL: analysis layer. Abbreviations of the four MSC types: 2–2: 2-in-2-out, 2–1: 2-in-1-out, 1–2: 1-in-2-out, 1–1: 1-in-1-out. (c) Statistical results for the effect of the MSC type on the changes observed at different generations (Figure 1). The effect of the MSC type has been analyzed separately for the generations upstream (−5 to −1) and downstream (1 to 5) of the MSC. The statistical test has been performed in R with the function anova_test() as a two-way mixed ANOVA with Bonferroni correction. Upper: There is a significant simple main effect of the factor MSC type at all generations except generation 4 and 5. Lower table: Pairwise t-test to determine for which MSC types there is a significant difference in the changes observed per generation. Only pairs with a significant difference are listed. Case 1: 2-in-2-out, Case 2: 2-in-1-out, Case 3: 1-in-2-out, Case 4: 1-in-1-out. p-adj.: adjusted p-value, sign: significance. (d) Statistical results for the effect of the MSC type on the changes in inflow rate for analysis boxes of different volumes (Figure 2b–e). The statistical test has been performed in R with the function anova_test() as a two-way mixed ANOVA with Bonferroni correction. Upper: There is a significant simple main effect of the factor MSC type for all volume factors < 2.75. Lower: Pairwise t-test to determine for which MSC types there is a significant difference in the changes observed per volume factor. Only pairs with a significant difference are listed. Case 1: 2-in-2-out, Case 2: 2-in-1-out, Case 3: 1-in-2-out, Case4: 1-in-1-out. p-adj.: adjusted p-value, sign: significance. (e) Statistical results for the characteristics of different MSC types (Figure 5f–k). The statistical test has been performed in with the Python library scipy.stats. The Kruskal–Wallis test showed a significant difference between supplied tissue volume, flow rate, and number of paths in both microvascular networks (MVNs, all p-values<0.001). Below the p-values of the pairwise comparison with the Mann-Whitney U test are listed. Upper: p-values for MVN1. Lower: p-values for MVN2. Abbreviations for the MSC types: 2–2: 2-in-2-out, 2–1: 2-in-1-out, 1–2: 1-in-2-out, 1–1: 1-in-1-out. ns: not significant. (f) Absolute differences between averaged flow rates in all capillaries at two time points t1 and t2. The time difference between the two time points is 20 s. Left: The absolute differences for an averaging interval of 10 turnover times (ToT) are displayed. Middle and left: The differences for averaging intervals of 5 ToTs and 3 ToTs are shown. The absolute differences between the averaged results increase for smaller averaging intervals. For an averaging interval of 10 ToT for 94% of all vessels, the absolute difference is smaller than 0.1 µm3 ms−1. This value decreases to 91% and 87% for an averaging interval of 5 ToT and 3 ToT, respectively.
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