Time-averaged simulations results for bi-phasic blood flow simulations in realistic microvascular networks for multi-capillary dilation scenarios mimicking pericyte ablation

Documentation to reproduce in silico analyses related to the manuscript
Pericyte remodelling is deficient in the aged brain and contributes to impaired capillary flow and structure

by

Andrée-Anne Berthiaume, Franca Schmid, Stefan Stamenkovic, Vanessa Coelho-Santos, Cara D. Nielson, Bruno Weber, Mark W. Majesky and Andy Y. Shih

Published in
Nature Communications (doi: 10.1038/s41467-022-33464-w)

All simulations are performed based on the in silico blood flow model with discrete red blood cell (RBC) tracking as described in Schmid et al., 2017, PLoS Comp Biol (doi: 10.1371/journal.pcbi.1005392). The bi-phasic blood flow simulations have been performed in two realistic microvascular networks from the somatosensory cortex of the mouse first published in Blinder et al., 2013, Nature Neuroscience (doi: 10.1038/nn.3426). 

For further information and instructions please contact Franca Schmid (franca.schmid@unibe.ch, orcid.org/0000-0002-0689-9366).

Simulation results:

All time-averaged simulation results are saved as vascular graphs building on the python library igraph and stored as python pickle files (Python 2.7). For each simulation two files are available: verticesDict.pkl and edgesDict.pklcontaining all vertex and edge specific data, respectively. A summary of the vertex and edge attributes is provided below. The folder Baseline contains the simulation results for microvascular network 1 (MVN1) and MVN2 for the reference simulation, i.e. without any dilation. Folder Dilated contains the simulation results mimicking the four pericyte ablation scenarios. Subfolders dc_x.x contain the simulation results for the different diameter changes. Note that, folder dc_0.0 contains no new simulation results but is a dummy folder containing the information about the vessels to be dilated for the different dilation scenarios (namely edge attribute: toDilate and base_capillary). 

Reproducing figure 8:

Panels a-c: created by illustrating the simulation results with the open source software Paraview (v5.7.0).
Panels d-f & h: can be generated by executing make_all_figures.py in Python 2.7 within the provided folder structure.
Panel g: can be generated by executing make_figure_8g.py after installation of the the vgm-framework (further information see below). 

Output: All created Figures are saved in the folder Figures. The associated source data is available in Excel format in the folder SourceData.

Edge attributes:

diameter: vessel diameter [µm]
mainAV: 1 if ascending venule main branch, 0 otherwise
connectivity: vertex tuple to define location of edge
flow: flow rate [µm³/ms]
mainDA: 1 if descending arteriole main branch, 0 otherwise
nkind: 0: pial artery, 1: pial vein, 2: descending arteriole, 3: ascending venule, 4: capillary
htt: tube hematocrit [-]
toDilate: 1 if vessel is dilated for the current dilation scenario, 0 otherwise
base_capillary: 1 if vessel is the base capillary of the current dilation scenario, 0 otherwise

Vertex attributes:

index: vertex index
pressure: pressure [mmHg]
nkind: 0: pial artery, 1: pial vein, 2: descending arteriole, 3: ascending venule, 4: capillary
coords: vertex coordinates x,y,z [µm]
pBC: pressure boundary conditions at inflow vertices [mmHg], None at internal nodes

Obtaining simulation results:
General:

• Running bi-phasic blood flow simulations requires setting-up the vgm-framework available at: https://github.com/Franculino/vgm.git (v.1.0).
• vgm is written in Python 2.7 and builds on standard python libraries.
• vgm has been used on macOS, Ubuntu and Windows Systems.
• Installation time < 5min. Further details available within the vgm README.
• Runtime depends on the network size, the chosen blood flow model and the initial conditions (e.g. ~8hrs for a Restart simulation of MVN1 with the bi-phasic blood flow model, see Restarty.py).
• scripts/Test.py provides an example how a simulation can be initiated. A Demo case is provided (details see below).
• Output: sampledict_BackUp_xx.pkl
• The bi-phasic blood flow model can be applied on all kind of microvascular graphs.

Specific for current application:

• Simulations are a restart on the statistical steady state of the baseline cases.
• All relevant pre-processing functions for the current study are available in scripts/find_stroke_locations.py. Further details are available from the definition of the different functions.
• The simulations are initiated with scripts/Restart.py.
• To obtain the time-averaged simulation results scripts/01_put_together_sampledicts.py and scripts/02_convergenceDiscrete.py need to be executed. This results in the file G_averaged.pkl that is used for further analyses.

Demo:

• Contains a small hexagonal microvascular network to test the code.
• 1) Run Test.py to start the simulation
• 2) Run 01_put_together_sampledicts.py
• 3) Run 02_convergenceDiscrete.py to obtain time-averaged results (G_averaged.pkl)