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Description
Maintaining a stable oxygen supply to the brain is essential to meet its high metabolic demands and sustain cognitive function. Assessing how microvascular changes affect cerebral energy supply is challenging due to complex capillary networks and small-scale vascular alterations. To address this, we developed a computational model of oxygen transport incorporating microvascular perfusion heterogeneity.
Our approach employs a mixed-dimensional framework, representing the vascular network as a 1D graph embedded in 3D brain tissue. Unlike conventional models, it does not assume equilibrium between oxygen partial pressure (PO2) in red blood cells (RBCs) and plasma, capturing inter-vessel differences in oxygen unloading dynamics. Coupled non-linear PDEs are solved at steady state within the open-source framework DuMux [\cite{A}].
The model computes PO2 in tissue, plasma, and RBCs across 13 tissue volumes (0.064 mm³) obtained by two-photon microscopy in mice [\cite{B}], each with ~1100 capillaries. Tissue hypoxia is rare, affecting ~15% of cells, mainly distal to descending arterioles or in low-vascular-density areas. Capillary stalling, linked to aging and disease, was assessed via 160 single-capillary occlusion simulations. While domain-averaged PO2 remained stable, local oxygenation patterns changed notably, with 27% of cells showing PO2 changes >1 mmHg. Strongest effects occurred in capillaries with high baseline flow [\cite{C}] or high RBC oxygen saturation (~25% of cases).
Bibliography
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title = {{DuMux} 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling},
volume = {81},
issn = {08981221},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0898122120300791},
doi = {10.1016/j.camwa.2020.02.012},
language = {en},
urldate = {2026-03-09},
journal = {Computers \& Mathematics with Applications},
author = {Koch, Timo and Gläser, Dennis and Weishaupt, Kilian and Ackermann, Sina and Beck, Martin and Becker, Beatrix and Burbulla, Samuel and Class, Holger and Coltman, Edward and Emmert, Simon and Fetzer, Thomas and Grüninger, Christoph and Heck, Katharina and Hommel, Johannes and Kurz, Theresa and Lipp, Melanie and Mohammadi, Farid and Scherrer, Samuel and Schneider, Martin and Seitz, Gabriele and Stadler, Leopold and Utz, Martin and Weinhardt, Felix and Flemisch, Bernd},
month = jan,
year = {2021},
pages = {423--443},
}
@article{B,
title = {The cortical angiome: an interconnected vascular network with noncolumnar patterns of blood flow},
volume = {16},
copyright = {http://www.springer.com/tdm},
issn = {1097-6256, 1546-1726},
shorttitle = {The cortical angiome},
url = {https://www.nature.com/articles/nn.3426},
doi = {10.1038/nn.3426},
language = {en},
number = {7},
urldate = {2026-03-09},
journal = {Nature Neuroscience},
author = {Blinder, Pablo and Tsai, Philbert S and Kaufhold, John P and Knutsen, Per M and Suhl, Harry and Kleinfeld, David},
month = jul,
year = {2013},
pages = {889--897},
}
@article{C,
title = {The severity of microstrokes depends on local vascular topology and baseline perfusion},
volume = {10},
issn = {2050-084X},
url = {https://elifesciences.org/articles/60208},
doi = {10.7554/eLife.60208},
abstract = {Cortical microinfarcts are linked to pathologies like cerebral amyloid angiopathy and dementia. Despite their relevance for disease progression, microinfarcts often remain undetected and the smallest scale of blood flow disturbance has not yet been identified. We employed blood flow simulations in realistic microvascular networks from the mouse cortex to quantify the impact of single-capillary occlusions. Our simulations reveal that the severity of a microstroke is strongly affected by the local vascular topology and the baseline flow rate in the occluded capillary. The largest changes in perfusion are observed in capillaries with two inflows and two outflows. This specific topological configuration only occurs with a frequency of 8\%. The majority of capillaries have one inflow and one outflow and is likely designed to efficiently supply oxygen and nutrients. Taken together, microstrokes bear potential to induce a cascade of local disturbances in the surrounding tissue, which might accumulate and impair energy supply locally.
,
A blockage in one of the tiny blood vessels or capillaries of the brain causes a ‘microstroke’. Microstrokes do not cause the same level of damage as a major stroke, which is caused by a blockage in a larger blood vessel that completely cuts off oxygen to a part of the brain for a period. But microstrokes do increase the risk of developing conditions like dementia – including Alzheimer’s disease – later in life.
People with these neurodegenerative conditions have fewer capillaries in their brains. The capillaries make up a mesh-like network of millions of vessels that supply most of the energy and oxygen to the brain. Repeated microstrokes may contribute to progressive loss of capillaries over time. Reduced numbers of capillaries may increase memory loss and other brain difficulties.
To better understand how microstrokes affect blood flow in the brain, Schmid et al. created a computer model to simulate blood flow in capillaries in the mouse brain. Then, they modeled what happens to the blood flow when one capillary is blocked. The experiments showed that the configuration of the blocked capillary determines how much blood flow in neighboring capillaries changes. Blockages in capillaries with two vessels feeding in and two vessels feeding out caused the greatest blood flow disturbances. But these 2-in-2-out vessels only make up about 8\% of all brain capillaries. Blockages in capillaries with different configurations with respect to feeding vessels had less effect.
The experiments suggest that most microstrokes have limited effects on blood flow on the scale of the entire brain because of redundancies in the capillary network in the brain. However, the ability of the capillary network to adapt and reroute blood flow in response to small blockages may decrease with aging. Over time, ministrokes in a single capillary may set off a chain reaction of disturbed blood flow and more blockages. This may decrease energy and oxygen supplies explaining age- and disease-related brain decline. Better understanding the effects of microstrokes on blood flow may help scientists develop new ways to prevent such declines.},
language = {en},
urldate = {2026-03-09},
journal = {eLife},
author = {Schmid, Franca and Conti, Giulia and Jenny, Patrick and Weber, Bruno},
month = may,
year = {2021},
pages = {e60208},
}
