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Percolation phenomenon: the effect of capillary network rarefaction
1Department of Physiology, Medical College of Wisconsin, Milwaukee 53226.
Microvascular Research
|January 1, 1993
Summary
Microvascular network resistance increases significantly only after functional capillary density drops by over 30%. A critical percolation threshold exists, below which resistance rises sharply, especially when low-flow capillaries are removed.
Area of Science:
- Physiology
- Biophysics
- Computational Biology
Background:
- Microvascular networks are crucial for tissue oxygenation.
- Understanding how network structure affects resistance is vital for studying blood flow regulation.
- Functional capillary density is a key indicator of microcirculatory health.
Purpose of the Study:
- To investigate the relationship between microvascular network resistance and functional capillary density.
- To determine the impact of capillary rarefaction on network resistance and flow distribution.
- To identify the percolation threshold in a simulated microcirculatory network.
Main Methods:
- Computer simulation of a spinotrapezius muscle microcirculatory network.
- Modeling based on measured vessel length and diameter data.
- Simulating progressive capillary rarefaction by stepwise random removal.
- Calculating flow distribution and network resistance after each removal step.
Main Results:
- Network resistance showed minimal increase for functional capillary density decreases <30%.
- Capillary flow and its variance remained stable despite flow redistribution up to 30% reduction.
- Network resistance increased exponentially beyond 30% capillary loss, approaching infinity at the percolation threshold (56-62%).
- Preferential removal of low-flow capillaries lowered the percolation threshold.
Conclusions:
- Microvascular networks exhibit resilience to moderate capillary loss.
- A critical functional capillary density (percolation threshold) exists, beyond which network resistance escalates dramatically.
- Network robustness is influenced by the pattern of capillary loss, with preferential removal of underperfused vessels being more detrimental.
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