The development of retinal blood vessels has extensively been used as a model to study vascular pattern formation. To date, various quantitative measurements, such as size distribution have been performed, but the relationship between pattern formation mechanisms and these measurements remains unclear. In the present study, we first focus on the islands (small regions subdivided by the capillary network). We quantitatively measured the island size distribution in the retinal vascular network and found that it tended to exhibit an exponential distribution. We were able to recapitulate this distribution pattern in a theoretical model by implementing the stochastic disappearance of vessel segments around arteries could reproduce the observed exponential distribution of islands. Second, we observed that the diameter distribution of the retinal artery segment obeyed a power law. We theoretically showed that an equal bifurcation branch pattern and Murray's law could reproduce this pattern. This study demonstrates the utility of examining size distribution for understanding the mechanisms of vascular pattern formation.
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