The quantitative estimation of microvessels in microvascular networks

A novel method is presented that greatly facilitates the determination of vessel segment number and density in both simple and complex microvascular networks. This approach was applied to microvascular networks represented by the Bra-Ket operator technique and accurately predicted the number of vessel segments in both tree-branched and loop-branched (arcade) networks. The method was then applied to the complex hexagonal array network described by Engelson et al. for gastrointestinal mucosa and accurately yielded an average vessel segment number of three around each hexagonal loop. This new method may be used for conveniently estimating tissue microvascular densities, such as vessel rarefaction or proliferation, and for the modelling of microvascular networks.