The Domain Method

The construction of a domain around a capillary (red in the figure) is straightforward. Draw lines (purple/black) mid between adjacent capillaries (blue) and where these intersect, they form a polygon (black) around the central capillary. The polygon and its area (yellow) are the domain. Mathematically, it is a form of tesselation, Voronoi tesselation, and centroidal because the capillary is central (centre of gravity); and the lines are called perpendicular bisectors of (virtual) lines connecting the capillaries.

Originally, the domain method was developed as a tool to determine the distribution of intercapillary distances ⁽²⁾, but it is easier to take the distribution of domain areas instead.

Tissue domains are a special case of tesselation since their distribution appears to be lognormal ⁽¹⁾ – as for the distances between the capillaries. This makes comparison between cases easy because a lognormal distribution is characterized with two parameters, a mode or mean or median value and a skewness (often denoted as logSD). Tissues can be compared by comparing these parameters. It turns out that skewness is almost the same for different muscle tissue, even for different species, and in that case comparison can be restricted to the other parameter. Whether this similar skewness, of about 0.06-0.07, is a natural phenomenon, e.g., caused by how a muslce develops, has not been investigated so far.

Then, there is the possibility to combine domains with other tissue features. Most obvious: cell cross sections. From such methods, conclusions about their relation with the capillaries can be derived ⁽³⁾.

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