Geometric and Topological Analysis of Arteriolar Networks in the Rat Gluteus Maximus Muscle: One Network to Rule Them All?

Introduction A detailed evaluation of in vivo geometry and topology of skeletal muscle arteriolar networks is essential to understanding microvascular blood flow regulation. Beyond increasing understanding of skeletal muscle hemodynamics, such data provides critical experimental inputs for theoretical blood flow simulation studies. Generally, past studies have relied on data collected from vascular casting experiments or data collected from incomplete microvascular trees or segments. The objective of this study was to comprehensively analyze the geometry and topology of complete arteriolar networks within the rat gluteus maximus (GM) muscle. The data generated were used to generate an index of geometric/topological homology across GM networks and produce essential experimental data to use as inputs for future theoretical studies of hemodynamics. Methods The rat GM provides the ideal experimental model to study locomotive skeletal muscle. Its planar geometry and uniform thinness enable access (within a single focal plane) to its entire microcirculation for microscopic imaging and perturbation. Using intravital videomicroscopy, the GM (n=4) was scanned under baseline conditions and photomontages were compiled (~400 images per network). Photomontages were registered to a MATLAB x–y coordinate system and scaled digital networks were generated. Arteriolar diameters and lengths were measured along the arteriolar network and a centrifugal ordering algorithm was applied, resulting in arterioles ranging from 1 st (feed) to 9 th (terminal) order. Mean diameters, lengths, and number of segments were outputted and grouped with respect to arteriolar order. Results The coefficients of variation at each order were consistently greater for lengths than diameters. The relationships of arteriolar diameter and segment length as a function of vessel order were fitted with an exponential decay function and resulted in relatively stronger goodness of fit values for diameters (R 2 = 0.62 to 0.75) than lengths (R 2 = 0.32 to 0.53), suggesting greater predictability and homology between arteriolar diameter and vessel order. Topological analyses were extended to plotting the logarithm of diameters and lengths as a function of vessel order in an effort to validate Horton's laws in the GM and derive diameter, length, and bifurcation ratios. Finally, a “mean” arteriolar network that describes all relevant geometric and topological parameters was explored. Conclusion This study provides the first comprehensive analysis of rat GM topology and geometry. The data presented herein will serve as ideal experimental inputs for future computational studies of skeletal muscle hemodynamics and microvascular blood flow regulation. Support or Funding Information NSERC

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