A planar fractal analysis of the arterial tree of the human thyroid gland: implications for additive manufacturing of 3D ramified scaffolds

It is currently known that a number of human vascular systems have a fractal geometry. Since we have recently developed a technique to prototype single arterial branches of human soft tissue organs by additive layer manufacturing (AM), we have explored the possibility that auto-similarity in vessel branching represents a key variable for accurate computational modeling of the organ three-dimensional (3D), macro / microscopic anatomy, and its reproduction by inverse engineering. To this purpose, ramification features of the intra-lobar arteries of the human thyroid were studied using injection-corrosion casts of a cadaveric gland. Vessel diameters, ramification angles and branch lengths were measured by light microscopic, computer-aided optical metrology. Distribution of morphological variables was considered on a cumulative basis, and special focus was given to the branching laws. To reduce the bias of vascular distortion due to the pressure of intra-vascular resin injection, measures were made dimensionless through the use of a scaling parameter set on the vascular caliber of major afferent arteries. In addition, using high resolution micro-tomography (mCT Skyscan 1172, Bruker micro-CT) equipped with CTAn software and the Otsu algorithm for segmentation, spaces occupied by vascular branches (referred to as Volume of Interests, VOI) were selected, and their planar fractal dimension calculated (Mandelbrot 1982). Finally, a computational simulation of the vascular tree was achieved using a mixed, stochastic / deterministic algorithm, based on diffusion limited aggregation (DLA; Witten and Sander, 1981), constrained by mean values of vascular variables. Ratios among decreasing cast calibers, ramification angles and branch lengths, respectively, were found strictly interrelated, mCT-VOI depicted fractal dimensions, and DLA simulation led to a fractal-like organization consistent with real data morphometrics. In summary, thyroid arterial geometry reliably exhibited a degree of auto-similarity, suggesting that fractality is a key feature for computational modeling and eventual AM of 3D vascular networks of the human thyroid.