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Fractal properties have been demonstrated in literature for several human vascular systems. In the frame of the investigation of additive manufacturing (AM) as a viable solution to prototype single arterial branches of human soft tissue organs, the paper provides a fractal analysis of the arterial tree of the human thyroid gland. The possibility that the thyroid arterial structure may be described as auto-similar is investigated, by studying injection-corrosion casts of the cadaveric gland. Vessel branching is analyzed by measuring branch diameters, ramification angles, and vessel lengths with the use of an optical microscope. Metrological results are made dimensionless by applying, as a scaling parameter, the caliber of major arteries. Data are then studied on a cumulative basis and processed to infer general rules for vessel branching. High resolution microtomography (mCT) is used to determine the spaces occupied by vascular branches and calculate their planar fractal dimension. Finally, the vascular tree has been simulated by a mixed, stochastic / deterministic algorithm based on diffusion limited aggregation (DLA), in which mean values of vascular variables are set as constraints. The purpose of this research is to understand if fractality can be reliably assumed for computational modeling of the organ anatomy, in order to be able to produce, by AM, more representative physical prototypes and scaffolds. The finding allow to affirm that the human thyroid arterial structure exhibits a degree of auto similarity.

Strategies for reducing the effect of cumulative rounding errors in geometric numerical integration are outlined. The focus is, in particular, on the solution of separable Hamiltonian systems using explicit symplectic integration methods and on solving orthogonal matrix differential systems using projection. Examples are given that demonstrate the advantages of an increment formulation over the standard implementation of conventional integrators. We describe how the aforementioned special purpose integration methods have been set up in a uniform, modular and extensible framework being developed in the problem solving environment Mathematica. © 2002 Elsevier Science B.V. All rights reserved.

This paper focuses on the solution of separable Hamiltonian systems using explicit symplectic integration methods. Strategies for reducing the effect of cumulative rounding errors are outlined and advantages over a standard formulation are demonstrated. Procedures for automatically choosing appropriate methods are also described. © Springer-Verlag 2002.