NEW CONCEPTS IN THE STUDY OF TISSUE VASCULARIZATION - A MATHEMATICAL-MODEL OF SKIN VASCULARIZATION

A preliminary study demonstrated the existence of a fractal structure for perforator arterial vessels of the skin and proved to be a useful tool to compare vascular trees on the basis of their complexity. Fract al analysis of axial-perforator arteriovenous vascular trees was perfo rmed on the skin of mice after injection of the arterial network by in dia ink. Fractal analysis was performed by box counting. Fractal dimen sion D was determined for 35 venous and 31 arterial perforator vessels (D = 1.302 and 1.264, respectively) and 5 venous and 3 arterial axial vessels (D = 1.374 and 1.328, respectively) (gamma(2) greater than or equal to 0.985). All vascular networks show a fractal structure, char acterized by a specific D. These values are relatively constant; Dis a function of the anatomic and physiologic characteristics. There was n o significant difference between venous and arterial networks, nor was there between axial and perforator networks (p < 0.05); this demonstr ates a similar efficacy in terms of perfusion of the skin. A computer simulation based on fractal theory has been developed to reproduce the two kinds of vascular networks. Fractals are the result of a construc tion procedure that is repeated and repeated so that the iteration of a very simple rule can produce seemingly complex shapes, such as vascu lar networks. The basic module that is repeated in the whole structure is Y-shaped and is termed the generator; this generator is applied to a basic structure, called the initiator. After a few iterations, a va scular network is obtained. The difference between axial and perforato r vascular networks is the choice of the initiator, whereas the genera tor is identical. The growth of the two kinds of perfusions appears in the same tissue environment; there is no reason why, in the same tiss ue, for an identical physiologic function, there should be a differenc e in the growing pattern of these vessels. Only the origin of these bl ood vessels is different, and this is taken into account by the model in having different initiators; this explains the difference in macros copic aspects. Finally, several variables of this mathematical model a re discussed.