Pg. Vico et al., NEW CONCEPTS IN THE STUDY OF TISSUE VASCULARIZATION - A MATHEMATICAL-MODEL OF SKIN VASCULARIZATION, Plastic and reconstructive surgery, 94(1), 1994, pp. 174-179
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.