Abstract (EN):
Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the
principle of energy minimization, Murray found restrictions for the relation between the diameters and
also between the angles of the branches. It is known that bifurcations are prone to the development of
atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index
(OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions)
were evaluated in this work. All of them were normalized by the size of the outflow branches. The
relation between Murray¿s laws and the size of low WSS regions was analysed in detail. It was found that
the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between
the cross section areas of the outflow branches and the cross section area of the main branch. Large
regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent
of the ratio between the diameters of the outflow branches. Since the expansion ratio in
bifurcations following Murray¿s law is kept in a small range (1 and 1.25), all of them have regions of low
WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions
with low WSS values and, therefore, Murray¿s law does not lead to atherosclerosis minimization. A study
on the effect of the angulation of the bifurcation suggests that the Murray¿s law for the angles does not
minimize the size of low WSS regions.
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica