Vascular Branching
163
(5.3.20)
The fraction
of
the pressure pulse that
is
reflected at the junction due
to unmatched branching vessel characteristic impedances is
2,
-zm
-
1-2,
12,
-
(5.3.2 1)
where
Z,
and
Zd
are the characteristic impedances of the mother and
daughter vessels, respectively.
This
latter leads to a junction reflection
of
l-nZm/Z,
1+nZ,
/Z,
r,
=
If we let
PI
and
2,
=-
Pm
z,
=-
Am
A,
then, for n equal branches, we obtain
where
4
Am
A,
=n--
(5.3.22)
(5.3.23)
(5.3.24)
(5.3.25)
is
the area ratio
(A,)
and c,/cI
is
the velocity ratio, related to the ratio of
elastic properties
of
the branching vessels:
