o_1977r8vv9vk1ts2ms0kd8pksa.pdf

58 T. Kiserud
Fig. 5.2. The impact of geometry on the velocity profile.
The profile changes from a parabolic shape to a more
blunted (flat) shape at converging vessel lumen (upper
panel). A funnel-shaped geometry with increasing diameter
is associated with reduced velocities at the periphery and
a more or less maintained axial velocity resulting in a
pointed velocity profile (lower panel). (From [2])
Factors Modifying the Velocity Profile
Fig. 5.3. Two-dimensional velocity profile in the ductus venosus
predicted by computer modelling (a). Note the
skewed profile and the small negative velocity component
estimated by using the present geometrical details. (From
[16])
The acceleration of blood, as seen in the isthmus of
the ductus venosus, also represents a transition of the
velocity profile from the parabolic (V mean /V max = 0.5)
to a more blunted profile (Fig. 5.1). There is now theoretical
and experimental proof that the blood velocity
profile at the ductus venosus inlet is partially
blunted with V mean /V max = 0.7 [15±17], which has
been used when calculating volume flow in the ductus
venosus [12, 13]. This value of the ratio is applicable
with the high ductus venosus velocities seen during
the second half of pregnancy. It is less certain that it
applies to the low velocities of early pregnancy.
Curvature, bifurcation or other changes in blood
flow direction cause changes in the velocity profile.
The blood starts spiralling along the wall of the curvature
and the velocity profile is commonly dislodged
towards the periphery of the vessel cross section. Depending
on the geometrical details, dimensions and
viscosity (i.e. Reynold's number), and the magnitude
of the velocity, the velocity profile may show a proportion
of negative (reversed) velocity (Fig. 5.3).
It is also worth noting that the velocity and its
profile starts to change before the blood has reached
the narrow section of a constriction, and gradually
returns to parabolic or more pointed velocity profile
on the other side of the constriction, again depending
on geometrical details (Fig. 5.4). An example would
be the physiological constriction of the umbilical vein
at the abdominal inlet. The abrupt expansion of the
umbilical vein diameter after the constriction at the
abdominal wall makes the blood slow down and regain
parabolic flow within a short distance. In some
cases this expansion is extensive and permits vortex
formation (whirls) and may be misinterpreted as an
aneurysm instead of a ªpost-stenotic dilatationº. In
contrast, the tapering geometry of the ductus venosus
central to the isthmic inlet maintains the high axial
velocity for a longer distance (Fig. 5.4).
During pulsation the velocity profile is continuously
changing. That is of particular interest in early
pregnancy when the Doppler recording of the ductus
venosus is used to identify risk groups of chromosomal
aberration. During atrial contraction the velocity
may retard to reach the zero line or beyond. Commonly,
there may be both positive and negative velocities
at the same time (Fig. 5.5, left). Apart from interference
of signals from neighboring vessels (umbilical
vein or liver), both the negative and positive recordings
could be genuine ductus venosus signals representing
a transitional change of the velocity profile
containing both negative and positive velocities at the
same time (Fig. 5.5, right). The degree of such
changes depends on the velocity, vessel diameter, viscosity
and pulse frequency, and can be predicted by
using the Womersley equation [1]; thus, the results of
the studies in early pregnancy using the zero or reversed
velocity in the ductus venosus recorded during
atrial contraction depend on how the velocity is