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Chapter 5
Venous Hemodynamics
Torvid Kiserud
In recent years evaluation of the venous system has
become a compulsory part of the haemodynamic assessment
of the fetus, but the underlying mechanisms
of our Doppler recordings are still incompletely understood.
The present chapter is not intended to solve
all that, but rather to address important hemodynamic
issues from a clinical point of view to help clinicians
use and interpret venous Doppler recordings.
For the interested reader more extensive discussions
of blood flow dynamics are available in the literature
[1±5].
Velocity Profile in Veins
Parabolic Blood Velocity Profile
and Flow Calculation
In a straight section of the umbilical vein with a
steady velocity, the distribution of the velocity across
the cross-sectional area of the vessel is assumed to be
parabolic with the highest velocity (V max ) in the center
of the cross section (Fig. 5.1). The ratio of the
average velocity across the vessel (V mean ) and the
V max characterizes the velocity profile. For parabolic
flow, the ratio V mean /V max is 0.5.
For calculating volume flow we need the averaged
velocity across the vessel area. We can derive that by
tracing the weighted mean velocity (V w.mean ) of the
Doppler recording. Ideally, with a strictly parabolic
flow, the relation would be V w.mean =V mean = 0.5 V max .
This is particularly useful since the intensity-weighted
mean velocity (V w.mean ) derived from the Doppler
shift is easily influenced by low-velocity signals from
the vessel wall or neighboring vessels, or from loss of
low-velocity recordings due to filters, or loss of the
weakest signals when travelling through the tissues.
Secondly, the V w.mean represents the average of the velocities
recorded in the sample volume (Doppler
gate), which is not identical to the vessel cross-section.
The sample volume may cover the vessel incompletely
or asymmetrically. The low velocities at the
periphery of the vessel are more likely to be underrepresented
than the high axial velocities of the center.
In short, we have two ways of calculating blood
flow:
and
p…D=2† 2 V w:mean
p…D=2† 2 0:5V max
Fig. 5.1. The velocity profile represents the velocity distribution
across the vessel and is characterized by the V mean /
V max ratio. The steady blood flow in the umbilical vein has
a parabolic velocity profile (i.e. ratio 0.5). The accelerated
blood at the ductus venosus inlet has a partially blunted
velocity profile corresponding to a ratio of 0.7, while at the
cardiac outlets the profile is even more blunted (e.g. ratio
0.97). (From [17])
the latter being the more robust, provided the velocity
actually is parabolic.
That may not always be the case. For example, the
velocity profile is found to be more blunted the first
few centimetres after the umbilical vein has left the
placenta [6]. During acceleration or retardation the
velocity profile changes, and variation in geometry,
branching and curvature alter the velocity profile
(Fig. 5.2). These changes are further determined by
the viscosity of the blood and dimension of the vessel
expressed in the Reynold's number [1]. These facts
favor the use of V w.mean , which is not dependent on a
known profile factor; thus, it has not been determined
which method is the best, and the literature
has examples of both methods [7±14].