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a Chapter 4 Spectral Doppler Sonography: Waveform Analysis and Hemodynamic Interpretation 47
between placental angiomorphologic changes and the
Doppler indices has been investigated by several
workers. This section summarizes these findings and
presents a brief description of basic hemodynamic
concepts relevant for Doppler validation studies.
Experimental Approaches to Hemodynamic
Validation of Doppler Indices
Experimental procedures to validate Doppler indices
hemodynamically often require not only the direct
measurement of relevant hemodynamic parameters,
such as pressure and flow, but also controlled alterations
of the circulatory state. Such interventions are
too invasive to be performed in relation to human
pregnancy because of risks to the mother and fetus.
This limitation has led to the utilization of physical
and animal models. In vitro circulatory simulation
exemplifies the physical model and has been used
widely to investigate complex hemodynamic phenomena.
Nonbiologic materials are used for prototyping
circulatory systems for this type of simulation. In an
intact organism it may be difficult to perform comprehensive
hemodynamic measurements without profoundly
altering the physiologic state of the preparation.
Indeed, it may be impossible to conduct certain
hemodynamic experiments in vivo because of the inherent
complexities of modeling. It is also well recognized
that the fundamental hydrodynamics principles
are equally applicable to explaining circulatory phenomena
in a physical simulation and in a biologic
system. The principles of in vitro simulation for hemodynamic
studies have been comprehensively reviewed
by Hwang [31]. More specifically, hemodynamic
parameters for designing an in vitro circulatory
system for validation the Doppler indices have
been reviewed by Maulik and Yarlagadda [32]. Regarding
animal models, lambfetuses and newborns
have been used in both acute and chronic preparations.
These models have been utilized traditionally
to elucidate the circulatory phenomenon in human
fetuses.
Arterial Input Impedance:
Basic Concepts and Relevance
to Doppler Waveform Analysis
The relevant aspects of peripheral circulatory dynamics
are briefly reviewed here. Specifically, the basic
principle of arterial input impedance and its relevance
to Doppler waveform analysis are discussed.
Traditionally, opposition to flow has been expressed
in terms of peripheral resistance (Z pr ), which is the
ratio of mean pressure (P m ) to mean flow (Q m ):
Z pr ˆ P m =Q m
…10†
Although peripheral resistance has been the prevalent
concept for describing the opposition to flow, it is applicable
only to steady, nonpulsatile flow conditions.
Flow of blood in the arterial system, however, is a
pulsatile phenomenon driven by myocardiac contractions
with periodic rise and fall of pressure and flow
associated with systole and diastole of the ventricles.
The pressure and flow pulses, thus generated, are
profoundly affected by the downstream circulatory
conditions, specifically the opposition to flow offered
by the rest of the arterial tree distal to the measurement
point in the peripheral vascular bed. The idea
of vascular impedance provides the foundation for
understanding this complex phenomenon in a pulsatile
circulation. Vascular impedance is analogous to
electrical impedance in an alternating current system.
Womersley [33] showed that the equations dealing
with electrical impedance are applicable to solving
the problems of vascular impedance. It should be
noted in this context that the idea of vascular resistance
is analogous to the principle of electrical resistance
in direct-current electrical transmissions.
Closely related to impedance is the phenomenon
of wave reflection in a vascular tree. The shape of
pressure and flow waves at a specific vascular location
results from the interaction of the forward propagating
(orthograde) waves with the reflected backward
propagating (retrograde) waves [34, 35].
P m ˆ P o ‡ P r
Q m ˆ Q o ‡ Q r
…11†
…12†
where P is pressure, Q is flow, m is the measured
wave, o is the orthograde wave, and r is the retrograde
wave. The presence of reflected pressure and
flow waves in the arterial circulation has long been
recognized by hemodynamics experts. Comprehensive
analysis and understanding of the phenomenon was
facilitated by using the analogy of the theory of electrical
current transmission. The existence of wave reflections
in the circulatory system is evident from the
observation that as one obtains samples along the
arterial tree from the heart to the periphery the
pulsatility of pressure waves progressively increases
and that of the flow or flow velocity waves declines.
Consequently, pressure and slow waves acquire distinctly
differing configurations as they propagate
down the arterial tree. The phenomenon has been
analyzed mathematically by separating the observed
pressure and flow waves into their constituent orthograde
and retrograde components [35]. It should be
noted that the forward propagating waves of pressure
and flow demonstrate the same configuration. When
wave reflection occurs, the retrograde flow waves are