Ultrasound Physics & Instrumentation
4th Edition
Volume II
Companion Presentation
Frank R. Miele
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Volume II Outline
 Chapter 7: Doppler
 Chapter 8: Artifacts
 Chapter 9: Bioeffects
 Chapter 10: Contrast and Harmonics
 Chapter 11: Quality Assurance
 Chapter 12: Fluid Dynamics
 Chapter 13: Hemodynamics
 Level 2
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Removing Assumptions Made
In Chapter 13: Fluid Dynamics, the basic equations were derived based
on the following assumptions:
 The flow conduit is a rigid, cylindrical tube
 The flow is steady state, laminar flow
 The fluid is Newtonian
In this chapter, we remove these restrictions which clearly do not hold
true for blood flow.
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The Assumption of Steady State Flow
The driving pressure for blood flow is highly pulsatile, as shown in the
figure below. Since the driving pressure is dynamic, there are many
changes which affect flow relative to the simplified equations introduced
in the previous chapter.
R
P
Q
S
T
Fig. 1: (Pg 776)
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The Assumption of Rigid Flow Conduits
The arteries are elastic and not rigid conduits for flow. This elasticity is
important since:
 The elasticity allows the aorta to be capacitive
 The capacitance of the aorta allows energy to be stored in the walls
of the aorta, to provide energy to propel blood during diastole
 Run off from the capacitive aorta through the resistive arterioles and
capillaries reduces the pulsatility, improving heart efficiency.
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Pressure Volume Relationship
(Compliant Vessel)
The simplified law expresses that the
rate of change in pressure is
proportional to the rate of change in
volume. As seen by this graph, the
compliance of the vessel (non-rigid flow
conduit) is not linear, explaining the
naming of the equation as “simplified”.
In reality, there is a non-linear
relationship between a change in
pressure and the resulting change in
volume.
Fig. 2: (Pg 778)
(A 25% increase in pressure at 100
mmHg results in a 50% increase in
volume.)
(Redrawn from Berne, R.M. and Levy,
M.N., Cardiovascular Physiology)
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Pressure Volume Relationship
(Compliant vs. Non-compliant Vessel)
Compliant
Non-Compliant
In this graph we see what happens
to flow with an increase in pressure
for a non-compliant vessel. At
lower pressures, the relationships is
relatively linear, but at higher
pressures, an increase in pressure
results in virtually no increase in
volume.
(A 25% increase in pressure at 100
mmHg results in only a 7% increase
in volume.)
Fig. 3: (Pg 779)
(Redrawn from Berne, R.M. and Levy,
M.N., Cardiovascular Physiology)
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Single Flow Conduit “Tacit” Assumption
Although not explicitly stated, the equations were all derived making the
simplistic assumption of a single flow conduit. The effective resistance
of multiple flow conduits can become relatively complex based on the
geometry of the multiple vessels.
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Series Resistance
For flow conduits in series (the exit of one connected to the input of the
next) the effective (overall) resistance is simply the sum of resistances
of each individual component, as shown below.
Fig. 4: (Pg 780)
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Parallel Resistance
For flow conduits in parallel (the inputs connected to each other and the
outputs connected to each other) the effective (overall) resistance is
more complicated to calculate than a series resistance. The inverse
effective resistance is calculated as the sum of the individual inverse
resistances as shown below.
Fig. 5: (Pg 780)
Note the effective resistance decreases with increasing parallel vessels.
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Example of Series Resistance
For this simple case as shown below, we see that the effective
resistance of four shorter segments connected in series is simply four
times the resistance of one short segment. Equivalently, four shorter
segments connected in series have the same effective resistance as
one longer segment of the same diameter.
Fig. 6: (Pg 781)
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Example of Parallel Resistance
Notice that by placing the same four short segments in parallel, the
effective resistance now decreases by a factor of four, as shown below.
Fig. 7: (Pg 781)
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Comparing Parallel with Larger Diameter
Be careful not to assume that
the resistance would be the
same for a vessel of four
times the radius r, as for four
vessels in parallel each of
radius r. As shown, the
effective resistance for a
single larger diameter vessel
is much less than for the
parallel combination (in fact
64 times less).
Fig. 8: (Pg 782)
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Parallel Series Network
Applying the rules we learned for series and parallel combinations, the
effective resistance for the following network is calculated as:
R eff  R1 
R2
4
 R3
To view specific
calculation refer to
page 783
Fig. 9: (Pg 783)
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The Assumption of Smooth Straight
Vessels
The amount of energy lost by
transporting blood over rough
vessel surfaces is obviously
greater than the energy lost
transporting over smooth
surfaces. This fact is important
since the determination of
disease severity does not take
into account changes in frictional
energy losses associated with
the geometry of the lesion.
Fig. 10: (Pg 785)
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“Discretized” Energy Loss
This figure demonstrates frictional and viscous energy losses as is
existing in discrete layers as a means to more simply visualize energy
loss.
“Lossless” Flow
Viscous Energy Flow
Frictional Energy Loss Flow
Fig. 11: (Pg 786)
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Energy Losses with Varying Stages
Disease
This diagram demonstrates how energy losses increase with
decreasing vessel size as a result of increased frictional and viscous
energy loss (using the “discretized” model of the previous slide).
Fig. 12: (Pg 786)
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Velocity Profiles
The following diagram demonstrates the boundary effects on the flow
profile through varying vessel sizes.
Fig. 13: (Pg 787)
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The Cardiovascular System
This figure shows a
simplified model of the
cardiovascular system,
demonstrating the key
functions required.
Fig. 14: (Pg 789)
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Arterial Vessel Sizes
Varying vessel diameter is a
principal mechanism in
controlling the effective
resistance throughout the
arterial system. Control of
the resistance is critical to
control pressure decrease
as well as regulate
volumetric flow (as indicated
by the simplified law).
Fig. 15: (Pg 790)
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Complex Resistance Network of the
Arterial System
Fig. 16: (Pg 791)
Even though there are
increasing numbers of vessels
progressing from the left heart
toward the periphery, the
resistance decreases in
progression from the low
resistance of the aorta to the
relatively high resistance of
the arterioles. The effective
resistance in the capillaries is
still very high, although
generally lower than the
resistance of the arterioles
because of the sheer number
of capillaries.
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Relative Resistances
The following graph (linear and logarithmic) display the resistance of the
vessels relative to the resistance of the aorta. Note the high resistance
of the arterioles given rise to the terminology of the arterioles as the
“resistance component” of the cardiovascular system.
Fig. 17: (Pg 792)
Fig. 18: (Pg 792)
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Velocity versus Total Cross Sectional
Area
The velocity of the flow is
controlled primarily by the
varying total cross sectional
area of the vessels.
According to the volumetric
flow equation (continuity), for
a fixed volume, as the area
increases the velocity
decreases, as seen in the
associated figure.
Fig. 19: (Pg 794)
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Pressure Across the Arterial System
Important Characteristics:
1. Slight increase in pulse
pressure from aorta to
small arteries
2. Pulsatility is damped at
level of arterioles
3. Rapid pressure drop
occurs at arterioles
4. Significant pressure drop
occurs across capillaries
5. Pressures in venous side
are very low and relatively
“steady-state”
Fig. 20: (Pg 795)
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The Venous System
The pressure in the venous system (as seen in the diagrams from a
few of the last slides) is relatively low. The result is that people often
underestimate the role of the venous system as a subsystem of the
cardiovascular system. Specifically, the capacitance of the venous
system is critical to controlling the mean circulatory pressure.
Note: The venous system is referred to as the “capacitive” component
of the cardiovascular system.
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Blood Volume Distribution
(patient at rest)
 65 – 70% in the veins and venules
 10 - 12% in the systemic arteries
 5% in the heart
 5% in the pulmonary veins
 5% in the systemic capillaries
 3% in the pulmonary capillaries
 3% in the pulmonary arteries
Can you see why the venous system is referred to as the capacitive component
of the CV system?
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Reference for Hydrostatic Pressure
By referencing the
hydrostatic pressure to the
right atrium of the heart, the
central pressure of a patient
does not need to be
corrected by the hydrostatic
pressure differences for
different height patients.
The result of referencing
the RA as 0 mmHg is that
the hydrostatic pressure is
considered negative in the
head for a standing patient.
Fig. 21: (Pg 799)
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Calf Muscle Pump
The calf muscle pump helps overcome the effect of gravity to aid with
venous return for a patient in the standing position. By muscle
contraction, the venous volume is ratcheted back toward the right heart
through a series of valves which open and close with muscle contraction.
Fig. 22: (Pg 800)
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Transmural Pressure
The transmural pressure is a measure of the difference of the pressure
inside the vessel (intravascular pressure) relative to the pressure outside
the vessel (tissue pressure). Note that the transmural pressure is always
referenced from the inside of the vessel to the outside of the vessel.
Intravascular Pressure
(lower)
Intravascular Pressure
(higher)
Tissue Pressure
(higher)
Tissue Pressure
(lower)
Fig. 23: (Pg 801)
Fig. 24: (Pg 801)
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Sub-critical Disease
At the sub-critical stage of disease, the energy losses under normal
metabolic demand are small enough that the body can adequately
compensate, and the end organ is adequately perfused. Since
perfusion requirements are met, the patient is asymptomatic for normal
metabolic demand.
Fig. 25: (Pg 803)
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What Would Happen with Disease and
NO Arteriole Compensation
In comparison to the pressure
graph of the normal system
(shown on an earlier slide),
notice the pressure decreases
across the large arteries
(whereas previously the
pressure was maintained or
actually slightly increased). The
large pressure drop across the
arterioles now results in
inadequate pressure to provide
flow across the capillaries and
the rest of the CV system.
Fig. 26: (Pg 804)
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Normal versus Diseased Arteries with
Adequate Compensation
In comparison to the graph of the
last slide, notice now that there is a
decrease in the pressure dropped
across the capillaries to
compensate for the pressure loss
across the arteries as a result of
the disease. The decrease in
pressure drop across the arterioles
results from the decreased
resistance from vasodilation of the
arterioles. The result is now
adequate pressure to perfuse the
end organ.
Fig. 27: (Pg 805)
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Inadequate Compensation
(More Severe Disease)
In this case, the energy loss
across the arteries is so great
because of the more significant
increase in resistance that the
arterioles are unable to
adequately compensate. As a
result, there is inadequate
perfusion of the end organ and
the patient is symptomatic even
at rest (rest pain).
Fig. 28: (Pg 805)
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Pressure Gradient with Normal
Volumetric Demand
To fully appreciate this slide, a comparison must be made with the next
slide. Notice that with the normal metabolic demand, the pressure drop
as depicted below is related to 4 times the velocity v squared.
Fig. 29: (Pg 806)
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Increase in Pressure Gradient with
Increase in Volumetric Demand
In comparison to the normal volumetric demand, an increase in demand
by a factor of four, as can occur with exercise, results in a factor of 4
increase in velocity. Now notice that the pressure gradient, as depicted
below, is related to 4 times the square of 4v. This represents an
increase in the pressure gradient by a factor of 16. This fact explains
why exercising a patient often unmasks sub-critical disease.
Fig. 30: (Pg 806)
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Critical Stenoses
When the disease becomes critical, the amount of energy lost to
frictional and viscous effects become so severe, that volume is not
maintained across the lesion. As depicted below, a point is reached at
which there is a narrow stream of flow at a high velocity with most of the
flow traveling at a relatively low velocity (“string flow”).
Fig. 31: (Pg 807)
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Velocity and Flow Changes with
Percentage Stenosis
Notice that the volumetric flow is
maintained for percentage
decreases in cross-sectional area up
to about 75%. Past 75%, the
volume begins to drop rapidly.
Notice that as the percent stenosis
increases, the velocity increases to
maintain the volumetric flow.
Eventually, the increased energy
loss related to frictional and viscous
losses dominates and the peak
velocity decreases precipitously.
Fig. 32: (Pg 808)
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Spectral Doppler Assessment of
Hemodynamics
Spectral Doppler displays velocity information versus time. From the
Doppler spectrum, the peak velocities, the mean velocities, the
variance in velocity, and acceleration/deceleration can be visualized
and measured. By understanding the hemodynamic laws which govern
flow and relating those concepts to velocity and changes in velocity,
Doppler can therefore be used to assess many hemodynamic
situations.
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Systolic Acceleration and Pressure
Step 1: Relate pressure with volume change.
P  Q  R
S o as the pressure increases, the volum e increases
Fig. 33: (Pg 809)
Step 2: Relate volume change with velocity change.
Q  v  area
S o as the volum e increases, the velocity increases
Fig. 34: (Pg 809)
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Measuring Acceleration
Fig. 35: (Pg 810)
A cceleration 
v
t
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Doppler Risetime for a Diseased Vessel
With proximal disease, the volume of flow cannot increase as rapidly with
increasing systolic pressure, decreasing the acceleration. The decrease
in acceleration results in a longer risetime. Typically, a risetime of
greater than 144 msec is indicative of a flow limiting proximal stenosis.
Fig. 36: (Pg 810)
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Spectral Windows
The presence of a spectral window implies the presence of laminar flow.
The converse is not necessarily true. The absence of a spectral window
does not necessarily imply the absence of laminar flow (turbulence). The
loss of the spectral window can be affected by many parameters such as
proximity of the sample volume to the vessel wall, a large sample volume
or CW Doppler, overgaining, spectral broadening, etc.
Fig. 37: (Pg 811)
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Spectral Display of Turbulence
In this case, the absence of the spectral window is indicative of turbulence
resulting from a renal artery stenosis.
Fig. 38: (Pg 812)
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Relating Pressure Characteristics with
Spectral Characteristics
Parabolic velocity
profile from slowly
varying profiles
Graphical
representation of rapid
acceleration
Fig. 39: (Pg 813)
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Resulting “flattened”
velocity profile
Arterial Signal Components
The normal lower extremity
arterial signal is multi-phasic
with a rapid, antegrade
acceleration during systole
followed by one or more
diastolic components
a: rapid acceleration
a
b: short flow reversal caused
by high resistance of
distal bed
c
b
Fig. 42: (Pg 815)
c: diastolic forward flow
component.
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Doppler Indices
R esistive I ndex:
A-B

Systolic  D iastolic
A
Systolic
P u lsatility In d ex :
A-B

S ysto lic  D ia sto lic
v
m ea n velo city
S ystolic D ia stolic R atio:
A
B
Fig. 43: (Pg 817)
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
Systolic
D iastolic
Bruits in Doppler
Fig. 44: (Pg 818)
Doppler Bruit
Fig. 45: (Pg 819)
Fig. 46: (Pg 819)
Harmonic Bruit
Fluttering Bruit
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Flow Examples
The following slides are taken from the animation CD demonstrating
various flow conditions and states (videos courtesy of Flometrics of
Solana Beach California). It is very beneficial to review the animation
CD for more in depth descriptions.
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Stent Entrance (Animation)
(Pg 820 A)
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Stent Exit (Animation)
(Pg 820 B)
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Blood Reservoir (Side View)
(Animation)
(Pg 820 C)
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Blood Reservoir (Top View)
(Animation)
(Pg 820 D)
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Carotid Bifurcation Flow (Animation)
(Pg 821 A)
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Flow in an Aneurysm (Animation)
(Pg 821 B)
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