Volume II Companion Presentation Frank R. Miele Pegasus Lectures, Inc. Ultrasound Physics & Instrumentation 4th Edition Volume II Companion Presentation Frank R. Miele Pegasus Lectures, Inc. Pegasus Lectures, Inc.

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Volume II Outline Pegasus Lectures, Inc. 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 Pegasus Lectures, Inc.

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. Pegasus Lectures, Inc.

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. P Q S T R Fig. 1: (Pg 776) Pegasus Lectures, Inc.

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. Pegasus Lectures, Inc.

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. (A 25% increase in pressure at 100 mmHg results in a 50% increase in volume.) Fig. 2: (Pg 778) (Redrawn from Berne, R.M. and Levy, M.N., Cardiovascular Physiology) Pegasus Lectures, Inc.

Pressure Volume Relationship (Compliant vs. Non-compliant Vessel) 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. Compliant Non-Compliant (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) Pegasus Lectures, Inc.

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. Pegasus Lectures, Inc.

Series Resistance Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

Parallel Resistance Pegasus Lectures, Inc. 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. Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Parallel Series Network Applying the rules we learned for series and parallel combinations, the effective resistance for the following network is calculated as: To view specific calculation refer to page 783 Fig. 9: (Pg 783) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

“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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Velocity Profiles Pegasus Lectures, Inc. The following diagram demonstrates the boundary effects on the flow profile through varying vessel sizes. Fig. 13: (Pg 787) Pegasus Lectures, Inc.

The Cardiovascular System This figure shows a simplified model of the cardiovascular system, demonstrating the key functions required. Fig. 14: (Pg 789) Pegasus Lectures, Inc.

Arterial Vessel Sizes Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

Complex Resistance Network of the Arterial System 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. Fig. 16: (Pg 791) Pegasus Lectures, Inc.

Relative Resistances Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Pressure Across the Arterial System Important Characteristics: Slight increase in pulse pressure from aorta to small arteries Pulsatility is damped at level of arterioles Rapid pressure drop occurs at arterioles Significant pressure drop occurs across capillaries Pressures in venous side are very low and relatively “steady-state” Fig. 20: (Pg 795) Pegasus Lectures, Inc.

The Venous System Pegasus Lectures, Inc. 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. Pegasus Lectures, Inc.

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? Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Calf Muscle Pump Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

Intravascular Pressure Intravascular Pressure 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 (higher) Tissue Pressure (lower) Intravascular Pressure (lower) Tissue Pressure (higher) Fig. 23: (Pg 801) Fig. 24: (Pg 801) Pegasus Lectures, Inc.

Sub-critical Disease Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Critical Stenoses Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

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. Pegasus Lectures, Inc.

Systolic Acceleration and Pressure Step 1: Relate pressure with volume change. Fig. 33: (Pg 809) Step 2: Relate volume change with velocity change. Fig. 34: (Pg 809) Pegasus Lectures, Inc.

Measuring Acceleration Fig. 35: (Pg 810) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Spectral Windows Pegasus Lectures, Inc. 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) Pegasus Lectures, Inc.

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) Pegasus Lectures, Inc.

Relating Pressure Characteristics with Spectral Characteristics Parabolic velocity profile from slowly varying profiles Graphical representation of rapid acceleration Resulting “flattened” velocity profile Slow Deceleration Acceleration Fig. 39: (Pg 813) Pegasus Lectures, Inc.

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 c b a: rapid acceleration b: short flow reversal caused by high resistance of distal bed c: diastolic forward flow component. Fig. 42: (Pg 815) Pegasus Lectures, Inc.

Doppler Indices Fig. 43: (Pg 817) Pegasus Lectures, Inc.

Bruits in Doppler Pegasus Lectures, Inc. Fig. 44: (Pg 818) Doppler Bruit Harmonic Bruit Fluttering Bruit Pegasus Lectures, Inc.

Flow Examples Pegasus Lectures, Inc. 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. Pegasus Lectures, Inc.

Stent Entrance (Animation) (Pg 820 A) Pegasus Lectures, Inc.

Stent Exit (Animation) (Pg 820 B) Pegasus Lectures, Inc.

Blood Reservoir (Side View) (Animation) (Pg 820 C) Pegasus Lectures, Inc.

Blood Reservoir (Top View) (Animation) (Pg 820 D) Pegasus Lectures, Inc.

Carotid Bifurcation Flow (Animation) (Pg 821 A) Pegasus Lectures, Inc.

Flow in an Aneurysm (Animation) (Pg 821 B) Pegasus Lectures, Inc.

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