Quantitative Doppler and Hemodynamics

Tzong Huei Chen

Andrew Maslow

Albert C. Perrino Jr.

When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind.

—Lord Kelvin

HEMODYNAMICS IS THE STUDY OF blood flow and its associated forces. The objective of this chapter is to describe the use of Doppler echocardiography for the quantitative assessment of hemodynamics. Although two-dimensional (2D) echocardiography displays cardiac dimensions and motion, it does not readily assess cardiac blood flow and pressures. In contrast, Doppler echocardiography provides excellent assessments of hemodynamics that compare favorably with more invasive measurements. Quantitative Doppler assessments of blood flow, chamber pressures, valvular disease, pulmonary vascular resistance (PVR), ventricular function (systolic and diastolic), and anatomic defects illustrate the power of this technique.

The accuracy of the Doppler evaluation depends on the ability to minimize interference from neighboring blood flows and aligning the ultrasound beam near parallel to the blood flow of interest. Traditionally, transthoracic echocardiography was a superior approach because it offered multiple windows and angles from which blood flow could be interrogated. The introduction of multiplane transesophageal echocardiography (TEE) has increased the number of imaging windows and angles from which the heart can be evaluated with TEE and has greatly facilitated accurate hemodynamic evaluation.

VOLUMETRIC FLOW CALCULATIONS

Doppler Measurements of Stroke Volume and Cardiac Output

Principles

In many clinical instances, knowledge of the volumetric flow rate is desired. Cardiac output (CO) and stroke volume (SV) are familiar examples. It is important not to confuse blood flow velocity, which is the speed at which blood flows (expressed in centimeters per second), with volumetric flow rate, which assesses the amount of blood that flows (expressed in cubic centimeters per second). The volumetric flow rate (Q) at any point in time equals the blood flow velocity (v) times the cross-sectional area (CSA) of the conduit.

Q = v × CSA

To determine the volumetric flow with echocardiography, a Doppler measurement of the instantaneous blood flow velocities is combined with a 2D measurement of the CSA.

In the clinical setting, the volume of blood ejected during each cardiac cycle, known as the SV, is an important parameter of cardiac performance. To calculate the SV, the instantaneous velocities during systole are traced from the spectral display, and the internal software package of the echocardiographic system calculates the time-velocity integral (TVI), which is expressed in centimeters (Fig. 6.1). Conceptually, the TVI represents the cumulative distance, commonly referred to as the stroke distance, that the red cells have traveled during the systolic ejection phase. When the stroke distance is multiplied by the CSA (in square centimeters) of the conduit (e.g., aorta, mitral valve [MV], pulmonary artery [PA]) through which the blood has traveled, the SV (in cubic centimeters) is obtained (1,2,3,4,5,6,7). CO, which expresses volumetric flow in cubic centimeters per minute, is estimated from the product of the SV and the heart rate (HR).

Echocardiographic Technique for Doppler Measurements of Stroke Volume

The SV and CO are best measured with TEE at the left ventricular outflow tract (LVOT) or aortic valve (AoV) (1,2,3,4,5,6,7). These locations offer several advantages to the clinical echocardiographer. First, the entire ejected SV
traverses these structures, whereas it does not in more distant vessels, allowing the total SV to be calculated. Second, Doppler interrogation typically assesses blood flow from only a small fraction of the total CSA of the vessel, and therefore SV calculations assume that the measured velocity reflects the mean flow velocity throughout the cross-section of the vessel. This assumption is most accurate when blood flow is laminar and has the same velocity across the entire vessel, a situation known as a blunt or flat flow profile (Fig. 6.2). Because blood accelerates along the truncated LVOT during systole, the velocity profile has a blunt, uniform pattern rather than the parabolic pattern seen in the ascending aorta or PA. Consequently, the LVOT and AoV are attractive because the risk for sampling blood velocities that are not reflective of the average blood flow velocity is reduced. Third, the LVOT and ascending aorta are more circular and the CSA changes less during the cardiac cycle. Multiplane TEE offers excellent windows at these sites for both Doppler blood flow measurements and 2D or three-dimensional (3D) echocardiographic measurements of the CSA. Several clinical studies have confirmed that the CO measurements obtained by TEE compare favorably with those obtained by thermodilution (1,2,3,5,6,7).

FIGURE 6.1 Determination of stroke volume. Volumetric flow can be determined from a combination of area and velocity measurements. In this example, flow through the ascending aorta is used to determine the stroke volume. Integrating the Doppler-derived flow velocities over time (known as the time-velocity integral) during a single cardiac cycle calculates the stroke distance. The cross-sectional area measurement is obtained with two-dimensional echocardiography. The product of these two measurements, conceptualized as a cylinder, is the stroke volume. CSA, cross-sectional area; AoV, aortic valve.

LVOT or transaortic valvular flows are most reliably obtained from the transgastric (TG) long-axis and the deep TG long-axis views because the blood flow is aligned nearly parallel to the ultrasound beam. It is critical to interrogate blood flow carefully through minor alterations in the probe position and multiplane angle to obtain the optimal Doppler spectral signal. The maximal velocity profile with a dense spectral signal is sought.

Calculation of the Left Ventricular Outflow Tract Stroke Volume

The TVI of the LVOT (TVI_LVOT) is measured by positioning the pulsed-wave (PW) Doppler sample volume in the LVOT immediately proximal (or subvalvular) to the AoV (TG long-axis and deep TG longaxis views) (Fig. 6.3).

FIGURE 6.2 Common flow profiles. A: The acceleration of the blood flow as it enters the truncated left ventricular outflow tract leads to a “flat” profile in which velocities are uniform. As blood travels in the ascending aorta, the effects of wall friction and a curved conduit result in an asymmetric and parabolic flow profile. B: When blood is forced through a narrow opening, laminar flow is replaced with turbulence. In this illustration, aortic stenosis has created a narrow, highvelocity jet encased by turbulent flow.

The CSA for the LVOT is most easily obtained from the mid-esophageal (ME) LVOT view. The CSA is then calculated from a measurement of the LVOT diameter as follows:

CSA_LVOT = π(diameter/2)²
The CSA for the LVOT can also be measured using 3D echocardiography. After acquiring a full-volume dataset, 3D analytical software is used to obtain a cross-section through the short axis of the LVOT and directly measure its area. This method may be more accurate because of the elliptical shape of the LVOT and because it enables measurement of area and not diameter; that is, potential error is not increased by an order of magnitude during the conversion from diameter to area.
Finally, the SV and CO are calculated using the following equations:

SV_LVOT = TVI_LVOT × CSA_LVOT

CO_LVOT = SV_LVOT × HR = TVI_LVOT × CSA_LVOT × HR

Calculation of the Transaortic Valve Stroke Volume

The TVI across the AoV is measured by directing the continuous wave (CW) Doppler beam through the AoV orifice from the TG long-axis or deep TG long-axis view (Fig. 6.4).
The CSA of the valve is best estimated by planimetry of the equilateral triangle-shaped orifice observed in midsystole (6). The AoV is viewed in cross-section from the ME AoV short-axis window, and frame-by-frame review is used to capture the valve in midsystole. Planimetry of the triangle-shaped orifice yields the effective CSA. This measurement can be performed using both 2D and 3D echocardiography.
Finally, the SV and CO are calculated using the following equations:

SV_AoV = TVI_AoV × CSA_AoV

CO_AoV = SV_AoV × HR = TVI_AoV × CSA_AoV × HR

Calculation of the Stroke Volume of the Right Side of the Heart

Alternatively, right-sided flows and diameters can be analyzed from the main PA or the right ventricular outflow tract (RVOT). PW or CW Doppler analysis proceeds after the main PA is imaged from high-esophageal
windows at the level of the superior mediastinal vessels (Fig. 6.5) or the RVOT is imaged from TG windows at 110- to 150° rotation of the transducer and rightward turn of the TEE probe. In all cases, the maximal velocity profile is sought. Flow across the MV is measured by placing the sample volume at the level of the mitral annulus to obtain the transmitral TVI, which is then multiplied by the area of the MV annulus. Compared with the diameters of the LVOT and ascending aorta, the diameters of the main PA and MV fluctuate more during the cardiac cycle, and these measurements are less reliable than those from the LVOT and AoV (4). In addition, the MV orifice is not circular, and its size changes during diastole.

FIGURE 6.3 The CO can be calculated using the cross-sectional area of the left ventricular outflow tract (CSA_LVOT) and the time-velocity integral of blood flow through the LVOT (TVI_LVOT) during systole. CSA_LVOT can be calculated from a measurement of the LVOT diameter (2.2 cm) in the mid-esophageal aortic valve long-axis view using the equation π(D_LVOT/2)², assuming a circular orifice and can also be measured directly using three-dimensional echocardiography (4.0 cm²). Multiplying the CSA by TVI_LVOT (21 cm) measured using pulsed-wave (PW) Doppler in the deep transgastric left ventricular outflow window yields a stroke volume of 80 or 84 mL depending on if the CSA is determined using twoor three-dimensional echocardiography, while the CO, determined by multiplying stroke volume by the heart rate of 81 bpm, is 6.4 L/min or 6.7 L/min, respectively. LVOT, left ventricular outflow tract; LA, left atrium; LV, left ventricle; RV, right ventricle; Ao, ascending aorta; CO, cardiac output; D, diameter; CSA, cross-sectional area; TVI, time-velocity integral; HR, heart rate; SV, stroke volume.

Regurgitant Volume

Regurgitant volume is the quantity of blood that flows back through a regurgitant lesion in a single cardiac cycle. The total SV traversing a regurgitant valve during systole is greater than that in a normal valve. For a regurgitant valve, the total SV equals the regurgitant volume plus the SV delivered to the peripheral circulation. The regurgitant volume can be calculated as the difference between the total forward flow through the regurgitant valve and the total forward flow through a reference valve.

Regurgitant volume = forward flow through regurgitant valve – forward flow through reference valve

FIGURE 6.4 The CO can be calculated using the cross-sectional area of the AoV orifice during maximum opening (CSA_AoV) and the time-velocity integral of blood flow across the aortic valve (TVI_AoV) during systole. CSA_AoV can be calculated using planimetry in the mid-esophageal aortic valve short-axis view with two-dimensional echocardiography (3.2 cm²) or using three-dimensional echocardiography (3.1 cm²). Multiplying the CSA by the time-velocity integral of blood flow across the AoV (TVI_AoV = 25 cm) measured using continuous wave (CW) Doppler in the deep transgastric left ventricular outflow window yields a stroke volume of 78 or 80 mL depending on if the CSA is determined using two- or three-dimensional echocardiography, while the CO, determined by multiplying stroke volume by the heart rate of 80 bpm, is 6.4 L/min or 6.2 L/min, respectively. AoV, aortic valve; LA, left atrium; LV, left ventricle; RV, right ventricle; Ao, ascending aorta; CO, cardiac output; CSA, cross-sectional area; TVI, time-velocity integral; HR, heart rate; SV, stroke volume.

In the case of mitral regurgitation (MR) (in the absence of significant AoV disease), the SV across the AoV can be used as the true SV.

Regurgitant volume_MV = forward flow through MV – flow through AoV

RV_MV (mL) = SV_MV – SV_AoV

However, there is a significant potential for error in the mitral flow measurements because the MV orifice is not circular (4), and its diameter changes during the cardiac cycle.

Similarly, the aortic regurgitant volume can be calculated as follows:

Regurgitant volume_AV = forward flow through AoV – flow through MV

The regurgitant fraction is simply the ratio of the regurgitant volume to the total SV through the diseased valve and is typically expressed as a percentage.

Regurgitant fraction (%) = regurgitant volume/forward flow

Alternative techniques to measure the severity of valvular regurgitation are discussed in Chapters 8 and 11.

FIGURE 6.5 Calculation of cardiac output from the MPA can be performed from the mid-esophageal view seen in the right panel from which the MPA diameter (2.8 cm) can be measured. The PW Doppler beam is aligned with blood flow in the pulmonary artery, and at the same site where the MPA diameter is measured. The MPA time-velocity integral (TVI) is assessed using PW Doppler. The cross-sectional area of the pulmonary artery (π(D_MPA/2)²) is calculated to be 6.2 cm² and manual tracing of the spectral display of pulmonary blood velocities shows a TVI of 10.5 cm. When multiplied by the cross-sectional area, the stroke volume is calculated to be 64.6 mL/beat and when multiplied by the heart rate, the CO is calculated to be 5.3 L/min. MPA, main pulmonary artery; Ao, ascending aorta; CO, cardiac output; D, diameter; CSA, crosssectional area; TVI, time-velocity integral; HR, heart rate; SV, stroke volume.

Intracardiac Shunts

The ratio of pulmonic to systemic SV, Q_p/Q_s, is important in assessing the severity of shunts and in guiding treatment. Intracardiac shunts are assessed by calculating the SV (8). By measuring the left-sided (LVOT or AoV) and right-sided (PA or RVOT) SVs, one can determine Q_p/Q_s:

Q_p/Q_s = SV_{Right heart (e.g., PA, RVOT)}/SV_{Left heart (e.g., LVOT, AoV)}

These measurements are often combined with 2D and color Doppler data to provide a complete assessment of congenital lesions.

Valve Area: The Continuity Equation

The principle of conservation of mass is the basis of the continuity equation, which is commonly used to measure the AoV area (Fig. 6.6B) (9). The continuity equation simply states that the volume of blood passing through one site (e.g., the LVOT) is equal to the mass or volume of blood passing through another site (e.g., the AoV). Of course, there must be no intervening channels for this principle to apply. By using the principle of volumetric flow, discussed earlier, the continuity equation can be applied clinically.

Volumetric flow₁ = Volumetric flow₂

CSA₁ × TVI₁ = CSA₂ × TVI₂

CSA₁ = CSA₂ × TVI₂/TVI₁

To calculate the area of the AoV:

Area_AoV = Area_LVOT × (v_LVOT/v_AoV)

Area_AoV = π(D_LVOT/2)² × (v_LVOT/v_AoV)

where D_LVOT is the diameter of the LVOT and v_LVOT is the velocity in the LVOT.

FIGURE 6.6 Calculating the pressure gradient and valve area. A: Bernoulli equation. The simplified Bernoulli equation states that the pressure drop (P₂ – P₁ = Δ4P) across a stenotic orifice is four times the square of the velocity of the high-velocity jet. P₁, blood pressure proximal to stenosis; v₁, flow velocity proximal to stenosis; P₂, blood pressure distal to stenosis; v₂, flow velocity through stenosis. B: Continuity equation. The continuity equation is often described as the principle of “what goes in must come out.” Accordingly, flow proximal to the stenosis (A₁ × v₁) should equal flow through the stenosis (A₂ × v₂). A₁, cross-sectional area proximal to stenosis; v₁, flow velocity proximal to stenosis; A₂, cross-sectional area of stenosis; v₂, flow velocity through stenosis.

TEE assessments of LVOT and aortic flows and of LVOT diameter were described earlier in the section “Doppler Measurements of Stroke Volume and Cardiac Output.” The continuity equation is the basis for assessments based on the proximal isovelocity surface area method (10,11,12), which is described in detail in Chapter 9. The velocities of the LVOT and the AoV can be obtained separately using PW and CW Doppler, respectively, or simultaneously during CW Doppler, this latter being referred to as a double-envelope technique. Whether obtained separately or simultaneously, the basis of the equation is the ratio of the two velocities (v_LVOT/v_AoV). A velocity ratio <0.25 is consistent with severe AoV stenosis.

INTRACARDIAC PRESSURES AND PRESSURE GRADIENTS: THE BERNOULLI EQUATION

Pressure gradients are used to estimate intracavitary pressures and assess conditions such as valvular disease (e.g., aortic stenosis), septal defects, outflow tract abnormalities (e.g., LVOT obstruction), and major vessel pathology (e.g., coarctation). As blood flows across a narrowed or stenotic orifice, blood flow velocity increases. The increase in velocity is related to the degree of narrowing. The Bernoulli equation describes
the relation between the increases in blood flow velocity and the pressure gradient across the narrowed orifice (13):

ΔP = 1/2ρ		(dv/dt)dx + R(v)
Convection	Flow	Viscous
acceleration	acceleration	friction

where P is the pressure gradient across the area of interest (mm Hg), ρ is the density of blood (1.06 × 10³ kg/m³), v₁ is the peak velocity of blood flow proximal to the area of interest (m/s), and v₂ is the peak velocity of blood flow across the area of interest (m/s).

In clinical practice, the Bernoulli equation is simplified by ignoring the effects of flow acceleration, viscous friction, and the velocity proximal to the area of interest (v₁) because:

Peak flows are of interest in clinical measurements. During peak flow, the flow acceleration is virtually nonexistent and thus can be ignored.
Viscous friction contributes significantly only in discrete orifices with an area of less than 0.25 cm². Blood flow is thought to be constant for orifices with an area greater than this, so that viscous friction is also eliminated in the Bernoulli calculation.
For clinically significant lesions, v₂ is substantially greater than v₁, such that is approximated by just .

The elimination of these factors yields the simplified Bernoulli equation:

Therefore, a pressure gradient is obtained in clinical echocardiography by the straightforward process of measuring the peak velocity of blood flow across the lesion of interest (Fig. 6.6A). However, when v₁ is greater than 1.4 m/s then the Modified Bernoulli equation is considered to account for the higher proximal velocity:

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