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Two-dimensional and Doppler imaging can be used to obtain comprehensive hemodynamic data, but it should be remembered that these data, while providing a more objective measure of cardiac performance, should always be interpreted within the context of the patient's clinical condition.
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In circulation, the blood flow and velocity are phasic, ie, change throughout the cardiac cycle. A Doppler spectrum of the velocity of blood flowing through a conduit will yield a curve during systole that has velocity (cm/s) on the y-axis and time (s) on the x-axis. When this curve is integrated, it yields a velocity-time integral (VTI) in units of centimeters (velocity [cm/s] time [s] = VTI [cm]). The VTI is a manifestation of the stroke distance (ie, the distance the stroke volume travels over time during a single systolic ejection period). The product of VTI (cm) and cross-sectional area (CSA; cm2) will yield stroke volume (SV; cm3):
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Stroke Volume (SV) = Stroke Distance (VTI) × Cross-Sectional Area (CSA)
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Cardiac output can then be calculated as:
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Cardiac Output = Stroke Volume × Heart Rate
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Cardiac index can be calculated as:
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Cardiac Index = Cardiac Output/Body Surface Area
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The calculation of SV through a conduit assumes laminar flow, a flat flow profile in which velocities are uniform, constant diameter of the conduit, velocity measured at the same point as the diameter, velocity measured represents the mean velocity during the entire ejection period, and accurate measurement of the conduit diameter (a common source of error). Stroke volume can be measured at any conduit in the heart; however, the preferred site for such calculation is the left ventricular outflow tract (LVOT) (Figure 4–6). Other intracardiac sites such as the pulmonic and mitral valves have a dynamic conduit diameter during the cardiac cycle, and at times the velocity profile is parabolic, where velocities vary across the parabola.
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In echocardiography, it is assumed that a conduit or orifice, such as the LVOT, is circular. The CSA is calculated from the diameter measurements by using the equation for area of a circle:
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The diameter of the LVOT is calculated from the midesophageal long-axis window, and LVOT VTI is calculated from the deep transgastric window (Figure 4–7).
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Measurement of Intracardiac Shunts
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The ratio of pulmonary (Qp) to systemic (Qs) flow is a useful parameter to assess the magnitude of shunting, with a ratio greater than 1.5 generally considered significant. Qp/Qs calculation requires calculation of the stroke volume at the right ventricular outflow tract (RVOT) and the left ventricular outflow tract (LVOT). Thus, for atrial or ventricular shunts:
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Qp/Qs = (CSARVOT × TVIRVOT)/(CSALVOT × TVILVOT)
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For shunts occurring through a patent ductus arteriosus:
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Qp/Qs = (CSALVOT × TVILVOT)/(CSARVOT × TVIRVOT)
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Assuming a constant flow of fluid through a conduit at a certain velocity, if there is a stenosis in the conduit, the velocity of fluid will increase at the site of stenosis to conserve flow. This concept is known as the continuity of flow and sometimes as the conservation of flow:
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FlowLarger Conduit = FlowStenosis
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As described above, constant flow (cm3/s) in a conduit is the product of cross-sectional area (CSA) of the conduit (cm2) and the average velocity of the fluid (cm/s). Thus,
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CSALarger Conduit × VelocityLarger Conduit = CSAStenosis × VelocityStenosis
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When three variables are known, the fourth is easily determined with this equation, commonly known as the continuity equation.
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In aortic stenosis, flow across the aortic valve is equal to the flow across the LVOT (Figure 4–8) and in order to determine the stenotic area, the continuity equation can be reordered as:
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Mitral valve area can also be similarly calculated, but it must be remembered that the transmitral flow must be the same as left ventricular SV, a condition that is met only in the absence of ventricular shunts and mitral and aortic regurgitation.
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The principles of flow conservation can also be applied to assess regurgitant volumes and fractions. For this calculation, one valve is considered the “reference valve,” but it should be remembered that the assumption that the mitral valve orifice is circular may not always be valid. In the absence of aortic stenosis or regurgitation (see Chapters 7 and 9), SVLVOT can be substituted for SVAortic Valve
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Velocity Acceleration
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When molecules move within a large cavity toward a small orifice, as in stenotic and regurgitant lesions, the velocity increases over a large area and the velocity profile is hemispherical, with the cavity of the hemisphere facing the orifice. The velocity over the surface of the hemisphere is the same (isovelocity), and because it is proximal to the orifice, the surface area is known as proximal isovelocity surface area (PISA). The product of the (iso)velocity (cm/s) and the surface area of the hemispherical velocity profile (cm2) yields the flow (cm3).
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If the flow approaching the orifice is examined with color-flow Doppler, with the color scale set so that the accelerated velocity exceeds the Nyquist limit, aliasing will take place and a semicircular shell of a contrasting color will appear to cap the orifice (Figure 4–9). To obtain this shell, the baseline for the color scale should be shifted in the direction of the jet of interest (eg, towards the transesophageal echocardiography [TEE] transducer for mitral regurgitation). The semicircular shell is in fact a hemisphere in three dimensions, and its surface area can be calculated as that of a sphere:
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The velocity at the surface of the hemispherical velocity profile is the Nyquist limit (aliasing velocity) on the color-flow Doppler scale. Thus,
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By the principle of conservation of flow, the flow through an orifice is the same as the flow where the PISA is located:
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In the setting of stenosis, the valve area can be calculated by reordering the equation as:
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For a regurgitant lesion, the calculation of the effective regurgitant orifice area (EROA) employs the peak velocity of the regurgitant jet so that:
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The PISA radius should be measured at the same time as the peak velocity of the jet, and this can be more readily accomplished using color M-mode imaging. PISA has been validated for mitral valve assessment, but is not commonly applied to TEE assessment of the aortic valve. PISA is performed in diastole and on the left atrial side for assessment of mitral stenosis severity, and during systole and on the left ventricular side for calculation of the EROA (Figure 4–10). Summarizing, the assessment of the mitral valve:
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True hemispheric shells require a flat valve surface area, and because the mitral valve surface area is not flat, an angle correction term is sometimes used to increase the accuracy of volumetric flow assessment:
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where α is the angle subtended by the mitral leaflets (see Figure 4–9). However, this technique of angle correction is limited by the inability to readily measure α with existing ultrasound system software.
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Measurement of Pressure
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A Dutch-Swiss mathematician, Daniel Bernoulli, in 1798 proposed the principle that the total energy in a steady flowing fluid column remains constant, such that when the velocity (kinetic energy) increases, it is accompanied by a simultaneous decrease in pressure (potential energy). This principle helped to explain the development of a pressure gradient across a narrowing, ie, there is an increase in distal velocity with a simultaneous drop in pressure (Figure 4–13). The Bernoulli equation can be applied to compressible and noncompressible fluids or even gases, and is expressed as:
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- P1 – P2 = Pressure difference between the two locations
- ρ = Mass density of blood (gm/cm3)
- V1 = Velocity proximal to stenosis (m/s)
- V2 = Velocity at vena contracta (m/s)
- dv/dt = Acceleration
- s = Distance over which flow accelerates
- R = Viscous resistance
- μ = Viscosity
- v = Velocity of blood flow (m/s)
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During routine clinical echocardiography, acceleration at peak velocities (dv/dt) is zero and viscous acceleration is negligible, and hence both terms can be ignored. One-half of the mass density of blood (1/2ρ) is equal to 4 (after correction for units of measure), hence the Bernoulli equation can be modified as:
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The proximal velocity (V1) is also generally very low and can often (but not always) be ignored, thus further simplifying the equation:
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Limitations of the Bernoulli Equation
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Significant error can be introduced into the calculation in specific situations when the assumptions inherent in simplifying the equation are violated. For example, flow acceleration (inertial force) can become significant with some prosthetic valves, where a greater than normal force is required to open the valve. Similarly, the presence of viscous friction is negligible with laminar flow, but should be accounted for in lesions with tubular obstructions greater than 4 cm in length and orifices less than 0.1 cm2. The simplified Bernoulli equation also ignores the proximal velocity (V1), but in conditions such as high cardiac output states, sub-aortic obstruction, significant aortic regurgitation, and intracardiac shunts, the proximal velocity (V1) can be significant (>1.5 m/s), leading to an overestimation of the pressure gradient if the modified (rather than the simplified) Bernoulli equation is not applied. Finally, alterations in the blood viscosity, such as an increase in hematocrit to 60%, may lead to an underestimation of gradients, as 1/2 ρ may be higher from an increase in the mass density of blood.
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Applications of the Bernoulli Equation
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Peak and Mean Gradients The Bernoulli equation is most commonly used to determine the peak instantaneous gradients across stenotic valves. The peak instantaneous gradient is measured with continuous-wave Doppler, and most echocardiography machines can automatically calculate the peak gradient by simply positioning the cursor at the highest point of the velocity envelope (Figure 4–14).
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Peak Instantaneous Gradient = 4 × (VPeak)2
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Mean pressure gradients are calculated as the average of multiple successive peak instantaneous peak gradients measured over time during the particular ejection phase (see Figure 4–14).
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Intracardiac Pressure Measurements Estimation of intracardiac chambers is one of the most common forms of application of the modified Bernoulli equation. This method requires the presence of a regurgitant jet or the presence of a shunt jet. The estimation of intracardiac pressures is performed in the following steps (Figure 4–15)2:
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Utilization of continuous-wave Doppler to measure the peak velocity of the jet
Conversion of peak velocity into pressure gradient with the Bernoulli equation
Estimation of pressure in the origination chamber (POC)
Estimation of pressure in the receiving chamber (PRC)
Calculation of pressures (Figure 4–15):
POC = 4v2 + PRC
PRC = POC − 4v2
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Using this methodology, numerous intracardiac pressures can be measured depending upon the presence or absence of regurgitation jets:
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Right Heart Pressures
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Right ventricular systolic pressure (RVSP) using tricuspid regurgitant (TR) jet
RVSP = 4 (VPeak TR)2 + Right Atrial Pressure (CVP)
In the absence of pulmonic stenosis or right ventricular outflow tract obstruction, RVSP is equal to pulmonary artery systolic pressure.
Right ventricular systolic pressure in the presence of a ventricular septal defect (VSD)
RVSP = Left Ventricular Systolic Pressure − 4 (VPeak VSD)2
Pulmonary artery mean pressures (PAMP) using pulmonary regurgitant (PR) jet
PAMP = 4 (VPeak PR)2 + Right Atrial Pressure (CVP)
Pulmonary artery diastolic pressures (PADP) using pulmonary regurgitant (PR) jet
PADP = 4 (VEnd-Diastolic PR)2 + Right Atrial Pressure (CVP)
Pulmonary artery systolic pressure (PASP) in the presence of a patent ductus arteriosus (PDA)
PASP = Systolic Blood Pressure − 4 (VPeak PDA)2
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Left atrial pressure (LAP) from a mitral regurgitant (MR) jet
LAP = Left Ventricular Systolic Pressure − 4 (VPeak MR)2
In the absence of aortic stenosis or left ventricular outflow tract obstruction, systolic blood pressure can be substituted for left ventricular systolic pressure.
Left atrial pressure in the presence of a patent foramen ovale (PFO)
LAP = 4 (VPeak PFO)2 + Right Atrial Pressure (CVP)
Left ventricular end-diastolic pressure (LVEDP) from an aortic regurgitant (AR) jet
LVEDP = Diastolic Blood Pressure − 4 (VEnd-Diastolic AR)2
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Measurement of Resistance
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Systemic vascular resistance (SVR) and pulmonary vascular resistance (PVR) are typically calculated from invasive hemodynamic measurements; however, Doppler echocardiography can provide a noninvasive assessment of vascular resistance. Units for measuring vascular resistance are dyne·s·cm−5, pascal seconds per cubic meter (Pa·s/m3), or mm Hg/L/min, which is referred to as a Wood unit (WU). The WU value is multiplied by 8 to convert to Pa·s/m3 or by 80 to obtain the value in dys·n·cm−5. Normal SVR values range from 10 to 14 WU, while a normal PVR is 1 WU.
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The ratio of peak mitral regurgitant velocity to the time-velocity integral of the LVOT flow (VMR/ TVILVOT) measured by Doppler echocardiography has been shown by Abbas et al7 to correlate positively with SVR measurements (WU) obtained invasively (r = 0.84, 95% CI = 0.7 to 0.92). Furthermore, a calculated ratio greater than 0.27 identified patients with elevated SVR (>14 WU) with 70% sensitivity and 77% specificity, whereas a ratio less than 0.2 had a 92% sensitivity and 88% specificity to identify SVR less than 10 WU.
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Similarly, Doppler echocardiography has been shown to provide a clinically reliable noninvasive method to determine PVR8:
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where VTR = peak tricuspid regurgitant velocity and TVIRVOT = right ventricular outflow tract time-velocity integral. Furthermore, the ratio of VTR/TVIRVOT compared favorably to invasive PVR measurements (r = 0.93, 95% CI = 0.87 to 0.96), and a ratio greater than 0.175 had a sensitivity of 77% and a specificity of 81% to determine PVR greater than 2 WU.8 Scapellato et al9 have also described a method of estimating PVR using the preejection period (PEP), acceleration time (AcT), and total systolic time (TT) derived from pulmonary systolic flow:
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PVR = −0.156 + {1.154 × [(PEP/AcT)/TT)]}
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Although these methods have the advantage of being simple and easily applicable, they may not be as reliable in patients with pulmonary arterial hypertension (PAH). More recently, Haddad et al10 reported that the ratio of systolic pulmonary artery pressure/(HR × TVIRVOT) correlated very well with invasive measurements of PVR indexed to body surface area (PVRI; r = 0.86; 95% CI = 0.76 to 0.92). A cutoff value of 0.076 provided a sensitivity of 86% and specificity of 82% to determine PVRI greater than 15 WU/m2. A cutoff value of 0.057 increased sensitivity to 97% but decreased specificity to 65%. Similarly, Kouzu et al11 showed that the ratio of the peak tricuspid regurgitant pressure gradient over the time–velocity integral of right ventricular outflow (PGTR/TVIRVOT) provided a reliable estimation of PVR over a wide range of PAH values and from various causes, including intracardiac shunts. In addition, a PGTR/TVIRVOT ratio greater than 7.6 was suggestive of poor prognosis for patients with PAH without an intracardiac shunt.
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Measurement of Contractility
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A relatively load-independent index of left ventricular systolic performance is peak dP/dt, or the maximum rate of rise of left ventricular pressure during systole. The echocardiographic method for deriving this parameter is based on the continuous-wave Doppler recording of the mitral regurgitant spectrum, wherein the time for velocity to rise from 1 m/s to 3 m/s is measured, and the pressure change from 1 m/s to 3 m/s is calculated by the Bernoulli equation as 32 mm Hg (4 × 32 − 4 × 12). dP/dt is then calculated with the following equation:
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Left Ventricular dP/dt = 32 × 1000/dt in Milliseconds
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Normal values for this parameter are 1610 ± 290 mm Hg/s. Although relatively afterload dependent, dP/dt is preload dependent.
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Right ventricular dP/dt may be calculated by using the continuous-wave tricuspid regurgitant spectrum in a manner analogous to the approach used for left ventricular dP/dt. Because even hypertensive right ventricular pressures are typically lower than those of the left ventricle, the convention is to make the calculation based on the rise in velocity between 1 and 2 m/s. The pressure change from 1 m/s to 2 m/s is calculated by the Bernoulli equation as 12 mm Hg (4 × 22 − 4 × 12). dP/dt is then calculated as:
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Right Ventricular dP/dt = 12 × 1000/dt in Milliseconds
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A value greater than 1000 mm Hg/s is generally associated with normal right ventricular function.