Blood flow profiles

Flow is calculated as the product of the average velocity and cross‐sectional area (CSA) of the vessel. If flow was constant, laminar, and homogenous across the vessel this would be relatively easy to do. However, in the cardiovascular system, flow is pulsatile and the flow velocity varies across the cross‐section of the vessel or orifice. The distribution of flow velocities across the vessel is called the flow velocity profile. In a straight, rigid tube with steady laminar flow, flow velocities are highest in the center and lowest in the periphery. This yields a parabolic velocity profile across the vessel with the highest velocities in the center of the spectral Doppler envelope and the lowest velocities at its edges. In contrast, flow entering a tube from a reservoir has a relatively flat velocity profile at the vessel inlet, that is, all velocities are similar across the vessel cross‐sectional area. The flat flow velocity profile at the inlet of the vessel gradually becomes parabolic as flow propagates through the vessel. Because the velocity profile at the vessel inlet is flat, spectral Doppler measurement of the peak velocity at the vessel inlet is more representative of the average velocity. The transition from a flat to a parabolic velocity profile occurs because of the viscous drag between the vessel wall and the adjacent fluid with concomitant acceleration of flow in the center of the vessel. Consequently, when the velocity profile is parabolic, the maximum velocity significantly overestimates the mean velocity, which is the parameter needed to calculate flow. For example, in the branch pulmonary arteries, the flow velocity profile is parabolic and a three‐dimensional assessment would be required to derive the true average velocity for flow calculations [1,2]. Likewise, a small Doppler sample volume that captures local velocities may not represent the average velocity across the entire cross‐sectional area of the vessel if it is placed either in a region of local turbulence or in a region of local high‐velocity laminar flow. One can picture this as a river with fast flow in the center and slow flow at the edges. Sampling the flow in one region will not reflect the average velocity across the entire width of the river. Likewise, sampling flow velocity in a region where the water is turbulent due to rocks does not represent the average velocity of the river across its width. Over the coming years, assessment of blood flow using echocardiography is expected to change rapidly as high frame‐rate speckle tracking imaging noninvasively directly assesses the velocity and direction of flow [4].

Other factors also influence flow profiles. At vascular bifurcations, such as the carotid artery bifurcation [5], the greater central velocity in the carotid artery results in a skewed velocity profile in the internal carotid artery, with greater velocity flow adjacent to the bifurcation. In curved vessels, such as the aortic arch, the flow profile in the curved segment depends on the flow profile at the entrance to the curve. If parabolic, the maximum velocity is shifted toward the outer wall with flow velocity slowing along the inner wall and vortex development or even flow reversal [6] (Video 6.1). In contrast, if the flow profile is flat at the entrance to the curve, centrifugal forces produce higher pressure (lower velocities) at the outer aspect of the curve, and lower pressures (higher velocities) at the inner curvature of the vessel. For example, the flow profile in the ascending aorta is generally flat (velocities are equal across the whole cross‐sectional area), and therefore the flow velocities are generally highest along the inner curvature of the aortic arch.

The Coanda effect

The Coanda effect refers to a flow profile where the tendency of a stream of fluid is to follow a convex surface, rather than a straight line. In the heart, the Coanda effect causes jets to adhere to the chamber or vessel wall and can significantly affect Doppler assessment of valvar regurgitation and shunts. Examples include aortic regurgitation jets that track along the valve cusp or the ventricular septal surface and mitral regurgitation (MR) jets that hug the atrial wall (Figure 6.2, Video 6.2). The Coanda effect is actually a manifestation of the Bernoulli principle, which is described in further detail later. The larger decrease in flow velocity along the inner surface of the jet, away from the vessel wall, increases the pressure relative to the outer surface of the jet where velocities are higher, thereby pushing the jet toward the vessel wall. Because of the Coanda effect, and in general because of eccentric jets, multiple echocardiographic views should be obtained in order to achieve the narrowest insonation angle between the ultrasound beam and direction of flow and hence capture the highest velocity.

Characteristics of flow through a narrow orifice, the vena contracta, and the phenomenon of pressure recovery

When flow approaches a narrowing, the flow streamlines converge to enter the orifice. This pushes the streamlines close together so that the diameter of the jet passing through the orifice is smaller than the size of the anatomical orifice itself (known as the anatomic orifice area (AOA)). The narrowest region of the jet at or immediately after it emerges from the orifice is called the vena contracta. Because the vena contracta is the smallest CSA through which the flow passes it is also known as the effective orifice area (EOA). The flow velocity is highest and pressure lowest at this point. It is the EOA and not the AOA that determines the hemodynamic importance of a narrowing. Therefore, the hemodynamic effect of a stenosis can be significantly greater than would be predicted on the basis of the actual orifice size. The size of the vena contracta is relatively independent of flow rate and driving pressure for a fixed orifice [7]. The vena contracta is measured from color Doppler [8–10], correlates closely with the actual EOA [11] and severity of valve regurgitation [12], and is therefore used to judge the severity of valvar regurgitation. Downstream of the vena contracta, the streamlines begin to diverge at the periphery of the jet, forming a central core of laminar flow that persists for a variable distance (Figure 6.3).

The high‐velocity edges of the central core shear against the stagnant flow around the central jet, creating eddies that gradually engulf the central core and the surrounding area (Figure 6.4). A common error is to assume that aliasing of the color Doppler signal distal to the orifice implies turbulence when in reality it is the turbulent flow of the parajet region creating the aliasing, not high flow velocity. More distally in the vessel, downstream from the stenotic orifice, the phenomenon of pressure recovery becomes important. Let us dwell on this for a moment as pressure recovery impacts Doppler measurements. The Bernoulli equation, which is subsequently discussed, implies that the conversion of pressure to velocity is reversible, and that velocity can be converted to pressure. When blood flows across a narrow orifice, velocity rises and pressure falls, with the lowest pressure associated with the narrowest portion of the jet at the vena contracta. Distal to this point, as the flow stream widens and the flow velocity diminishes, the pressure rises again, a phenomenon known as pressure recovery [13]. In essence, pressure recovery occurs because not all kinetic energy across the stenosis is dissipated as turbulence, and some of the flow becomes laminar again. However, pressure recovery is always incomplete because some energy is lost due to friction along the boundaries of the outflow jet (Figure 6.5). The amount of energy lost in this transition depends on the shape of the outlet chamber and can be clinically significant. For example, in aortic stenosis there is an inverse relationship between the size of the aortic root (which is often dilated) and the amount of pressure recovery distal to the stenotic aortic valve [14]. The larger the aortic root, the less the pressure recovery, and the higher the gradient across the valve. Similarly, pressure recovery is less in eccentric jets [14] (Video 6.1). Therefore, for any given orifice size, the functional severity of stenosis is greater in eccentric jets, both because of a greater pressure loss (smaller effective orifice area) and because of diminished pressure recovery.

When a Doppler sample is placed at, or immediately distal to the vena contracta, pressure recovery has not yet occurred and even though the measured gradient is true, it will overestimate the net gradient. The more clinically relevant parameter is the actual pressure in the vessel that incorporates the recovered pressure. Hence, due to pressure recovery the net gradient from the LV to the aorta will be lower than that measured at the vena contracta, where pressure recovery has not yet occurred. Accordingly, the LV pressure will not be as elevated as would be expected from the measured Doppler gradient. Therefore, a large gradient measured at the vena contracta of the aortic valve may not be hemodynamically important if the LV systolic pressure is not significantly elevated. Consequently, correcting the Doppler gradient for pressure recovery improves the correlation between Doppler and catheter measured gradients in infants with congenital aortic stenosis [15]. Other factors can influence the prediction of stenosis severity based on the vena contracta. Gilon et al. [16] showed that doming stenotic aortic valves have a much smaller impact on the reduction in valve area at the level of the vena contracta than flat valves.

Quantification of blood flow and the measurement of cardiac output

Calculation of cardiac output (CO), its change over time, and its response to intervention is potentially useful, especially in critically ill patients. There are two methods commonly used to measure blood flow and specifically stroke volume by echocardiography. The first uses M‐mode, 2D, or 3D echocardiography to calculate the change in chamber volume between end‐diastole and end‐systole to yield the stroke volume (Figure 6.6). The stroke volume multiplied by heart rate yields CO, which can be indexed to body surface area to yield cardiac index. Alternatively, as previously mentioned, flow can be quantified as the product of the average flow velocity and the CSA of the vessel or a cylindrical structure. The flow velocity is obtained by Doppler and the CSA is obtained by M‐mode, 2D, or 3D echocardiography. As previously mentioned, it is the average velocity that is required to calculate flow. If flow is laminar and the flow velocity profile flat, then the average velocity is relatively easy to calculate. However, because blood flow is pulsatile and because the velocity flow profile is often parabolic, all velocities within the Doppler spectral envelope must be summed and integrated to yield the average velocity. Integrating all flow velocities across the Doppler spectral envelope is called the time velocity integral (TVI, in meters). The integration of velocity yields the stroke distance, that is, the distance (or length) the column of blood has moved in one heartbeat. The TVI multiplied by the CSA of the vessel or valve yields the stroke volume (SV): SV = TVI × CSA. Although this sounds complex, in practice this is relatively easy to do with digital echocardiography. A Doppler sample is placed at the structure of interest (e.g., left ventricular outflow tract (LVOT)), a pulsed spectral Doppler is acquired, and the average flow velocity across the CSA is calculated by integrating all the velocities encapsulated in the Doppler spectral display. This is achieved by digitally tracing the Doppler spectral envelope (Figure 6.7c). To simplify the calculation, the CSA is usually calculated as a circle (πr²). CO is most commonly measured at the aortic valve as the normal aortic valve annulus diameter can be measured with good accuracy and reproducibility, and the true CSA is relatively close to being a circle (Figure 6.7a). Pulsed‐wave (PW) Doppler rather than continuous‐wave (CW) Doppler should be used to ensure that the velocity sample is obtained in the LVOT or at the annulus where the flow profile is relatively flat (Figure 6.7c). Otherwise, more distal flow acceleration may be captured by the CW sample resulting in spuriously high flow velocities and erroneously high calculation of the CO. The Doppler sample is placed in the LVOT a few millimeters below the valve in an apical five‐chamber, three‐chamber, or subxiphoid view. The aortic valve diameter can be measured from these positions, although usually the parasternal long‐axis view is used (Figure 6.7b). Because the aortic annulus diameter does not vary much through the cardiac cycle, the timing of the measurement is not crucial, although it is usually performed in mid‐systole when the aortic leaflets are open and the attachment of the valve cusps to the vessel wall (the hinge points) can be discerned (Figure 6.7b). The volume crossing the aortic valve (the product of CSA and TVI) in one cardiac cycle yields the stroke volume (SV), which multiplied by heart rate provides the cardiac output: CO = SV × HR. The CO can be further indexed to body surface area to yield the cardiac index.

In theory, flow at other locations can be sampled in a similar fashion, but measurements are less accurate than at the aortic valve. For example, when the pulmonary valve annulus can be seen clearly from subxiphoid or parasternal short‐axis views, right ventricular (RV) stroke volume and hence pulmonary flow can be calculated by measuring the pulmonary annulus and by placing a PW Doppler sample in the RV outflow tract. Calculation of pulmonary flow in addition to aortic flow should permit calculation of the pulmonary versus aortic flow ratio (Qp/Qs) to evaluate the magnitude of intracardiac shunts [17]. In practice, measurement of the pulmonary valve area is subject to error due to poorer visualization of the pulmonary valve, which leads to inaccurate measurements of the pulmonary annulus diameter [17].

Because the annulus diameter is squared to calculate the CSA, a small measurement error of the annulus diameter will result in a large error when calculating the CSA. This error is further amplified if the measurement is used to calculate a ratio such as Qp/Qs. Consequently, relatively small measurement errors by echocardiography can have a large impact on CO measurements or derived ratios such as the Qp/Qs. Because much of the error stems from inaccuracies in measurement of the valve diameter some authors have suggested using simplifications of this principle to approximate the Qp/Qs using just the ratio of the peak velocities and ratio of the annulus diameters of the pulmonary and aortic valves as follows [18]:

(6.1)

In practice, due to the inaccuracies of calculating Qp/Qs by echocardiography, this measurement is not routinely used. Rather, considerations such as the patient’s clinical status and left‐sided chamber enlargement determine clinical decisions such as the need to close a ventricular septal defect. Similarly, measurement of flow across the atrioventricular valves would be useful to calculate the severity of valve regurgitation. However, measurement accuracy is limited by the elliptical shape of the atrioventricular valve annuli, the change in their shape over the cardiac cycle, and the large magnitude of atrioventricular valve motion relative to the ultrasound transducer.

Because a large source of error in calculating blood flow/stroke volume by echocardiography is the calculation of the CSA, some have proposed using the TVI alone to assess relative changes in cardiac output. If we assume that the CSA of the aortic or pulmonary valves, for example, remains relatively constant over the cardiac cycle and relatively constant from one examination to the next over short periods of time, then any change in the TVI should reflect a change in CO. This method has been used in a number of clinical situations. For example, in pulmonary hypertension, assessment of the TVI serially over time can reflect changes in CO. This imperfect measure of RV performance has been shown in some studies to correlate with patient outcomes in pulmonary arterial hypertension (PAH) [19]. Hemodynamic parameters derived from RV stroke volume, calculated from the pulmonary valve diameter and VTI and pulmonary pressures, such as stroke work, are associated with outcomes in children with pulmonary hypertension [20,21]. The change in TVI as a measure of change in CO can also be used to optimize pacemaker settings during cardiac resynchronization therapy. Multiple measurements of the TVI at different pacemaker settings are made at the same session in a relatively short period of time. The change in TVI between settings allows evaluation of which pacemaker setting yields the highest CO [22]. One should be cognizant, however, of the important factors influencing TVI. Just as stroke volume is highly influenced by preload and afterload, TVI is similarly influenced by loading conditions. Likewise, CO is the product of heart rate and stroke volume. Therefore, a change in TVI when heart rate has changed may not in itself reflect a change in CO. 3D echocardiography measurement of stroke volume and ventricular volumes may yield more accurate measurements of flow. For example, the ratio of RV stroke volume to RV end‐systolic volume has been suggested to reflect RV–pulmonary arterial coupling, and this ratio correlated with clinical outcomes in pediatric pulmonary hypertension [23].

Estimation of pressure gradients and the Bernoulli equation

One of the key and most common hemodynamic assessments in clinical practice is the measurement of pressure gradients across valves or vessels. Common examples in pediatric cardiology include measurement of pressure gradients across stenotic valves (e.g., aortic or pulmonary valve stenosis), assessment of pressure gradients across a ventricular septal defect to determine whether it is restrictive to pressure, and measurement of the pressure gradient from the RV to the right atrium (RA) across the tricuspid valve to assess RV systolic pressures (Figure 6.8). Measurement of pressure gradients by echocardiography is done by measuring flow velocities, which are then translated into pressure gradients using the Bernoulli principle. It is important to remember, regardless of the particular example, that echocardiography cannot measure absolute pressures and that only the difference in pressures across a structure (i.e., the pressure gradient) is measured. For example, if the gradient across an atrial septal defect is low, this does not automatically imply that left atrial pressure is low, as RA pressure may be elevated. The absolute pressures in the left and right atria remain unknown and can only be estimated by echocardiography using indirect methods which will not be discussed here.

The Bernoulli equation is based on the principle of conservation of energy, that is, the total amount of energy at all points within a closed system must be constant. Applied to blood flow this means that if a valve or vessel area decreases, the flow velocity must increase. Again, think of the example of a river. If the river narrows, the flow quickens to maintain the same flow volume. Although in clinical echocardiography we almost always use a condensed, boiled‐down version of the full Bernoulli equation, it is worthwhile discussing the elements that make up the full equation as they explain some of the common pitfalls encountered when using the simplified version. The full Bernoulli equation incorporates three elements: (i) convective (kinetic) acceleration; (ii) flow acceleration; and (iii) viscous friction (Figure 6.9). Convective (kinetic) acceleration describes the increase in flow velocity between two points. The velocities at these two points are the v₁ (proximal) and v₂ (distal) in the Bernoulli equation. Acceleration of any mass requires force, and in the circulation the force accelerating blood is largely supplied by contraction of the myocardium. The direct “force” accelerating blood through a narrowing is provided by the pressure drop across the narrowing. A constriction in a blood vessel causes acceleration of blood flow through the narrowing and a change in its kinetic energy proportional to the square of the velocity. The increase in kinetic energy is associated with a concomitant decrease in potential energy. This component of the Bernoulli equation is the one most important to clinicians and is encapsulated in the simplified Bernoulli equation used in clinical practice. The second component in the complete Bernoulli equation is flow acceleration. When flow is pulsatile the flow velocity at any given location will increase and decrease with each heartbeat, with some energy loss due to viscous friction. However, when matched for phase, the velocity at a location varies little from beat to beat, and this component of the Bernoulli equation is disregarded in the modified version used in clinical practice. The third component of the complete Bernoulli equation relates to energy lost due to viscous forces. Viscous friction is the resistance that slows blood flow due to friction between blood layers and between blood and the vessel wall (imagine squeezing through a narrow tunnel). Although the true magnitude of viscous losses is difficult to estimate, when the velocity is high enough, or the structure large enough, the viscous losses may be neglected and are dropped from the modified Bernoulli equation. When estimating gradients across valves for example, viscous friction can be neglected. In contrast, the viscous friction component can be important in small or stenotic vessels. Therefore, the simplified Bernoulli equation does not perform well when calculating gradients across a small vessel such as a Blalock–Taussig shunt.

The condensed and simplified Bernoulli equation,

(6.2)

most commonly used in clinical practice, therefore takes only the first component of the full equation into account. The “4” is a rounded‐up conversion factor that converts velocity into pressure units of mmHg. It is also important to note that the simplified equation only includes v₂, or the blood flow velocity distal to the narrowing. For large pressure differences, the initial velocity (v₁) is small compared with the distal velocity (v₂), and can be ignored. However, when v₁ is relatively large compared to the distal velocity (i.e., when it is 2 m/s or more) it should be accounted for and the modified equation should be (Figure 6.10):

(6.3)

Likewise, the simplified Bernoulli equation cannot be used to quantify intraventricular flow or flow across unobstructed LV inflow or outflow tracts [25]. The Bernoulli equation performs best across discrete stenoses. When there is a long‐segment narrowing, the simplified Bernoulli equation will overestimate the gradient. This can be commonly seen, for example, when assessing gradients across long‐segment narrowing in the aortic isthmus (i.e., diffuse aortic coarctation). Other technical factors can be important sources of error. Beyond the alignment of the ultrasound beam with the direction of the blood flow, the image quality will influence the spectral Doppler measurement and hence the estimation of peak velocity. A common example in clinical practice is underestimating the peak velocity and hence RV systolic pressure when the tricuspid regurgitation spectral envelope is incomplete. Careful adjustment of gain and reject settings, as well as sampling the jet from multiple views to ensure the highest velocity, is paramount. Contrast with agitated saline can be used to enhance the spectral display intensity, although this necessitates placement of an intravenous catheter. One must also be cognizant of where the Doppler sample is placed and, if there is more than one jet, which jet is being sampled. For example, when trying to sample the LVOT in hypertrophic cardiomyopathy, the MR jet, which is in close proximity, must be avoided. Similarly, a jet across a ventricular septal defect can contaminate the estimation of RV systolic pressure using the tricuspid regurgitation jet. This can also be a problem when trying to determine the pressure gradient across RV muscle bundles associated with a ventricular septal defect where a high‐velocity ventricular septal defect jet can contaminate the flow acceleration across the closely related muscle bundles (Video 6.3).

The configuration of the spectral jet can also provide clues not only on the severity of the obstruction in terms of peak velocity, but also to its mechanism. Dynamic muscular obstructions often have a curved, dagger‐like profile. Sometimes, multiple contours can be seen simultaneously, pointing to multilevel obstruction. This is commonly seen in multilevel RV obstruction in unrepaired tetralogy of Fallot (Figure 6.11, Videos 6.4 and 6.5). Gradients should be obtained at a stable heart rate. The presence of premature beats affects filling and hence stroke volume and can lead to errors in assessment of the true gradient (Figure 6.12a and b).

Differences in catheter and Doppler measured pressure gradients

Calculation of pressure differences based on Doppler measurement of flow velocities has become a staple of patient care. However, the conversion of velocity to pressure using the modified Bernoulli equation is imperfect. Likewise, there are several factors that contribute to differences in the pressure gradient measured invasively in the catheterization laboratory versus those assessed noninvasively by Doppler. It is worthwhile to consider these briefly.

1. Velocity measurement error. As previously discussed, Doppler measures only the component of velocity in the direction of the ultrasound beam. Therefore, an off‐angle Doppler sample results in underestimation of the true velocity.
   
2. Pressure measurement error in the catheterization lab. Inadequately calibrated pressure transducers, disturbance of the flow by the catheter itself, and measurement of stagnation pressure can each lead to pressure measurement errors at cardiac catheterization and therefore differences between echocardiographic and catheter measurements (even the “gold‐standard” of catheter measurements is imperfect).
   
3. Physiologic differences in the patient state between studies. The interval between the echocardiographic study and catheterization as well as differences in the hemodynamic state of a fasting, sedated patient in the catheterization laboratory compared with the awake and sometimes uncooperative child having an echocardiogram will influence measurements of gradients. Doppler gradients in the awake child are usually higher than those measured under general anesthesia in the catheterization laboratory
   
4. Peak‐to‐peak versus peak pressure differences. Catheter calculations are generally based on the peak pressure difference between two chambers even though these occur at different times. Doppler measurements, on the other hand, estimate the peak instantaneous pressure drop. These values are different, and this becomes important predominantly in mild stenosis. Calculating the instantaneous pressure gradient at 50–55% of ejection has been found to correlate better than simply the mean or peak Doppler gradient with the catheter measured peak‐to‐peak systolic gradient in children with congenital aortic stenosis [26].

   

   
   
5. Pressure recovery. The phenomenon of pressure recovery has been discussed previously. Because Doppler techniques do not detect pressure recovery, they may overestimate pressure gradients [27]. In contrast, a catheter positioned downstream from a stenotic valve measures recovered pressure, but measuring the maximum pressure drop within the vena contracta is generally not possible [28]. Similarly, if the catheter is positioned close to the vena contracta, the pressure gradient may be overestimated as pressure recovery, which can continue for 5–10 cm downstream, has not fully occurred. Also, smaller peak velocities are associated with a greater degree of pressure recovery, resulting in greater relative differences between catheter and Doppler estimates of pressure differences even though the absolute differences tend to be small. Pressure recovery has been found to explain much of the difference between catheter and Doppler measurements, especially in children with mild to moderate valve stenosis and small‐size downstream vessels [29]. Correcting the Doppler gradient for pressure recovery can improve the correlation between Doppler and catheter measured gradients in infants with congenital aortic stenosis [15,29].
   
6. Inaccuracies introduced by use of the simplified Bernoulli equation. As previously discussed, use of the simplified Bernoulli equation assumes that the proximal velocity is negligible and that viscous effects are small. Tunnel‐like stenoses, eccentric jets, and prosthetic valves are all subject to greater viscous effects and the simplified Bernoulli equation may be inaccurate in these situations.

Although it is theoretically possible to estimate the catheter peak‐to‐peak gradient based on the peak instantaneous echocardiographic Doppler gradient using regression equations derived from comparative studies [30], in practice most laboratories do not do so.

Assessment of valvar stenosis and regurgitation in clinical practice

Valve stenosis imposes a pressure load on the pumping chamber. The severity of this load is proportional to the magnitude of the stenosis and therefore quantifying valvar stenosis is important. In valvar regurgitation, the regurgitant volume influences the ventricular response and is the parameter of interest. In both valvar stenosis and regurgitation, the ventricular response to the abnormal loading is the key parameter that determines clinical decision making and is therefore an integral part of the hemodynamic assessment. Consequently, assessment of ventricular hypertrophy, enlargement, and function is as or more important in aortic stenosis and regurgitation than quantitative assessment of the stenosis or regurgitant volume itself. Nonetheless, in asymptomatic children with preserved ventricular function and dimensions, the severity of stenosis is used to decide on the timing of intervention, both for the aortic and pulmonary valves. Although Doppler echocardiography is a valuable tool to assess valvar stenosis and regurgitation, it is important to recognize the many limitations to these methods. It is equally important to remember that sometimes simple clues can provide useful information on the severity of a hemodynamic lesion. For example, a pulsatile abdominal aorta on 2D imaging suggests that more proximal arch obstruction or aortic coarctation is not severe. Likewise, flow reversal in the abdominal aorta suggests that aortic regurgitation is at least of moderate severity or that flow across a patent arterial duct is substantial. The key points in the assessment of native valvar stenosis and regurgitation are summarized in Table 6.2.

Assessment of native valvar stenosis

There are several Doppler echocardiography methods to judge the severity of valvar stenosis. One of these is to measure the stenotic valve area relative to body surface area. This theoretically can be achieved by direct planimetry of the valve area from 2D images and perhaps more accurately by 3D echocardiography [31]. However, direct measurement of the AOA is often not possible or reliable. Moreover, even if the actual AOA could be accurately measured, this would still underestimate the severity of the stenosis, because, as previously detailed, the effective orifice area and not the anatomic orifice area determines the severity of the stenosis. Therefore, assessment of valvar stenosis using the CSA has largely relied on measurement of blood flow using the continuity equation rather than on direct measurement. The continuity equation is commonly used in adult cardiology, but is less commonly used in pediatric laboratories for reasons that will be subsequently detailed. The continuity equation is based on the dictum that if there are no intracardiac shunts or valvar regurgitation, flow across all four cardiac valves is equal and, specifically, flow across the aortic and mitral valves is equal; otherwise blood would rapidly accumulate in the LV. Therefore, based on the calculation of blood flow we detailed previously, the continuity equation for the left‐sided valves is

(6.4)

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