It is further modified in clinical cardiology as:
In the presence of severe AS, V2 is usually significantly greater than V1 and thus V1 is omitted and the equation is further simplified into:
Errors of assumption occur when V1 is omitted and the simplified equation is applied, and V1 is >1.5 m/s as seen with hyperdynamic states, dynamic outflow obstruction, and moderate to severe aortic regurgitation or when V2 is <3.0 m/s. This causes an overestimation of the noninvasively derived ΔP. In such cases, V1 should be included in the equation [6–8].
Simplification of the Bernoulli equation also neglects the final term in the calculation, R (μ), which represents energy loss due to viscous friction, where R is viscous resistance and μ is viscosity. Though less common, failing to recall this component may result in an overestimation of pressure gradients in anemic patients [1] or an underestimation in milder degrees of AS with laminar flow where viscous losses are more significant [9].
Erroneous noninvasive overestimates of ΔP may also occur due to inadvertently mistaking an eccentric mitral regurgitation jet for AS jet [8] (Case 1, seen in Fig. 9.1). This is particularly true when the mitral regurgitation jet is eccentric as with mitral valve prolapse, with hypertrophic obstructive cardiomyopathy and associated systolic anterior motion of the mitral valve leaflets and mitral regurgitation, and with the use of the non-imaging probe (Pedoff). Less commonly, tricuspid regurgitation jet may also be mistaken for aortic stenosis.
Fig. 9.1
Case 1: Error of Measurement. 50 year/old female presents for echocardiographic evaluation after her primary care physician noted a new murmur on routine physical examination. Echo reveals markedly eccentric severe mitral regurgitation jet due to severe prolapse of the posterior mitral leaflet on TTE (a–left) and TEE (a–right). Doppler signal is wrongfully noted as AV Doppler, which is actually that of the eccentric mitral regurgitation jet (b). Normal Excursion of the AV is noted on 2D (c)
The aortic stenosis spectral flow pattern is a systolic ejection flow and occurs upon opening of the aortic valve, progresses to a peak at some point during systole and ceases at the closure of the aortic valve. As this flow occurs during left ventricular ejection only, it will not be present during isovolumic ventricular contraction time (IVCT) or isovolumic ventricular relaxation time (IVRT). This fact helps differentiate the aortic stenosis flow pattern from the holosystolic flow of mitral insufficiency or tricuspid insufficiency. These latter two flow patterns, although occasionally confused with aortic stenosis due to their occurrence during systole, are holosystolic in nature. These regurgitant jets therefore begin immediately upon cessation of diastolic inflow velocities through the AV valves and continue throughout systole until, and sometimes into the next diastolic flow pattern. Careful examination of the timing of the turbulent systolic jet low pattern is necessary to avoid confusion and mistaking these jets for an aortic stenotic flow pattern.
Systolic turbulence due to left ventricular outflow tract obstruction may be noted from the same windows used to interrogate the aortic valve, particularly when using the Pedoff probe. The continuous wave flow pattern in this pathologic entity differ from aortic stenosis in that the peak velocity of the jet tends to be in a much later part of systole and tends to be maximal in the late phase of systole and the velocity is usually negligible or very low in the early to mid-portion of systole.
Invasively, ∆P is obtained via a double lumen single catheter, dual catheters, or pull back of a single catheter across the AV. Poor balancing, air bubbles in transducers, or the positioning of the transducer either too high or too low in relation to the patient may account for errors. Moreover, utilizing the pressure difference between the left ventricular catheter and the femoral line rather than the ascending aorta as a surrogate for trans-aortic gradient may overestimate ΔP in the presence of descending aortic or iliac stenosis [10]. Inherent errors in estimating the cardiac output may also account for errors of area measurement as may occur with utilizing an erroneous constant, utilizing estimated rather than measured O2 consumption with Fick method, or using the thermodilution method with severe tricuspid regurgitation, atrial fibrillation, or low cardiac output [11].
High Flow States
Due to the quadratic and direct relationship between pressure gradient and flow, a high flow state may cause elevated gradients (both Doppler ∆Pmax and invasive ∆Pnet) in the absence of significant AS. Moreover, as note above, high flow may increase the LVOT V1 component of the simplified Bernoulli equation to >1.5 m/s and ignoring it will also overestimate ∆P.
High flow may occur with fever, severe anemia, pregnancy, thyrotoxicosis, arterio-venous fistulas, and thiamine deficiency [8]. Case 2, seen in Fig. 9.2, demonstrates a patient on hemodialysis admitted with fever and chills causing a hyperdynamic state with increased flow across the AV.
Fig. 9.2
Case 2: High flow states. 64 year/old male on chronic hemodialysis, admitted for fevers/chills. The patient was found to have sepsis, likely secondary to a chronic indwelling line infection. Trans-thoracic echocardiogram was initially obtained to evaluate for obvious cardiac valve vegetation. Pulse wave Doppler (left) and Continuous wave Doppler (right) across the AV demonstrating increased velocities as well as an AV velocity <3 m/s. Thus the modified Bernoulli rather than the simplified equation should be used 
. The actual ΔPMIG across the AV is 
. The actual ΔPMIG across the AV is Conversion of a high flow/high gradient AS in the presence of a dialysis shunt to a paradoxically low flow low gradient AS with shunt compression has been reported [12]. In a patient on dialysis with an AV fistula and mild to moderate AS, the increased flow from the AV shunt, may increase the gradient noted on both Doppler and catheterization into the severe range. In addition, the cardiac output may be markedly elevated by invasive measures. This leads to a large AVA by the Gorlin equation in the mild to moderate range of severity. However, the increase flow may only marginally increase the Doppler LVOT TVI, causing the Doppler-estimated AVA to remain in the severe range. Hence, reverse area/gradient mismatch will be only noted on cardiac catheterization.
In addition, aortic regurgitation may also increase transaortic flow leading to an increase in the AVvel and thus the ∆P, particularly in the presence of combined valve stenosis and regurgitation. In patients with at least moderate combined AV disease, the progressive increase AVvel has been recently linked to worse outcomes, especially in patients with bicuspid aortic valve disease [13].
Pressure Recovery
In the presence of significant Prec, reverse area/gradient mismatch is only present by Doppler-derived mean gradient (∆Pmean) and EOA assessments of AS severity. However, catheter-derived ∆Pmean is lower and concordant to the higher invasively derived EOA resulting in Doppler/catheter discordance. The Prec phenomenon is clinically relevant in patients with a small ascending aorta diameter and moderate aortic stenosis [14–16] (Case 3, seen in Fig. 9.3).
Fig. 9.3
Case 3: Pressure recovery: significant pressure recovery in a patient with moderate aortic stenosis and small aortic diameter (Doppler-only reverse area/gradient mismatch). 80 year/old female with a history of an undetermined degree of aortic stenosis presents for TAVR evaluation. Echocardiography: AVvel : 3.5 m/s, ΔP mean : 30mmHg, ΔPMIG : 50mmHg (bottom right), Dimensionless index (VTI): 0.16, EOA Dop (VTI): 0.6 cm 2 , iEOA: 0.33 cm2/m2, GOA by planimetry is 1.3 cm 2 (top right), aortic diameter: 2.2 cm (bottom left), 
, noninvasive absolute P rec = 14 mmHg (using ΔPmean), relative Prec (Prec/ Doppler ΔPmean) 15/34 = 44 %. Note that the AV is thickened and restricted (red arrow, top left), however, appears only moderately stenosed. Catheterization: 
, noninvasive absolute P rec = 14 mmHg (using ΔPmean), relative Prec (Prec/ Doppler ΔPmean) 15/34 = 44 %. Note that the AV is thickened and restricted (red arrow, top left), however, appears only moderately stenosed. Catheterization: In a study of 1,563 patients with AS, 47.5 % initially classified as severe were reclassified as moderate after accounting for Prec [4]. A clinically relevant Prec (>20 % of ∆Pmax) was present in 16.8 % of patients [4]. After accounting for Prec via calculation of energy loss index (ELI), reclassification into moderate AS occurred more often in patients with a smaller ascending aorta (<3.0 cm) and lower trans-aortic velocities, regardless of flow state. However, the absolute magnitude of Prec was greater in the presence of higher trans-aortic velocities (>3.33 m/s) [4]. This was discussed in more detail in Chap. 3.
Eccentric Jet
Conversely, in the presence an eccentric jet across the AV (as in cases of a bicuspid AV, non uniform calcification of cusps, and uneven restriction of AV leaflets) (Fig. 9.4), there is an increase in pressure loss as the eccentric jet collides with the ascending aortic wall with resultant energy loss due to heat, flow separation, and vortex formation. The latter will also cause a decrease in the absolute and relative Prec [17–20]. As a result of both increased in pressure loss as well as decreased Prec, both the Doppler- and catheter-derived ∆Pmean will be higher compared to the GOA. As such, there is Doppler/catheter concordance and reverse area/gradient mismatch is present on both Doppler and catheter-derived assessments. The greatest proportion of increase in both Doppler ∆Pmax and catheter ∆Pnet, and decline in EOA induced by jet eccentricity occurs by an angle of 30° and to a higher degree in the presence of more severe AS [18]. We have recently published a review highlighting several cases of an eccentric jet leading to reverse area/gradient mismatch [17].
Fig. 9.4
Eccentric (a) (left) and centric (b) (right) jets across the aortic valve as viewed above the valve from the aorta as demonstrated on 3D color in two different
Aortic Valve Geometry
As mentioned above, a pliable domed AV with a gradually narrowed orifice (funnel-shaped) will have a larger EOA for a given gradient that is almost similar to the GOA in dimension (a higher coefficient of orifice contraction) (Fig. 9.5). Conversely, a relatively flat AV with abrupt narrowing (sharp-edged) will lead to increase in disparity between the EOA and the GOA and a smaller EOA for a given gradient and [21] with reverse area gradient mismatch. A bicuspid AV will lead to a smaller EOA and higher ∆Pmean for a given GOA with a low coefficient of orifice contraction [22].
Fig. 9.5
The relationship between GOA, EOA, and the coefficient of orifice contraction (EOA/GOA). With a more gradually narrowed GOA (left), the EOA is almost equal to the GOA and the CC is close to 1. However, with a more abrupt narrowing (right), the EOA is more distal and smaller than the GOA
Increased LVOT Diameter
Similarly, increased LVOT diameter will lead to more initial drop of pressure as blood flow converges towards the AV. Thus, with larger LVOT diameters, there is an elevation in both Doppler ∆Pmax and invasive ∆Pnet that is disproportionate to the degree of area stenosis. However, Doppler and invasive gradients are close to each other with a reverse area/gradient mismatch noted by both modalities [18–20]. Thus for a given geometric AVA, a larger LVOT diameter yields a higher gradient, higher AVVel, and a smaller dimensionless index (DI). Moreover, the larger the LVOT size compared to that of the GOA, the lower the EOA and the contraction coefficient with disproportionately high gradients [11].
The impact of LVOT diameter on Doppler-derived Pmean was further elucidated in a recent Doppler study of about 10,000 patients. In this study, an AVA of 1 cm2 corresponded to a Pmean of 42 mmHg, AVVel of 4.1 m/s, and a DI of 0.22 in patients with a large LVOTD (>2.3 cm). While it corresponded to a Pmean of 35 mmHg, AVVel 3.8 m/s, and a DI of 0.29 in patients with an average LVOTD (2–2.2 cm). Finally, it corresponded to a Pmean of 29 mmHg, AVVel 3.5 m/s, and a DI of 0.36 in patients was with a small LVOTD (1.7–1.9 cm) [23].
All the above factors may occur independently or simultaneously. A patient with a bicuspid aortic valve, dilated aorta, eccentric jet, moderate to severe aortic regurgitation may experience markedly elevated Doppler and invasive gradients across the AV, despite the absence of severe reduction in the GOA, is demonstrated in Case 4, seen in Fig. 9.6.
