{'fraction_non_alphanumeric': 0.04249096851883709, 'fraction_numerical': 0.018120305063363724, 'mean_word_length': 4.860215053763441, 'pattern_counts': {'":': 0, '<': 4, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Calculation of Aortic VAlve and LVOT Areas by a Modified Continuity Equation Using Different Echocardiography Methods: The CAVALIER Study

Background: The area of the left ventricular outflow tract (ALVOT) represents a major component of the continuity equation (CE), which is, i.a., crucial to calculate the aortic valve (AV) area (AAV). The ALVOT is typically calculated using 2D echo assessments as the measured anterior–posterior (a/p) extension, assuming a round LVOT base. Anatomically, however, usually an elliptical shape of the LVOT base is present, with the long diameter extending from the medial–lateral axis (m/l), which is not recognized by two-dimensional (2D) echocardiography. Objective: We aimed to compare standard and three-dimensional (3D)-echocardiography-derived ALVOT calculation and its use in a standard CE (CEstd) and a modified CE (CEmod) to calculate the AAV vs. computed tomography (CT) multi-planar reconstruction (MPR) measurements of the anatomical ALVOT, and AAV, respectively. Methods: Patients were selected if 3D transthoracic echocardiography (TTE), 3D transesophageal echocardiography (TEE), and cardiac CT were all performed, and imaging quality was adequate. The ALVOT was assessed using 2D calculation, (a/p only), 3D-volume MPR, and 3D-biplane calculation (a/p and m/l). AAV was measured using both CEstd and CEmod, and 3D-volume MPR. Data were compared to corresponding CT analyses. Results: From 2017 to 2018, 107 consecutive patients with complete and adequate imaging data were included. The calculated ALVOT was smaller when assessed by 2D- compared to both 3D-volume MPR and 3D-biplane calculation. Calculated AAV was correspondingly smaller in CEstd compared to CEmod or 3D-volume MPR. The ALVOT and AAV, using data from 3D echocardiography, highly correlated and were congruent with corresponding measurements in CT. Conclusion: Due to the elliptic shape of the LVOT, use of measurements and calculations based on 2D echocardiography systematically underestimates the ALVOT and dependent areas, such as the AAV. Anatomically correct assessment can be achieved using 3D echocardiography and adapted calculations, such as CEmod.


Introduction
Echocardiographic assessment of the left ventricular outflow tract (LVOT) area (A LVOT ) using transthoracic (TTE) or transesophageal echocardiography (TEE) is a key component for the calculation of various hemodynamic states, such as stroke volume [1], cardiac output and index [2][3][4], and-most crucially-the calculation of the aortic valve (AV) area (A AV ) [5,6]. The underlying principle is the theorem of a steady flow system in communicating conduits. Here, the laminar flow through the conduit is equal to the product of the mean velocity times the cross-sectional area of the conduit, with SV = VTI LVOT (SV = stroke volume; VTI = velocity time integral). When calculating the A AV , this principle is used to form the so-called (standard) continuity equation (CE std ) as the ratio of constant flows through the LVOT and the following (smaller) aortic valve are inversely proportional to the corresponding areas, i.e., A AV ·VTI AV = A LVOT ·VTI LVOT , A AV = A LVOT · VTI LVOT VTI AV .
In clinical practice, the A LVOT is calculated by measuring the anterior-posterior (a/p) diameter of the LVOT in the parasternal long axis only, thus assuming a round shape of the LVOT's cross-sectional area, as described in the formula A LVOT = π· DiameterLVOT 2 2 [6]. However, it has been shown that the shape of the LVOT is eccentric, i.e., elliptical in shape, with the longer diameter extending from the medial-lateral axis (m/l), which is not recognized by 2D echocardiography [7]. In consequence, cardiac hemodynamics, and/or the anatomical aortic valve area, are underestimated [8][9][10].
This study aimed to assess multiple 2D and 3D measurements and calculations of the A LVOT and A AV in both TTE and TEE, and compare their performance and validity to the "gold standard" of the CT analysis.

Patient Selection
We prospectively screened consecutive patients undergoing imaging for different clinical indications. Patients were included if both 3D-TTE and 3D-TEE were performed, as well as cardiac CT analysis. The study conformed to the Declaration of Helsinki. All patients provided written informed consent, and the study was approved by the local ethics committee (EK 111032015).

Echocardiography
Imaging was acquired using Philips IE33 and EPIQ CVx ultrasound machines, equipped with either X5-1 TTE probes and X7-2t or X8-2t TEE probes. Analysis of the imaging data was carried out by two experienced echocardiographers (KS and TFR), using Philips QLAB (all Philips Health Systems N.V., Koninklijke, The Netherlands). First, A LVOT was calculated using the standard approach, employing 2D-echocardiography assessment of the long axis, with stdA LVOT = π· DiameterLVOT a/p 2 2 . Second, 3DA LVOT was assessed using planimetry in multiplanar reconstruction (MPR) from 3D-echocardiography datasets. Third, to appreciate the elliptic form of the LVOT in a calculation, ellipticA LVOT = π· DiameterLVOT a/p · DiameterLVOT m/l 4 was devised from 3D-biplane echocardiography, incorporating both a/p and m/l diameters of the LVOT ( Figure 1A,B  (C) Planimetry of CTA LVOT (transparent white, 4.901 cm 2 ) using 3D-volume MPR. A LVOT -area of the LVOT, assessed using different methods; CT-computed tomography TEE-transesophageal echocardiography.

CT
CT measurements served as the "gold standard" comparator to the echocardiographic measurements and calculations. Using planimetry in MPR, variables measured by CT were CTA LVOT ( Figure 1C) and CTA AV . Analysis of the data was carried out by two experienced specialists (KS and TFR), using 3mensio structural heart (3mensio Medical Imaging, Bilthoven, The Netherlands). Imaging was acquired using Siemens SOMATOM Force (Siemens Healthineers, Erlangen, Germany).
The comparisons of values included correlation and Bland-Altman analyses to assess the congruence using bias and limits of agreement between the different techniques [11]. Normality distribution was tested using the Kolmogoroff-Smirnoff test. Bias between measurements was assessed using a paired or unpaired Student's t-test, or a Wilcoxon signed-rank test, as appropriate. Differences between parameters for multiple groups was assessed by analysis of variance or by the Kruskal-Wallis test, as appropriate. Statistical significance was defined as a two-tailed p-value < 0.05. Significance criteria in multiple testing were adjusted by the Bonferroni method. All analyses were performed using R (version 3.0.2, 2013, The R Foundation for Statistical Computing, Vienna, Austria).

Results
From 2 January 2017 to 28 December 2018, 421 patients were examined. Complete data were available for 107 patients (Supplementary Figure S1). Baseline characteristics showed a median age of 74 years, and a higher prevalence of the male sex (55%). Further details, including comorbidities, are shown in Table 1. Left ventricular dimensions showed normal median ranges in diastole (LVEDD 47 mm [42, 54]) and systole (LVESD 32 mm [25,40]). Median LVEF was 57% [41,65]. No or mild aortic stenosis (AS) was present in 50% of cases, while moderate AS was present in 10%, and severe AS in 40% of cases (Table 2). Calculating stdA LVOT from the a/p dimension yielded more than 20% lower values in all echocardiography assessments compared to CT (p < 0.001). Both 3D-volume MPR (p = 0.14) and use of the novel equation ellipticA LVOT (p = 0.20) showed no significant difference (Figure 2A-C). Details of the comparisons of LVOT measurements by the different imaging methodologies are summarized in Table 3.
All echocardiographic measurements correlated significantly and strongly with CT (all p < 0.001; Figure 3). Congruence of stdA LVOT measurements with "gold standard" of CT was low, irrespective of TTE or TEE. In contrast, 3D-volume MPR and ellipticA LVOT showed high congruence with CT ( Figure 3). The strongest correlations and congruence were found in TEE when using either 3D planimetry for ellipticA LVOT   All echocardiographic measurements correlated significantly and strongly with CT (all p < 0.001; Figure 3). Congruence of stdA measurements with "gold standard" of CT was low, irrespective of TTE or TEE. In contrast, 3D-volume MPR and ellipticA showed high congruence with CT ( Figure 3). The strongest correlations and congruence were found in TEE when using either 3D planimetry for ellipticA    Regarding the AV, where CEstd, CEmod, and 3D-volume MPR were used to receive the AAV, results are in principle similar to LVOT assessments. The stdA showed smaller values than the 3DA and ellipticA measurements (Table 4, Figure 2D-F). The lowest bias and the best congruence were found in TTE using 3D-biplane modA (bias 0.06, LOA: −0.45, 0.56) and in TEE using both 3D-volume MPR for 3DA (bias −0.03, LOA: −0.38, 0.32) and 3D biplane for modA (bias −0.04, LOA: −0.4, 0.32). The highest bias and least congruence were seen using any stdA (Supplementary Figure S2).  Regarding the AV, where CE std , CE mod , and 3D-volume MPR were used to receive the A AV , results are in principle similar to LVOT assessments. The stdA AV showed smaller values than the 3DA AV and ellipticA AV measurements (Table 4, Figure 2D-F). The lowest bias and the best congruence were found in TTE using 3D-biplane modA AV (bias 0.06, LOA: −0.45, 0.56) and in TEE using both 3D-volume MPR for 3DA AV (bias −0.03, LOA: −0.38, 0.32) and 3D biplane for modA AV (bias −0.04, LOA: −0.4, 0.32). The highest bias and least congruence were seen using any stdA AV (Supplementary Figure S2).

Discussion
Accurate measurement of the A LVOT is pivotal to correctly calculating left cardiac hemodynamic states and/or the A AV to assess the severity in AS, using the continuity equation. Our study offers comparison of a wide spectrum of different echocardiographic imaging methods to the "gold standard" of CT data as a reference. The principles used to receive A LVOT and A AV were either calculation (stdA LVOT and ellipticA LVOT ; stdA AV and modA AV ), or planimetry using MPR (3DA LVOT and 3DA AV ). The echocardiographic methods employed were common 2D echocardiography (stdA LVOT and stdA LVOT ), 3Dbiplane interrogation (ellipticA LVOT and modA AV ), and 3D-volume planimetry (3DA LVOT and 3DA AV ), in both TTE and TEE, respectively.
In this study, we have shown that first, the A LVOT underestimated the anatomic area when the standard echo calculation was used, compared to CT. This was irrespective of the echocardiography approach used. Second, 3DA LVOT assessed using planimetry in 3D echocardiography showed excellent congruence and correlation with CT measurements for both 3D-TTE and 3D-TEE. 3D-TEE was superior to 3D-TTE in both congruence and correlation. Third, the adapted formula to calculate an elliptic LVOT's anatomy, ellipticA LVOT , also showed both excellent correlation and congruence with CT measurements for both 3D-TTE and 3D-TEE. Again, 3D-TEE was superior to 3D-TTE in both congruence and correlation. Fourth, using the CE std leads to underestimating the anatomic A AV , irrespective of the echocardiography approach used. Fifth, while 3DA AV showed excellent correlation to CT for both 3D-TTE and 3D-TEE, congruence of 3D-TEE measurements was conspicuously superior. Finally, using the adapted ellipticA LVOT in the CE mod showed modA AV also had excellent correlation and congruence with CT measurements for both 3D-TTE and 3D-TEE-again with superior performance of 3D-TEE.
Our findings of underappreciating both the A LVOT and A AV when using the standard echocardiographic interrogation technique are in line with current data. Different methods have been proposed for correcting this flaw, e.g., using a fixed correction factor [12], evaluating the aortic annulus instead of the LVOT, as it becomes "more" round in shape during systole [13], or using the A LVOT as directly measured using CT or 3D-TTE planimetry [10,14]. As the LVOT comes in different shapes and sizes, including round-based LVOTs, a fixed correction factor, while maybe statistically correct, seems less appropriate for the assessment of the individual patient. Then, the data suggesting that the aortic annulus becomes "more" round in shape during systole have been challenged by other studies, which rather suggests that the aortic annulus is just as elliptical as the LVOT [15][16][17]. Furthermore, correct placement of the pulsed-wave Doppler (PWD) sample volume to acquire the appropriate measurements of the velocity (and thus gradient), as well as the velocity time integral of the flow, is highly challenging when the aortic annulus is chosen as the point of interrogation: since the aortic annulus moves up and down during the cardiac cycle, the sample volume of the PWD will not stay at the correct site. Hence, there is a very high risk of either measuring the speed at the level of the LVOT (velocities may be lower), or at the level of the (stenotic) aortic valve (thus yielding much higher velocities), instead of the aortic annulus. Concerning planimetry of the LVOT using 3D data, our results support the assumption that its use from MPR in either 3D echocardiography or CT seems to be a more accurate approach. However, even though echocardiography is widely available, 3D-MPR analysis is not. This is caused by multiple factors: Not all echo machines can acquire 3D volumes. If 3D volumes can be obtained, analysis is dependent on specific (and often expensive) software, e.g., QLAB, EchoPac (GE Healthcare, Chicago, IL, USA), TOMTEC (TOMTEC Imaging Systems GmbH, Unterschleissheim, Germany), 3Mensio, and others. Finally, if these requirements can be fulfilled, 3D-volume analysis using MPR requires special training and is sometimes not feasible [18]. On the other hand, 3D biplane is much more available, has both a higher spatial and temporal resolution than 3D-volume imaging, and assessment is very similar to the 2D imaging physicians are used to. Our data also show 3D-TEE is superior to all other echocardiographic approaches. However, the use of both the ellipticA LVOT and the CE mod , yielding the modA AV , offer attractive alternatives, even if they are based on the more available 3D-biplane interrogation and TTE, respectively. Circumventing 3D evaluation in favor of direct 2D-TTE planimetry in the parasternal short axis of either the A LVOT and/or the A AV should be discouraged. First, oblique cut-planes, and second, lower image quality of TTE-especially relevant in calcified AS-can easily lead to incorrect measurements [19,20].
Recent guidelines still advocate the use of standard echocardiographic interrogation to assess and grade AS, although the problem of underestimating both the A LVOT and A AV is well-known [6,21]. The reason is that despite assuming a circular LVOT shape in the continuity equation, use of this calculation has shown to be a strong predictor of clinical outcomes. This suggests that aortic stenosis might be of relevance earlier than a progression of the anatomic A AV below 1 cm 2 . This is somewhat backed by the observation that treatment of asymptomatic patients with severe AS shows a mortality benefit [22]. Hemodynamics seem even more complex in patients with moderate AS and reduced LVEF, prompting the TAVR UNLOAD trial [23][24][25]. In this light, use of a CE std yielding imprecise results hardly seems satisfying-scientifically and clinically. Anatomically correct echocardiographic assessment and grading of the underlying disease is a necessity void of compromises.

Study Limitations
As this study was held at one center only, the external validity might be questionable. For instance, differences in personnel and logistics in general and differences in TTE, and TTE operator experience in particular, can cause wide variations on the outcome. However, there were only a limited number of highly qualified TTE and TEE operators, following the same protocol during the examinations. Additionally, the data were re-evaluated by two blinded cardiologists, both experts in echocardiography. With the single-center character of the study, a selection bias cannot be ruled out. However, as the study population was an "all comers" selection, comprised of patients with a very heterogeneous disease spectrum, this seems less likely.
Differences in imaging quality were not addressed specifically. Image quality in the study population was generally good. Decreased image quality will most likely lead to different results. In these cases, CT angiography analysis might prove to be superior to echocardiography.

Conclusions
The LVOT area, as well as the aortic valve area, is systematically underestimated when using standard calculations based on 2D-echocardiography interrogations, due to the eccentricity of the LVOT. The use of 3D echocardiography is significantly superior due to its good correlation and its data being congruent with CT analysis. The use of adapted formulas designed to recognize the elliptic LVOT shape also yielded excellent correlation and congruence with CT data, with the underlying echocardiographic method of 3D biplane being widely available and easy to use.  Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Conflicts of Interest:
The authors declare no conflict of interest for this study.