Relative Aortic Valve Stiffness: A New Parameter Quantifying Aortic Stenosis

Structured Abstract

Background

Aortic stenosis (AS) quantification relies on transvalvular gradients or aortic valve opening area (AVA), two measures that inherently depend on the instantaneous transvalvular flow rate (Q). We present a new quantification method for AS based on new modelling where AVA saturates with increasing Q, contradicting the assumption of linear Q-AVA-relation currently predominant in the literature.

Objective

Development of a new method for the quantification of AS.

Methods

In 141 patient undergoing transesophageal echocardiography, AVA was obtained frame-by-frame over an entire systole from 3D echocardiograms using multiplanar reconstruction. Q was retrieved by Doppler- and 3D echocardiography of the left ventricular outflow tract. A sigmoid Q-AVA relation was fitted with a machine learning algorithm. The measured and the predicted AVA were compared between a parametrized linear and sigmoid Q-AVA-relation model. A relative aortic valve stiffness (rAVS) was calculated, and an isostiffness nomogram was constructed. Cox proportional hazard modelling was used to look for predictors of rehospitalization-free survival

Results

Compared to the linear model, the sigmoid model consistently better predicted measured AVA in all AS severity groups. Within severity groups, rAVS remained robust and constant, a property not shared by the linear model. A ROC-Analysis revealed a rAVS-value of 1.51 as the best cut-off for distinguishing severe from non-severe AS. Cox proportional hazard modelling showed its value as an independent predictor of rehospitalization-free survival.

Conclusions

We present a new method for the quantification of AS that could help simplify the diagnosis of patients with low-flow, low-gradient AS.

Abbreviations

AIC

Akaike information criteria

AS

aortic stenosis

AVA

aortic valve opening area

va-ECMO

veno-arterial extracorporeal membrane oxygenation

LVOT

left ventricular outflow tract

Q

transvalvular flow rate (through aortic valve)

rAVS

relative aortic valve stiffness, the stenosis parameter introduced in this study

ROC

receiver operating characteristic

TEE

transesophageal echocardiography

Introduction

The assessment of aortic stenosis (AS) severity has an important clinical impact. It determines the prognosis and the therapeutic approach, ranging from watchful waiting to valve replacement. AS severity is primarily diagnosed echocardiographically by assessing the transvalvular gradients and the aortic valve opening area (AVA). In the presence of severe AS, normal instantaneous transvalvular flow rate (Q) values through the valve are often not achieved because of an underlying ventricular disease. In the case of reduced Q, severe AS may exhibit low gradients and smaller AVA. Such a low-Q, low-gradient constellation is present in approximately 40% of patients with severe, symptomatic AS (1). The term “low-flow low-gradient AS” has therefore become popular in echocardiography. In these patients, the diagnosis is cumbersome and additional tests, such as stress tests, may be necessary to better characterize the flow rate-dependent aortic valve opening behavior (2,3). With regard to its ability to increase Q, dobutamine has been shown to be ineffective in numerous situations, especially in low-Q with normal ejection fraction, an entity also referred to as paradoxical low-flow, low-gradient AS. We previously suggested that a volume challenge may be superior for this purpose (4). In addition, pharmacologic adrenergic stimulation may trigger complications in severe AS, such as ischemia and tachyarrhythmia. Clinicians often restrain themselves from using such an approach, particularly in the concomitant presence of coronary artery disease. Therefore, a new method for the prediction of maximal AVA is desirable. It should be robust in the presence of low-Q without the need for stress stimuli.

Our approach considers that a range of different Q is present during every systolic ejection, and that the instantaneous AVA follows accordingly: the dynamics of pulsatile flow and subsequent aortic valve opening - from closed at the onset of systole to its maximal opening - has the potential to allow projecting the AVA to any hypothetical (and physiologically unreachable) Q value. In previous studies, we suggested that the Q-AVA-relation does not follow a linear path, but that a saturation of AVA occurs at high Q (5,6). This seems obvious considering that AVA is constrained by the dimensions of the supporting structures, such as the aortic annulus. Previous methods did not take this into account, portraying a linear Q-AVA-relation regardless of the anatomical constraints (“projected AVA”) (7,8). The premise of this approach was that if Q can be increased during the stress test, a theoretical AVA can be projected at a standardized Q (set arbitrarily to 250ml/s) by linear extrapolation. Undoubtedly, this method has the merit that AVA values become more comparable regardless of Q. Our method, however, differs in three aspects: First, a saturating (sigmoid) Q-AVA-relation must also be considered, as previously suggested. Second, there should be a robust prediction of maximal possible AVA from low Q situations in clinical routine, obviating the need for a stress test. Third, a new parameter of AS severity should be deducible by parametrizing a sigmoid Q-AVA-relation, i.e. the relative aortic valve stiffness, rAVS (6). We hypothesize that this new parameter is superior in assessing AS severity than the previous linear model in humans. Its clinical impact is assessed using a Cox proportional hazard model for analyzing rehospitalisation-free survival.

Methods

Patient Recruitment

One hundred forty-one consecutive patients referred to our laboratory for transesophageal echocardiography (TEE) were prospectively included with the aim of achieving a similar number of patients with normal aortic valve, mild, moderate and severe AS. The severity of AS was defined using the continuity equation as follows: severe aortic stenosis: AVA < 1.0 cm², moderate aortic stenosis: 1.0 cm² ≥ AVA < 1.5 cm², mild aortic stenosis: 1.5 cm² ≥ AVA < 2.5 cm², normal aortic valve: AVA > 2.5 cm². As there is no threshold value between normal aortic valve and mild aortic stenosis, we arbitrarily classified patient with AVA > 2.5 cm² as having a normal aortic valve. Exclusion criteria were: age < 18 years, aortic valvular prosthesis, more than mild aortic regurgitation, infective endocarditis of the aortic valve, hypertrophic obstructive cardiomyopathy (HOCM), more than mild mitral regurgitation, and atrial fibrillation.

An additional 21 patients hospitalized at the intensive care unit (ICU) under va-ECMO (veno-arterial extracorporeal membrane oxygenation) undergoing routine TEE-guided weaning procedure were also included. These patients were only included if they showed a morphologically normal aortic valve.

The study was approved by the Ethics Committee of the Canton of Bern, Switzerland (KEK 2019-00666 and KEK 2021-01134).

Echocardiographic Data Acquisition

TEE images were acquired using EPIQ CVx ultrasound machines equipped with an X8-2T probe (Philips, Amsterdam, Netherlands). Pulsed-wave Doppler signals in the left ventricular outflow tract (LVOT) and continuous-wave Doppler signals in the aortic valve were recorded in the transgastric view. A single-beat 4D dataset zoomed on the aortic valve was acquired in the transesophageal short axis view (60°) at a frame rate of at least 50Hz to maximize temporal resolution with the narrowest field of view encompassing only the aortic valve during systole to retain a good spatial resolution. A second single-beat 4D dataset on the LVOT was acquired with a lower frame rate (20-50Hz) to favor spatial over temporal resolution. Furthermore, 2D scans in the mid-esophageal four-chamber and two-chamber view were obtained. In va-ECMO patients, all acquisitions were repeated for every weaning step after allowing a steady state of 2 minutes.

Echocardiographic Measurements

All measurements were performed offline by independent, experienced echocardiographers in Tomtec Arena (Tomtec, Unterschleissheim, Germany) equipped with multiplanar reconstruction functionalities. In each frame k of the 4D dataset of the aortic valve and using multiplanar reconstruction, the instantaneous AVA (AVA[k]) was manually traced in the most distal plane orthogonal to the flow, where all the borders of the cusps were visible over the entire ejection (see supplemental material, DOI: https://doi.org/10.6084/m9.figshare.31338727). A single, mid-systolic LVOT area was also measured planimetrically following the inner edge of the aortic valve from the corresponding 4D dataset using multiplanar reconstruction as previously described (9). The stroke volume was calculated with the Doppler method by multiplying the systolic velocity time integral in systole by the LVOT area (10).

Cardiac output was obtained by multiplying the stroke volume by the heart rate. The maximal and average value of the transvalvular aortic velocity and transvalvular aortic gradient where obtained. Left ventricular ejection fraction (LVEF) was calculated using the biplanar Simpson rule.

Similarly to the AVA[k] data acquisition, Q was also measured to create individual {Q[k],AVA[k]} data pairs. The following procedure was performed using custom software written in Python programming language: The contour of the pulsed-wave Doppler signal in the LVOT was manually traced on the calibrated DICOM image file (figure 1, left panel), yielding an instantaneous velocity profile. This profile was then resampled to the frequency given by the AVA[k] dataset (middle panel), thus allowing to create a {Q[k],AVA[k]} dataset containing temporally aligned, simultaneous data pairs (right panel). In order to take into account the valve dimension of the patient, Q was divided by the LVOT area, which corresponds to the velocity.

Figure 1. Obtaining Coinciding Q-AVA-Datapairs.

The pulsed-wave Doppler signal in the LVOT was manually traced (left panel), then resampled according to the available frames of the echocardiographic 3D scan of the aortic valve (middle panel, green frame lines). This allowed obtaining coinciding Q-AVA-datapairs (right lower panel). Normalization with the LVOT area were applied to the parameters (see text).

Definition of the Linear and Sigmoid Models Describing the Q-AVA-Relation

The relation between AVA[k] and Q[k] was modelled with two equations as previously described (6). The first assumed a linear relation, reflecting the linear assumption of the current literature (7,8) (Equation 1), whereas the second assumed a staturating, sigmoid relation (Equation 2):

$$AV{A}_1={\theta }_1\cdot \frac{Q}{LVO{T}_{area}}\cdot {\theta }_2{ }^{rAVS}$$ Equation 1

$$AV{A}_2=\frac{{\theta }_3}{rAV{S}^{{\theta }_4}}(\frac{1}{e^{\left(\frac{-Q\cdot {\theta }_5}{LVO{T}_{\mathit{\text{area}}}}\right)+1}}-0.5)$$ Equation 2

where AVA₁ and AVA₂ are the respective predicted AVA for each model, θ_1-5 are the hyperparameters to be fitted on the training set and to be kept constant for all the valves of the test sets in AS patients.

Hyperparameter Fitting, Definition of rAVS and AVA Prediction Schemes

The first regression machine learning training step consisted in fitting the model’s hyperparameters (θ_1-5) using patients with normal aortic valves, including our va-ECMO-patients. The Levenberg-Marquardt algorithm was used. The rAVS-values were predefined as equal to 1 as a reference of normal opening in this first training. A k-fold (k=5) cross-validation algorithm was used to internally validate the results of the first step. In this step, the {Q,AVA} data pairs of all the normal valves were randomly split in five groups. The hyperparameters (θ_1-5) were fitted on the training set constituted by four of the groups. With the obtained hyperparameters (θ_1-5), rAVA and AVA were predicted on the last remaining fifth group constituting the test set. This procedure was performed five time for each group sequentially defined as the test group. Mean and standard deviation for the hyperparameters (θ_1-5), rAVA and mean squared error (MSE) for AVA prediction were reported. Due to the small amount of data, we decided to fix one of the parameter done on all the data points. θ₄ seemed to be most robustly converging to a certain value which we decided to fix in the later stages so as to limit the number of parameters in the model and so, further reduce potential overfitting In the second training step, the retrieved hyperparameter values where used as constants to fit the individual rAVS-values in AS patients.

Particular attention was payed to the prediction of maximal AVA from low Q, because this represents the low-flow situation frequently encountered in clinical routine in the presence of diseased ventricles. Four prediction schemes with a stepwise loss of high Q training data were therefore introduced: The 70%-, 50%-, 30%, and the 10%-scheme. The percentage number in the scheme name indicates the lower Q range used for training (second training set) to predict AVA in the remaining higher Q range, the test set. Figure 2 illustrates these prediction schemes. We previously described this method in detail in our in-vitro study (6).

Figure 2. Examples Illustrating the Prediction Schemes.

A patient with mild (upper panels) and with severe (lower panels) AS are illustrated. Per design, the 70% prediction schemes predict the upper AVA values (range with red dots) from the lower 70% of the Q range (black dots). The predicted values for the linear model are depicted as green dots, whereas the predicted values of the sigmoid model are shown as blue dots. On the other extreme, i.e. the 10% prediction scheme, AVA is predicted using only the lowest 10% of the Q range, which increases the prediction uncertainty. The deviation of the green and blue dots from the measured red dots determine the models’ prediction capabilities. Note that in the patient with severe stenosis, the measured AVA values saturate at a lower level compared to the patient with mild stenosis.

To further increase prediction robustness in low Q situations, we included patients with normal aortic valves that were under va-ECMO (Cardiohelp, Getinge Group, Germany) and mechanical ventilation (Hamilton C6, Hamilton-Medical, Bonaduz, Switzerland) at our intensive care unit. During va-ECMO, intracardiac blood flow is drastically reduced (11), but it can be varied during the ECMO-weaning procedure (12,13). This provides the unique opportunity to study the Q-AVA-relation in an unphysiologically low range of Q.

Prediction Accuracy: Comparison between the two Models

AVA prediction accuracy was assessed by quantifying the full-range agreement between Q[k] and AVA[k] in both, the linear and the sigmoid model. The model’s goodness of fit was determined by the Akaike information criteria (AIC), with lower AIC values indicating a better fit (14). A linear regression analysis between predicted and measured AVA[k] was also performed for each model and scheme.

Determining the rAVS Threshold for the Distinction between Severe and Non-Severe AS

A receiver operating characteristic (ROC) analysis with computation of its area under the curve (AUC) was performed to discriminate between severe from non-severe AS in all patients. The ROC analysis was performed for both, the linear and the sigmoid model. The AUCs were compared using the Hanley-McNeil test.

Construction of the Isostiffness Nomogram

The mean of the isostiffness line with its confidence interval was computed for each AS severity group. The isostiffness line corresponding to the rAVS-value best capable of differentiating between severe and non-severe AS was computed with the Youden’s index in the ROC analysis and was additionally plotted in the nomogram.

Statistical Methods

Patients with AVA > 2.5 cm² undergoing TEE in our echocardiographic laboratory or undergoing va-ECMO-weaning were pooled to construct the normal isostiffness line (rAVS = 1 by definition). The baseline variables are given as pooled data in the normal group, i.e. including the va-ECMO patients. Between-group comparisons were performed by analysis of variance (ANOVA), and a post-hoc Tukey test. Trend significance was computed by ANOVA linear trend testing.

A Cox proportional hazards model was used to separately determine the influence of AVA and rAVS on the rehospitalization rate. Rehospitalisation of any cause was defined as the endpoint. Additional independent variables included diabetes, smoking, the presence of other cardiovascular diseases (including pulmonary embolism, heart failure, coronary heart disease), cerebrovascular diseases, chronic respiratory diseases (including COPD, emphysema, asthma, pulmonary fibrosis), as well as malignant tumors. The variance inflation factor (VIF) was calculated to exclude relevant multicollinearity.

Statistical analyses were performed on R (RStudio, R Core Team 2023).

Results

Baseline Characteristics

A total number of 141 patients were included with 3705 {Q,AVA} data pairs. The baseline characteristics are given in table 1. There were 50 patients with normal aortic valves and 32, 33 and 27 with mild, moderate and severe AS respectively. Within those groups there were 21 patients analyzed during ECMO-weaning of which 14, 5 and 2 where classified as normal mild and moderate aortic stenosis.

Table 1. Baseline Characteristics.

	normal	mild AS	moderate AS	severe AS	p value
n	50	32	33	27	-
male (%)	74	56	64	33	0.005
age (y)	58 ± 14	73 ± 10	78 ± 6	76 ± 17	<0.001
height (cm)	173 ± 9	170 ± 9	169 ± 7	165 ± 10	0.003
weight (kg)	82 ± 16	77 ± 14	81 ± 14	76 ± 16	0.261
body surface area (m2)	1.96 ± 0.23	1.88 ± 0.20	1.91 ± 0.17	1.82 ± 0.18	0.043
LVEF (%)	51 ± 19	51 ± 18	53 ± 15	53 ± 11	0.868
heart rate (min−1)	76 ± 16	75 ± 19	71 ± 16	76 ± 11	0.593
SVI (ml/m2)	29.5 ± 11.7	30.0 ± 10.8	34.3 ± 12.9	29.9 ± 9.7	0.286
cardiac index (l/min/m2)	2.2 ± 0.9	2.1 ± 0.7	2.3 ± 0.7	2.2 ± 0.7	0.769
AV mean velocity (m/s)	0.84 ± 0.23	1.13 ± 0.39	1.86 ± 0.52	2.16 ± 0.54	<0.001
AV peak velocity (m/s)	1.20 ± 0.35	1.61 ± 0.58	2.63 ± 0.69	2.90 ± 0.74	<0.001
mean gradient (mmHg)	3.0 ± 1.5	5.7 ± 3.9	14.8 ± 8.4	19.8 ± 10.1	<0.001
peak gradient (mmHg)	6.2 ± 3.4	11.7 ± 8.1	29.5 ± 15.3	35.9 ± 19.2	<0.001
AVA max (cm2)	3.20 ± 0.72	1.88 ± 0.30	1.22 ± 0.14	0.79 ± 0.11	<0.001
AVA mean (cm2)	2.22 ± 0.53	1.31 ± 0.32	0.80 ± 0.14	0.48 ± 0.09	<0.001
Q max (ml/s)	312 ±114	286 ± 88	329 ±126	264 ± 73	0.087
Q mean (ml/s)	216 ± 76	192 ± 59	220 ± 82	182 ± 55	0.095
LVOT area (cm2)	4.24 ± 0.83	3.74 ± 0.87	4.02 ± 0.81	3.74 ± 0.75	0.025

Baseline characteristics for each group of aortic stenosis severity. Patients under va-ECMO and patients with normal aortic valves undergoing elective TEE in our echocardiography laboratory are pooled in the normal group.

Abbreviations: AV = aortic valve; AVA = aortic valve opening area; LVEF = left ventricular ejection fraction; LVOT = left ventricular outflow tract; Q = flow; SVI = stroke volume index; va-ECMO = veno-arterial extracorporeal membrane oxygenation.

Hyperparameters, rAVS and AVA prediction

The k-fold (k=5) cross-validation yielded the following mean results rounded to the fourth decimal: θ₁ = 0.0945±0.0001, θ₂ = 0.0945±0.0001 for the average of the 5 training runs, MSE on the prediction of AVA on the tests runs = 0.042±0.003cm² and an rAVS of 0.9434±0.2491 (for the linear model, equation 1) and θ₃ = 1.4234±0.0133, θ₅ = 0.0446±0.0008 (θ₄ parameter was set fixed to 3.000 based on exploratory fitting runs) for the average of the 5 training runs, MSE on the prediction of AVA on the tests runs = 0.026±0.003cm² and an rAVS of 0.929±0.234 (for the sigmoid model, equation 2).

The mean rAVS-values for the various AS severity groups, schemes and models are shown in figure 3. In both, the linear and the sigmoid model, rAVS gradually increased along the AS severity groups, showing that a higher rAVS-value reflects a more stenosed valve. In the sigmoid group, rAVS-values remained consistent in the 70%, 50% and 30% scheme, a property not shared by the linear model. Here, there was a statistically significant trend towards a decrease in rAVS when the highest Q-range was increasingly omitted from the prediction. Figure 4 depicts the correlation plots of the predicted versus measured AVA in all AS patients. Here, it can be appreciated that the sigmoid model outperformed the linear model in all prediction schemes, but it was particularly more robust when prediction was enforced from low Q values (50% and 30% schemes). Accordingly, the AIC was better (i.e. more negative) in the sigmoid model throughout all prediction schemes: -23597 vs -21031 in the 70% scheme, -18750 vs -16990 in the 50% scheme, -13341 vs -12328 in the 30% scheme, -7933 vs -7428 in the 10% scheme. Similarly, MSE of the linear regressions were more favorable in the sigmoid model (6.6 vs 14.1, 4.9 vs 12.4, 4.7 vs 14.8, and 6.3 vs 23.0 x10^-6, respectively). The 10% scheme introduced a large scatter in both models, which is to be expected as the training set was extremely small.

Figure 3. The relative Aortic Valve Stiffness Values (rAVS).

Bar plot of the rAVS-values for the various AS severity groups, prediction schemes (70% to 10%) and the two models (linear and sigmoid). The plot not only illustrates the increasing rAVS-values with increasing AS severity, but also the stability of rAVS in the sigmoid model within the severity groups. * p=0.01, **p<0.0001 in ANOVA linear trend testing.

Figure 4. Regression Plots of Predicted versus Measured AVA.

The graphs illustrate how the disparity between measured and predicted AVA values widens as prediction difficulty increases, progressing from the 70% to the 10% scheme. It is visually evident that the scatter is more prominent in the linear model (green) as compared to the sigmoid model (blue). The corresponding statistical confirmation can be found in the text.

ROC Analysis

In the ROC analysis performed in all AS patients and using the 70% scheme of the sigmoid model, the AUC was 0.88 for a rAVS-threshold of 1.51. This value represented the rAVS that discriminated severe from non-severe with an accuracy of 0.85 (figure 5). The same ROC analysis using the linear model yielded an AUC of 0.83, and the rAVS-threshold was also 1.51 with an accuracy of 0.72. With increasing data scarcity for AVA prediction, the AUC diminished, remaining slightly higher in the sigmoid than in the linear model, but these differences did not achieve statistical significance.

Figure 5. ROC-Analyses.

ROC-analyses for the detection of severe AS in all models and schemes. The area under the curve (AUC) decreased gradually with smaller training sets in both models. The sigmoid model showed consistently higher AUC values compared to the linear model, although these inter-model differences did not reach statistical significance.

Isostiffness Nomogram and rAVS-Formula

The isostiffness nomograph is depicted in figure 6. The lines for the various AS severities are well distinct. Since the flow Q is normalized to the LVOT area, the unit on the x-axis corresponds to the velocity in the pulsed-wave Doppler signal. Using this nomogram, a LVOT flow velocity (V) and a simultaneous AVA value (normalized to the LVOT area) can be used to estimate the rAVS, i.e. a Doppler measurement and a structural assessment. Points below the black isostiffness line (rAVS = 1.51) are indicative for severe AS with the accuracy reported in the ROC analysis.

Figure 6. Isostiffness Nomogram.

The sigmoid Q-AVA-relation is depicted for various AS severity grades: green = normal AVA, blue = mild, brown = moderate, red = severe. The black line corresponds to the Q-AVA-relation for a rAVS-value of 1.51 (i.e. value best discriminating severe from non-severe). The dotted lines represent the confidence intervals. Using this graph, the individual rAVS-value can be determined by relating a flow velocity measurement in the LVOT with a planimetric measurement of the AVA, the latter normalized by the planimetric LVOT area.

An alternative, more quantitative method is the direct calculation of rAVS using the following formula derived from our sigmoid model (equation 2), using the fitted hyperparameters:

$$rAVS=\sqrt[3]{\frac{LVO{T}_{area}\cdot 1.423\cdot \left(\frac{1}{e^{\left(-V\cdot 0.045\right)}+1}-0.5\right)}{AVA}}$$

, where LVOT area and AVA are given in cm² and V in cm/s, respectively.

Survival Data

The results of the Cox proportional hazard model for the survival free from rehospitalization is given in table 2. The follow-up period was 1299 ± 220 days. There were 75 hospitalizations events reported in the cohort. A relevant multicollinarity between the test-variables could be excluded, as all VIF were <5. Whereas AVA<1cm² did not emerge as an independent predictor, rAVS ≥1.51 significantly predicted rehospitalization-free survival. The same analysis with overall survival did not show any statistical significance due to the low number of casualties in our population. A Kaplan-Meier curve for severe and non-severe AS population according to rAVS can be found in figure 7.

Table 2. Rehospitalization-free survival, Cox Proportional Hazard Model, HR: Hazard ratio.

	VIF	HR	95%-CI	p-Value
Analysis with AVA
Diabetes	1.43	0.84	0.49 to 1.42	0.51
Smoking	1.92	0.95	0.59 to 1.54	0.85
Cardiovascular diseases	1.62	0.83	0.51 to 1.35	0.46
Cerebrovascular diseases	1.31	0.95	0.56 to 1.60	0.85
Chronic pulmonary diseases	1.21	1.88	0.94 to 3.77	0.08
Malignant cancer	1.18	1.21	0.63 to 2.28	0.56
AVA < 1cm2	2.08	0.82	0.65 to 1.03	0.10
Analysis with rAVS
Diabetes	1.79	0.88	0.49 to 1.61	0.68
Smoking	1.71	0.97	0.55 to 1.71	0.91
Cardiovascular diseases	2.00	0.84	0.47 to 1.50	0.54
Cerebrovascular diseases	1.27	1.01	0.53 to 1.93	0.99
Chronic pulmonary diseases	1.23	1.72	0.74 to 4.02	0.21
Malignant cancer	1.27	1.34	0.60 to 2.97	0.47
rAVS ≥ 1.51	2.57	1.26	1.02 to 1.55	0.03
rAVS ≥ 1.51 male subgroup	2.84	1.04	0.76 to 1.42	0.83
rAVS ≥ 1.51 male subgroup	2.62	1.53	1.09 to 2.14	0.01

Figure 7. Isostiffness Nomogram.

A Kaplan-Meier curve showing the difference in hospitalization rate between the severe and non-severe AS population according to rAVS.

Discussion

In this study, we developed a model to simplify the classification system for AS severity in humans. Our research indicates that a sigmoid model offers improved accuracy in predicting AVA at any clinically reasonable flow. The model’s robustness is evident as it consistently predicts rAVS, even when only the lowest 30% of Q-values are available, a capability not shared by the linear model. This tool intends to assess AS severity across various flow rates, LVOT and valve sizes, and providing personalized valve stiffness values through a single nomogram or formula. In our study, a stiffness value greater than 1.51 demonstrated high accuracy in distinguishing between severe and non-severe AS. The approach eliminates the need for a stress test, requiring only a single simultaneous echocardiographic Q-AVA data pair. In particular, rAVS can be used in both cases of classical (LVEF <50%) and paradoxical (LVEF ≥ 50%) low-flow, low-gradient AS, as our model covers the whole spectrum of theoretical Q encountered in the clinic and does not make any assumption regarding systolic or diastolic dysfunction of the LV. This could be a particular additional useful tool to help simplify the challenging low-flow, low-gradient AS classification. The current results are consistent with our previous observations. In a pooled analysis from transthoracic echocardiograms that included inotropic stress and volume challenge testing in patients with severe AS, a saturating Q-AVA-relation could also be demonstrated (5). Interestingly, the linear, projected AVA method applied in saturating data led to the apparently paradox situation that a stress stimulus can increase maximal AVA, while simultaneously decreasing the projected AVA. This paradox is caused by the fact that a straight line between two points in a saturating curve is always a secant whose slope depends on the localization of the two points, i.e. of the instantaneous flow rates. In a particularly effective stress test, the upper point is farther in the saturating part of the curve, diminishing the slope of the secant, and ultimately leading to a lower projected AVA despite an increased maximal AVA. The same phenomenon can be observed without any stress test in this study, particularly in moderate and severe AS (figure 3): When most high Q values are included in the prediction, the linear model tends to produce the highest rAVS values (hence the flattest secant), and vice versa. The sigmoid model, on the other hand, shows a very stable stiffness measurement even when high Q-values are deliberately excluded from the training scheme. The sigmoid model therefore shows more robustness in estimating valvular stiffness in the low Q range and more Q-independent consistency in general. Although their hemodynamical state is altered with respect to the normal population, patients under va-ECMO offer a unique opportunity of observing the opening behavior if the aortic valve under very low-flow conditions. The method is theoretically also applicable in bicuspid aortic valves, but this study does not provide specific data in these patients. It should be further noted that the method has not yet been tested for prosthetic aortic valves.

Our new method also suggests its clinical relevance, as a severe stenosis as assessed using rAVS significantly and independently predicts rehospitalisation-free survival. Interestingly, AVA was not an important variable associated with rehospitalization. We think that this might be due the small patient sample size and we still believe that this remains a valuable clinical marker. For overall survival analyses, a new and adequately powered study is needed. Finally it would be conceivable to use this method with cardiac magnetic resonance as the same measurements can be retrieved with this other imaging modality (16).

Limitations

This study lacks an independent measure of AS severity beyond echocardiography, which would have been preferable. The study design mandated the inclusion of patients with normal aortic valves and mild AS, making alternative standards like computed tomography or cardiac catheterization unfeasible in this population. Although we did show that AVA with respect to Q also follows a sigmoid behavior in patients with low-flow, low-gradient AS undergoing diagnostic dobutamine stress echocardiography (5), this imaging modality, recommended in the guidelines for such patients was not used in the present study.

It is important to note that our method is not suitable for cases with significant LVOT obstruction, such as hypertrophic obstructive cardiomyopathy (HOCM). In HOCM, the aortic valve opening exhibits a unique behavior characterized by intense turbulences and dynamic systolic pressure drops in close proximity to the valve. This condition is beyond the intended scope of our study. These patients were excluded from our study and caution is therefore advised against using echocardiographic data from these patients to assess AS severity using our method. Furthermore, our analysis focuses solely on adult individuals. Acknowledging the challenge of extending our results to pediatric echocardiography, we intentionally designed the normalization of AVA to the LVOT area to facilitate testing in the presence of smaller structures without significant parameter alterations. However, specific validation with pediatric data is necessary to confirm the applicability of our method in children. Moreover, due to the asynchronous sampling of Q and AVA with assumption of a constant heart cycle length, patients with atrial fibrillation were not included in this study. Those patients as well as patients with mitral regurgitation should be included in a future study to evaluate the diagnostic yield of our method in those subpopulations.

It needs also to be noted that as our method was performed with data collected with TEE, it is probably not transposable to transthoracic echocardiography were the quality of AVA planimetry is too often insufficient. Planimetry on 4D dataset is also technically demanding. Nevertheless it should be seen as a useful additional measurement for patients in which an uncertain diagnosis of AS warrants the realization of a TEE. Despite the fact that the standard deviation encompasses normal stroke volume indices, the mean stroke volume indices is low across all the AS severity groups. This model needs to be validated in patients with higher/normal stroke volume indices. Although we did not test intra- or interobserver variability in rAVS per se, we did show a good intra- (ICCs 0.99, 95% CI 0.98 to 0.99, p <0.001) and interobserver (ICCs 0.98, 95% CI 0.99 to 0.99, p <0.001) variability for AVA measurements in a previous work on the same dataset (17).

The goal of our study was to provide a new quantification method of AS with a small number of measurement, backed up by survival data. We did not include the myocardial dysfunction measured by global longitudinal strain or late gadolinium enhancement in our model as mentioned in the literature (18). Moreover, as LVOT area and AVA are known for large measurement variability, which affects our method as well as the classical one, the use of artificial intelligence to automatically segment those areas should probably be sought after to improve the reproducibility of the measurements.

For our validation process, it was essential to maintain a consistent heart rate. Since all TEEs were conducted under sedation, there might have been fluctuations in sedation depth leading to hemodynamic changes (19–22). To address this concern, we took measures to ensure stable sedation levels, including the use of automated target-controlled infusions (TCI) of propofol.

The non-simultaneous acquisition of Q and AVA data posed a challenge in ECMO patients. The assessment of normal opening behavior (illustrated by the green curve in figure 6) under extreme low-flow conditions was complicated by the onset of ‘pulsus alternans’, i.e. cardiac output fluctuating on a beat-to-beat basis. This was addressed by selecting the signals from the most vigorous outputs.

We acknowledge the relatively limited size of our monocentric patient cohort for establishing full conviction not only in the ROC curve comparisons, but also in machine learning algorithms in general. A validation of our finding in other centers is needed. The theoretical risk of non-independent data exists as there was multiple measures per patient. The frame-by-frame echocardiographic analyses, however, were performed with a well-defined prediction goal, and an algorithm specialized on smaller sample sizes was used. The compilation of 3705 manually acquired Q-AVA data pairs provides a reassuring foundation. Furthermore, the data quality corresponds to the current state of the art in TEE, as only experienced echocardiographers meticulously conducted all 3D image acquisitions, as well as all AVA and LVOT area measurements using multiplanar reconstruction. The influence of hemodynamic fluctuations (due to sedation or va-ECMO settings) on measurement reliability and external applicability needs more evaluation in other centers.

Conclusions

We propose a new, single parameter for the quantification of AS that incorporates the transvalvular flow conditions.

Perspectives

Competencies

This study offers a new way to quantify AS without the need for commonly used terms like “low-flow”, “paradoxical” or “pseudo-severe”. This was not achieved by neglecting flow conditions, but by integrating them into a single parameter that characterizes the stiffness of the aortic valve itself.

Translational Outlook

Given the clinical importance of AS quantification, our method deserves solid clinical testing in a large population, where the statistical power is sufficient to enhance robustness of rAVS-cut off values, to establish its impact on outcome, and to delineate the limitations that may be imposed by other cardiac co-morbidities.

New & Noteworthy.

Aortic stenosis (AS) quantification relies on transvalvular gradients or aortic valve opening area (AVA). We present a new quantification method for AS based on new modelling of the aortic valve opening behavior. We fitted a sigmoid relation between flow rate and AVA and retrieved the “relative aortic valve stiffness” (rAVS). We could demonstrate its superior association with clinical endpoints compared to previous models in AS and provide a simple tool for its calculation using echocardiography.

Central Illustration.

Example of our new method for AS quantification using a nomogram. The saturating curves represent the isostiffness lines for normal aortic valves (green), mild (blue), moderate (orange), and severe (red) AS. The thick solid black line represents the relative aortic valve stiffness (rAVS) value that best discriminated between severe and non-severe AS. The individual point in the nomogram results from relating the pw-Doppler velocity in the LVOT to the AVA (normalized by the LVOT area). Any resulting point located below the black lines (as in this example) is indicative for severe AS. Alternatively, rAVS can be calculated directly with a formula provided in the manuscript without the use of the nomogram. This method allows quantifying AS by incorporating the flow conditions in a single parameter, and therefore eliminates the need for commonly used terms like “low-flow”, “paradoxical” or “pseudo-severe”.