Accuracy of continuity equation in aortic stenosis and irregular heart rhythm (5–10 beats average)
Authors: Romero Puche A J , Andreu Cayuelas J M , Cambronero Sanchez F , Cerdan Sanchez M C , Garcia-Escribano I , Vicente Vera T 
Published: October 2022

Abstract

Introduction
Continuity equation is the cornerstone of aortic valve area (AVA) calculation in patients with aortic stenosis (AS). In patients with irregular rhythms (IR) - especially atrial fibrillation (AF)-, values of velocity-time integral (VTI) at left ventricular outflow tract (LVOT) and aortic valve (AV) vary between heart beats. The usual recommendation is to average the measurements of 5 or 10 beats in both locations. However, original papers describing continuity equation, from which that recommendation arises (refs 1 & 2), only included 3 and 2 AF patients, respectively. To our knowledge, there are not clinical studies to support this procedure and its accuracy has not been established.
In contrast, in a previous study our team had evaluated the accuracy of the double envelope technique to assess both LVOT and AV VTI in the same beat, with a 7.8% (CI 95%: 5.8–10.3) difference (error) in the estimation of AVA when compared to pulsed wave of LVOT in patients with stable sinus rhythm.

Purpose
To evaluate how dispersion in VTIs due to IR impacts on variability of AVA calculations.

Methods
For each patient, we recorded multiple measurements of VTI in both LVOT and AV (mean 36.8 beats, range 29–47) per patient and location). Reference AVA was estimated using the average of all these measurements. To estimate the accuracy of averaging 5 or 10 heart beats, we created a computer code which simulated the AVA calculation using random samples of these measurements, and calculated the difference between true AVA and that obtained in the simulation (expressed as percentage of the true value). The process was iterated 10,000 times to obtain the distribution of differences and to estimate its mean value.
Data handling and graphic representation was performed with Python 3.9.6 and Pyodbc, Pandas, NumPy, Matplotlib and Seaborn libraries.

Results
We included data from 8 patients with AS and IR (Age: 71 to 89, mean 82.5 years; Aetiology: degenerative (100%); Sex: 3 males / 5 females; Rhythm: AF [7], atrial flutter [1]; Severity: severe [3], moderate [4], mild [1]). Mean difference in AVA calculations was 8.2% (range: 5.1–13.5%). With 10 beats, mean difference was 5.7% (range: 3.6–9.5%).
Figute 1 shows violin plot with distribution in each patient of recorded VTIs at both AV (left) and LVOT (right). To ease visualization, data are expressed as percentage of mean values. Fig 2 shows how that variability results in inaccuracy of AVA calculations with 5 (left) or 10 beats (right). Note that in many cases, possible results are located on both sides of the severity threshold of 1 cm2 (red line).

Conclusion
AVA assessment using 5 beats average results in a mean difference (error) of 8.2%, which can be reduced to a mean of 5.7% using 10 beats. These differences are comparable with the previously observed with the double envelope technique (7.8%).

Funding Acknowledgement
Type of funding sources: None.