## Background

Measurement of left atrial (LA) volume (LAV) is recommended for quantification of LA size. Only LA anteroposterior diameter (LAd) is available in a number of large cohorts, trials, or registries. The aim of this study was to evaluate whether LAV may be reasonably estimated from LAd.

## Methods

One hundred forty consecutive patients referred to our outpatient clinics were prospectively enrolled to measure LAd from the long-axis view on two-dimensional echocardiography. LA orthogonal dimensions were also taken from apical four- and two-chamber views. LAV was measured using the Simpson, area-length, and ellipsoid (LAV _{e }) methods. The first 70 patients were the learning series and the last 70 the testing series (TeS). In the learning series, best-fitting regression analysis of LAV-LAd was run using all LAV methods, and the highest values of *F *were chosen among the regression equations. In the TeS, the best-fitting regressions were used to estimate LAV from LAd.

## Results

In the learning series, the best-fitting regression was linear for the Spearman method ( *r *^{2 }= 0.62, *F *= 111.85, *P *= .0001) and area-length method ( *r *^{2 }= 0.62, *F *= 112.24, *P *= .0001) and powered for the LAV _{e }method ( *r *^{2 }= 0.81, *F *= 288.41, *P *= .0001). In the TeS, the *r *^{2 }value for LAV prediction was substantially better using the LAV _{e }method ( *r *^{2 }= 0.89) than the Simpson ( *r *^{2 }= 0.72) or area-length ( *r *^{2 }= 0.70) method, as was the intraclass correlation (ρ = 0.96 vs ρ = 0.89 and ρ = 0.89, respectively). In the TeS, the sensitivity and specificity of LA dilatation by the estimated LAV _{e }method were 87% and 90%, respectively.

## Conclusions

LAV can be estimated from LAd using a nonlinear equation with an elliptical model. The proposed method may be used in retrospective analysis of existing data sets in which determination of LAV was not programmed.

## Highlights

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LAV can be estimated from LA linear dimension using nonlinear equations.

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The most reliably estimated LAV is obtained using the ellipsoid model.

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The proposed method might be helpful for retrospective analysis of existing data sets in which determination of LAV was not programmed.

Left atrial (LA) dilatation is a potent marker of cardiovascular (CV) risk, associated with incident heart failure, atrial arrhythmias, and stroke. Assessment of echocardiographic M-mode or two-dimensional (2D) LA anteroposterior diameter (LAd) has been, for a long time, the only available noninvasive method to determine LA size. However, estimation of 2D and, more recently, three-dimensional LA volume (LAV), are more accurate, though the difference of prognostic power of LAV versus LAd has not been extensively investigated. Recent chamber quantification recommendations suggest biplane LAV as the most reliable method to assess LA size. Of note, the 2005 American Society of Echocardiography and European Association of Echocardiography recommendations also suggested normal values of LAd, which, however, were not adopted in the 2015 update.

Attempts have been made to find the best way to identify LA dilatation and to determine its prognostic role in different clinical and epidemiologic settings in which LAV is not available. Although current recommendations strongly suggest adopting LAV as standard for the quantification of LA size, LAd is present in large databases and is still used on an epidemiologic scale. Thus, the estimation of LAV from LAd might be helpful for a number of cohorts and registries in which the determination of LAV was not programmed, such as the initial cohort of the Framingham Heart Study, the Strong Heart Study, the Campania Salute Network, Progetto Ipertensione Umbria Monitoraggio Ambulatoriale, and others.

LAV is biologically related to LAd, though it is unreasonable to think that this relation (i.e., between a linear and a three-dimensional measure) would be linear. Accordingly, we designed this study to verify whether LAV may be estimated from LAd, in a consecutive series of new patients seen in our cardiology outpatient clinics.

## Methods

## Patients

We analyzed 2D echocardiograms from 140 patients (63% men; mean age, 61 ± 17 years) prospectively enrolled from January to March 2015 and seen in our outpatient echocardiographic laboratory. Written informed consent for the use of their data was obtained.

## Echocardiographic Evaluation

Two-dimensional echocardiograms were recorded using a commercially available echocardiographic system (iE33; Philips, Amsterdam, the Netherlands). All images were digitally recorded, and measurements were obtained using the commercially available software package on the same machine acquiring video clips. All measurements were obtained by averaging at least three consecutive cardiac cycles. Left ventricular (LV) ejection fraction and LV mass were computed as previously reported. LV hypertrophy was defined as previously prognostically validated.

We recorded parasternal long-axis view and apical four- and two-chamber views at the time of maximal LA size, at LV end-systole, with the subject in the left lateral supine position, as suggested by American Society of Echocardiography and European Association of Cardiovascular Imaging recommendations. LAd was measured from the long axis, orthogonal to the aortic root, at the level of the sinus of Valsalva using the leading edge–to–leading edge convention ( Figure 1 ). LA transverse ( *T *) and longitudinal ( *L *) dimensions were taken from the apical four- and two-chamber views using the inner edge–to–inner edge method ( Figure 1 ). Their mean values were used to compute LAV, using the ellipsoid model (LAV _{e }), applying the following formula :

LAV e = 4 3 π × D 2 × T 2 × L 2 .

The outline of the LA endocardium was also traced from the apical four-chamber (A1) and two-chamber (A2) views, excluding the area under the mitral valve annulus, atrial appendage, and pulmonary veins, according to Simpson’s rule. Automatic volume calculation was obtained by a computer software package using the modified Simpson disk summation method (LAV _{S }) and the longitudinal dimensions, measured in both orthogonal apical views ( Figure 1 ).

Finally from the same area and length measurements from the orthogonal apical windows, we also calculated LAV using the area-length method (LAV _{al }) using the following equation :

LAV al = 8 3 π × A 1 × A 2 L .

## Statistical Analysis

Data are expressed as mean ± SD. Statistical analysis was performed using SPSS version 21.0 (IBM, Armonk, NY). Intraobserver variability was assessed on paired readings obtained by the same observer (M.-A.L.). Interobserver variability was assessed on paired readings obtained by the second observer (G.C.). The first reading of each observer was considered for the statistical analysis of interobserver variability. Student’s *t *test of the mean differences between readings (intraobserver and interobserver) ( *x *_{1 }− *x *_{2 }) was used to determine the significance of the systematic difference (bias) for each source of variability. The percentage bias was computed as the percentage difference in the means by the following equation: 100[( *x *_{1 }− *x *_{2 })/( *x *_{1 }− *x *_{2 })/2]. The Pearson correlation coefficients for paired measurements were also calculated. The precision of the measurements (random variability) was computed as the mean of the absolute value of the differences, [(Σ| *x *_{1 }− *x *_{2 }|)/ *n *], where *n *is the number of subjects. The percentage precision was determined as 100[(Σ| *x *_{1 }− *x *_{2 }|)/ *n *]/[( *x *_{1 }+ *x *_{2 })/2], whereas the repeatability coefficient was determined as 1.96 × SD of the absolute value of the differences.

Patients were divided into two series according to the sequence of presentation to our outpatient clinics. The first 70 patients were analyzed as the derivation group (learning series), and the last 70 patients represented the validation group (testing series). To verify or reject the assumption of linearity, in the learning series, we ran a best-fitting regression analysis between LAd and LAV measured with the three reported methods and compared *F *values among the following regression models: linear, logarithmic, quadratic, cubic, compound, power, S, growth, and exponential. The *F *value, which compares the fits of different regression models in relation to their variance, expresses the statistical significance of the different models. Although *r *^{2 }(the coefficient of determination) provides an estimate of the strength of a relationship and gives information on how much variance of the dependent variable can be explained by the independent variable, it does not provide a formal hypothesis test for the relationship. The *F *test determines whether this relationship is statistically significant. The *F *value follows the *r *^{2 }value in regression models with one independent factor but is more accurate in expressing the strength and the significance when multiple factors are imputed, such as in quadratic and cubic modeling, when *r *^{2 }might be greater but the *F *value lower. For testing analyses, we used the regression models corresponding to the highest values of *F *in each of the methods of calculation of LAV and compared the predicted with the observed values in the test series.

To evaluate the degree of accuracy of estimation of LAV in the test series, intraclass correlation between estimated and measured LAV was run using a two-way random-effects model. To evaluate the limits of agreement between observed and estimated LAV _{e }and LAV _{S }, Bland-Altman plots were used. To evaluate the practical applicability of the LAV estimation, we analyzed the accuracy for definition of LA dilatation, using cut points proposed by Kuznetsova *et al *., using an elliptical model, and based on an allometric exponent of height to normalize LAV to body size.