A method for measuring the angle between left atrial and left ventricular long axes using 3D echocardiography

Left ventricle (LV) optimized views are routinely used for left atrial (LA) volume and strain measurements on 2D echocardiography. This might be a source of the error because of the variation of the angle between the left atrial and left ventricle long axes (LA‐LV angle), leading to foreshortening of the LA.


INTRODUCTION
Left atrial size and function are established prognostic markers for adverse cardiovascular and cerebrovascular events, as well as cardiac and all-cause mortality. 1,2The most common way to evaluate left atrial (LA) structure and function is by using 2D echocardiography.The current guidelines 3 recommend 2D assessment of LA volume and function as the primary method.The recommended method is still the biplane disk summation technique, as there are insufficient data and standardized methodology to recommend 3D echocardiography as the primary method. 3However, the correlation with 2D measurements and the true LA volume is moderate at best 4 and 2D assessment, unlike 3D, consistently underestimates LA volume when compared to magnetic resonance imaging (MRI). 5e 2D views of the left heart are optimized along the left ventricle (LV) long axis in the guidelines. 3If the axes of the LA and LV are not codirectional, this might reasonably cause foreshortening of the LA and thus inaccurate measurements of the LA parameters.Using cardiac MRI, the concept of the angle between the LA and LV long axes (LA-LV angle) measurement has recently been established. 6To our knowledge only a single study has previously utilized this concept in CT imaging, concerning only volume measurements, and has found only minor differences in 2D volume calculation accuracy with respect to the LA-LV angle. 7Using echocardiography, atrial-focused views have been shown to yield better LA volume estimations than traditional LV-focused views, 8 but the determinants of this difference-such as, possibly, the LA-LV angle-have not been known previously.Even atrial-focused views may still misrepresent true LA size due to difficulty to verify a non-foreshortened view and due to constraints regarding acoustic windows 9 -indeed, getting a 2D view aligned to the LA axis would sometimes require absurd acoustic windows through the intestine. 10garding strain measurements, 2D imaging has been shown to overestimate LA strain compared to 3D imaging, and the difference in LA length between 2D and 3D images correlate with this error. 10This difference could at least partially be explained by the LA-LV angle, since 2D measurements of the LA are acquired only in 2-and 4-chamber views, and the measurement error of LA length could well be increased when the LA axis does not lay in those planes-as is often the case. 9en in what is traditionally thought of as a non-foreshortened LA 2D view, the length of the LA is shorter than in 3D view, 10 supporting this idea.
To the best of our knowledge, there are no studies investigating the concept of the angle between LA and LV-or any angle measurements at all-using 2D or 3D echocardiography.Indeed, the published angle measurements using 3D ultrasound have been mostly restricted to the Cobb angle of the spine 11 and the frontomaxillary facial angle of the fetus, 12 using fundamentally different techniques than what would be used with TTE.Neither have any previous studies to our knowledge sought to validate the cardiac angle measurements using in vitro models, regardless of the imaging modality.
Hence, we conducted this 3D echocardiographic study to evaluate whether angle measurement is possible and repeatable using phan-toms and further, to study whether it is feasible in human subjects.
We first establish the concept by using simple wooden phantoms to demonstrate that it is entirely possible to measure angles reliably using 3D echocardiography.Next, we use different phantoms made of agaragar to more accurately model the chambers of the human heart to find whether similar measurements can be performed in a more humanlike phantom.Finally, we pilot this measurement in a small number of human hearts in vivo.If the LA-LV angle could be measured and found to be partially responsible for the error of 2D echocardiographic measurements of the LA, it could help us find the patients for whom such measurements are unacceptably inaccurate.

Definitions
We considered the LV long axis to be the line defined by the LV apex and the center of the mitral annulus. 3The choice of LA long axis was more complex, as the center of LA roof has not been conclusively defined in the literature.Anatomically, it is the point at the center of the four pulmonary vein ostia, but these are often not all discernable using 3D TTE.
In our pilot studies we attempted to define it as the point in the LA wall furthest from the center of the mitral annulus, but this method produced inconsistent results, as such a point is often not explicit and may lie in an opening of a pulmonary vein, even when the veins are excluded from the LA volume.Similar problems arose when attempting to define it as the center of the LA in the most distant (from the mitral annulus) of the slices orthogonal to LV axis which still intersect the LA.
Thus, we defined LA long axis to be the line that starts at the center of mitral orifice and is at equal distances from the atrial walls up to the roof of the LA, thus avoiding the problems that pulmonary veins or the left atrial appendage might cause, and indeed, avoiding the need to define the exact center point of the LA roof altogether.
In prior ultrasound publications the definition of the 4-chamber plane has been descriptive without detailing specific anatomic markers, and to the best of our knowledge, a rigorous definition of the plane in the context of 3D echo does not exist.Hence we used a definition that was previously established using cardiac CT, 13 according to which the 4-chamber plane is the plane defined as the LV axis and the point of the right ventricular (RV) free wall which is the furthest from that axis.This definition is unambiguous and easily adapted to 3D echocardiography.
LA-LV angle was defined to be the angle between LA and LV axes such that the angle is zero if the axes are co-directional.The axis deviation from the 4-chamber plane was defined to be the angle between the 4-chamber plane and the LA axis such that the deviation is zero if the LA axis lies on the 4-chamber plane.If this deviation was directed anterior, the angle had a plus sign, and if inferior, a minus sign.
As the focus of interest is the LA maximum volume, all measurements were taken in LV end-systole, defined as the frame just before the mitral valve starts to open.This definition has been shown to be superior to ECG-derived triggers. 14The angles were measured in arc degrees.

F I G U R E 1
A wooden phantom used to simulate cardiac axes, and the corresponding ultrasound image.Points corresponding to the left ventricle apex (Apex; red sphere), left atrial roof (LA; blue sphere), right ventricle (RV; green sphere) and mitral valve orifice center (MV; yellow sphere) are depicted.The sides of the triangle in the top-left ultrasound image are measured and the angle deviation calculated from those..

Materials
Eight wooden phantoms using three skewers each of 3 mm diameter, and hot-setting adhesive were constructed.Two skewers representing the LV axis and the 4-chamber plane were joined with the adhesive, and a third skewer was joined in varying angles of approximately 20−40 degrees to represent the LA axis.The point at which the axes of these skewers met was considered the mitral orifice center.The skewers were joined such that the deviation from the 4-chamber plane was also varied (Figure 1).The LA-LV angles and their deviations from the 4-chamber plane were measured directly using a protractor.These measurements were performed in a separate session on a different day from the ultrasound measurements, in order not to cause bias during ultrasound analysis.The rationale behind using wooden phantoms was to study the concept of angle measurement in as simple a phantom as possible.
The angle measurement using a protractor gives a standard against which the ultrasound measurements could be compared and avoids In order to better mimic real cardiac tissue, we also constructed another set of nine phantoms made of 2.5% agar-agar solution in water.This is the most widely used material for soft tissue substitution described in the literature 15 and has been effectively used for imaging cardiac casts with ultrasound. 16In order to be able to accurately determine the LA-LV angle of these phantoms while avoiding bias from using specific molds in a known exact angle, we cast the agar solution onto a level sheet and cut it into shapes made of two cuboids representing LA and LV, approximately 20 × 25 × 40 mm each in size, with a varying angle between these cuboids, which was then measured using a protractor, similar to the wooden phantoms.Dimensions slightly smaller than a typical adult heart were chosen, as agar requires high surface-tovolume ratio to properly congeal. 15To unambiguously define the points representing the LA roof and the LV apex, the tips of these cuboids were cut into a pyramid shape, the tips of which represented these points.In order to represent the 4-chamber plane, a short piece of a wooden skewer was inserted into the cuboid representing LV into varying angles (Figure 2).The center of the mitral orifice was considered to be the midpoint of the plane joining the cuboids.
Finally, to better reflect the shape of the cardiac chambers, a third set of four phantoms using a 3% agar-agar solution augmented with .5% wheat flour for enhanced contrast 17 and 1% sodium chloride for enhanced stiffness 18 were prepared using tubular polyethylene molds of 35 mm inner diameter.Two of these tubes were joined side by side to represent LV and RV, and a third tube, one end cut to varying angles, was joined to the construction (Figure 3).Angles were measured using a protractor similar to the previous phantoms.The LA and LV axes were considered to be the centerlines of the respective tubes, the LV apex and LA roofs to be the distal points of these centerlines, and the center of the mitral orifice to be the point where these lines intersected.

Ultrasound imaging
We used a similar imaging protocol as described previously. 16A GE Vivid E95 device with a 4Vc-D probe (GE Vingmed Ultrasound AS, Horten, Norway) was used for all imaging.The phantoms were immersed in a 20-l water tank for imaging.No contrast agent was used for the wooden phantoms, or for the phantoms augmented with flour and salt.For the cuboid agar phantoms, a small amount of dried and ground seeds of Plantago Ovata was added to the water tank to enhance the echogenity of water and thus increase the visibility of the phantoms, while also mimicking the blood volume of the cardiac chambers having less contrast than the surrounding tissue.A coarse cloth was fixed in the bottom of the tank to lessen reverberation artifacts.
The wooden phantoms were attached to a pedestal at the bottom of the tank, and a wooden skewer was used to hold the agar phantoms in the middle of the tank.The probe was covered with a sterile transducer cover, with ultrasound gel between the lens and the cover, and suspended above the tank using a tripod so that the lens was just beneath the surface of the water.The phantoms were positioned to an apical ultrasound window, the part representing LV apex was facing upwards.
The LV axis of the phantoms was not exactly positioned parallel to the ultrasound beam to more simulate real-life conditions.In vivo imaging was performed by one of the researchers (V.J.) for patients who had a clinical indication for echocardiography.Ten patients were chosen for the study.A single-cycle full-volume 3DE scan using the same machine as with the phantoms was acquired so that the entire LA, LV and a large portion of RV were visible, to be able to reconstruct the 4-chamber view from these images.If available, a six-cycle image was recorded for reproducibility analysis, otherwise another single cycle recording was used for these analyses.The average frame rate for single cycle images was 24.1 Hz, similar to in vitro imaging.

The senior medical director of Helsinki University Hospital Diagnostic
Center reviewed and approved this data collection.Since this was a retrospective study of data obtained during routine clinical care, the need for Ethics Committee approval was waived.

Image analysis
Offline image analysis was performed using GE EchoPAC Plug-in version 204 (GE Vingmed Ultrasound AS, Horten, Norway).The Flexi-Slice mode of EchoPAC, and its 4D marker functionality which allows to mark a point in the 3D image, were used.A reconstructed 4-chamber view was acquired so that LV long axis is exactly vertical, and a 4D marker (marker name in parentheses) was placed at LV apex (Apex) and mitral annulus center (MV).Images were scrolled with cine loop to determine the true LV apex, while otherwise the analyses were performed with an image frozen to LV end systole.A third marker was placed in the right ventricle (RV) to mark the 4-chamber plane as the plane defined by these three points.Using MV as the hinge point, the image was tilted and rotated to find the approximate LA axis as described, and rotations around this axis were used to further specify the final axis.A point on the intersection of this line and the LA roof was marked (LA).Since we were only interested in angles, the exact location of this point does not matter if it lies on the correct line.Next, the image was tilted and rotated back to the 4-chamber view, as marked previously, with the LV axis as the vertical axis.The LA axis deviation from the 4-chamber plane could be measured by considering the triangle defined by the projection of MV, RV, LA markers onto a plane orthogonal to the LV axis (Figure 4), so that this deviation is the angle between the two lines defined by MV and RV, and MV and LA projections, respectively.These projections are readily visible in the 4D image of Flexi-Slice.As there is no function in EchoPAC to measure angles from these images, we used the caliper function to measure the sides of the triangle defined by the previous projections of MV, RV and LA and used basic trigonometry to calculate the angle.
The LA-LV angle itself was measured by rotating the 4-chamber view around the LV axis such that the imaging plane contains the LA marker, that is, to the plane that is determined by the Apex, MV and LA markers.From this view, the angle between the LA and LV axes is readily visible, and again calculated using trigonometry, after measuring the sides of the right triangle determined by MV, LA and the projection of LA onto the LV axis (Figure 5).
An equivalent analysis protocol was performed with the phantoms (Figure 1).The images were frozen to a suitable frame before analysis.As the phantoms were still, the difference between the frames was miniscule.
To assess repeatability of the measurements, the same images were analyzed twice by the same researcher (L.V.).To assess reproducibility, two separate images of the same phantom or human heart were analyzed.

Data analyses
IBM SPSS for Windows version 28 (Armonk, NY, USA) and Microsoft

Excel for Microsoft 365 MSO version 2206 (Microsoft Corporation,
Redmond, WA, USA) were used for statistical and data analyses.
For the phantoms, protractor measurements were considered to be the true angles.Paired differences of the ultrasound measurements to the true angles were calculated, separately for the wooden and the agar phantoms.For the analyses, the data from both types of agar phantoms were combined.The means of these differences were considered bias.
Pearson correlation coefficients were calculated.The same methods, in addition to intraclass correlation coefficients (two-way mixed testing for absolute agreement), were applied to the repeatability and reproducibility measurements, and for the measurements of the human hearts.Bland-Altman difference plots 19 were used to visualize the data.

Phantoms
The true LA-LV angle of the wooden phantoms ranged from 17 to 41 degrees (mean 30.1), and the axis deviation from the 4-chamber plane ranged from −2 to 54 degrees (mean 26.1).The true LA-LV angle of the agar phantoms ranged from 18 to 60 degrees (mean 39.1), and the axis deviations ranged from −65 to 43 degrees (mean −.5).
There was excellent correlation to the true measurements (Pearson correlations .96 to .99), with minimal bias (−.9 to 1.2 degrees) in general (Table 1, Figures 6-7).The deviations from the 4-chamber plane were slightly less repeatable and reproducible (Pearson correlations .91 to .97)than the LA-LV-angles (Pearson correlations .94 to .98).The reproducibility and repeatability were similar, likely since the phantoms were still, and thus the difference between different images of the same phantom is small.

Human subjects
The human subjects had LV end-diastolic volume ranging from 49 to 138 mL (mean 106) and LA maximum volume from 43 to 162 mL (mean The ultrasound angle measurements of the phantoms as compared to the true angles, with reproducibility and repeatability analyses.

DISCUSSION
In this study we investigated a novel method to determine the angle between the axes of the left ventricle and left atrium, and its deviation from the 4-chamber plane, using 3D echocardiography.The method is based on marking anatomic points of reference in the 3D echocardiogram and measuring the angles between these points.We tested its feasibility, repeatability and reproducibility using multiple types of phantoms and volume data of actual patients.To the best of our knowledge, this measurement has not been done with ultrasound previously.
We found the angle and axis deviation measurements to be feasible and repeatable.Still, there are multiple factors that could be a source of error in the measurement.The most susceptible is the choice of the LA axis, since the often irregular and rounded shape of the LA renders it impossible to determine a true anatomic axis, so an approximation must necessarily be used.The pulmonary vein ostia are often not all discernable using 3D ultrasound, and thus it is impossible to determine the point at the center of those openings.Thus, after studying

F I G U R E 7
The difference between true and measured LA-LV axis deviations of the phantoms.

TA B L E 2
The ultrasound measurements of the human subjects, with reproducibility and repeatability analyses.

Reproducibility of 4-chamber deviation measurement
Bias (95% CI), degrees .2(−2.8 to 3.1) 2.6 (−2.9 to 8.0) .5 (−2.9 to 3.9)  Also, if the angle itself is small, it may be more difficult to determine the deviation from the 4-chamber plane, since a slight movement of the LA axis could produce large variations in the 4-chamber plane deviation.The ultrasound phantoms are susceptible to artifacts: for instance, the wooden phantom was constructed with skewers of 3 mm diameter, yet due to the edge enhancing property of ultrasound, the ultrasound measured thickness was found to be around 11 mm, varying with the direction relative to the ultrasound beam.Thus, the axis of such a skewer was not explicit.Similar issues were faced in a previous study 16 and are to a degree a given property of the modality of ultrasound.We circumvented these types of issues, however, by using multiple types of phantoms and performing multiple measurements each.
While the process of using offline measurements, 4D markers and the need for external trigonometric calculations may be unfeasible for routine usage, the concept of this measurement has now been established.A quick approximate way to take similar measurements online using only 2D ultrasound could be to acquire a 4-chamber view with the mitral orifice in the center of the image, rotate the transducer (virtually or not) until the LA length appears the largest, and calculate or eyeball the rotation of the transducer relative to the starting position (which would correspond to the angle deviation from the 4-chamber plane) and the angle between LA and LV axes in the image thus acquired.If these angles are found to be large, it might be concluded that traditional 2D measurements of the LA would yield results that are less accurate than usual.The feasibility of this accelerated method however needs further evaluation.
In addition to the feasibility of the angle measurement, it makes geometrical sense that a plane cutting the LV along its axis would not cut the LA in a manner conducive to accurate measurements if the LA axis deviates from this plane to a large degree.The effect of this, that is, how the angle affects measurements of LA volume and strain with 2D methods, was not the focus of this method validation study and needs to be studied further.

CONCLUSION
The angle between the LA and LV axes and its deviation from the 4chamber plane are novel echocardiographic parameters, which can be feasibly and repeatably measured using 3D ultrasound, and the effect of which on the accuracy of 2D ultrasound measurements as compared to 3D remains to be seen.
bias since it is a direct physical measurement.The protractor measurements were carried out similarly in all the different types of phantoms.The LA-LV angles were measured by placing the base line of the protractor along the part representing the LV axis, and the origin to the part representing the mitral orifice center, and reading the degree marks where the LA axis intersects the degree scale.The deviations from the 4-chamber plane were measured in a similar fashion by placing the base of the protractor along the 4-chamber plane, and the origin to the part representing the mitral orifice center, and reading the degree marks where the LA axis intersects the degree scale.

F I G U R E 2
An agar-agar phantom used to simulate left sided cardiac chambers axes, and the corresponding ultrasound image.The skewer depicts the cardiac four chamber plane.Points corresponding to the left ventricle apex (Apex; red sphere), left atrial roof (LA; blue sphere), right ventricle (RV; green sphere) and mitral valve orifice center (MV; yellow sphere) are depicted.

ZoomedF I G U R E 3
4D view was used for image acquisition, adjusting recorded volume so that the frame rate was 17−19 Hz, which is a typical frequency for single cycle imaging.Imaging over 6 cardiac cycles (with the ECG recorded from the researcher) was also tested and found not to markedly affect image quality with these phantoms, and the final analyses were performed from single cycle images.Neither was the image quality improved with the reduction of the volume rate.Multiple acquisitions per phantom were performed to assess the reproducibility of the measurements, with a slight movement of the probe between measurements.An agar-agar phantom used to simulate the right ventricle and the left sided cardiac chambers, and the corresponding ultrasound image.Points corresponding to the left ventricle apex (Apex; red sphere), left atrial roof (LA; blue sphere; not visible on this ultrasound projection), right ventricle (RV; green sphere) and mitral valve orifice center (MV; yellow sphere) are depicted.

F I G U R E 4 F I G U R E 5
Markers used for the determination of the deviation of the left atrium-left ventricle angle from the 4-chamber plane.Left ventricle apex (Apex; red sphere), left atrial roof (LA; blue sphere), right ventricle (RV; green sphere) and mitral valve orifice center (MV; yellow sphere) are depicted.Determination of the left atrium (LA)-left ventricle (LV) angle.LV long axis (red sphere-yellow sphere) is shown and the volume is rotated along this axis to show the LA roof (blue sphere).The sides of the right triangle thus formed are measured, and the angle calculated.

F 9
I G U R E 8 Repeated LA-LV angle measurements of the human subjects.LA axis deviation from the 4-chamber plane, repeated measurements, mean, degrees Repeated LA-LV axis deviations of the human subjects.multiple different definitions, we settled on the LA long axis being the line that starts at the center of mitral orifice and is at equal distances from the atrial walls up to the roof of the LA.In contrast, the LV apex, the center of the mitral orifice and the 4-chamber plane are rather easily determined explicitly in vivo.The concept of the LA-LV angle is quite novel, and to our knowledge there are no studies examining the transient factors that affect it: for example, how much do the breathing phase or the position of the patient affect the measurement.The stage of the cardiac cycle probably has an effect, but we have standardized this by taking all measurements in end systole.Still, with the current knowledge, these factors make it impractical to directly compare the LA-LV angles obtained using different imagining modalities.
The difference between true and measured LA-LV axes of the phantoms.