Relationship between left atrial reservoir strain, volumes, and geometry: Insights from simple theoretical model

Left atrial (LA) volume is related to LA reservoir strain (LAS_R ), but the relationship is not fully resolved. We sought to model the relationship between LA end-diastolic and end-systolic volumes (LAEDV and LAESV) and LAS_R based on a geometrical approach to exploit the relationship between LAS_R and volume.

Modeling the LA as a hemisphere with radius r, LAS_R was recognized to vary linearly with r and LA volume with r³ . Expanding this cubic relation as a Taylor series resulted in a simple linear equation: LAESV/LAEDV = 1 + 3 × LAS_R . To validate this, 52 transthoracic echocardiograms were analyzed from 18 patients who underwent transcatheter edge-to-edge repair (TEER) with MitraClip with serial assessment pre-procedure, 1 month post-clip, and 12 months post-TEER. Linear regression was performed to compare the geometric equation to a statistical model created by a line of best fit to relate LAESV/LAEDV to LAS_R .

The statistical and geometric model both resulted in a strong correlation (r = .8, p < .001, respectively). The slope of the line in the statistical model was 3.3, which was statistically indistinguishable from the expected slope of 3 based on the geometric model (Figure 2A). Using the geometric model to compare the measured versus calculated LAESV/LAEDV also resulted in a strong correlation (r = .8, p < .001)(Figure 2B).

We describe the relationship between LA volume and strain mathematically by considering the geometry of the LA. This model enhances our understanding of the interaction between atrial strain and volume. Further research is necessary to validate this using 3D atrial volumes in a broader cohort of subjects.