Regularization-Free Strain Mapping in Three Dimensions, With Application to Cardiac Ultrasound

Abstract

Quantifying dynamic strain fields from time-resolved volumetric medical imaging and microscopy stacks is a pressing need for radiology and mechanobiology. A critical limitation of all existing techniques is regularization: because these volumetric images are inherently noisy, the current strain mapping techniques must impose either displacement regularization and smoothing that sacrifices spatial resolution, or material property assumptions that presuppose a material model, as in hyperelastic warping. Here, we present, validate, and apply the first three-dimensional (3D) method for estimating mechanical strain directly from raw 3D image stacks without either regularization or assumptions about material behavior. We apply the method to high-frequency ultrasound images of mouse hearts to diagnose myocardial infarction. We also apply the method to present the first ever in vivo quantification of elevated strain fields in the heart wall associated with the insertion of the chordae tendinae. The method shows promise for broad application to dynamic medical imaging modalities, including high-frequency ultrasound, tagged magnetic resonance imaging, and confocal fluorescence microscopy.

Three-dimensional myocardial strain correlates with murine left ventricular remodelling severity post-infarction

“…Another advantage of the presented technique lies in its ability to yield reproducible measures of 3D strain. Unlike existing techniques, which often rely on displacement regularization prior to strain estimation, the DDE method estimates the 3D deformation gradient tensor directly during voxel intensity mapping as reported previously [19]. This results in a noise-insensitive algorithm that provides a more accurate and precise strain-field estimation when compared with displacement-based methods, as supported by in silico validation [19].…”

“…We implemented a direct deformation estimation (DDE) algorithm in Matlab to estimate the 3D deformation gradient tensor as described previously (figure 1d; [19] reference template, we iteratively optimized a warping function that best mapped the affine transformation of this region from the template image to a deformed image at the next time point. The warping function was optimized by best matching voxel intensities between the template and deformed image.…”

“…Unlike existing techniques, which often rely on displacement regularization prior to strain estimation, the DDE method estimates the 3D deformation gradient tensor directly during voxel intensity mapping as reported previously [19]. This results in a noise-insensitive algorithm that provides a more accurate and precise strain-field estimation when compared with displacement-based methods, as supported by in silico validation [19]. We demonstrate the reproducibility of our 3D strain measurements in electronic supplementary material, figure S7, which highlights similarities in the bullseye strain maps of all 15 healthy mice imaged at baseline.…”

“…Recent developments in non-invasive four-dimensional (4D) imaging techniques have made it possible for researchers to reconstruct volumetric maps of patient-or mouse-specific LV geometries throughout a cardiac cycle [14][15][16], opening the possibility for three-dimensional (3D) strain mapping of the heart. Indeed, several groups have quantified regional differences in 3D strain in both healthy [17,18] and ischaemic left ventricles [19][20][21], with results revealing significant strain reductions within infarcted tissue. However, these studies either evaluated strain at only sparse time points [19,20] or relied on contrast agents to quantify strain in the remodelling infarct [21].…”

“…A thorough longitudinal study investigating changes in the spatial distribution of 3D myocardial strain in a murine model of acute MI has not yet been conducted. Here, we integrated high-resolution 4D ultrasound imaging [14] with 3D strain mapping [19] to monitor cardiac remodelling over 28 days. By employing two surgical mouse models to induce ischaemic damage with varying severities, we identified unique remodelling patterns that differed between ischaemia-reperfusion and permanent ligation models.…”