Automatic quantification of regional left ventricular deformation in volumetric ultrasound data remains challenging. Many methods have been proposed to extract myocardial motion, including techniques using block matching, phase-based correlation, differential optical flow methods, and image registration. Our lab previously presented an approach based on elastic registration of subsequent volumes using a B-spline representation of the underlying transformation field. Encouraging results were obtained for the assessment of global left ventricular function, but a thorough validation on a regional level was still lacking. For this purpose, univentricular thick-walled cardiac phantoms were deformed in an experimental setup to locally assess strain accuracy against sonomicrometry as a reference method and to assess whether regions containing stiff inclusions could be detected. Our method showed good correlations against sonomicrometry: r(2) was 0.96, 0.92, and 0.84 for the radial (ε(RR)), longitudinal (ε(LL)), and circumferential (ε(CC)) strain, respectively. Absolute strain errors and strain drift were low for ε(LL) (absolute mean error: 2.42%, drift: -1.05%) and ε(CC) (error: 1.79%, drift: -1.33%) and slightly higher for ε(RR) (error: 3.37%, drift: 3.05%). The discriminative power of our methodology was adequate to resolve full transmural inclusions down to 17 mm in diameter, although the inclusion-to-surrounding tissue stiffness ratio was required to be at least 5:2 (absolute difference of 39.42 kPa). When the inclusion-to-surrounding tissue stiffness ratio was lowered to approximately 2:1 (absolute difference of 22.63 kPa), only larger inclusions down to 27 mm in diameter could still be identified. Radial strain was found not to be reliable in identifying dysfunctional regions.

A plethora of techniques for cardiac deformation imaging with 3D ultrasound, typically referred to as 3D speckle tracking techniques, are available from academia and industry. Although the benefits of single methods over alternative ones have been reported in separate publications, the intrinsic differences in the data and definitions used makes it hard to compare the relative performance of different solutions. To address this issue, we have recently proposed a framework to simulate realistic 3D echocardiographic recordings and used it to generate a common set of ground-truth data for 3D speckle tracking algorithms, which was made available online. The aim of this study was therefore to use the newly developed database to contrast non-commercial speckle tracking solutions from research groups with leading expertise in the field. The five techniques involved cover the most representative families of existing approaches, namely block-matching, radio-frequency tracking, optical flow and elastic image registration. The techniques were contrasted in terms of tracking and strain accuracy. The feasibility of the obtained strain measurements to diagnose pathology was also tested for ischemia and dyssynchrony.

A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value problems may have regular (i.e. sufficiently smooth) stationary solutions. This class of close-to-equilibrium patterns includes stationary solutions that emerge due to the Turing instability of a spatially constant stationary solution. The main result of this work is instability of all regular patterns. It suggests that stable stationary solutions arising in models with non-diffusive components must be far-from-equilibrium exhibiting singularities. Such discontinuous stationary solutions have been considered in our parallel work [Stable discontinuous stationary solutions to reaction-diffusion-ODE systems, preprint (2021)].

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Effect of the out-of-plane (OOP) movement amplitude on estimates of global displacements (radial, circumferential) and strains (radial , circumferential ) was studied in an ellipsoidal model of the left ventricle using finite-element modeling (FEM), synthetic ultrasonic data, and short-axis view. This effect was assessed using median of the absolute relative error (RE) of the global parameters. FEM provided node displacements for synthetic ultrasonic data and reference data generation. Displacements were estimated using block-matching (BM) and B-spline (BS) methods. FEM-derived data analysis, free from errors resulting from speckle tracking, indicated that the tissue motion introduced REs of global strain estimates below 4.5%. The effect of the OOP motion amplitude on strain estimates was strain specific and depended on the displacement estimation method. In the case of , the increase of the OOP amplitude resulted in quasi-linear increase of the RE from approximately 10% to 15%. The modulus of the end-systolic (ES) errors of the estimates almost linearly increased with increasing OOP amplitude approximately from 10% to 16%. REs of the estimate were close to 80% and 40%, respectively, in the case of the BM and BS methods, and increased with increasing OOP amplitude. The modulus of the ES errors of the estimates in the case of the BS method was about -40% and showed low sensitivity to the OOP amplitude; in the BM case, these errors varied approximately from -70% to -58% for OOP amplitude from 0 to 15 mm.