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A mechanics–based analysis of data from three-dimensional speckle tracking echocardiography can help to infer useful clinical data about the state of myocardium. Precisely, we recently conjectured that principal strain lines in the left ventricle change in presence of heart disease, and used data from healthy subjects and patients to support our conjecture. Here, we set the first steps of our analysis relative to the left atrium, describing our method of acquisition, and discussing the key mechanical characteristics delivered by the echocardiographic device for healthy subjects and patients affected by hypertrophic cardiomyopathy.

Transporting deformations from a template to a different one is a typical task of the shape analysis. In particular, it is necessary to perform such a kind of transport when performing group-wise statistical analyses in Shape or Size and Shape Spaces. A typical example is when one is interested in separating the difference in function from the difference in shape. The key point is: given two different templates (Formula presented.) and (Formula presented.) both undergoing their own deformation, and describing these two deformations with the diffeomorphisms (Formula presented.) and (Formula presented.), then when is it possible to say that they are experiencing the same deformation? Given a correspondence between the points of (Formula presented.) and (Formula presented.) (i.e. a bijective map), then a naïve possible answer could be that the displacement vector (Formula presented.), associated to each corresponding point couple, is the same. In this manuscript, we assume a different viewpoint: two templates undergo the same deformation if for each corresponding point couple of the two templates the condition (Formula presented.) holds or, in other words, the local metric (non linear strain) induced by the two diffeomorphisms is the same for all the corresponding points.

In a previous contribution, a new Riemannian shape space, named TPS space, was introduced to perform statistics on shape data. This space was endowed with a Riemannian metric and a flat connection, with torsion, compatible with the given metric. This connection allows the definition of a Parallel Transport of the deformation compatible with the three-fold decomposition in spherical, deviatoric, and non-affine components. Such a parallel transport also conserves the Γ-energy, strictly related to the total elastic strain energy stored by the body in the original deformation. A new approach is here presented in order to calculate the bending energy on the body alone (body bending energy) and to restrict it exclusively within physical boundaries of objects involved in the deformation analysis. The novelty of this new procedure resides in the fact that we propose a new metric to be preserved during the TPS direct transport. This allows transporting the shape change more coherently with the mechanical meaning of the deformation. The geometry of the TPS space is then further discussed in order to better represent the relationship between the Γ-energy, the strain energy, and the so-called bending energy densities.

A mechanics–based analysis of data from three–dimensional speckle tracking echocardiography is proposed, aimed at investigating deformations in myocardium and at assessing shape and function of distinct strain lines corresponding to the principal strain lines of the cardiac tissue. The analysis is based on the application of a protocol of measurement of the endocardial and epicardial principal strain lines, which was already tested on simulated left ventricles. In contrast with similar studies, it is established that endocardial principal strain lines cannot be identified with any structural fibers, not even along the systolic phase and is suggested that it is due to the capacity of the endocardial surface to contrast the dilation of the left ventricle. A mechanics-based analysis of data from three-dimensional speckle tracking echocardiography is proposed, aimed at investigating deformations in myocardium and at assessing shape and function of distinct strain lines corresponding to the principal strain lines of the cardiac tissue. The analysis is based on the application of a protocol of measurement of the endocardial and epicardial principal strain lines, which was already tested on simulated left ventricles. In contrast with similar studies, it is established that endocardial principal strain lines cannot be identified with any structural fibers, not even along the systolic phase and is suggested that it is due to the capacity of the endocardial surface to contrast the dilation of the left ventricle.

We present and discuss a method to infer noninvasively information on the fibre architecture in real human left ventricle walls. The method post-processes the echocardiographic data acquired by three-dimensional speckle tracking echocardiography through a MatLab-based protocol, already presented, discussed and validated. Our results indicate the difference between the role of endocardial and epicardial principal strain lines, at the systolic peak, and set the bases for possible future investigations aimed to analyse the onset of specific cardiac diseases through noninvasive analysis of LV fibre architecture. Moreover, we set a rational statistical analysis to investigate the reliability of the proposed method.

The aim of this paper is to emphasise the role of the primary strain-line patterns in a human left ventricle (LV) within the complex system that is the heart. In particular, a protocol is proposed for the measurement of the principal strain lines (PSL) in the walls of the LV; this protocol is tested by means of a computational model which resembles a human LV. When the analysis is focused on the epicardial surface, PSL can be used to derive information on the directions of muscle fibres during the entire cardiac cycle, not only the systolic phase.

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.