Geometry Does Impact on the Plane Strain Directions of the Human Left Ventricle, Irrespective of Disease.

The directions of primary strain lines of local deformation in Epicardial and Endocardial layers have been the subject of debate in recent years. Different methods led to different conclusions and a complete assessment of strain direction patterns in large and variable (in terms of pathology) cohorts of healthy and diseased patients is still lacking. Here, we use local deformation tensors in order to evaluate the angle of strain lines with respect to the horizontal circumferential direction in both Epi- and Endo-layers. We evaluated this on a large group of 193 subjects including 82 healthy control and 111 patients belonging to a great variety of pathological conditions. We found that Epicardial strain lines obliquely directed while those of Endocardium are almost circumferential. This result occurs irrespective of pathological condition. We propose that the geometric vinculum characterizing Endocardium and Epicardium in terms of different lever arm length and orientation of muscular fibers during contraction inescapably requires Endocardial strain lines to be circumferentially oriented and this is corroborated by experimental results. Further investigations on transmural structure of myocytes could couple results presented here in order to furnish additional experimental explanations.

Stress-free morphing by means of compatible distortions.

We study the morphing of three-dimensional objects within the framework of nonlinear elasticity with large distortions. A distortion field induces a target metric, and the configuration which is effectively realized by a material body is the one that minimizes the distance, measured through the elastic energy, between the target metric and the actual one. Morphing through distortions might have a paramount feature: the resulting configurations might be stress-free; if this is the case, the distortions field is called compatible. We maintain that the morphing through compatible distortions is a key strategy exploited by many soft biological materials, which can exhibit very large shape-change in response to distortions controlled by stimuli such as chemicals or temperature changes, while keeping their stress state almost null. Thus, the study of compatible distortions, and of the related shape-changes, is quite important. Here, we show a blueprint for stress-free morphing based on the notions of metric tensor and of Riemann curvature which can be used to design large morphing of three-dimensional objects.

The heart function as a motor-brake system.

The controversy between passive and active ventricular filling has been debated for decades and the question about the existence of an active diastole remains open. In this work, we advocate the model of active diastole by considering the heart as a suction pump and we add some more clues to support this point of view by the analysis of the pressure-volume (PV) loops of the left heart, comprising of the left ventricle (LV) and atrium (LA). Our working hypothesis is based on the dichotomy motor-brake: the cardiac muscle can act as a motor, when shortening against a load, or as a brake, when lengthening to a load. We discuss our hypothesis by means of a lumped model of the left heart, where both chambers are considered as hollow spherical shells. The notion of active stretch, introduced to describe the contractile behavior of the muscle fibers, plays a major role in our model. Then, the contraction of the muscle is related to the pressure and volume of the chamber through a nonlinear hyperelastic energy density function. Despite its simplicity, the model enlightens some important features of the LV-LA coupling and of the pumping function of the heart. Based on experimental PV data of the left heart of a normal human subject, it is shown that the contraction patterns of the LV and LA are synchronized with each other and have distinguishing features in each phase of the cardiac cycle. These results highlight the interplay between the two chambers and support the idea that the heart may act as a suction pump functioning in turn as a motor or a brake in order to meet specific demands in each phase of the cardiac cycle.