Valerio Varano

Torsion of the human left ventricle: Experimental analysis and computational modeling

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.

Modeling Helicoid to Spiral-Ribbon Transitions of Twist-Nematic Elastomers

Nematic Elastomers (NEs) possess very interesting properties stemming from the interaction between liquid crystal order and rubber elasticity. For such materials, thermally induced phase transition from the isotropic to the nematic phase may induce very large distortions, which in turn can affect the overall configuration of a macroscopic specimen. The behavior of NEs can be well modeled within the theory of finite elasticity with distortions; here, we test a theoretical model against fancy shapes formation; in particular, we deal with the many different shapes that a thin, slender bar, made of NE, may assume as a consequence of its chiral symmetry during solvent evaporation and subsequent heating. Our goal has been to replicate with numerical experiments the phenomena of shape formation in chiral NEs, and our results constitute a noteworthy assessment of the physical model underlying the numerical solutions.

4D-Analysis of Left Ventricular Heart Cycle Using Procrustes Motion Analysis

The aim of this study is to investigate human left ventricular heart morphological changes in time among 17 healthy subjects. Preliminarily, 2 patients with volumetric overload due to aortic insufficiency were added to our analyses. We propose a special strategy to compare the shape, orientation and size of cardiac cycle’s morphological trajectories in time. We used 3D data obtained by Speckle Tracking Echocardiography in order to detect semi-automated and homologous landmarks clouds as proxies of left ventricular heart morphology. An extended Geometric Morphometrics toolkit in order to distinguish between intra- and inter-individual shape variations was used. Shape of trajectories with inter-individual variation were compared under the assumption that trajectories attributes, estimated at electrophysiologically homologous times are expressions of left ventricular heart function. We found that shape analysis as commonly applied in Geometric Morphometrics studies fails in identifying a proper morpho-space to compare the shape of morphological trajectories in time. To overcome this problem, we performed a special type of Riemannian Parallel Transport, called “linear shift”. Whereas the two patients with aortic insufficiency were not differentiated in the static shape analysis from the healthy subjects, they set apart significantly in the analyses of motion trajectory’s shape and orientation. We found that in healthy subjects, the variations due to inter-individual morphological differences were not related to shape and orientation of morphological trajectories. Principal Component Analysis showed that volumetric contraction, torsion and twist are differently distributed on different axes. Moreover, global shape change appeared to be more correlated with endocardial shape change than with the epicardial one. Finally, the total shape variation occurring among different subjects was significantly larger than that observable across properly defined morphological trajectories.

A 1D higher gradient model derived from Koiter’s shell theory

A thin rectangular plate is modelled as an (initially flat) shell. Following Koiter, the two fundamental forms of the deformed middle surface are then used to define the strain measures of the body. On the middle surface of the plate two local coordinates are introduced: we will call them longitudinal and transversal, respectively. It is assumed that the components of the displacement field which characterize the middle surface kinematics can be expressed as a product of two functions: one defined along the longitudinal coordinate and one defined along the transversal coordinate. Given an explicit expression of the latter functions, the 2D plate fields are reduced to 1D ones. The functions of the transversal coordinate are chosen so that the stretch along it together with the membrane shear vanish. It is worth noting that the linearization of these constraints leads to the well-known Vlasov’s assumptions. It is shown that by modelling each side of a thin walled beam as a 1D continuum, the entire assembly can be reduced to a 1D model as well. This procedure gives rise to an hyperelastic 1D beam model in which at least the warping effect is taken into account. The main features of the model are shown by means of some simple applications.

A New 4D Trajectory-Based Approach Unveils Abnormal LV Revolution Dynamics in Hypertrophic Cardiomyopathy

The assessment of left ventricular shape changes during cardiac revolution may be a new step in clinical cardiology to ease early diagnosis and treatment. To quantify these changes, only point registration was adopted and neither Generalized Procrustes Analysis nor Principal Component Analysis were applied as we did previously to study a group of healthy subjects. Here, we extend to patients affected by hypertrophic cardiomyopathy the original approach and preliminarily include genotype positive/phenotype negative individuals to explore the potential that incumbent pathology might also be detected. Using 3D Speckle Tracking Echocardiography, we recorded left ventricular shape of 48 healthy subjects, 24 patients affected by hypertrophic cardiomyopathy and 3 genotype positive/phenotype negative individuals. We then applied Generalized Procrustes Analysis and Principal Component Analysis and inter-individual differences were cleaned by Parallel Transport performed on the tangent space, along the horizontal geodesic, between the per-subject consensuses and the grand mean. Endocardial and epicardial layers were evaluated separately, different from many ecocardiographic applications. Under a common Principal Component Analysis, we then evaluated left ventricle morphological changes (at both layers) explained by first Principal Component scores. Trajectories’ shape and orientation were investigated and contrasted. Logistic regression and Receiver Operating Characteristic curves were used to compare these morphometric indicators with traditional 3D Speckle Tracking Echocardiography global parameters. Geometric morphometrics indicators performed better than 3D Speckle Tracking Echocardiography global parameters in recognizing pathology both in systole and diastole. Genotype positive/phenotype negative individuals clustered with patients affected by hypertrophic cardiomyopathy during diastole, suggesting that incumbent pathology may indeed be foreseen by these methods. Left ventricle deformation in patients affected by hypertrophic cardiomyopathy compared to healthy subjects may be assessed by modern shape analysis better than by traditional 3D Speckle Tracking Echocardiography global parameters. Hypertrophic cardiomyopathy pathophysiology was unveiled in a new manner whereby also diastolic phase abnormalities are evident which is more difficult to investigate by traditional ecocardiographic techniques.

Non-invasive assessment of functional strain lines in the real human left ventricle via speckle tracking echocardiography

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.

Evaluation of the strain-line patterns in a human left ventricle: a simulation study.

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.

A Generalized Continuum Formulation for Composite Microcracked Materials and Wave Propagation in a Bar

A multifield continuum is adopted to grossly describe the dynamical behavior of composite microcracked solids. The constitutive relations for the internal and external (inertial) actions are obtained using a multiscale modeling based on the hypotheses of the classical molecular theory of elasticity and the ensuing overall elastodynamic properries allow us to take properly into account the microscopic features of these materials. Referring to a one-dimensional microcracked bar, the ability of such a continuum to reveal the presence of internal heterogeneities is investigated by analyzing the relevant dispersive wave propagation properties. Scattering of traveling waves is shown to be associated with the microcrack density in the bar.

Homeostatic Left Heart integration and disintegration links atrio-ventricular covariation’s dyshomeostasis in Hypertrophic Cardiomyopathy

Left ventricle and left atrium are and have been practically always analyzed separately in common clinically and non-clinically oriented cardiovascular investigations. Both classic and speckle tracking echocardiographic data contributed to the knowledge about deformational impairments occurring in systo-diastolic differences. Recently new trajectory based approaches allowed a greater awareness about the entire left ventricle or left atrium revolution and on their deficiencies that take place in presence of hypertrophic cardiomyopathy. However, surprisingly, the concomitant function of the two left heart chambers has not been analyzed for their geometrical/mechanical relationship. For the first time we study here, by acquiring left ventricle and left atrial geometries on the same heartbeat, the trajectory attributes of the entire left heart treated as a whole shape and the shape covariation of its two subunits. We contrasted healthy subjects with patients affected by hypertrophic cardiomyopathy. We found impaired left heart trajectory mainly in terms of orientation and size. More importantly, we found profound differences in the direction of morphological covariation of left ventricle and left atrium. These findings open to new perspectives in pathophysiological evaluation of different diseases by allowing the appreciation of concomitant functioning of both left heart whole geometry and of its two chambers.

Growth-induced compatible strains

We studied the time evolution problem driven by growth for a non-Euclidean ball which at its initial state is equipped with a non-compatible distortion field. The problem is set within the framework of non-linear elasticity with large growing distortions. No bulk accretive forces are considered, and growth is only driven by the stress state. We showed that, when stress-driven growth is considered, distortions can evolve along different trajectories which share a common attracting manifold; moreover, they eventually attain a steady and compatible form, to which there corresponds a stress-free state of the ball.