Non-invasive prediction of genotype positive-phenotype negative in hypertrophic cardiomyopathy by 3D modern shape analysis.

NEW FINDINGS: What is the central question of this study? Can impaired deformational indicators for genotype positive for hypertrophic cardiomyopathy in subjects that do not exhibit a left-ventricular wall hypertrophy condition (G+LVH-) be determined using non-invasive 3D echocardiography? What is the main finding and its importance? Using 3D-STE and modern shape analysis, peculiar deformational impairments can be detected in G+LVH- subjects that can be classified with good accuracy. Moreover, the patterns of impairment are located mainly on the apical region in agreement with other evidence coming from previous biomechanical investigations. ABSTRACT: We propose a non-invasive procedure for predicting genotype positive for hypertrophic cardiomyopathy (HCM) in subjects that do not exhibit a left-ventricular wall hypertrophy condition (G+LVH-); the procedure is based on the enhanced analysis of medical imaging from 3D speckle tracking echocardiography (3D-STE). 3D-STE, due to its low quality images, has not been used so far to detect effectively the G+LVH- condition. Here, we post-processed echocardiographic images exploiting the tools of modern shape analysis, and we studied the motion of the left ventricle (LV) during an entire cycle. We enrolled 82 controls, 21 HCM patients and 11 G+LVH- subjects. We followed two steps: (i) we selected the most impaired regions of the LV by analysing its strains; and (ii) we used shape analysis on these regions to classify the subjects. The G+LVH- subjects showed different trajectories and deformational attributes. We found high classification performance in terms of area under the receiver operating characteristic curve (∼90), sensitivity (∼78) and specificity (∼79). Our results showed that (i) G+LVH- subjects present important deformational impairments relative to healthy controls and (ii) modern shape analysis can efficiently predict genotype by means of a non-invasive and inexpensive technique such as 3D-STE.

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.

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.

Local and global energies for shape analysis in medical imaging.

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.

The decomposition of deformation: New metrics to enhance shape analysis in medical imaging.

In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between Centroid Size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall's size-and-shape space without losing Kendall's original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy.

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.

Left Atrial trajectory impairment in Hypertrophic Cardiomyopathy disclosed by Geometric Morphometrics and Parallel Transport.

The analysis of full Left Atrium (LA) deformation and whole LA deformational trajectory in time has been poorly investigated and, to the best of our knowledge, seldom discussed in patients with Hypertrophic Cardiomyopathy. Therefore, we considered 22 patients with Hypertrophic Cardiomyopathy (HCM) and 46 healthy subjects, investigated them by three-dimensional Speckle Tracking Echocardiography, and studied the derived landmark clouds via Geometric Morphometrics with Parallel Transport. Trajectory shape and trajectory size were different in Controls versus HCM and their classification powers had high AUC (Area Under the Receiving Operator Characteristic Curve) and accuracy. The two trajectories were much different at the transition between LA conduit and booster pump functions. Full shape and deformation analyses with trajectory analysis enabled a straightforward perception of pathophysiological consequences of HCM condition on LA functioning. It might be worthwhile to apply these techniques to look for novel pathophysiological approaches that may better define atrio-ventricular interaction.

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.

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.