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

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 Rie-mannian 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 threefold decomposition in spherical, deviatoric and non affine components. Such a Parallel Transport also conserves the-energy, strictly related to the total elastic strain energy stored by the body in the original deformation. New machinery is here presented in order to calculate the bending energy on the body only (body bending energy) in order 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 conserve 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 developed in order to better represent the relationship between the-energy, the strain energy and the so called bending-energy densities

Systo-Diastolic LV Shape Analysis by Geometric Morphometrics and Parallel Transport Highly Discriminates Myocardial Infarction

We present a procedure that detects myocardial infarction by analyzing left ventricular shapes recorded at end-diastole and endsystole, involving both shape and statistical analyses. In the framework of Geometric Morphometrics, we use Generalized Procrustes Analysis, and optionally an Euclidean Parallel Transport, followed by Principal Components Analysis to analyze the shapes. We then test the performances of different classification methods on the dataset. Among the different datasets and classification methods used, we found that the best classification performance is given by the following workflow: full shape (epicardium+endocardium) analyzed in the Shape Space (i.e. by scaling shapes at unit size); successive Parallel Transport centered toward the Grand Mean, in order to detect pure deformations; final statistical analysis via Support Vector Machine with radial basis Gaussian function. Healthy individuals show both a stronger contraction and a shape difference in systole with respect to pathological subjects. Moreover, endocardium clearly presents a larger deformation when contrasted with epicardium. Eventually, the solution for the blind test dataset is given. When using Support Vector Machine for learning from the whole training dataset and for successively classifying the 200 blind test dataset, we obtained 96 subjects classified as normal and 104 classified as pathological. After the disclosure of the blind dataset this resulted in 95% of total accurracy with sensitivity at 97% and specificity at 93%