Abstract: Early diagnosis and accurate treatment of Left Ventricle (LV) dysfunction significantly increases the patient survival. Impairment of LV contractility due to cardiovascular diseases is reflected in its motion patterns. Recent advances in medical imaging, such as Magnetic Resonance (MR), have encouraged research on 3D simulation and modelling of the LV dynamics. Most of the existing 3D models consider just the gross anatomy of the LV and restore a truncated ellipse which deforms along the cardiac cycle. The contraction mechanics of any muscle strongly depends on the spatial orientation of its muscular fibers since the motion that the muscle undergoes mainly takes place along the fibers. It follows that such simplified models do not allow evaluation of the heart electro-mechanical function and coupling, which has recently risen as the key point for understanding the LV functionality . In order to thoroughly understand the LV mechanics it is necessary to consider the complete anatomy of the LV given by the orientation of the myocardial fibres in 3D space as described by Torrent Guasp. We propose developing a 3D patient-sensitive model of the LV integrating, for the first time, the ven- tricular band anatomy (fibers orientation), the LV gross anatomy and its functionality. Such model will represent the LV function as a natural consequence of its own ventricular band anatomy. This might be decisive in restoring a proper LV contraction in patients undergoing pace marker treatment. The LV function is defined as soon as the propagation of the contractile electromechanical pulse has been modelled. In our experiments we have used the wave equation for the propagation of the electric pulse. The electromechanical wave moves on the myocardial surface and should have a conductivity tensor oriented along the muscular fibers. Thus, whatever mathematical model for electric pulse propa- gation [4] we consider, the complete anatomy of the LV should be extracted. The LV gross anatomy is obtained by processing multi slice MR images recorded for each patient. Information about the myocardial fibers distribution can only be extracted by Diffusion Tensor Imag- ing (DTI), which can not provide in vivo information for each patient. As a first approach, we have computed an average model of fibers from several DTI studies of canine hearts. This rough anatomy is the input for our electro-mechanical propagation model simulating LV dynamics. The average fiber orientation is updated until the simulated LV motion agrees with the experimental evidence provided by the LV motion observed in tagged MR (TMR) sequences. Experimental LV motion is recovered by applying image processing, differential geometry and interpolation techniques to 2D TMR slices [5]. The pipeline in figure 1 outlines the interaction between simulations and experimental data leading to our patient-tailored model.

Abstract: There is general consensus that myocardial fiber architecture should be modelled in order to fully understand the electromechanical properties of the Left Ventricle (LV). Diffusion Tensor magnetic resonance Imaging (DTI) is the reference image modality for rapid measurement of fiber orientations by means of the tensor principal eigenvectors. In this work, we present a mathematical framework for across subject comparison of the local geometry of the LV anatomy including the fiber architecture from the statistical analysis of DTI studies. We use concepts of differential geometry for defining a parametric domain suitable for statistical analysis of a low number of samples. We use Riemannian metrics to define a consistent computation of DTI principal eigenvector modes of variation. Our framework has been applied to build an atlas of the LV fiber architecture from 7 DTI normal canine hearts.

Abstract: The problem of texture segmentation and interpretation is one of the main concerns in the field of document analysis. Graphical documents often contain areas characterized by a structural texture whose recognition allows both the document understanding, and its storage in a more compact way. In this work, we focus on structural linial textures of regular repetition contained in plan documents. Starting from an atributed graph which represents the vectorized input image, we develop a method to segment textured areas and recognize their placement rules. We wish to emphasize that the searched textures do not follow a predefined pattern. Minimal closed loops of the input graph are computed, and then hierarchically clustered. In this hierarchical clustering, a distance function between two closed loops is defined in terms of their areas difference and boundary resemblance computed by a string matching procedure. Finally it is noted that, when the texture consists of isolated primitive elements, the same method can be used after computing a Voronoi Tesselation of the input graph.

Abstract: Deep understanding of myocardial structure may help to link form and funcion of the heart unraveling crucial knowledge for medical and surgical clinical procedures and studies. In this work we introduce two visualization techniques based on DT-MRI streamlining able to decipher interesting properties of the architectural organization of the heart.