Abstract: Distortion of Left Ventricle (LV) external anatomy is related to some dysfunctions, such as hypertrophy. The architecture of myocardial fibers determines LV electromechanical activation patterns as well as mechanics. Thus, their joined modelling would allow the design of specific interventions (such as peacemaker implantation and LV remodelling) and therapies (such as resynchronization). On one hand, accurate modelling of external anatomy requires either a dense sampling or a continuous infinite dimensional approach, which requires non-Euclidean statistics. On the other hand, computation of fiber models requires statistics on Riemannian spaces. Most approaches compute separate statistical models for external anatomy and fibers architecture. In this work we propose a general mathematical framework based on differential geometry concepts for computing a statistical model including, both, external and fiber anatomy. Our framework provides a continuous approach to external anatomy supporting standard statistics. We also provide a straightforward formula for the computation of the Riemannian fiber statistics. We have applied our methodology to the computation of complete anatomical atlas of canine hearts from diffusion tensor studies. The orientation of fibers over the average external geometry agrees with the segmental description of orientations reported in the literature.

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 [1] 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 [2]. 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 [3].
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
Figure 1: Scheme for the Left Ventricle Patient-Sensitive Model.
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: Les malalties cardiovasculars afecten les propietats contràctils de la banda ventricular i provoquen una variació de la funció del Ventricle Esquerre (VE) . Només els indicadors locals (strains, la deformació del teixit) són capaços de detectar anomalies en territoris específics del VE . Patrons de normalitat regionals d’aquests paràmetres serien d’utilitat a l’hora de valorar-ne la funció .
Presentem un Domini Paramètric Normalitzat (DPN) que permet comparar dades de diferents pacients i definir Patrons de Normalitat Regional (PNR)

Abstract: Els canvis en la dinàmica del Ventricle Esquerre (VE) reflecteixen la majoria de malalties cardiovasculars . Els avenços en imatge mèdica han impulsat la recerca en models i simulacions de la dinàmica 3D del VE . La majoria dels models existents sols consideren l’anatomia externa del VE i no permeten una avaluació de l’acoblament electromecànic . Donat que la mecànica d’un muscle depèn de la orientació de les seves fibres, un model realista hauria d’incloure la disposició espacial de la banda ventricular helicoidal (BVH) .
Proposem desenvolupar un model del VE adaptat a cada pacient que integri, per primer cop, l’anatomia de la banda ventricular, l’anatomia externa del VE i la seva funcionalitat, per a una millor determinació del patró d’activació electromecànica