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Debora Gil, Jaume Garcia, Aura Hernandez-Sabate, & Enric Marti. (2010). "Manifold parametrization of the left ventricle for a statistical modelling of its complete anatomy " In 8th Medical Imaging (Vol. 7623, 304). SPIE.
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.
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Jaume Garcia, Albert Andaluz, Debora Gil, & Francesc Carreras. (2010). "Decoupled External Forces in a Predictor-Corrector Segmentation Scheme for LV Contours in Tagged MR Images " In 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 4805–4808).
Abstract: Computation of functional regional scores requires proper identification of LV contours. On one hand, manual segmentation is robust, but it is time consuming and requires high expertise. On the other hand, the tag pattern in TMR sequences is a problem for automatic segmentation of LV boundaries. We propose a segmentation method based on a predictorcorrector (Active Contours – Shape Models) scheme. Special stress is put in the definition of the AC external forces. First, we introduce a semantic description of the LV that discriminates myocardial tissue by using texture and motion descriptors. Second, in order to ensure convergence regardless of the initial contour, the external energy is decoupled according to the orientation of the edges in the image potential. We have validated the model in terms of error in segmented contours and accuracy of regional clinical scores.
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Joel Barajas, Jaume Garcia, Karla Lizbeth Caballero, Francesc Carreras, Sandra Pujades, & Petia Radeva. (2006). "Correction of Misalignment Artifacts Among 2-D Cardiac MR Images in 3-D Space " In 1st International Wokshop on Computer Vision for Intravascular and Intracardiac Imaging (CVII’06) (Vol. 3217, pp. 114–121). Copenhagen (Denmark).
Abstract: Cardiac Magnetic Resonance images offer the opportunity to study the heart in detail. One of the main issues in its modelling is to create an accurate 3-D reconstruction of the left ventricle from 2-D views. A first step to achieve this goal is the correct registration among the different image planes due to patient movements. In this article, we present an accurate method to correct displacement artifacts using the Normalized Mutual Information. Here, the image views are treated as planes in order to diminish the approximation error caused by the association of a certain thickness, and moved simultaneously to avoid any kind of bias in the alignment process. This method has been validated using real and syntectic plane displacements, yielding promising results.
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Debora Gil, Jaume Garcia, Ruth Aris, Guillaume Houzeaux, & Manuel Vazquez. (2009). "A Riemmanian approach to cardiac fiber architecture modelling " In R. L. R. V. L. Nithiarasu (Ed.), 1st International Conference on Mathematical & Computational Biomedical Engineering (pp. 59–62). Swansea (UK).
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.
Keywords: cardiac fiber architecture; diffusion tensor magnetic resonance imaging; differential (Rie- mannian) geometry.
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