Modeling and simulation of the electric activity of the heart using graphic processing units

Mathematical modelling and simulation of the electric activity of the heart (cardiac electrophysiology) offers and ideal framework to combine clinical and experimental data in order to help understanding the underlying mechanisms behind the observed respond under physiological and pathological conditions. In this regard, solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi- scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This thesis develops around the implementation of an electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA) for GPU computing. The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting and the finite element method for space discretization. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50× for three-dimensional problems when using an implicit scheme for the parabolic equation, whereas accelerations reach values up to 100× for the explicit implementation. The implemented solver has been applied to study pro-arrhythmic mechanisms during acute ischemia. In particular, we investigate on how hyperkalemia affects the vulnerability window to reentry and the reentry patterns in the heterogeneous substrate caused by acute regional ischemia using an anatomically and biophysically detailed human biventricular model. A three dimensional geometrically and anatomically accurate regionally ischemic human heart model was created. The ischemic region was located in the inferolateral and posterior side of the left ventricle mimicking the occlusion of the circumflex artery, and the presence of a washed-out zone not affected by ischemia at the endocardium has been incorporated. Realistic heterogeneity and fi er anisotropy has also been considered in the model. A highly electrophysiological detailed action potential model for human has been adapted to make it suitable for modeling ischemic conditions (hyperkalemia, hipoxia, and acidic conditions) by introducing a formulation of the ATP-sensitive K+ current. The model predicts the generation of sustained re-entrant activity in the form single and double circus around a blocked area within the ischemic zone for K+ concentrations bellow 9mM, with the reentrant activity associated with ventricular tachycardia in all cases. Results suggest the washed-out zone as a potential pro-arrhythmic substrate factor helping on establishing sustained ventricular tachycardia.Colli-Franzone P, Pavarino L. A parallel solver for reaction-diffusion systems in computational electrocardiology, Math. Models Methods Appl. Sci. 14 (06):883-911, 2004.Colli-Franzone P, Deu hard P, Erdmann B, Lang J, Pavarino L F. Adaptivity in space and time for reaction-diffusion systems in electrocardiology, SIAM J. Sci. Comput. 28 (3):942-962, 2006.Ferrero J M(Jr), Saiz J, Ferrero J M, Thakor N V. Simulation of action potentials from metabolically impaired cardiac myocytes: Role of atp-sensitive K+ current. Circ Res, 79(2):208-221, 1996.Ferrero J M (Jr), Trenor B. Rodriguez B, Saiz J. Electrical acticvity and reentry during acute regional myocardial ischemia: Insights from simulations.Int J Bif Chaos, 13:3703-3715, 2003.Heidenreich E, Ferrero J M, Doblare M, Rodriguez J F. Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology, Ann. Biomed. Eng. 38 (7):2331-2345, 2010.Janse M J, Kleber A G. Electrophysiological changes and ventricular arrhythmias in the early phase of regional myocardial ischemia. Circ. Res. 49:1069-1081, 1981.ten Tusscher K HWJ, Panlov A V. Alternans and spiral breakup in a human ventricular tissue model. Am. J.Physiol. Heart Circ. Physiol. 291(3):1088-1100, 2006.<br /

Sustained reentry in a 3d regionally ischemic human heart. A simulation study

In this work, we have studied the vulnerable window and propagation patterns in a human heart during acute ischemia. A 3-D biventricular model of a human heart with realistic heterogeneity and fiber orientations has been considered. The ischemic region was located in the anterior left ventricular wall mimicking the occlusion of the circumflex artery. The electrical activity of the tissue was modeled with the monodomain model along with a modified version of the ten Tusscher 2006 ionic model. The model predicts the generation of sustained re-entrant activity in the form of a rotor around the ischemic zone. Patterns in the form of figure-of-eight were also observed within the vulnerable window. The re-entrant activity originates in the endocardial surface and propagates transmurally towards the epicardium

Simulación de la actividad eléctrica del corazón utilizando unidades de procesamiento gráfico (GPU)

En los últimos años, las técnicas de observación celular y molecular han mejorado paulatinamente, lo que ha permitido avanzar en el conocimiento de los mecanismos que gobiernan la electrofisiología cardiaca a nivel celular y su relación con la señal bioeléctrica a nivel de tejido, órgano y superficie (electrocardiograma). En este sentido, la modelización matemática se ha convertido en una importante herramienta en la investigación de la biofísica celular y la electrofisiología. Los modelos matemáticos de células cardíacas pueden ser acopladas a modelos de tejido y ser empleados para simular la actividad eléctrica del corazón bajo condiciones normales y patológicas, así como bajo los efectos de medicamentos anti- y pro-arrítmicos. Uno de los objetivos de la modelización y simulación numérica es el de reproducir los experimentos, entender los fenómenos físicos involucrados que no pueden ser observados a través de ellos y el poder predecir esos fenómenos. Los modelos matemáticos de la electrofisiología del corazón describen de qué manera se propaga la onda eléctrica a través del tejido cardíaco y su relación con procesos que ocurren a escala celular. Los modelos involucrados en este trabajo, consisten en sistemas de ecuaciones diferenciales ordinarios (EDO) que modelan la electrofisiología de una célula, acoplados a un sistema de ecuaciones diferenciales en derivadas parciales (EDP) que gobiernan la propagación de la señal eléctrica a través del tejido. El gran nivel de detalle electrofisológico de los modelos celulares subyacentes, convierte la simulación de la actividad eléctrica de un órgano como el corazón, en un desafío computacional de considerable envergadura. El reto desde el punto de vista computacional se encuentra en el correcto manejo de las diferentes escalas de tiempo y espacio existentes en el problema. Las constantes de tiempo involucradas en la cinética de los modelos iónicos van desde una fracción de milisegundo (corriente de sodio), hasta los cientos de milisegundos (corriente de calcio), lo cual implica desde un punto de vista numérico, pasos de integración del orden de centésimas de milisegundo. Por otro lado, la rápida despolarización de la membrana celular (el potencial de membrana varía 120mV en menos de un milisegundo), sumado a la relativamente baja velocidad de conducción del ventrículo (entorno a los 55 cm/s de velocidad media), implica que el frente de despolarización se desarrolla en pocos milímetros, dando lugar a la necesidad de emplear discretizaciones muy finas con la finalidad de obtener resultados fiables. De esta manera, la simulación de un solo latido cardíaco (800 ms de simulación), en una geometría real del corazón humano, conlleva resolver un problema con millones de grados de libertad y simulaciones que pueden requerir miles de pasos de tiempo. El objetivo principal de este trabajo es abordar la solución numérica del problema de electrofisología cardiaca en arquitecturas GPU (Graphic Processor Units) para cálculo de altas prestaciones aprovechando el alto nivel de paralelización de esta arquitectura. Para ello se implementó en C++ y CUDA un programa de elementos finitos para resolver el modelo mono-dominio para la simulación de la propagación de la actividad eléctrica en el corazón acoplado a modelos electrofisiológicos detallados

Evaluación biomecánica de dos implantes intramedulares para el alivio de la patología del dedo en garra

La patología del dedo en garra puede ser tratada de forma pasiva o mediante diferentes intervenciones quirúrgicas. El presente estudio se centra en la cirugía más común de todas, la artrodesis. Se estudian los efectos que produce añadir dos tipos de implante intramedular, uno neutral y otro angulado, en la articulación media del segundo dedo. Para lograrlo se ha realizado un modelo de elementos finitos del pie humano, obtenido a partir de la tomografía computarizada de un paciente. En primer lugar, se ha realizado la segmentación de cada uno de los 28 huesos que conforman el pie humano, distinguiendo en cada uno la parte cortical de la parte esponjosa. Una vez generados los volúmenes 3D de los huesos se han creado los cartílagos de unión, responsables de transmitir los esfuerzos entre los huesos. A continuación, se han introducido los implantes al modelo y se ha realizado un mallado volumétrico, permitiendo así el posterior cálculo numérico mediante elementos finitos. Una vez que se ha obtenido la malla de elementos tetraédricos el siguiente paso es colocar los ligamentos y tendones, los cuales se han simplificado mediante elementos barra 2D. Por último, se aplican las cargas y condiciones de contorno y se lanzan a calcular cada uno de los tres casos de estudio: pie sano, implante neutral e implante angulado, para posteriormente comparar los resultados obtenidos en cada uno de ellos. A la vista de los resultados obtenidos en el cálculo se puede concluir que ambos tipos de implante corrigen con eficacia esta deformidad, sin embargo, las tensiones y desplazamientos obtenidos en cada caso son diferentes. El implante angulado genera menos tensiones en las falanges, pero, debido a su forma angulada, las tensiones sobre el propio implante son considerablemente superiores al caso de implante neutral. Por esto mismo se recomienda el uso de implante neutral ya que se reduce el riesgo de rotura. Al comparar estos resultados con los obtenidos en el modelo previo del que dispone el grupo de investigación del Área de Mec. de Medios Continuos y Teor. de Estructuras de la Universidad de Zaragoza se ha observado que la discrepancia de resultados es relevante. Tras analizar en detalle ambos modelos se ha concluido que la principal causa de esta discrepancia es la diferencia en las técnicas de modelado utilizadas en cada uno de los modelos, sobre todo en lo que se refiere a la segmentación del cortical y esponjoso de las falanges. En el presente estudio se ha contado con una tomografía de mayor resolución (292 tacs frente a 93) y con un software más actual, lo que ha permitido realizar una segmentación más precisa y obtener así un modelo más realista. Se ha observado que el espesor y calidad de la capa cortical influyen notablemente en los resultados de tensiones, aunque no tanto en los desplazamientos

Numerical Assessment of the Structural Effects of Relative Sliding between Tissues in a Finite Element Model of the Foot

Penetration and shared nodes between muscles, tendons and the plantar aponeurosis mesh elements in finite element models of the foot may cause inappropriate structural behavior of the tissues. Penetration between tissues caused using separate mesh without motion constraints or contacts can change the loading direction because of an inadequate mesh displacement. Shared nodes between mesh elements create bonded areas in the model, causing progressive or complete loss of load transmitted by tissue. This paper compares by the finite element method the structural behavior of the foot model in cases where a shared mesh has been used versus a separated mesh with sliding contacts between some important tissues. A very detailed finite element model of the foot and ankle that simulates the muscles, tendons and plantar aponeurosis with real geometry has been used for the research. The analysis showed that the use of a separate mesh with sliding contacts and a better characterization of the mechanical behavior of the soft tissues increased the mean of the absolute values of stress by 83.3% and displacement by 17.4% compared with a shared mesh. These increases mean an improvement of muscle and tendon behavior in the foot model. Additionally, a better quantitative and qualitative distribution of plantar pressure was also observed.Fac. de Enfermería, Fisioterapia y PodologíaTRUEMinistry of Economy Government of SpainCONACYT, Mexicopu

Computational methodology to determine fluid related parameters on non regular three-dimensional scaffolds

The application of three-dimensional (3D) biomaterials to facilitate the adhesion, proliferation, and differentiation of cells has been widely studied for tissue engineering purposes. The fabrication methods used to improve the mechanical response of the scaffold produce complex and non regular structures. Apart from the mechanical aspect, the fluid behavior in the inner part of the scaffold should also be considered. Parameters such as permeability (k) or wall shear stress (WSS) are important aspects in the provision of nutrients, the removal of metabolic waste products or the mechanically-induced differentiation of cells attached in the trabecular network of the scaffolds. Experimental measurements of these parameters are not available in all labs. However, fluid parameters should be known prior to other types of experiments. The present work compares an experimental study with a computational fluid dynamics (CFD) methodology to determine the related fluid parameters (k and WSS) of complex non regular poly(L-lactic acid) scaffolds based only on the treatment of microphotographic images obtained with a microCT (lCT). The CFD analysis shows similar tendencies and results with low relative difference compared to those of the experimental study, for high flow rates. For low flow rates the accuracy of this prediction reduces. The correlation between the computational and experimental results validates the robustness of the proposed methodology.The authors gratefully acknowledge research support from the Spanish Ministry of Science and Innovation through research project DPI2010-20399-C04-01. The Instituto de Salud Carlos III (ISCIII) through the CIBER initiative and the Platform for Biological Tissue Characterization of the Centro de Investigacion Biomedica en Red en Bioingenieria, Biomateriales y Nanomedicina (CIBER-BBN) are also gratefully acknowledged.Acosta Santamaría, VA.; Malvé, M.; Duizabo, A.; Mena Tobar, A.; Gallego Ferrer, G.; García Aznar, J.; Doblare Castellano, M.... (2013). Computational methodology to determine fluid related parameters on non regular three-dimensional scaffolds. Annals of Biomedical Engineering. 41(11):2367-2380. https://doi.org/10.1007/s10439-013-0849-8S236723804111Acosta Santamaría, V., H. Deplaine, D. Mariggió, A. R. Villanueva-Molines, J. M. García-Aznar, J. L. Gómez Ribelles, M. Doblaré, G. Gallego Ferrer, and I. Ochoa. Influence of the macro and micro-porous structure on the mechanical behavior of poly(l-lactic acid) scaffolds. J. Non-Cryst. Solids 358(23):3141–3149, 2012.Adachi, T., Y. Osako, M. Tanaka, M. Hojo, and S. J. Hollister. Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials 27(21):3964–3972, 2006.Adamczyk, Z., and T. G. M. Vandeven. Deposition of particles under external forces in laminar-flow through parallel-plate and cylindrical channels. J. Colloid Interface Sci. 80(2):340–356, 1981.Alberich, B. A., D. Moratal, J. L. Escobar, J. C. Rodríguez, A. Vallés-Lluch, L. Martí-Bonmatí, et al. Microcomputed tomography and microfinite element modeling for evaluating polymer scaffolds architecture and their mechanical properties. J. Biomed. Mater. Res. B Appl. Biomater. 91B(1):191–202, 2009.Al-Munajjed, A., M. Hien, R. Kujat, J. P. Gleeson, and J. Hammer. Influence of pore size on tensile strength, permeability and porosity of hyaluronan-collagen scaffolds. J. Mater. Sci. Mater. Med. 19(8):2859–2864, 2008.Alves da Silva, M. L., A. Martins, A. R. Costa-Pinto, V. M. Correlo, P. Sol, M. Bhattacharya, S. Faria, R. L. Reis, and N. M. Neves. Chondrogenic differentiation of human bone marrow mesenchymal stem cells in chitosan-based scaffolds using a flow-perfusion bioreactor. J. Tissue Eng. Regen. Med. 5(9):722–732, 2011.Ansys (2010) CFX Theory User Manual. Canonsburg, PA: Ansys Software.Brígido, R. D., J. M. Estellés, J. A. Sanz, J. M. García-Aznar, and M. S. Sánchez. Polymer scaffolds with interconnected spherical pores and controlled architecture for tissue engineering: fabrication, mechanical properties, and finite element modeling. J. Biomed. Mater. Res. B Appl. Biomater. 81B(2):448–455, 2007.Byrne, P. D., D. Lacroix, J. A. Planell, D. J. Kelly, and P. J. Prendergast. Simulation of tissue differentiation in a scaffold as a function of porosity, Young’s modulus and dissolution rate: application of mechanobiological models in tissue engineering. Biomaterials 28:5544–5554, 2007.Chor, M. V., and W. Li. A permeability measurement system for tissue engineering scaffolds. Meas. Sci. 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Mater Sci. 46:273–282, 2001.Gong, S., H. Wang, Q. Sun, S. T. Xue, and J. Wang. Mechanical properties and in vitro biocompatibility of porous zein scaffolds. Biomaterials 27(20):3793–3799, 2006.Gutierrez, R. A., and E. T. Crumpler. Potential effect of geometry on wall shear stress distribution across scaffold surfaces. Ann. Biomed. Eng. 36(1):77–85, 2008.Hammer, D. A., and D. Lauffenburger. A dynamic-model for receptor-mediated cell adhesion to surfaces. Biophys. J. 52(3):475–487, 1987.Ho, S. T., and D. W. Hutmacher. A comparison of micro CT with other techniques used in the characterization of scaffolds. Biomaterials 27(8):1362–1376, 2006.Ho, M. H., P. Y. Kuo, H. J. Hsieh, T. Y. Hsien, L. T. Hou, J. Y. Lai, and D. M. Wang. Preparation of porous scaffolds by using freeze-extraction and freeze-gelation methods. Biomaterials 25(1):129–138, 2004.Hutmacher, D. W., J. T. Schantz, C. X. Lam, K. C. Tan, and T. C. Lim. State of the art and future directions of scaffold-based bone engineering from a biomaterials perspective. J. Tissue Eng. Regen. Med. 1(4):245–260, 2007.Izal, I., P. Aranda, P. Sanz-Ramos, P. Ripalda, G. Mora, F. Granero-Moltó, H. Deplaine, J. L. Gómez-Ribelles, G. G. Ferrer, V. Acosta, I. Ochoa, J. M. García-Aznar, E. J. Andreu, M. Monleón-Pradas, M. Doblaré, and F. Prósper. Culture of human bone marrow-derived mesenchymal stem cells on of poly(l-lactic acid) scaffolds: potential application for the tissue engineering of cartilage. Knee Surg. Sports Traumatol. Arthrosc., 2012.Kapur, S., D. J. Baylink, and K. H. Lau. Fluid flow shear stress stimulates human osteoblast proliferation and differentiation through multiple interacting and competing signal transduction pathways. Bone 32(3):241–251, 2003.Karande, T. S., J. L. Ong, and C. M. Agrawal. Diffusion in musculoskeletal tissue engineering scaffolds: design issues related to porosity, permeability, architecture, and nutrient mixing. Ann. Biomed. Eng. 32(12):1728–1743, 2004.Kelly, D. J., and P. J. Prendergast. Mechano-regulation of stem cell differentiation and tissue regeneration in osteochondral defects. J. Biomech. 38(7):1413–1422, 2005.Kreke, M. R., L. A. Sharp, Y. W. Lee, and A. S. Goldstein. Effect of intermittent shear stress on mechanotransductive signaling and osteoblastic differentiation of bone marrow stromal cells. Tissue Eng. Part A 14(4):529–537, 2008.Lacroix, D., A. Chateau, M. P. Ginebra, and J. A. Planell. Micro-finite element models of bone tissue-engineering scaffolds. Biomaterials 27(30):5326–5334, 2006.Lacroix, D., and P. J. Prendergast. A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading. J. Biomech. 35(9):1163–1171, 2002.Li, S., J. R. De Wijn, J. Li, P. Layrolle, and K. De Groot. Macroporous biphasic calcium phosphate scaffold with high permeability/porosity ratio. Tissue Eng. 9:535–548, 2003.Melchels, F. P. W., B. Tonnarelli, A. L. 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Vulnerability in regionally ischemic human heart. Effect of the extracellular potassium concentration

Ventricular tachycardia and ventricular fibrillation are two types of cardiac arrhythmias that usually occur during acute ischemia and frequently lead to sudden death. Pro-arrhythmic mechanisms related to acute ischemia have been extensively investigated, although often in animal models rather than in human. In this work, we investigate how hyperkalemia affects the vulnerable window to reentry and the reentry patterns in the heterogeneous substrate caused by acute regional ischemia using an anatomically and biophysically detailed human biventricular model. The ischemic region was located in the inferolateral and posterior side of the left ventricle, mimicking the occlusion of the circumflex artery, and includes a wash-out zone not affected by ischemia located in the endocardium. Realistic heterogeneity and fiber anisotropy have been considered in the model. An electrophysiologically detailed human action potential model has been modified to simulate ischemic conditions. The model predicts the generation of sustained reentrant activity in the form of single and double circuits around an area of block within the ischemic zone for K+concentrations below 9 mM, with the reentrant activity corresponding to ventricular tachycardia in all cases. Our results also suggest that the wash-out zone is a potential pro-arrhythmic factor that favors sustained ventricular tachycardia

Trabajos de grado en Comunicación, resúmenes analíticos 2012-2015

Se entiende el sistema de investigación como el proceso integrado mediante el cual asignaturas y proyectos de investigación institucional posibilitan la realización de ejercicios de investigación por parte de los estudiantes del Programa de Comunicación de la Pontificia Universidad Javeriana Cali. El sistema plantea la interacción entre las asignaturas del núcleo de formación (asignaturas teóricas, talleres, y de gestión) y las asignaturas que contribuyen a la formulación, escritura y realización del trabajo de grado en la Carrera de Comunicación; tales asignaturas son: Métodos de investigación en comunicación (300CMG051), Proyecto de grado (300CMG015) y Trabajo de grado (300CMG018). Del tránsito por este sistema de investigación se espera que los estudiantes consoliden competencias para el abordaje crítico de fenómenos sociales, donde la comunicación puede ofrecer una vía interpretativa, analítica o resolutiva. Asimismo, se espera que la participación activa de los estudiantes en los proyectos institucionales de investigación permita la consecución de una comunidad académica activa, participativa y reflexiva en torno al lugar que tiene la comunicación en la comprensión de la vida social en la ciudad, la región, el país y el mundo. Este proceso es agenciado por el grupo de investigación Procesos y Medios de Comunicación de la Pontificia Universidad Javeriana Cali. A continuación se presenta una breve descripción del grupo y sus líneas

Migraciones en América Central: Políticas, territorios y actores

Migraciones en América Central. Políticas, territorios y actores procura ofrecer un acercamiento a las diversas dimensiones de la experiencia migratoria en Centroamérica. Cuatro puntos de partida caracterizan este libro: el carácter público de la convocatoria, la dimensión colectiva del trabajo, la perspectiva regional que se nutre del contraste y comparación de casos y, en cuarto lugar, la convocatoria que da origen a este libro. Lo anterior ha permitido contar con una tarea concreta para darle forma a las expectativas del trabajo público, colectivo y regional.UCR::Vicerrectoría de Docencia::Ciencias Sociales::Facultad de Ciencias Sociales::Escuela de Ciencias de la Comunicación ColectivaUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Sociales::Instituto de Investigaciones Sociales (IIS