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<p>Engineered monolayers created by using microabrasion and micropatterning methods have provided a simplified in vitro system to study the effects of anisotropy and fiber direction on electrical propagation. Interpreting the behavior in these culture systems has often been performed using classical computer models with continuous properties. Such models, however, do not account for the effects of random cell shapes, cell orientations and cleft spaces inherent in these monolayers on the resulting wavefront conduction. Additionally when the continuous computer model is built to study impulse propagations, the intracellular conductivities of the model are commonly assigned to match impulse conduction velocity of the model to the experimental measurement. However this method can result in inaccurate intracellular conductivities considering the relationship among the conduction velocity, intracellular conductivities and ion channel properties. In this study, we present novel methods for modeling a monolayer cardiac tissue and for estimating intracellular conductivities from an optical mapping. First, in the proposed method for modeling a monolayer of cardiac tissue, the factors governing cell shape, cell-to-cell coupling and the degree of cleft space are not constant but rather are treated as spatially random with assigned distributions. This approach makes it possible to simulate wavefront propagation in a manner analogous to performing experiments on engineered monolayer tissues. Simulated results are compared to reported experimental data measured from monolayers used to investigate the role of cellular architecture on conduction velocities and anisotropy ratios. We also present an estimate for obtaining the electrical properties from these networks and demonstrate how variations in the discrete cellular architecture affect the macroscopic conductivities. The simulation results agree with the common assumption that under normal ranges of coupling strengths, tissues whose cell shapes and connectivity show relatively uniform distributions can be represented using continuous models with conductivities derived from random discrete cellular architecture using either estimates. The results also reveal that in the presence of abrupt changes in cell orientation, local estimates of tissue properties predict smoother changes in conductivities that may not adequately predict the discrete nature of propagation at the transition sites. Second, a novel approach is proposed to estimate intracellular conductivities from the optical mapping of the monolayer cardiac tissue under subthreshold stimulus. This method uses a simplified membrane model, which represents the membrane as a second order polynomial of the membrane potential. The simplified membrane model and the intracellular conductivities are estimated from the optical mapping of the monolayer tissue under the subthreshold stimulus. We showed that the proposed method provides more accurate intracellular conductivities compared to a method using a constant membrane resistance.</p> / Dissertation

Accurate numerical simulation of reaction-diffusion systems can come with a high cost. A system may be stiff, and solutions may exhibit sharp localized features that require fine grids and small time steps to properly resolve the physical phenomena they represent. The development of efficient methods is crucial to cut down the demands of computational resources. In this thesis we consider the use of adaptive space and time methods driven by a posteriori error estimation. The error estimators for the spatial discretization are built from a variety of sources: the residual of the partial differential equation (PDE) system, gradient recovery operators and interpolation estimates. The interpolation estimates are anisotropic, not relying on classical mesh regularity assumptions. The adapted mesh is therefore allowed to include elements elongated in specified directions, as dictated by the type of solution being approximated. This thesis proposes an element-based adaptation method to be used for a residual estimator. This method avoids the usual conversion of the estimator to a metric, and instead applies the estimator to directly control the local mesh modifications. We derive a new error estimator for the L^2-norm in the same anisotropic setting and adjust the element-based adaptation algorithm to the new estimator. This thesis considers two new adaptive finite element settings for reaction-diffusion problems. The first is the extension to a PDE setting of an estimator for the time discretization with the backward difference formula of order 2 (BDF2), based on an estimator for ordinary differential equation (ODE) problems. Coupled with the residual estimator, we apply a space-time adaptation method. The second is the derivation of anisotropic error estimates for the monodomain model from cardiac electrophysiology. This model couples a nonlinear parabolic PDE with an ODE and this setting presents challenges theoretically as well as numerically. In addition to theoretical considerations, numerical tests are performed throughout to assess the reliability and efficiency of the proposed error estimators and numerical methods.

This thesis investigates the high-order hierarchical finite element method, also known as the finite element p-version, as a computationally-efficient technique for generating numerical solutions to the cardiac monodomain equation. We first present it as a uniform-order method, and through an a priori error bound we explain why the associated cardiac cell model must be thought of as a PDE and approximated to high-order in order to obtain the accuracy that the p-version is capable of. We perform simulations demonstrating that the achieved error agrees very well with the a priori error bound. Further, in terms of solution accuracy for time taken to solve the linear system that arises in the finite element discretisation, it is more efficient that the state-of-the-art piecewise linear finite element method. We show that piecewise linear FEM actually introduces quite significant amounts of error into the numerical approximations, particularly in the direction perpendicular to the cardiac fibres with physiological conductivity values, and that without resorting to extremely fine meshes with elements considerably smaller than 70 micrometres, we can not use it to obtain high-accuracy solutions. In contrast, the p-version can produce extremely high accuracy solutions on meshes with elements around 300 micrometres in diameter with these conductivities. Noting that most of the numerical error is due to under-resolving the wave-front in the transmembrane potential, we also construct an adaptive high-order scheme which controls the error locally in each element by adjusting the finite element polynomial basis degree using an analytically-derived a posteriori error estimation procedure. This naturally tracks the location of the wave-front, concentrating computational effort where it is needed most and increasing computational efficiency. The scheme can be controlled by a user-defined error tolerance parameter, which sets the target error within each element as a proportion of the local magnitude of the solution as measured in the H^1 norm. This numerical scheme is tested on a variety of problems in one, two and three dimensions, and is shown to provide excellent error control properties and to be likely capable of boosting efficiency in cardiac simulation by an order of magnitude. The thesis amounts to a proof-of-concept of the increased efficiency in solving the linear system using adaptive high-order finite elements when performing single-thread cardiac simulation, and indicates that the performance of the method should be investigated in parallel, where it can also be expected to provide considerable improvement. In general, the selection of a suitable preconditioner is key to ensuring efficiency; we make use of a variety of different possibilities, including one which can be expected to scale very well in parallel, meaning that this is an excellent candidate method for increasing the efficiency of cardiac simulation using high-performance computing facilities.

In mammalian hearts, initiation of the heartbeat occurs in a region of specialised pacemaker cells known as the sinoatrial node (SAN). The SAN is a highly complex spatially distributed structure which displays considerable cellular heterogeneity and is subject to complex electrotonic interactions with the surrounding atrial tissue. In this study, biophysically detailed ionic models of central and peripheral SAN pacemaker cells are described. These models are able to accurately reproduce experimental recordings of the membrane potential from central and peripheral SAN tissue. These models are used to investigate frequency synchronisation of electrically coupled cardiac pacemaker cells. Based on simulation results presented, it is proposed that cellular heterogeneity in the SAN plays an important role in achieving rhythm coordination and possibly contributes to the efficient activation of the surrounding atrial myocardium. This represents an important, previously unexplored, mechanism underlying pacemaker synchronisation and cardiac activation in vivo. A spatial-gradient model of action potential heterogeneity within the SAN is then formulated using a large-scale least squares optimisation technique. This model accurately reproduces the smooth spatial variation in action potential characteristics observed in the SAN. One and two dimensional models of the intact SAN are then formulated and three proposed models of SAN heterogeneity are investigated: 1) the discrete-region model, in which the SAN consists of a compact central region surrounded by a region of transitional pacemaker cells, 2) the gradient model, in which cells of the SAN exhibit a smooth variation in properties from the centre to the periphery of the SAN, and 3) the mosaic model, in which SAN and atrial cells are scattered throughout the SAN region with the proportion of atrial cells increasing towards the periphery. Simulation results suggest that the gradient model achieves frequency entrainment more easily than the other models of SAN heterogeneity. The gradient model also reproduces action potential waveshapes and a site of earliest activation consistent with experimental observations in the intact SAN. It is therefore proposed that the gradient model of SAN heterogeneity represents the most plausible model of SAN organisation.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T14:38:55Z No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:42:47Z (GMT) No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Made available in DSpace on 2018-01-23T13:42:47Z (GMT). No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) Previous issue date: 2017-08-28 / A fibrilação ventricular é uma arritmia cardíaca listada como uma das principais causas de morte no mundo industrializado, por isso, a importância do estudo do comportamento elétrico cardíaco. O equipamento mais indicado para tentar reverter este quadro de arritmia é o desfibrilador, que submete o tórax do paciente a um campo elétrico de alta energia. Entretanto essa técnica pode causar efeitos graves como queimaduras e dor intensa. Técnicas menos agressivas vêm sendo estudadas e consideram, por exemplo, protocolos com múltiplos estímulos de baixa energia. Observou-se que, nessas estratégias alternativas, a rede vascular cardíaca pode ter papel importante com relação ao padrões espaço-temporais gerados pelos estímulos. Nesta mesma direção, este trabalho apresenta um estudo computacional sobre a influência da rede vascular durante estímulos por campo elétrico em tecidos cardíacos. O fenômeno é capturado por um sistema não-linear de equações diferenciais parciais. Para resolver este modelo numericamente os Métodos de Volumes Finitos (MVF) e de Phase-Field (MPF) foram combinados buscando assim a caracterização geométrica de vasos arteriais durante simulações de desfibrilação de tecido cardíaco. Os resultados obtidos sugerem que os métodos usados (MVF+MPF) são adequados para o estudo de protocolo para desfibrilação cardíaca. / The ventricular fibrillation is a cardiac arrhythmia listed as one of the leading causes of death within the industrialized world, hence the study of cardiac electrical behavior is an important research area. The most used equipment for the reversal of this condition is the defibrillator, which subjects the patient's chest to a high-energy electric field. However, it can have serious effects such as burns and severe pain. Less aggressive techniques have been studied and considered, for example, protocols with multiple low energy stimuli. It was observed that, in this alternative technique, the cardiac vascular network may play an important role in relation to the spatial-temporal patterns generated by the stimuli. This work presents a computational study about the influence of the vascular network during electrical field stimuli in cardiac tissues. The phenomenon is described by a nonlinear system of partial differential equations. To solve this model numerically the Finite Volume Method (FVM) and the Phase-Field Method (PFM) were combined, thus seeking a better geometric characterization of arterial vessels during simulations of cardiac tissue defibrillation. The results obtained in this work suggest that these methods (FVM + PFM) are suitable for the protocol study for cardiac defibrillation.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-06T20:24:42Z No. of bitstreams: 1 joventinodeoliveiracampos.pdf: 3604904 bytes, checksum: aca8053f097ddcb9d96ba51186838610 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T20:27:39Z (GMT) No. of bitstreams: 1 joventinodeoliveiracampos.pdf: 3604904 bytes, checksum: aca8053f097ddcb9d96ba51186838610 (MD5) / Made available in DSpace on 2017-03-06T20:27:39Z (GMT). No. of bitstreams: 1 joventinodeoliveiracampos.pdf: 3604904 bytes, checksum: aca8053f097ddcb9d96ba51186838610 (MD5) Previous issue date: 2015-06-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta o método de lattice Boltzmann (MLB) para simulações computacionais da atividade elétrica cardíaca usando o modelo monodomínio. Uma implementação otimizada do método de lattice Boltzmann é apresentada, a qual usa um modelo de colisão com múltiplos parâmetros de relaxação conhecido como multiple relaxation time (MRT), para considerar a anisotropia do tecido cardíaco. Com foco em simulações rápidas da dinâmica cardíaca, devido ao alto grau de paralelismo presente no MLB, uma implementação que executa em uma unidade de processamento gráfico (GPU) foi realizada e seu desempenho foi estudado através de domínios tridimensionais regulares e irregulares. Os resultados da implementação para simulações cardíacas mostraram fatores de aceleração tão altos quanto 500x para a simulação global e para o MLB um desempenho de 419 mega lattice update per second (MLUPS) foi alcançado. Com tempos de execução próximos ao tempo real em um único computador equipado com uma GPU moderna, estes resultados mostram que este trabalho é uma proposta promissora para aplicação em ambiente clínico. / This work presents the lattice Boltzmann method (LBM) for computational simulations of the cardiac electrical activity using monodomain model. An optimized implementation of the lattice Boltzmann method is presented which uses a collision model with multiple relaxation parameters known as multiple relaxation time (MRT) in order to consider the anisotropy of the cardiac tissue. With focus on fast simulations of cardiac dynamics, due to the high level of parallelism present in the LBM, a GPU parallelization was performed and its performance was studied under regular and irregular three-dimensional domains. The results of our optimized LBM GPU implementation for cardiac simulations shown acceleration factors as high as 500x for the overall simulation and for the LBM a performance of 419 mega lattice updates per second (MLUPS) was achieved. With near real time simulations in a single computer equipped with a modern GPU these results show that the proposed framework is a promising approach for application in a clinical workflow.

The work deals with the foundations of bioelectric phenomena cardiomyocyte, then it is also part of this description of the heart conduction system and method of distribution in this system The next section is a description of the spread in the system, the very essence of the spread. In the last chapter analyzes the theory for the creation of computational models, which extend in one dimension or two dimensions

Les simulations numériques réalistes en électrophysiologie cardiaque ont un coût de calcul extrêmement élevé. Ce coût s’explique en grande partie par la raideur, à la fois en temps et en espace, d’une onde de « potentiel d’action » (PA). Par ailleurs, les phénomènes observés sont très instationnaires et s’étudient en temps long. Une description précise de la dynamique des PA est cruciale pour construire des modèles numériques pertinents d’un point de vue médical ou clinique. Cet aspect fondamental ne peut être contourné dans les études numériques réalistes.La raideur de l’onde de PA ne peut être captée numériquement qu’en ayant recours à des maillages très fins. Ces maillages très fins induisent un coût de calcul très important, et introduisent aussi des erreurs supplémentaires : les systèmes linéaires à résoudre deviennent très mal conditionnés. Au final, les erreurs numériques peuvent être particulièrement grandes dans les simulations alors que leur contrôle est évidemment essentiel pour assurer la fiabilité des résultats. Jusqu’à présent, très peu de résultats sont disponibles pour assurer cette fiabilité. Dans les faits, les erreurs sont la plupart du temps contrôlées par des procédés empiriques. Il existe quelques résultats théoriques étudiant la convergence et la stabilité des schémas numériques associés. En pratique, en plus d'avoir un contrôle de l'erreur sur le potentiel, il est aussi nécessaire d'avoir un contrôle de l’erreur sur des quantités macroscopiques décrivant la dynamique de l’onde de PA : temps d’activation, durée du PA, propriétés de restitution... Ces quantités ont en effet une interprétation physiologique qui permet de caractériser le caractère arythmogène des tissus.Les modèles sont des systèmes d’EDP de réaction-diffusion couplés avec des systèmes d’équations différentielles pouvant être très raides, les modèles ioniques. Ils sont actuellement discrétisés par éléments finis conforme (Lagrange) et par des schémas en temps d’ordre un ou deux. Dans ce travail, nous concevons et évaluons l’intérêt d'utiliser des méthodes d’ordre supérieure pour ces systèmes. Parallèlement nous introduisons d'une part une nouvelle classe de schémas appelé schémas exponentiel Adams Bashforth intégral (IEAB), et d'autre part des schémas Rush Larsen (RL) d'ordre élevé. Ces nouveaux schémas sont des schémas multipas de type exponentiels. Nous montrons qu'ils possèdent des bonnes propriétés de stabilité et permettent de faire face efficacement à la raideur des modèles ioniques. Les schémas que nous proposons sont comparés numériquement (en terme de précision, coût en temps de calcul et stabilité) à plusieurs schémas classiques, ainsi qu'aux schémas exponentiels (RL1, RL2) communément utilisés pour des simulations en électrophysiologie cardiaque. Nous proposons des techniques permettant de calculer avec précision les quantités d’intérêts cliniques (temps d’activation, de récupération, durée du potentiel d’action). Des résultats théoriques de convergence en temps et de convergence globale (espace et temps) sont énoncés et prouvés. Ces résultats sont ensuite illustrés numériquement à travers le modèle monodomaine et les modèles ioniques de Beeler Reuter, de Ten Tusscher et al. L’intérêt d'utiliser des schémas d'ordre élevés est aussi évalué sur des ondes spirales en 2D et 3D. / Realistic numerical simulations in cardiac electrophysiology have a computational cost of extremely high. This cost is largely explained by the stiffness both in time and space, of the action potential (AP) wave. Moreover, the observed phenomena are very unsteady and are studied in long time. A precise description of the dynamic of AP is crucial for constructing relevant numerical models, from a medical or clinical perspective. This fundamental aspect can not be circumvented in realistic numerical studies.The stiffness of AP wave can only be captured numerically, by using very fine meshes. In addition to the high computational cost, these very fine meshes also introduce additional errors : the linear systems to solve become very badly conditioned. In the end, the numerical errors can be particularly large whereas their control is obviously essential to ensure the reliability of the results. So far very few results are available to ensure this reliability. In practice, the errors are mostly controlled by empirical processes. In practice, in addition of having a control of the error on the potential, it is also necessary to have an error control on macroscopic quantities describing the dynamics of the AP wave : activation time, AP duration, properties of restitution ... These quantities have indeed a physiological interpretation which allows to characterize the arrhythmogenic character of the tissues.The models are systems of reaction diffusion PDE coupled with systems of differential equations that can be very stiffs (ionic models). They are currently discretized by conforming finite elements (Lagrange finite elements methods) and by schemes in time of order one or two. In this work, we design and evaluate the interest of using higher order methods for these systems. At the same time, we introduce on the one hand, a new class of schemes called Integral Exponential Adams Bashforth (IEAB) schemes and, on the other hand, high order Rush Larsen (RL) schemes. These new schemes are exponential time-stepping schemes. We show that they have good stability properties and can efficiently cope with the stiffness of ionic models. The schemes we propose are numerically compared (in terms of accuracy, CPU time and stability) with several classical schemes, as well as with the exponential schemes (RL1, RL2), commonly used for cardiac electrophysiology simulations. We propose good techniques for accurately calculating quantities of clinical interest (activation time, recovery time, duration of action potential). Theoretical results of convergence in time and global convergence (in space and time) are stated and proved. These results are then illustrated numerically through the monodomain model and the ionic models of Beeler Reuter, Ten Tusscher et al. The advantage of using high order schemes is also evaluated on spiral waves in 2D and 3D.

Thin-film-transistor (TFT) liquid crystal display (LCD) has been widely used in smartphones, pads, laptops, computer monitors, and large screen televisions, just to name a few. A great deal of effort has been delved into wide viewing angle, high resolution, low power consumption, and vivid color. However, relatively slow response time and low transmittance remain as technical challenges. To improve response time, several approaches have been developed, such as low viscosity liquid crystals, overdrive and undershoot voltage schemes, thin cell gap with a high birefringence liquid crystal, and elevated temperature operation. The state-of-the-art gray-to-gray response time of a nematic LC device is about 5 ms, which is still not fast enough to suppress the motion picture image blur. On the other hand, the LCD panel's transmittance is determined by the backlight, polarizers, TFT aperture ratio, LC transmittance, and color filters. Recently, a fringe-field-switching mode using a negative dielectric anisotropy (Δε) LC (n-FFS) has been demonstrated, showing high transmittance (98%), single gamma curve, and cell gap insensitivity. It has potential to replace the commonly used p-FFS (FFS using positive Δε LC) for mobile displays. With the urgent need of submillisecond response time for enabling color sequential displays, polymer-stabilized blue phase liquid crystal (PS-BPLC) has become an increasingly important technology trend for information display and photonic applications. BPLCs exhibit several attractive features, such as reasonably wide temperature range, submillisecond gray-to-gray response time, no need for alignment layer, optically isotropic voltage-off state, and large cell gap tolerance. However, some bottlenecks such as high operation voltage, hysteresis, residual birefringence, and slow charging issue due to the large capacitance, remain to be overcome before their widespread applications can be realized. The material system of PS-BPLC, including nematic LC host, chiral dopant, and polymer network, are discussed in detail. Each component plays an essential role affecting the electro-optic properties and the stability of PS-BPLC. In a PS-BPLC system, in order to lower the operation voltage the host LC usually has a very large dielectric anisotropy (Δε > 100), which is one order of magnitude larger than that of a nematic LC. Such a large Δε not only leads to high viscosity but also results in a large capacitance. High viscosity slows down the device fabrication process and increases device response time. On the other hand, large capacitance causes slow charging time to each pixel and limits the frame rate. To reduce viscosity, we discovered that by adding a small amount (~6%) of diluters, the response time of the PS-BPLC is reduced by 2X-3X while keeping the Kerr constant more or less unchanged. Besides, several advanced PS-BPLC materials and devices have been demonstrated. By using a large Δε BPLC, we have successfully reduced the voltage to <10V while maintaining submillisecond response time. Finally we demonstrated an electric fieldindeced monodomain PS-BPLC, which enables video-rate reflective display with vivid colors. The highly selective reflection in polarization makes it promising for photonics application. Besides displays in the visible spectral region, LC materials are also very useful electro-optic media for near infrared and mid-wavelength infrared (MWIR) devices. However, large absorption has impeded the widespread application in the MWIR region. With delicate molecular design strategy, we balanced the absorption and liquid crystal phase stability, and proposed a fluoro-terphenyl compound with low absorption in both MWIR and near IR regions. This compound serves as an important first example for future development of low-loss MWIR liquid crystals, which would further expand the application of LCs for amplitude and/or phase modulation in MWIR region.