Rodrigo Weber dos Santos

Comparing CUDA and OpenGL implementations for a Jacobi iteration

The use of the GPU as a general purpose processor is becoming more popular and there are different approaches for this kind of programming. In this paper we present a comparison between different implementations of the OpenGL and CUDA approaches for solving our test case, a weighted Jacobi iteration with a structured matrix originating from a finite element discretization of the elliptic PDE part of the cardiac bidomain equations. The CUDA approach using textures showed to be the fastest with a speedup of 31 over a CPU implementation using one core and SSE. CUDA showed to be an efficient and easy way of programming GPU for general purpose problems, though it is also easier to write inefficient codes.

Electroanatomical Characterization of Atrial Microfibrosis in a Histologically Detailed Computer Model

Fibrosis is thought to play an important role in the formation and maintenance of atrial fibrillation (AF). The propensity of fibrosis to increase AF vulnerability depends not only on its amount, its texture plays a crucial role as well. While the detection of fibrotic tissue patches in the atria with extracellular recordings is feasible based on the analysis of electrogram fractionation, as used in clinical practice to identify ablation targets, the classification of fibrotic texture is a more challenging problem. This study seeks to establish a method for the electroanatomical characterization of the fibrotic textures based on the analysis of electrogram fractionation. The proposed method exploits the dependence of fractionation patterns on the incidence direction of wavefronts which differs significantly as a function of texture. A histologically detailed computer model of the right atrial isthmus was developed for testing the method. A stimulation protocol was conceived which generated various incidence directions for any given recording site where electrograms were computed. A classification method is derived then for discriminating three types of fibrosis, no fibrosis (control), diffuse, and patchy fibrosis. Simulation results showed that electrogram fractionation and amplitudes and their dependence upon incidence direction allow a robust discrimination between different classes of fibrosis. Finally, to minimize the technical effort, sensitivity analysis was performed to identify a minimum number of incidence directions required for robust classification.

On the computational modeling of the innate immune system

In recent years, there has been an increasing interest in the mathematical and computational modeling of the human immune system (HIS). Computational models of HIS dynamics may contribute to a better understanding of the relationship between complex phenomena and immune response; in addition, computational models will support the development of new drugs and therapies for different diseases. However, modeling the HIS is an extremely difficult task that demands a huge amount of work to be performed by multidisciplinary teams. In this study, our objective is to model the spatio-temporal dynamics of representative cells and molecules of the HIS during an immune response after the injection of lipopolysaccharide (LPS) into a section of tissue. LPS constitutes the cellular wall of Gram-negative bacteria, and it is a highly immunogenic molecule, which means that it has a remarkable capacity to elicit strong immune responses. We present a descriptive, mechanistic and deterministic model that is based on partial differential equations (PDE). Therefore, this model enables the understanding of how the different complex phenomena interact with structures and elements during an immune response. In addition, the models parameters reflect physiological features of the system, which makes the model appropriate for general use.

A Macro Finite-Element Formulation for Cardiac Electrophysiology Simulations Using Hybrid Unstructured Grids

Abstract-Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large-scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem, which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for computing shape functions of finite elements (FEs). The technique generates macro FEs (MFEs) based on the local decomposition of elements into tetrahedral subelements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes (HMs) composed of different types of elements. MFEs are compared to classic standard FEs with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling, including bidomain and monodomain simulations in 2-D and 3-D for simple and complex tissue geometries. In problems with analytical solutions, MFEs displayed the same numerical accuracy of standard linear triangular and tetrahedral elements. In propagation simulations, conduction velocity and activation times agreed very well with those computed with standard FEs. However, MFEs offer a significant decrease in memory requirements. We conclude that HMs composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.

A transformation tool for ODE based models

This paper presents a tool for prototyping ODE (Ordinary Differential Equations) based systems in the area of computational modeling. The models, tailored during the project step of the system development, are recorded in MathML, a markup language built upon XML. This design choice improves interoperability with other tools used for mathematical modeling, mainly considering that it is based on Web architecture. The resulting work is a Web portal that transforms an ODE model documented in MathML to a C++ API that offers numerical solutions for that model.

ATX-II effects on the apparent location of M cells in a computational model of a human left ventricular wedge.

Introduction: The apparent location of the myocytes (M cells) with the longest action potential duration (APD) in a canine left ventricular (LV) wedge have been reported to shift after application of a sea anemone toxin, ATX‐II. This toxin slows inactivation of INa and thus prolongs APD. Thus, M cells may exhibit dynamic functional states, rather than being a static, anatomically discrete, myocyte population. In this study, we attempted to further define and understand this phenomenon using a mathematical model of the human ventricular myocyte action potential incorporated into an in silico “wedge” preparation. Our simulations demonstrate that even under conditions of a fixed population and ratio of epicardial, M, and endocardial myocytes, the apparent anatomical position (transmural location) of the myocytes with the longest APD can shift following ATX‐II treatment. This arises because the ATX‐II effect, modeled as a small increase in the late or persistent Na+ current, and consequent prolongation of APD significantly changes the electrotonic interactions between ventricular myocytes in this LV wedge preparation.

An Efficient Finite Element Approach for Modeling Fibrotic Clefts in the Heart

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

Experimental and theoretical ventricular electrograms and their relation to electrophysiological gradients in the adult rat heart

The electrical activity of adult mouse and rat hearts has been analyzed extensively, often as a prerequisite for genetic engineering studies or for the development of rodent models of human diseases. Some aspects of the initiation and conduction of the cardiac action potential in rodents closely resemble those in large mammals. However, rodents have a much higher heart rate and their ventricular action potential is triangular and very short. As a consequence, an interpretation of the electrocardiogram in the mouse and rat remains difficult and controversial. In this study, optical mapping techniques have been applied to an in vitro left ventricular adult rat preparation to obtain patterns of conduction and action potential duration measurements from the epicardial surface. This information has been combined with previously published mathematical models of the rat ventricular myocyte to develop a bidomain model for action potential propagation and electrogram formation in the rat left ventricle. Important insights into the basis for the repolarization waveform in the ventricular electrogram of the adult rat have been obtained. Notably, our model demonstrated that the biphasic shape of the rat ventricular repolarization wave can be explained in terms of the transmural and apex-to-base gradients in action potential duration that exist in the rat left ventricle.

Determination of Cardiac Ejection Fraction by Electrical Impedance Tomography - Numerical Experiments and Viability Analysis

Cardiac ejection fraction is a clinically relevant parameter that is highly correlated to the functional status of the heart. Today the non-invasive methods and technology that measure cardiac ejection fraction, such as MRI, CT and echocardiography do not offer a continuous way of monitoring this important parameter. In this work, we numerically evaluate a new method for the continuous estimation of cardiac ejection fraction based on Electrical Impedance Tomography. The proposed technique assumes the existence of recent Magnetic Resonance (MR) images of the heart to reduce the search space of the inverse problem. Simulations were performed on two-dimensional cardiac MRI images with electric potentials numerically obtained by the solution of the Poisson equation via the Boundary Element Method. Different protocols for current injection were evaluated. Preliminary results are presented and the potentialities and limitations of the proposed technique are discussed.

A three-dimensional computational model of the innate immune system

The Human Immune System is a complex system responsible for protecting the organism against diseases. Although understanding how it works is essential to develop better treatments against diseases, its complexity makes this task extremely hard. In this work a three-dimensional mathematical and computational model of part of this system, the innate immune system, is presented. The high computational costs associated to simulations lead the development of a parallel version of the code, which has achieved a speedup of about 72 times over its sequential counterpart.