Circ Res

Atrial fibrillation (AF) is the most common sustained arrhythmia in humans. The mechanisms that govern AF initiation and persistence are highly complex, of dynamic nature, and involve interactions across multiple temporal and spatial scales in the atria. This article aims to review the mathematical modeling and computer simulation approaches to understanding AF mechanisms and aiding in its management. Various atrial modeling approaches are presented, with descriptions of the methodological basis and advancements in both lower-dimensional and realistic geometry models. A review of the most significant mechanistic insights made by atrial simulations is provided. The article showcases the contributions that atrial modeling and simulation have made not only to our understanding of the pathophysiology of atrial arrhythmias, but also to the development of AF management approaches. A summary of the future developments envisioned for the field of atrial simulation and modeling is also presented. The review contends that computational models of the atria assembled with data from clinical imaging modalities that incorporate electrophysiological and structural remodeling could become a first line of screening for new AF therapies and approaches, new diagnostic developments, and new methods for arrhythmia prevention.DP1 HL123271/HL/NHLBI NIH HHS/United StatesDP1HL123271/DP/NCCDPHP CDC HHS/United States2015-04-25T00:00:00Z24763468PMC4043630vault:242

Atrial Fibrillation Mechanisms and Implications for Catheter Ablation

AF is a heterogeneous rhythm disorder that is related to a wide spectrum of etiologies and has broad clinical presentations. Mechanisms underlying AF are complex and remain incompletely understood despite extensive research. They associate interactions between triggers, substrate and modulators including ionic and anatomic remodeling, genetic predisposition and neuro-humoral contributors. The pulmonary veins play a key role in the pathogenesis of AF and their isolation is associated to high rates of AF freedom in patients with paroxysmal AF. However, ablation of persistent AF remains less effective, mainly limited by the difficulty to identify the sources sustaining AF. Many theories were advanced to explain the perpetuation of this form of AF, ranging from a single localized focal and reentrant source to diffuse bi-atrial multiple wavelets. Translating these mechanisms to the clinical practice remains challenging and limited by the spatio-temporal resolution of the mapping techniques. AF is driven by focal or reentrant activities that are initially clustered in a relatively limited atrial surface then disseminate everywhere in both atria. Evidence for structural remodeling, mainly represented by atrial fibrosis suggests that reentrant activities using anatomical substrate are the key mechanism sustaining AF. These reentries can be endocardial, epicardial, and intramural which makes them less accessible for mapping and for ablation. Subsequently, early interventions before irreversible remodeling are of major importance. Circumferential pulmonary vein isolation remains the cornerstone of the treatment of AF, regardless of the AF form and of the AF duration. No ablation strategy consistently demonstrated superiority to pulmonary vein isolation in preventing long term recurrences of atrial arrhythmias. Further research that allows accurate identification of the mechanisms underlying AF and efficient ablation should improve the results of PsAF ablation

Using delay differential equations in models of cardiac electrophysiology

In cardiac physiology, electrical alternans is a phenomenon characterized by long-short alternations in the action potential duration of cardiac myocytes that give rise to complex spatiotemporal dynamics in tissue. Experiments and clinical measurements indicate that alternans can be a precursor of life-threatening arrhythmias, such as cardiac _brillation. Despite the importance of alternans in the study of cardiac disease, many mathematical models developed to describe cardiac electrophysiology at the cellular level are not able to produce this phenomenon. As a potential remedy to this de_ciency, we introduce short time-delays in some formulations of existing cardiac cell models that are based on Ordinary Di_erential Equations (ODEs). Many processes within cardiac cells involve delays in sensing and responding to changes. In addition, delay di_erential equations (DDEs) are known to give rise to complex dynamical properties in mathematical models. In biological modeling, DDEs have been applied to epidemiology, population dynamics, immunology, and neural networks. Therefore, DDEs can potentially represent mechanisms that result in complex dynamics both at the cellular level and at the tissue level. In this thesis, we propose DDE-based formulations for ion channel models based on the Hodgkin-Huxley formalism that can induce alternans in single-cell simulations in many models found in the literature. We also show that these modi_cations can destabilize spiral waves and produce spiral breakups in two-dimensional simulations, which is a typical model of cardiac _brillation. However, the new DDE-based formulations introduce new computational challenges due to the need for storing and retrieving past values of variables. Therefore, we present novel numerical methods to overcome these challenges and enable e_cient DDE-based studies at the tissue level in standard computational environments. We _nd that the proposed methods decrease memory usage by up to 95% in cardiac tissue simulations compared to straightforward history management algorithms available in widely used DDE solvers.Em fisiologia cardíaca, alternans elétrica _e um fenômeno caracterizado pela alternância entre potenciais de ação longos e curtos que dá origem a complexos comportamentos espaço-temporais em tecido. Experimentos e medições clínicas indicam que alternans pode ser um precursor de perigosas arritmias, como fibrilação ventricular ou morte súbita. Apesar da importância do alternans no estudo de doenças cardíacas, muitos modelos matemáticos para a eletrofisiologia de células cardíacas não são capazes de reproduzir este fenômeno. Como um potencial remédio para esta deficiência, introduzimos curtos atrasos de tempo em algumas formulações de modelos preexistentes para células cardíacas que são baseados em Equações Diferenciais Ordinárias (EDOs). Vários processos em células cardíacas envolvem atrasos de sensibilidade e de resposta a mudanças em variáveis fisiológicas. Além disso, equações diferenciais com atraso (DDEs) são conhecidas por dar origem a complexas propriedades dinâmicas em modelos matemáticos. Em modelagem biológica, DDEs têm sido aplicadas em epidemiologia, dinâmica populacional, imunologia e redes neurais. Portanto, DDEs podem representar mecanismos que resultam em dinâmicas complexas tanto no nível celular, quanto no nível do tecido. Nesta tese, propomos formulações baseadas em DDEs para modelos de canais iônicos descritos pelo formalismo de Hodgkin-Huxley. Tais formulações são capazes de induzir alternans em simulações celulares envolvendo vários modelos encontrados na literatura. Nós também mostramos que essas modificações podem desestabilizar e quebrar ondas espirais em simulações bidimensionais de propagação elétrica, o que é típico de fibrilação cardíaca. Entretanto, as formulações propostas introduzem novos desafios computacionais devido à necessidade de armazenar e recuperar valores passados de variáveis. Deste modo, nós apresentamos novos métodos numéricos para superar tais desafios e permitir a eficiente simulação de modelos baseados em DDEs no nível do tecido cardíaco. Os métodos propostos foram capazes de diminuir o uso de memória em até 95% em comparação aos algoritmos largamente utilizados na solução numérica de DDEs. Assim, os novos modelos baseados em DDEs e os eficientes métodos numéricos propostos nesta tese contribuem para o estudo de arritmias cardíacas fatais através de modelagem computacional

Reactive interstitial and reparative fibrosis as substrates for cardiac ectopic pacemakers and reentries

This book constitutes the refereed proceedings of the 4th International Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2016, held in Granada, Spain, in April 2016. The 69 papers presented were carefully reviewed and selected from 286 submissions. The scope of the conference spans the following areas: bioinformatics for healthcare and diseases; biomedical image analysis; biomedical signal analysis; computational systems for modeling biological processes; eHealth; tools for next generation sequencing data analysis; assistive technology for people with neuromotor disorders; fundamentals of biological dynamics and maximization of the information extraction from the experiments in the biological systems; high performance computing in bioinformatics, computational biology and computational chemistry; human behavior monitoring, analysis and understanding; pattern recognition and machine learning in the -omics sciences; and resources for bioinformatics.Dangerous cardiac arrhythmias have been frequently associated with focal sources of fast pulses, i.e. ectopic pacemakers. However, there is a lack of experimental evidences that could explain how ectopic pacemakers could be formed in cardiac tissue. In recent studies, we have proposed a new theory for the genesis of ectopic pacemakers in pathological cardiac tissues: reentry inside microfbrosis, i.e., a small region where excitable myocytes and non-conductive material coexist. In this work, we continue this investigation by comparing different types of fibrosis, reparative and reactive interstitial fibrosis. We use detailed and modern models of cardiac electrophysiology that account for the micro-structure of cardiac tissue. In addition, for the solution of our models we use, for the first time, a new numerical algorithm based on the Uniformization method. Our simulation results suggest that both types of fibrosis can support reentries, and therefore can generate in-silico ectopic pacemakers. However, the probability of reentries differs quantitatively for the different types of fibrosis. In addition, the new Uniformization method yields 20-fold increase in cardiac tissue simulation speed and, therefore, was an essential technique that allowed the execution of over a thousand of simulations.Peer Reviewe