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 /

Art/Sci Nexus, 9 Evenings Revisited

Following the exhibition of Hybrid Bodies at KKW in 2016 Andrew Carnie and I were invited back to act as mentors to a group of young artists and scientists from all over Europe undertaking a week long workshop designed to lead to new art/science collaborations. We were also invited to present the Hybrid Bodies project at a one day public event preceding the workshop

Improved Hybrid/GPU Algorithm for Solving Cardiac Electrophysiology Problems on Purkinje Networks

Cardiac Purkinje fibres provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in-silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is based on operator splitting and is provided with three different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations in order to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all three implementations produce equivalent convergence rates, which shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all three implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure-GPU implementations outperform the pure-CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue

Aerospace Medicine and Biology. A continuing bibliography with indexes

This bibliography lists 244 reports, articles, and other documents introduced into the NASA scientific and technical information system in February 1981. Aerospace medicine and aerobiology topics are included. Listings for physiological factors, astronaut performance, control theory, artificial intelligence, and cybernetics are included

USSR Space Life Sciences Digest, issue 1

The first issue of the bimonthly digest of USSR Space Life Sciences is presented. Abstracts are included for 49 Soviet periodical articles in 19 areas of aerospace medicine and space biology, published in Russian during the first quarter of 1985. Translated introductions and table of contents for nine Russian books on topics related to NASA's life science concerns are presented. Areas covered include: botany, cardiovascular and respiratory systems, cybernetics and biomedical data processing, endocrinology, gastrointestinal system, genetics, group dynamics, habitability and environmental effects, health and medicine, hematology, immunology, life support systems, man machine systems, metabolism, musculoskeletal system, neurophysiology, perception, personnel selection, psychology, radiobiology, reproductive system, and space biology. This issue concentrates on aerospace medicine and space biology

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

Mathematical modeling approaches for the diagnosis and treatment of reentrant atrial tachyarrhythmias

[EN] Atrial tachyarrhythmias present a high prevalence in the developed world, and several studies predict that in the coming decades it will be increased. Micro or macro-reentrant mechanisms of the electrical wavefronts that govern the mechanical behavior of the heart are one of the main responsibles for the maintenance of these arrhythmias. Atrial flutter is maintained by a macro-reentry around an anatomical or functional obstacle located in the atria. In the case of atrial fibrillation, the hypothesis which describes high frequency rotors as dominant sources of the fibrillation and responsible for the maintenance of the arrhythmia, has been gaining relevance in the last years. However, the therapies that target high frequency sources have a limited efficacy with current techniques. Radiofrequency ablation allows the destruction of parts of the cardiac tissue resulting in the interruption of the reentrant circuit in case of macro-reentries or the isolation of micro-reentrant circuits. The non-invasive location of reentrant circuits would increment the efficacy of these therapies and would shorten surgery interventions. In parallel, pharmacological therapies modify ionic expressions associated to the excitability and electrical refractoriness of the cardiac tissue with the objective of hindering the maintenance of reentrant behaviors. These therapies require a deep knowledge of the ionic mechanisms underlying the reentrant behavior and its properties in order to be effective. The research in these mechanisms allows the evaluation of new targets for the treatment and thus may improve the efficacy in atrial fibrillation termination. In this thesis, mathematical modeling is used to go forward in the minimization of the limitations associated to these treatments. Body surface potential mapping has been evaluated, both clinically and by means of mathematical simulations for the diagnosis and location of macro-reentrant circuits. The analysis of phase maps obtained from multiple lead electrocardiographic recordings distributed in the whole torso allowed the discrimination between different reentrant circuits. It is the reason why this technique is presented as a tool for the non-invasive location of macro and micro-reentrant circuits. A population of mathematical models designed in this thesis based on the action potentials recordings of atrial cardiomyocites from 149 patients, allowed the evaluation of the ionic mechanisms defining the properties of reentrant behaviors. This study has allowed us defining the blockade of ICaL as a target for the pharmacological treatment. The blockade of this current is associated with the increase of the movement in the core of the rotor which easies the collision of the rotor with other wavefronts or anatomical obstacles promoting the extinction of the reentry. The variability observed between patients modeled in our population has allowed showing and explaining the mechanisms promoting divergent results of a single treatment. This is why the introduction of populations of models will allow the prevention of side effects associated to inter-subject variability and to go forward in the development of individualized therapies. These works are built through a simulation platform of cardiac electrophysiology based in Graphic Processing Units (GPUs) and developed in this thesis. The platform allows the simulation of cellular models, tissues and organs with a realistic geometry and shows features comparable to that of the platforms used by the most relevant electrophysiology research groups at the moment.[ES] Las taquiarritmias auriculares tienen una alta prevalencia en el mundo desarrollado, además diversos estudios poblacionales indican que en las próximas décadas ésta se verá incrementada. Los mecanismos de micro o macro-reentrada de los frentes de onda eléctricos que rigen el comportamiento mecánico del corazón, se presentan como una de las principales causas del mantenimiento de estas arritmias. El flutter auricular es mantenido por un macro-reentrada alrededor de un obstáculo anatómico o funcional en las aurículas, mientras que en el caso de la fibrilación auricular la hipótesis que define a los rotores de alta frecuencia como elementos dominantes y responsables del mantenimiento de la arritmia se ha ido imponiendo al resto en los últimos años. Sin embargo, las terapias que tienen como objetivo finalizar o aislar estas reentradas tienen todavía una eficacia limitada. La ablación por radiofrecuencia permite eliminar zonas del tejido cardiaco resultando en la interrupción del circuito de reentrada en el caso de macro-reentradas o el aislamiento de comportamientos micro-reentrantes. La localización no invasiva de los circuitos reentrantes incrementaría la eficacia de estas terapias y reduciría la duración de las intervenciones quirúrgicas. Por otro lado, las terapias farmacológicas alteran las expresiones iónicas asociadas a la excitabilidad y la refractoriedad del tejido con el fin de dificultar el mantenimiento de comportamientos reentrantes. Este tipo de terapias exigen incrementar el conocimiento de los mecanismos subyacentes que explican el proceso de reentrada y sus propiedades, la investigación de estos mecanismos permite definir las dianas terapéuticas que mejoran la eficacia en la extinción de estos comportamientos. En esta tesis el modelado matemático se utiliza para dar un paso importante en la minimización de las limitaciones asociadas a estos tratamientos. La cartografía eléctrica de superficie ha sido testada, clínicamente y con simulaciones matemática,s como técnica de diagnóstico y localización de circuitos macro-reentrantes. El análisis de mapas de fase obtenidos a partir de los registros multicanal de derivaciones electrocardiográficas distribuidas en la superficie del torso permite diferenciar distintos circuitos de reentrada. Es por ello que esta técnica de registro y análisis se presenta como una herramienta para la localización no invasiva de circuitos macro y micro-reentrantes. Una población de modelos matemáticos, diseñada en esta tesis a partir de los registros de los potenciales de acción de 149 pacientes, ha permitido evaluar los mecanismos iónicos que definen las propiedades asociadas a los procesos de reentrada. Esto ha permitido apuntar al bloqueo de la corriente ICaL como diana terapéutica. Ésta se asocia al incremento del movimiento del núcleo que facilita el impacto del rotor con otros frentes de onda u obstáculos extinguiéndose así el comportamiento reentrante. La variabilidad entre pacientes reflejada en la población de modelos ha permitido además mostrar los mecanismos por los cuales un mismo tratamiento puede mostrar efectos divergentes, así el uso de poblaciones de modelos matemáticos permitirá prevenir efectos secundarios asociados a la variabilidad entre pacientes y profundizar en el desarrollo de terapias individualizadas. Estos trabajos se cimientan sobre una plataforma de simulación de electrofisiología cardiaca de basado en Unidades de Procesado Gráfico (GPUs) y desarrollada en esta tesis. La plataforma permite la simulación de modelos celulares cardiacos así como de tejidos u órganos con geometría realista, mostrando unas prestaciones comparables con las de las utilizadas por los grupos de investigación más potentes en el campo de la electrofisiología.[CA] Les taquiarítmies auriculars tenen una alta prevalença en el món desenvolupat, a més diversos estudis poblacionals indiquen que en les pròximes dècades aquesta es veurà incrementada. Els mecanismes de micro o macro-reentrada dels fronts d'ona elèctrics que regeixen el comportament mecànic del cor, es presenten com una de les principals causes del manteniment d'aquestes arítmies. El flutter auricular és mantingut per una macro-reentrada al voltant d'un obstacle anatòmic o funcional en les aurícules, mentre que en el cas de la fibril·lació auricular la hipòtesi que defineix als rotors d'alta freqüència com a elements dominants i responsables del manteniment de l'arítmia s'ha anat imposant a la resta en els últims anys. No obstant això, les teràpies que tenen com a objectiu finalitzar o aïllar aquestes reentrades tenen encara una eficàcia limitada. L'ablació per radiofreqüència permet eliminar zones del teixit cardíac resultant en la interrupció del circuit de reentrada en el cas de macro-reentrades o l'aïllament de comportaments micro-reentrants. La localització no invasiva dels circuits reentrants incrementaria l'eficàcia d'aquestes teràpies i reduiria la durada de les intervencions quirúrgiques. D'altra banda, les teràpies farmacològiques alteren les expressions iòniques associades a la excitabilitat i la refractaritat del teixit amb la finalitat de dificultar el manteniment de comportaments reentrants. Aquest tipus de teràpies exigeixen incrementar el coneixement dels mecanismes subjacents que expliquen el procés de reentrada i les seues propietats, la recerca d'aquests mecanismes permet definir les dianes terapèutiques que milloren l'eficàcia en l'extinció d'aquests comportaments. En aquesta tesi el modelatge matemàtic s'utilitza per a fer un pas important en la minimització de les limitacions associades a aquests tractaments. La cartografia elèctrica de superfície ha sigut testada, clínicament i amb simulacions matemàtiques com a tècnica de diagnòstic i localització de circuits macro-reentrants. L'anàlisi de mapes de fase obtinguts a partir dels registres multicanal de derivacions electrocardiogràfiques distribuïdes en la superfície del tors permet diferenciar diferents circuits de reentrada. És per açò que aquesta tècnica de registre i anàlisi es presenta com una eina per a la localització no invasiva de circuits macro i micro-reentrants. Una població de models matemàtics, dissenyada en aquesta tesi a partir dels registres dels potencials d'acció de 149 pacients, ha permès avaluar els mecanismes iònics que defineixen les propietats associades als processos de reentrada. Açò ha permès apuntar al bloqueig del corrent ICaL com a diana terapèutica. Aquesta s'associa a l'increment del moviment del nucli que facilita l'impacte del rotor amb altres fronts d'ona o obstacles extingint-se així el comportament reentrant. La variabilitat entre pacients reflectida en la població de models ha permès a més mostrar els mecanismes pels quals un mateix tractament pot mostrar efectes divergents, així l'ús de poblacions de models matemàtics permetrà prevenir efectes secundaris associats a la variabilitat entre pacients i aprofundir en el desenvolupament de teràpies individualitzades. Aquests treballs es fonamenten sobre una plataforma de simulació de electrofisiologia cardíaca basat en Unitats de Processament Gràfic (GPUs) i desenvolupada en aquesta tesi. La plataforma permet la simulació de models cel·lulars cardíacs així com de teixits o òrgans amb geometria realista, mostrant unes prestacions comparables amb les de les utilitzades per els grups de recerca més importants en aquesta área.Liberos Mascarell, A. (2016). Mathematical modeling approaches for the diagnosis and treatment of reentrant atrial tachyarrhythmias [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62166TESI

Aerospace medicine and biology: A continuing bibliography with indexes, supplement 197, September 1979

This bibliography lists 193 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1979