Adaptive step ODE algorithms for the 3D simulation of electric heart activity with graphics processing units

In this paper we studied the implementation and performance of adaptive step methods for large systems of ordinary differential equations systems in graphics processing units, focusing on the simulation of three-dimensional electric cardiac activity. The Rush-Larsen method was applied in all the implemented solvers to improve efficiency. We compared the adaptive methods with the fixed step methods, and we found that the fixed step methods can be faster while the adaptive step methods are better in terms of accuracy and robustness. (c) 2013 Elsevier Ltd. All rights reserved.This work has been partially funded by Universitat Politecnica de Valencia through Programa de Apoyo a la InvestigaciOn y Desarrollo (PAID-06-11) and (PAID-05-12), by Generalitat Valenciana through projects PROMETEO/2009/013 and Ayudas para la realizacion de proyectos de I+D para grupos de investigacion emergentes GV/2012/039, and by Ministerio Espafiol de Economia y Competitividad through project TEC2012-38142-004.García Mollá, VM.; Liberos Mascarell, A.; Vidal Maciá, AM.; Guillem Sánchez, MS.; Millet Roig, J.; González Salvador, A.; Martínez Zaldívar, FJ.... (2014). Adaptive step ODE algorithms for the 3D simulation of electric heart activity with graphics processing units. Computers in Biology and Medicine. 44:15-26. https://doi.org/10.1016/j.compbiomed.2013.10.023S15264

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 /

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

Virtual Reality Games for Motor Rehabilitation

This paper presents a fuzzy logic based method to track user satisfaction without the need for devices to monitor users physiological conditions. User satisfaction is the key to any product’s acceptance; computer applications and video games provide a unique opportunity to provide a tailored environment for each user to better suit their needs. We have implemented a non-adaptive fuzzy logic model of emotion, based on the emotional component of the Fuzzy Logic Adaptive Model of Emotion (FLAME) proposed by El-Nasr, to estimate player emotion in UnrealTournament 2004. In this paper we describe the implementation of this system and present the results of one of several play tests. Our research contradicts the current literature that suggests physiological measurements are needed. We show that it is possible to use a software only method to estimate user emotion

Atrial location optimization by electrical measures for Electrocardiographic Imaging

[EN] Background: The Electrocardiographic Imaging (ECGI) technique, used to non-invasively reconstruct the epicardial electrical activity, requires an accurate model of the atria and torso anatomy. Here we evaluate a new automatic methodology able to locate the atrial anatomy within the torso based on an intrinsic electrical parameter of the ECGI solution. Methods: In 28 realistic simulations of the atrial electrical activity, we randomly displaced the atrial anatomy for +/- 2.5 cm and +/- 30 degrees on each axis. An automatic optimization method based on the L-curve curvature was used to estimate the original position using exclusively non-invasive data. Results: The automatic optimization algorithm located the atrial anatomy with a deviation of 0.5 +/- 0.5 cm in position and 16.0 +/- 10.7 degrees in orientation. With these approximate locations, the obtained electrophysiological maps reduced the average error in atrial rate measures from 1.1 +/- 1.1 Hz to 0.5 +/- 1.0 Hz and in the phase singularity position from 7.2 +/- 4.0 cm to 1.6 +/- 1.7 cm (p < 0.01). Conclusions: This proposed automatic optimization may help to solve spatial inaccuracies provoked by cardiac motion or respiration, as well as to use ECGI on torso and atrial anatomies from different medical image systems.This work was supported in part by: Generalitat Valenciana Grants [APOSTD/2017] and projects [GVA/2018/103]; Nvidia Corporation with GPU QUADRO P6000 donation.Gisbert Soler, V.; Jiménez-Serrano, S.; Roses-Albert, E.; Rodrigo Bort, M. (2020). Atrial location optimization by electrical measures for Electrocardiographic Imaging. Computers in Biology and Medicine. 127:1-8. https://doi.org/10.1016/j.compbiomed.2020.104031S18127Cuculich, P. S., Zhang, J., Wang, Y., Desouza, K. A., Vijayakumar, R., Woodard, P. K., & Rudy, Y. (2011). The Electrophysiological Cardiac Ventricular Substrate in Patients After Myocardial Infarction. Journal of the American College of Cardiology, 58(18), 1893-1902. doi:10.1016/j.jacc.2011.07.029Revishvili, A. S., Wissner, E., Lebedev, D. S., Lemes, C., Deiss, S., Metzner, A., … Kuck, K.-H. (2015). Validation of the mapping accuracy of a novel non-invasive epicardial and endocardial electrophysiology system. Europace, 17(8), 1282-1288. doi:10.1093/europace/euu339Haissaguerre, M., Hocini, M., Denis, A., Shah, A. J., Komatsu, Y., Yamashita, S., … Dubois, R. (2014). Driver Domains in Persistent Atrial Fibrillation. Circulation, 130(7), 530-538. doi:10.1161/circulationaha.113.005421PEDRÓN-TORRECILLA, J., RODRIGO, M., CLIMENT, A. M., LIBEROS, A., PÉREZ-DAVID, E., BERMEJO, J., … GUILLEM, M. S. (2016). Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation. Journal of Cardiovascular Electrophysiology, 27(4), 435-442. doi:10.1111/jce.12931Cuculich, P. S., Wang, Y., Lindsay, B. D., Faddis, M. N., Schuessler, R. B., Damiano, R. J., … Rudy, Y. (2010). Noninvasive Characterization of Epicardial Activation in Humans With Diverse Atrial Fibrillation Patterns. Circulation, 122(14), 1364-1372. doi:10.1161/circulationaha.110.945709Wang, Y., Schuessler, R. B., Damiano, R. J., Woodard, P. K., & Rudy, Y. (2007). Noninvasive electrocardiographic imaging (ECGI) of scar-related atypical atrial flutter. Heart Rhythm, 4(12), 1565-1567. doi:10.1016/j.hrthm.2007.08.019Milan Horáček, B., & Clements, J. C. (1997). The inverse problem of electrocardiography: A solution in terms of single- and double-layer sources on the epicardial surface. Mathematical Biosciences, 144(2), 119-154. doi:10.1016/s0025-5564(97)00024-2Rodrigo, M., Climent, A. M., Liberos, A., Hernandez-Romero, I., Arenal, A., Bermejo, J., … Guillem, M. S. (2018). Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality. IEEE Transactions on Medical Imaging, 37(3), 733-740. doi:10.1109/tmi.2017.2707413Dössel, O., Krueger, M. W., Weber, F. M., Wilhelms, M., & Seemann, G. (2012). Computational modeling of the human atrial anatomy and electrophysiology. Medical & Biological Engineering & Computing, 50(8), 773-799. doi:10.1007/s11517-012-0924-6Koivumäki, J. T., Seemann, G., Maleckar, M. M., & Tavi, P. (2014). In Silico Screening of the Key Cellular Remodeling Targets in Chronic Atrial Fibrillation. PLoS Computational Biology, 10(5), e1003620. doi:10.1371/journal.pcbi.1003620Garcia-Molla, V. M., Liberos, A., Vidal, A., Guillem, M. S., Millet, J., Gonzalez, A., … Climent, A. M. (2014). Adaptive step ODE algorithms for the 3D simulation of electric heart activity with graphics processing units. Computers in Biology and Medicine, 44, 15-26. doi:10.1016/j.compbiomed.2013.10.023Rodrigo, M., Climent, A. M., Liberos, A., Fernández-Avilés, F., Berenfeld, O., Atienza, F., & Guillem, M. S. (2017). Highest dominant frequency and rotor positions are robust markers of driver location during noninvasive mapping of atrial fibrillation: A computational study. Heart Rhythm, 14(8), 1224-1233. doi:10.1016/j.hrthm.2017.04.017Dolan, E. D., Lewis, R. M., & Torczon, V. (2003). On the Local Convergence of Pattern Search. SIAM Journal on Optimization, 14(2), 567-583. doi:10.1137/s1052623400374495Rodrigo, M., Guillem, M. S., Climent, A. M., Pedrón-Torrecilla, J., Liberos, A., Millet, J., … Berenfeld, O. (2014). Body surface localization of left and right atrial high-frequency rotors in atrial fibrillation patients: A clinical-computational study. Heart Rhythm, 11(9), 1584-1591. doi:10.1016/j.hrthm.2014.05.013Sanders, P., Berenfeld, O., Hocini, M., Jaïs, P., Vaidyanathan, R., Hsu, L.-F., … Haïssaguerre, M. (2005). Spectral Analysis Identifies Sites of High-Frequency Activity Maintaining Atrial Fibrillation in Humans. Circulation, 112(6), 789-797. doi:10.1161/circulationaha.104.517011Atienza, F., Almendral, J., Ormaetxe, J. M., Moya, Á., Martínez-Alday, J. D., Hernández-Madrid, A., … Jalife, J. (2014). Comparison of Radiofrequency Catheter Ablation of Drivers and Circumferential Pulmonary Vein Isolation in Atrial Fibrillation. Journal of the American College of Cardiology, 64(23), 2455-2467. doi:10.1016/j.jacc.2014.09.053Rodrigo, M., Climent, A. M., Liberos, A., Fernández-Avilés, F., Berenfeld, O., Atienza, F., & Guillem, M. S. (2017). Technical Considerations on Phase Mapping for Identification of Atrial Reentrant Activity in Direct- and Inverse-Computed Electrograms. Circulation: Arrhythmia and Electrophysiology, 10(9). doi:10.1161/circep.117.005008Miller, J. M., Kalra, V., Das, M. K., Jain, R., Garlie, J. B., Brewster, J. A., & Dandamudi, G. (2017). Clinical Benefit of Ablating Localized Sources for Human Atrial Fibrillation. Journal of the American College of Cardiology, 69(10), 1247-1256. doi:10.1016/j.jacc.2016.11.079Perez-Alday, E. A., Thomas, J. A., Kabir, M., Sedaghat, G., Rogovoy, N., van Dam, E., … Tereshchenko, L. G. (2018). Torso geometry reconstruction and body surface electrode localization using three-dimensional photography. Journal of Electrocardiology, 51(1), 60-67. doi:10.1016/j.jelectrocard.2017.08.035Schulze, W. H. W., Mackens, P., Potyagaylo, D., Rhode, K., Tülümen, E., Schimpf, R., … Dössel, O. (2014). Automatic camera-based identification and 3-D reconstruction of electrode positions in electrocardiographic imaging. Biomedical Engineering / Biomedizinische Technik, 59(6). doi:10.1515/bmt-2014-0018Ghanem, R. N., Ramanathan, C., Ping Jia, & Rudy, Y. (2003). Heart-surface reconstruction and ecg electrodes localization using fluoroscopy, epipolar geometry and stereovision: application to noninvasive imaging of cardiac electrical activity. IEEE Transactions on Medical Imaging, 22(10), 1307-1318. doi:10.1109/tmi.2003.818263Lee, J., Thornhill, R. E., Nery, P., Robert deKemp, Peña, E., Birnie, D., … Ukwatta, E. (2019). Left atrial imaging and registration of fibrosis with conduction voltages using LGE-MRI and electroanatomical mapping. Computers in Biology and Medicine, 111, 103341. doi:10.1016/j.compbiomed.2019.103341Weiss, E., Wijesooriya, K., Dill, S. V., & Keall, P. J. (2007). Tumor and normal tissue motion in the thorax during respiration: Analysis of volumetric and positional variations using 4D CT. International Journal of Radiation Oncology*Biology*Physics, 67(1), 296-307. doi:10.1016/j.ijrobp.2006.09.009Wikström, K., Isacsson, U., Nilsson, K., & Ahnesjö, A. (2018). Reproducibility of heart and thoracic wall position in repeated deep inspiration breath holds for radiotherapy of left-sided breast cancer patients. Acta Oncologica, 57(10), 1318-1324. doi:10.1080/0284186x.2018.1490027Messinger-Rapport, B. J., & Rudy, Y. (1986). The Inverse Problem in Electrocardiography: A Model Study of the Effects of Geometry and Conductivity Parameters on the Reconstruction of Epicardial Potentials. IEEE Transactions on Biomedical Engineering, BME-33(7), 667-676. doi:10.1109/tbme.1986.325756Messinger-Rapport, B. J., & Rudy, Y. (1990). Noninvasive recovery of epicardial potentials in a realistic heart-torso geometry. Normal sinus rhythm. Circulation Research, 66(4), 1023-1039. doi:10.1161/01.res.66.4.1023Coll-Font, J., & Brooks, D. H. (2018). Tracking the Position of the Heart From Body Surface Potential Maps and Electrograms. Frontiers in Physiology, 9. doi:10.3389/fphys.2018.01727Van der Waal, J., Meijborg, V., Schuler, S., Coronel, R., & Oostendorp, T. (2020). In silico validation of electrocardiographic imaging to reconstruct the endocardial and epicardial repolarization pattern using the equivalent dipole layer source model. Medical & Biological Engineering & Computing, 58(8), 1739-1749. doi:10.1007/s11517-020-02203-yChamorro-Servent, J., Dubois, R., & Coudière, Y. (2019). Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging. Frontiers in Physiology, 10. doi:10.3389/fphys.2019.0027

Retinal drug delivery: rethinking outcomes for the efficient replication of retinal behavior

The retina is a highly organized structure that is considered to be "an approachable part of the brain." It is attracting the interest of development scientists, as it provides a model neurovascular system. Over the last few years, we have been witnessing significant development in the knowledge of the mechanisms that induce the shape of the retinal vascular system, as well as knowledge of disease processes that lead to retina degeneration. Knowledge and understanding of how our vision works are crucial to creating a hardware-adaptive computational model that can replicate retinal behavior. The neuronal system is nonlinear and very intricate. It is thus instrumental to have a clear view of the neurophysiological and neuroanatomic processes and to take into account the underlying principles that govern the process of hardware transformation to produce an appropriate model that can be mapped to a physical device. The mechanistic and integrated computational models have enormous potential toward helping to understand disease mechanisms and to explain the associations identified in large model-free data sets. The approach used is modulated and based on different models of drug administration, including the geometry of the eye. This work aimed to review the recently used mathematical models to map a directed retinal network.The authors acknowledge the financial support received from the Portuguese Science and Technology Foundation (FCT/MCT) and the European Funds (PRODER/COMPETE) for the project UIDB/04469/2020 (strategic fund), co-financed by FEDER, under the Partnership Agreement PT2020. The authors also acknowledge FAPESP – São Paulo Research Foundation, for the financial support for the publication of the article.info:eu-repo/semantics/publishedVersio

Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation

[EN] Introduction Ablation of high dominant frequency (DF) sources in patients with atrial fibrillation (AF) is an effective treatment option for paroxysmal AF. The aim of this study was to evaluate the accuracy of noninvasive estimation of DF and electrical patterns determination by solving the inverse problem of the electrocardiography. Methods Four representative AF patients with left-to-right and right-to-left atrial DF patterns were included in the study. For each patient, intracardiac electrograms from both atria were recorded simultaneously together with 67-lead body surface recordings. In addition to clinical recordings, realistic mathematical models of atria and torso anatomy with different DF patterns of AF were used. For both mathematical models and clinical recordings, inverse-computed electrograms were compared to intracardiac electrograms in terms of voltage, phase, and frequency spectrum relative errors. Results Comparison between intracardiac and inverse computed electrograms for AF patients showed 8.8 ± 4.4% errors for DF, 32 ± 4% for voltage, and 65 ± 4% for phase determination. These results were corroborated by mathematical simulations showing that the inverse problem solution was able to reconstruct the frequency spectrum and the DF maps with relative errors of 5.5 ± 4.1%, whereas the reconstruction of the electrograms or the instantaneous phase presented larger relative errors (i.e., 38 ± 15% and 48 ± 14 % respectively, P < 0.01). Conclusions Noninvasive reconstruction of atrial frequency maps can be achieved by solving the inverse problem of electrocardiography with a higher accuracy than temporal distribution patterns.Pedrón-Torrecilla, J.; Rodrigo Bort, M.; M. Climent, A.; Liberos, A.; Pérez-David E; Bermejo, J.; Arenal, A.... (2016). Noninvasive Estimation of Epicardial Dominant High-Frequency Regions During Atrial Fibrillation. Journal of Cardiovascular Electrophysiology. 27(4):435-442. doi:https://doi.org/10.1111/jce.12931S43544227

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality

[EN] Electrocardiographic Imaging has become an increasingly used technique for non-invasive diagnosis of cardiac arrhythmias, although the need for medical imaging technology to determine the anatomy hinders its introduction in the clinical practice. This paper explores the ability of a new metric based on the inverse reconstruction quality for the location and orientation of the atrial surface inside the torso. Body surface electrical signals from 31 realistic mathematical models and four AF patients were used to estimate the optimal position of the atria inside the torso. The curvature of the L-curve from the Tikhonov method, which was found to be related to the inverse reconstruction quality, was measured after application of deviations in atrial position and orientation. Independent deviations in the atrial position were solved by finding the maximal L-curve curvature with an error of 1.7 +/- 2.4 mm in mathematical models and 9.1 +/- 11.5 mm in patients. For the case of independent angular deviations, the error in location by using the L-curve was 5.8 +/- 7.1 degrees in mathematical models and 12.4 degrees +/- 13.2 degrees in patients. The ability of the L-curve curvature was tested also under superimposed uncertainties in the three axis of translation and in the three axis of rotation, and the error in location was of 2.3 +/- 3.2 mm and 6.4 degrees +/- 7.1 degrees in mathematical models, and 7.9 +/- 10.7 mm and 12.1 degrees +/- 15.5 degrees in patients. The curvature of L-curve is a useful marker for the atrial position and would allow emending the inaccuracies in its location.This work was supported in part by Generalitat Valenciana under Grant ACIF/2013/021, in part by the Instituto de Salud Carlos III, Ministry of Economy and Competitiveness, Spain, under Grant PI13-01882, Grant PI13-00903, Grant PI14/00857, Grant TEC2013-46067-R, and Grant DTS16/00160, in part by the Spanish Society of Cardiology (Grant for Clinical Research in Cardiology 2015), and in part by the Spanish Ministry of Science and Innovation (Red RIC) under Grant PLE2009-0152.Rodrigo Bort, M.; Climent, AM.; Liberos Mascarell, A.; Hernández-Romero, I.; Arenal, A.; Bermejo, J.; Fernández-Avilés, F.... (2018). Solving Inaccuracies in Anatomical Models for Electrocardiographic Inverse Problem Resolution by Maximizing Reconstruction Quality. IEEE Transactions on Medical Imaging. 37(3):733-740. https://doi.org/10.1109/TMI.2017.2707413S73374037