Doctor of Philosophy

dissertationCine phase contrast (PC) magnetic resonance imaging (MRI) is a useful imaging technique that allows for the quantitative measurement of in-vivo blood velocities over the cardiac cycle. Velocity information can be used to diagnose and learn more about the mechanisms of cardio-vascular disease. Compared to other velocity measuring techniques, PC MRI provides high-resolution 2D and 3D spatial velocity information. Unfortunately, as with many other MRI techniques, PC MRI su ers from long acquisition times which places constraints on temporal and spatial resolution. This dissertation outlines the use of temporally constrained reconstruction (TCR) of radial PC data in order to signi cantly reduce the acquisition time so that higher temporal and spatial resolutions can be achieved. A golden angle-based acquisition scheme and a novel self-gating method were used in order to allow for exible selection of temporal resolution and to ameliorate the di culties associated with external electrocardiogram (ECG) gating. Finally, image reconstruction times for TCR are signi cantly reduced by implementation on a high-performance computer cluster. The TCR algorithm is executed in parallel across multiple GPUs achieving a 50 second reconstruction time for a very large cardiac perfusion data set

MR fingerprinting with simultaneous B1 estimation.

PURPOSE: MR fingerprinting (MRF) can be used for quantitative estimation of physical parameters in MRI. Here, we extend the method to incorporate B1 estimation. METHODS: The acquisition is based on steady state free precession MR fingerprinting with a Cartesian trajectory. To increase the sensitivity to the B1 profile, abrupt changes in flip angle were introduced in the sequence. Slice profile and B1 effects were included in the dictionary and the results from two- and three-dimensional (3D) acquisitions were compared. Acceleration was demonstrated using retrospective undersampling in the phase encode directions of 3D data exploiting redundancy between MRF frames at the edges of k-space. RESULTS: Without B1 estimation, T2 and B1 were inaccurate by more than 20%. Abrupt changes in flip angle improved B1 maps. T1 and T2 values obtained with the new MRF methods agree with classical spin echo measurements and are independent of the B1 field profile. When using view sharing reconstruction, results remained accurate (error <10%) when sampling under 10% of k-space from the 3D data. CONCLUSION: The methods demonstrated here can successfully measure T1, T2, and B1. Errors due to slice profile can be substantially reduced by including its effect in the dictionary or acquiring data in 3D. Magn Reson Med 76:1127-1135, 2016. © 2015 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.G.B. was funded by INFN CNS 5.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/mrm.2600

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

Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units

Anatomically realistic and biophysically detailed multiscale computer models of the heart are playing an increasingly important role in advancing our understanding of integrated cardiac function in health and disease. Such detailed simulations, however, are computationally vastly demanding, which is a limiting factor for a wider adoption of in-silico modeling. While current trends in high-performance computing (HPC) hardware promise to alleviate this problem, exploiting the potential of such architectures remains challenging since strongly scalable algorithms are necessitated to reduce execution times. Alternatively, acceleration technologies such as graphics processing units (GPUs) are being considered. While the potential of GPUs has been demonstrated in various applications, benefits in the context of bidomain simulations where large sparse linear systems have to be solved in parallel with advanced numerical techniques are less clear. In this study, the feasibility of multi-GPU bidomain simulations is demonstrated by running strong scalability benchmarks using a state-of-the-art model of rabbit ventricles. The model is spatially discretized using the finite element methods (FEM) on fully unstructured grids. The GPU code is directly derived from a large pre-existing code, the Cardiac Arrhythmia Research Package (CARP), with very minor perturbation of the code base. Overall, bidomain simulations were sped up by a factor of 11.8 to 16.3 in benchmarks running on 6-20 GPUs compared to the same number of CPU cores. To match the fastest GPU simulation which engaged 20 GPUs, 476 CPU cores were required on a national supercomputing facility

High-efficient Bloch simulation of magnetic resonance imaging sequences based on deep learning

Objective: Bloch simulation constitutes an essential part of magnetic resonance imaging (MRI) development. However, even with the graphics processing unit (GPU) acceleration, the heavy computational load remains a major challenge, especially in large-scale, high-accuracy simulation scenarios. This work aims to develop a deep learning-based simulator to accelerate Bloch simulation. Approach: The simulator model, called Simu-Net, is based on an end-to-end convolutional neural network and is trained with synthetic data generated by traditional Bloch simulation. It uses dynamic convolution to fuse spatial and physical information with different dimensions and introduces position encoding templates to achieve position-specific labeling and overcome the receptive field limitation of the convolutional network. Main Results: Compared with mainstream GPU-based MRI simulation software, Simu-Net successfully accelerates simulations by hundreds of times in both traditional and advanced MRI pulse sequences. The accuracy and robustness of the proposed framework were verified qualitatively and quantitatively. Besides, the trained Simu-Net was applied to generate sufficient customized training samples for deep learning-based T2 mapping and comparable results to conventional methods were obtained in the human brain. Significance: As a proof-of-concept work, Simu-Net shows the potential to apply deep learning for rapidly approximating the forward physical process of MRI and may increase the efficiency of Bloch simulation for optimization of MRI pulse sequences and deep learning-based methods.Comment: 18 pages, 8 figure

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 /

Frequency domain high density diffuse optical tomography for functional brain imaging

Measurements of dynamic near-infrared (NIR) light attenuation across the human head together with model-based image reconstruction algorithms allow the recovery of three-dimensional spatial brain activation maps. Previous studies using high-density diffuse optical tomography (HD-DOT) systems have reported improved image quality over sparse arrays. Modulated NIR light, known as Frequency Domain (FD) NIR, enables measurements of phase shift along with amplitude attenuation. It is hypothesised that the utilization of these two sets of complementary data (phase and amplitude) for brain activity detection will result in an improvement in reconstructed image quality within HD-DOT. However, parameter recovery in DOT is a computationally expensive algorithm, especially when FD-HD measurements are required over a large and complex volume, as in the case of brain functional imaging. Therefore, computational tools for the light propagation modelling, known as the forward model, and the parameter recovery, known as the inverse problem, have been developed, in order to enable FD-HD-DOT. The forward model, within a diffusion approximation-based finite-element modelling framework, is accelerated by employing parallelization. A 10-fold speed increase when GPU architectures are available is achieved while maintaining high accuracy. For a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, light propagation can be calculated at ∼0.25s per excitation source. Additionally, a framework for the sparse formulation of the inverse model, incorporating parallel computing, is proposed, achieving a 10-fold speed increase and a 100-fold memory efficiency, whilst maintaining reconstruction quality. Finally, to evaluate image reconstruction with and without the additional phase information, point spread functions have been simulated across a whole-scalp field of view in 24 subject-specific anatomical models using an experimentally derived noise model. The addition of phase information has shown to improve the image quality by reducing localization error by up to 59%, effective resolution by up to 21%, and depth penetration up to 5mm, as compared to using the intensity attenuation measurements alone. In addition, experimental data collected during a retinotopic experiment reveal that the phase data contains unique information about brain activity and enables images to be resolved for deeper brain regions

Doctor of Philosophy

dissertationAtrial fibrillation (AF) is the leading cause of ischemic stroke and is the most commonly observed arrhythmia in clinical cardiology. Catheter ablation of AF, in which specific regions of cardiac anatomy associated with AF are intenionally injured to create scar tissue, has been honed over the last 15 years to become a relatively common and safe treatment option. However, the success of these anatomically driven ablation strategies, particularly in hearts that have been exposed to AF for extended periods, remains poor. AF induces changes in the electrical and structural properties of the cardiac tissue that further promotes the permanence of AF. In a process known as electroanatomical (EAM) mapping, clinicians record time signals known as electrograms (EGMs) from the heart and the locations of the recording sites to create geometric representations, or maps, of the electrophysiological properties of the heart. Analysis of the maps and the individual EGM morphologies can indicate regions of abnormal tissue, or substrates that facilitate arrhythmogenesis and AF perpetuation. Despite this progress, limitations in the control of devices currently used for EAM acquisition and reliance on suboptimal metrics of tissue viability appear to be hindering the potential of treatment guided by substrate mapping. In this research, we used computational models of cardiac excitation to evaluate param- eters of EAM that affect the performance of substrate mapping. These models, which have been validated with experimental and clinical studies, have yielded new insights into the limitations of current mapping systems, but more importantly, they guided us to develop new systems and metrics for robust substrate mapping. We report here on the progress in these simulation studies and on novel measurement approaches that have the potential to improve the robustness and precision of EAM in patients with arrhythmias. Appropriate detection of proarrhythmic substrates promises to improve ablation of AF beyond rudimentary destruction of anatomical targets to directed targeting of complicit tissues. Targeted treatment of AF sustaining tissues, based on the substrate mapping approaches described in this dissertation, has the potential to improve upon the efficacy of current AF treatment options