High-order finite element methods for cardiac monodomain simulations

Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael; McCulloch, Andrew D.

doi:10.3389/fphys.2015.00217

Cited by 21 publications

(30 citation statements)

References 44 publications

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“…Vincent et al [2015] compared the convergence behavior of linear Lagrange, cubic-Hermite, and cubic Hermite-style serendipity interpolation methods for finite element simulations of cardiac electrophysiology in static meshes. They found that the high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements.…”

Section: Related and Previous Workmentioning

confidence: 99%

Biomechanics simulations using cubic Hermite meshes with extraordinary nodes for isogeometric cardiac modeling

Krishnamurthy

Gonzales

Sturgeon

et al. 2016

Computer Aided Geometric Design

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Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >= 5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

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Section: Related and Previous Workmentioning

confidence: 99%

Biomechanics simulations using cubic Hermite meshes with extraordinary nodes for isogeometric cardiac modeling

Krishnamurthy

Gonzales

Sturgeon

et al. 2016

Computer Aided Geometric Design

Self Cite

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“…The time reduction we achieve with our proposed towerDS approached 40.71% for a 256 3 mesh using the Tesla P100. For the 512 3 , we could reduce the execution time by 17.65% also using the Tesla P100.…”

Section: Single Gpu Performance Evaluationmentioning

confidence: 88%

“…[30][31][32] Several authors have tested GPU performance previously for different cardiac tissue models. 40,41 Some authors have addressed the problem of implementing a solution for a PDE like Equation (3) More recently, Kaboudian et al 46 proposed a WebGL-based approach to perform cardiac electrophysiology simulations on GPUs, using FDM and single precision. 40,41 Some authors have addressed the problem of implementing a solution for a PDE like Equation (3) More recently, Kaboudian et al 46 proposed a WebGL-based approach to perform cardiac electrophysiology simulations on GPUs, using FDM and single precision.…”

Section: Related Workmentioning

confidence: 99%

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Accelerating simulations of cardiac electrical dynamics through a multi‐GPU platform and an optimized data structure

Vasconcellos

Clua

Fenton

et al. 2019

Concurrency and Computation

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Simulations of cardiac electrophysiological models in tissue, particularly in 3D require the solutions of billions of differential equations even for just a couple of milliseconds, thus highly demanding in computational resources. In fact, even studies in small domains with very complex models may take several hours to reproduce seconds of electrical cardiac behavior.Today's Graphics Processor Units (GPUs) are becoming a way to accelerate such simulations, and give the added possibilities to run them locally without the need for supercomputers.Nevertheless, when using GPUs, bottlenecks related to global memory access caused by the spatial discretization of the large tissue domains being simulated, become a big challenge. For simulations in a single GPU, we propose a strategy to accelerate the computation of the diffusion term through a data-structure and memory access pattern designed to maximize coalescent memory transactions and minimize branch divergence, achieving results approximately 1.4 times faster than a standard GPU method. We also combine this data structure with a designed communication strategy to take advantage in the case of simulations in multi-GPU platforms.We demonstrate that, in the multi-GPU approach performs, simulations in 3D tissue can be just 4× slower than real time. KEYWORDScardiac electrophysiology models, GPU Computing, memory access optimization, parallel cardiac dynamics simulations INTRODUCTIONThe large increase of computational power over the last years shifted the bottleneck of different algorithms to the memory bandwidth and memory management. 1 One typical solution employed by hardware assemblers to minimize this issue is hardware hierarchical memory and memory locality optimization.Computational systems organize hierarchical memory system into levels. In the on-chip level, the registers are the fastest memory, with a high cost per byte and low capacity. Next, there are different cache levels according to the hardware architecture, typically called L1, L2, and so on.The main memory is the next level; here, the cost per byte is less than cache or registers, but latency is high. The last level is the secondary memory that has the highest latency with the lowest cost per byte. Overall, the cost per byte of each level determines the capacity and latency, which directly impact in performance.As each level of the hierarchical memory system has a different storage capacity and data is usually kept at the lowest memory level, computational systems must choose for each level which data will be prioritized to stay in memory and which will be removed when that memory level fills up. To do so, the computer memory system employs two fundamental principles, ie, temporal and spatial locality. 2 In general, these strategies aim to keep the most recently used data in the same memory level, since having to access higher memory levels drastically increases the time of the search.Based on the memory hierarchical principles, some researchers have tried to minimize memory system bottlenecks through s...

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“…Alternatively, other efforts point to reducing the complexity of the underlying cellular models [126]. At the same time, high-order spatial approximations are actively studied [8,9,266] as an alternative to the low-order finite-element discretizations that lead to problem sizes in the hundreds of millions, and naturally provide a unified spatial approximation framework for electromechanics simulations. Recent multiscale models for the mechanics of cardiac tissue include [41,111].…”

Section: Discussionmentioning

confidence: 99%

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

Quarteroni

Lassila

Rossi

et al. 2017

Computer Methods in Applied Mechanics and Engineering

211

205

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High-order finite element methods for cardiac monodomain simulations

Cited by 21 publications

References 44 publications

Biomechanics simulations using cubic Hermite meshes with extraordinary nodes for isogeometric cardiac modeling

Biomechanics simulations using cubic Hermite meshes with extraordinary nodes for isogeometric cardiac modeling

Accelerating simulations of cardiac electrical dynamics through a multi‐GPU platform and an optimized data structure

Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function

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