Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the Halting problem

Scarle, Simon

doi:10.1016/j.compbiolchem.2009.05.001

Cited by 20 publications

(15 citation statements)

References 31 publications

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“…The first published simulation of 2D wave propagation in cardiac arrhythmias model using GPU hardware was performed on an Xbox 360 and resulted in a speedup of more than for specific model parameters [28]. Our work is the first to report the simulation results of the 2D wave propagation using CUDA, OpenCL, and OpenACC to manually ( CUDA/OpenCL) and automatically (OpenACC) take advantage of the power of modern computational accelerators like GPUs and Intel Xeon Phi coprocessor.…”

Section: Discussionmentioning

confidence: 99%

Fast Acceleration of 2D Wave Propagation Simulations Using Modern Computational Accelerators

Wang

Xu²,

Cavazos³

et al. 2014

PLoS ONE

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Recent developments in modern computational accelerators like Graphics Processing Units (GPUs) and coprocessors provide great opportunities for making scientific applications run faster than ever before. However, efficient parallelization of scientific code using new programming tools like CUDA requires a high level of expertise that is not available to many scientists. This, plus the fact that parallelized code is usually not portable to different architectures, creates major challenges for exploiting the full capabilities of modern computational accelerators. In this work, we sought to overcome these challenges by studying how to achieve both automated parallelization using OpenACC and enhanced portability using OpenCL. We applied our parallelization schemes using GPUs as well as Intel Many Integrated Core (MIC) coprocessor to reduce the run time of wave propagation simulations. We used a well-established 2D cardiac action potential model as a specific case-study. To the best of our knowledge, we are the first to study auto-parallelization of 2D cardiac wave propagation simulations using OpenACC. Our results identify several approaches that provide substantial speedups. The OpenACC-generated GPU code achieved more than speedup above the sequential implementation and required the addition of only a few OpenACC pragmas to the code. An OpenCL implementation provided speedups on GPUs of at least faster than the sequential implementation and faster than a parallelized OpenMP implementation. An implementation of OpenMP on Intel MIC coprocessor provided speedups of with only a few code changes to the sequential implementation. We highlight that OpenACC provides an automatic, efficient, and portable approach to achieve parallelization of 2D cardiac wave simulations on GPUs. Our approach of using OpenACC, OpenCL, and OpenMP to parallelize this particular model on modern computational accelerators should be applicable to other computational models of wave propagation in multi-dimensional media.

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Section: Discussionmentioning

confidence: 99%

Fast Acceleration of 2D Wave Propagation Simulations Using Modern Computational Accelerators

Wang

Xu²,

Cavazos³

et al. 2014

PLoS ONE

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“…This is the typical assumption made by partial differential equation (PDE) models of large collections of cells where individual cell shapes do not play a role in the behavior of the tissue. Numerical computation of PDEs can achieve significant speedup on the GPU, but they have been discussed elsewhere [33,34] so we will not consider this representation any further. Discrete space or lattice representations divide space into discrete units, then cells occupy one or more spatial units thus defining the spatial extent of the cell.…”

Section: Modeling Methods For Biological Behaviorsmentioning

confidence: 99%

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

et al. 2010

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Background: Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models. Results: We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture. Conclusions: We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

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“…The electrophysiological equations of cardiac cells are of the reaction-diffusion type, for which GPUs have been shown to be superior to CPUs in both 2 and 3 dimensions with typical acceleration values between 5 and 40 depending on the algorithms used [25,33]. The first simulation of cardiac arrhythmias using GPUs actually was performed on an Xbox 360 [35] using the BCF model [2] (Fig. 7).…”

Section: Related Workmentioning

confidence: 99%

Toward real-time simulation of cardiac dynamics

Bartocci

Cherry

Glimm

et al. 2011

Proceedings of the 9th International Conference on Computational Methods in Systems Biology

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We show that through careful and model-specific optimizations of their GPU implementations, simulations of realistic, detailed cardiac-cell models now can be performed in 2D and 3D in times that are close to real time using a desktop computer. Previously, large-scale simulations of detailed mathematical models of cardiac cells were possible only using supercomputers. In our study, we consider five different models of cardiac electrophysiology that span a broad range of computational complexity: the two-variable Karma model, the four-variable Bueno-Orovio-Cherry-Fenton (BCF) model, the eight-variable Beeler-Reuter (BR) model, the 19-variable Ten Tusscher-Panfilov (TP) model, and the 67-variable Iyer-Mazhari-Winslow(IMW) model. For each of these models, we treat both their single-and double-precision versions and demonstrate linear or even sub-linear growth in simulation times with an increase in the size of the grid used to model cardiac tissue. We also show that our GPU implementations of these models can increase simulation speeds to near real-time for simulations of complex spatial patterns indicative of cardiac arrhythmic disorders, including spiral waves and spiral wave breakup. The achievement of real-time applications without the need for supercomputers may facilitate the adoption of modeling-based clinical diagnostics and treatment planning, including patient-specific electrophysiological studies, in the near future.

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Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the Halting problem

Abstract: Implications of the turing completeness of reactiondiffusion models, informed by GPGPU simulations on an XBox 360: Cardiac arrhythmias, re-entry and the halting problem.

Cited by 20 publications

References 31 publications

Fast Acceleration of 2D Wave Propagation Simulations Using Modern Computational Accelerators

Fast Acceleration of 2D Wave Propagation Simulations Using Modern Computational Accelerators

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

Toward real-time simulation of cardiac dynamics

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