An improved fast marching method and its application in Alzheimer's disease

Magnetic resonance diffusion tensor imaging (DTI) provides a noninvasive approach to characterize the fiber pathways in the human brain. Among the fiber tractography algorithms in DTI analysis, the fast marching (FM) method has been widely used in quantitatively analyzing the structural connectivity of the fibers and their changes. However, standard FM only considers the similarity and the principal direction information conveyed by two neighboring voxels. It may have poor tracking performance when image noise and fiber crossing are present. To solve this problem, we introduced an improved FM method employing a memory factor (MFFM) to better characterize the directionality of fiber propagation. Simulation showed that MFFM yields higher tracking accuracy, lower computational load, and better antinoise/crossing performance compared with standard FM. Finally, we applied MFFM to Alzheimer's disease (AD) DTI data to explore the impaired regional connectivity of fiber structure. The results augment the knowledge of the pathological alteration of white matter in AD. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 346–352, 2013     

Fractional anisotropy‐weighted front evolution algorithm for white matter tractography based on diffusion tensor imaging data

Tractography is one of the most important applications of diffusion tensor imaging (DTI) which noninvasively reconstructs 3D trajectories of the white matter tracts. Because of the intravoxel orientation heterogeneity of DTI data, some of tractography algorithms are unable to follow the correct pathways after the crossing and branching regions. Front propagation techniques are efficient methods in tracking the crossing fibers. A key parameter influencing the performance of these algorithms is the cost function which is mainly based on the colinearity of tensors' eigenvectors. The effect of the eigenvalues on the anisotropy strength of tensor has not been previously addressed in the definition of the speed function. In this article, a new speed function, based on the effect of diffusion anisotropy and the colinearity of eigenvectors is proposed. The performance of the suggested method on fiber tracking and crossing fiber detection has been evaluated using synthetic datasets, and the feasibility of the proposed method was shown by fiber tracking implemented on real DTI data. © 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 307–314, 2011     

Rapid computation of sodium bioscales using gpu‐accelerated image reconstruction

Quantitative sodium magnetic resonance imaging permits noninvasive measurement of the tissue sodium concentration (TSC) bioscale in the brain. Computing the TSC bioscale requires reconstructing and combining multiple datasets acquired with a non‐Cartesian acquisition that highly oversamples the center of k‐space. Even with an optimized implementation of the algorithm to compute TSC, the overall processing time exceeds the time required to collect data from the human subject. Such a mismatch presents a challenge for sustained sodium imaging to avoid a growing data backlog and provide timely results. The most computationally intensive portions of the TSC calculation have been identified and accelerated using a consumer graphics processing unit (GPU) in addition to a conventional central processing unit (CPU). A recently developed data organization technique called Compact Binning was used along with several existing algorithmic techniques to maximize the scalability and performance of these computationally intensive operations. The resulting GPU+CPU TSC bioscale calculation is more than 15 times faster than a CPU‐only implementation when processing 256 × 256 × 256 data and 2.4 times faster when processing 128 × 128 × 128 data. This eliminates the possibility of a data backlog for quantitative sodium imaging. The accelerated quantification technique is suitable for general three‐dimensional non‐Cartesian acquisitions and may enable more sophisticated imaging techniques that acquire even more data to be used for quantitative sodium imaging. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 29–35, 2013.     

图形处理器加速算法在复杂高层结构非线性响应分析中的应用

目前有限元分析软件多基于中央处理器的平台方式构建,在处理复杂高层结构非线性响应分析时暴露出计算耗时多、计算效率低以及对计算硬件要求高等问题。图形处理器由于其硬件构造的先天优势,可以提供十倍乃至上百倍于中央处理器的浮点运算和并行计算性能,因而为高层结构非线性计算所面临的瓶颈问题提供了一个切实可行的解决方法。该文在构建异构并行计算平台的基础上,提出一种适用于图形处理器加速的有限元并行数值计算方法。该方法利用精细化结构分析模型的自由度数据和图形处理器中的线程建立一一对应映射关系,对动力响应的隐式积分算法进行图形处理器线程级的并行化处理,并且结合EBE单元级的优化存储空间机制,降低系统方程组求解时对内存空间的需求。通过对比振动台试验结果对该方法进行验证,并对实际高层钢筋混凝土框筒结构工程进行弹塑性地震响应分析,结果显示该文所提方法在保证模型精度前提下能有效提高大型复杂高层结构非线性响应分析效率。     

Parallel particle swarm optimization on a graphics processing unit with application to trajectory optimization

In order to reduce the computational time, a fully parallel implementation of the particle swarm optimization (PSO) algorithm on a graphics processing unit (GPU) is presented. Instead of being executed on the central processing unit (CPU) sequentially, PSO is executed in parallel via the GPU on the compute unified device architecture (CUDA) platform. The processes of fitness evaluation, updating of velocity and position of all particles are all parallelized and introduced in detail. Comparative studies on the optimization of four benchmark functions and a trajectory optimization problem are conducted by running PSO on the GPU (GPU-PSO) and CPU (CPU-PSO). The impact of design dimension, number of particles and size of the thread-block in the GPU and their interactions on the computational time is investigated. The results show that the computational time of the developed GPU-PSO is much shorter than that of CPU-PSO, with comparable accuracy, which demonstrates the remarkable speed-up capability of GPU-PSO.     

Parallel implementation of spectral element method for Lamb wave propagation modeling

The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss–Lobatto–Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element‐by‐element vectors multiplication. Compute‐intensive operations are performed for a part of equation of motion derived at the degree of freedom level of 3D isoparametric spectral elements. The assembly is performed at the force vector in such a way that atomic operations are minimized. This is achieved by a new mesh coloring technique The proposed parallel implementation of spectral element method on GPU is applied for the first time for Lamb wave simulations. It has been found that computation on multicore GPU is up to 14 times faster than on single CPU. Copyright © 2015 John Wiley & Sons, Ltd.     

Calculation method for computer-generated holograms with cylindrical basic object light by using a graphics processing unit

It takes an enormous amount of time to calculate a computer-generated hologram (CGH). A fast calculation method for a CGH using precalculated object light has been proposed in which the light waves of an arbitrary object are calculated using transform calculations of the precalculated object light. However, this method requires a huge amount of memory. This paper proposes the use of a method that uses a cylindrical basic object light to reduce the memory requirement. Furthermore, it is accelerated by using a graphics processing unit (GPU). Experimental results show that the calculation speed on a GPU is about 65 times faster than that on a CPU.     

基于矢量DSP的并行化卷积算法

为了提场卷积算法在矢量!字信号处理器(DSP)上的执行效率,提出了一种高效的并行化卷积算法——基2并行短卷积(PSC R2)算法。该算法采用了基2短卷积运算结构,摆脱了传统并行化卷积算法的直接结构,从而有效降低了算法的循环次!。基于该算法结构,还提出了矢量DSP专用指令以匹配卷积的运算结构,保障算法执行效率。通过实际评估,证明了该算法在时间复杂度上仅为传统的内循环矢量化(VIL)算法的43%,为外循环矢量化(VOL)算法的55%,并且在存储空间开销上能够与传统算法基本持平。利用该算法,可以大幅降低移动通信和数字信号处理中的卷积、相关、滤波运算的时间复杂度。     

A rapid knowledge-based partial supervision fuzzy c-means for brain tissue segmentation with CUDA-enabled GPU machine

The proposed work aims to quicken the magnetic resonance imaging (MRI) brain tissue segmentation process using knowledge-based partial supervision fuzzy c-means (KPSFCM) with graphics processing unit (GPU). The proposed KPSFCM contains three steps: knowledge-based initialization, modification, and optimization. The knowledge-based initialization step extracts initial centers from input MR images for KPSFCM using Gaussian-based histogram smoothing. The modification step changes the membership function of PSFCM, which is guided by the labeled patterns of cerebrospinal fluid portion. Finally, the optimization step is achieved through size-based optimization (SBO), adjacency-based optimization (ABO), and parallelism-based optimization (PBO). SBO and ABO are algorithmic level optimization techniques in central processing unit (CPU), whereas PBO is a hardware level optimization technique implemented in GPU using compute unified device architecture (CUDA). Performance of the KPSFCM is tested with online and clinical datasets. The proposed KPSFCM gives better segmentation accuracy than 14 state-of-the-art-methods, but computationally expensive. When the optimization techniques (SBO and ABO) were included, the execution time reduces by 13 times in CPU. Finally, the inclusion of PBO yields 19 times faster than the optimized CPU implementation.     

GPU accelerated lattice Boltzmann model for shallow water flow and mass transport

A lattice Boltzmann method (LBM) for solving the shallow water equations (SWEs) and the advection–dispersion equation is developed and implemented on graphics processing unit (GPU)‐based architectures. A generalized lattice Boltzmann equation (GLBE) with a multiple‐relaxation‐time (MRT) collision method is used to simulate shallow water flow. A two‐relaxation‐time (TRT) method with two speed‐of‐sound techniques is used to solve the advection–dispersion equation. The proposed LBM is implemented to an NVIDIA ^® Computing Processor in a single GPU workstation. GPU computing is performed using the Jacket GPU engine for MATLAB ^® and CUDA. In the numerical examples, the MRT‐LBM model and the TRT‐LBM model are verified and show excellent agreement to exact solutions. The MRT outperforms the single‐relaxation‐time (SRT) collision operator in terms of stability and accuracy when the SRT parameter is close to the stability limit of 0.5. Mass transport with velocity‐dependent dispersion in shallow water flow is simulated by combining the MRT‐LBM model and the TRT‐LBM model. GPU performance with CUDA code shows an order of magnitude higher than MATLAB‐Jacket code. Moreover, the GPU parallel performance increases as the grid size increases. The results indicate the promise of the GPU‐accelerated LBM for modeling mass transport phenomena in shallow water flows. Copyright © 2010 John Wiley & Sons, Ltd.     

Rapid brain tissue segmentation process by modified FCM algorithm with CUDA enabled GPU machine

The proposed work introduces a modified method of fuzzy c means (FCM) algorithm using bias field correction and partial supervision techniques. The proposed method is named as bias corrected partial supervision FCM (BCPSFCM). The modified membership function takes the advantage of available knowledge from labeled patterns with the bias field correction. The experiment is tested on internet brain segmentation repository with their gold standard. The performance of the method is compared with three existing methods and 12 state of the art methods using dice coefficient, sensitivity, specificity, and accuracy. Accuracy of the proposed method reached upto 98%, 98%, and 99% of GM, WM, and CSF segmentation but required additional computation power from graphics processing unit (GPU). Further parallel BCPSFCM is proposed with the help of compute unified device architecture enabled GPU machine and the processing time is reduced up to 49 times than the serial implementation.     

Fast ultrasound beam prediction for linear and regular two-dimensional arrays

Real-time beam predictions are highly desirable for the patient-specific computations required in ultrasound therapy guidance and treatment planning. To address the longstanding issue of the computational burden associated with calculating the acoustic field in large volumes, we use graphics processing unit (GPU) computing to accelerate the computation of monochromatic pressure fields for therapeutic ultrasound arrays. In our strategy, we start with acceleration of field computations for single rectangular pistons, and then we explore fast calculations for arrays of rectangular pistons. For single-piston calculations, we employ the fast near-field method (FNM) to accurately and efficiently estimate the complex near-field wave patterns for rectangular pistons in homogeneous media. The FNM is compared with the Rayleigh-Sommerfeld method (RSM) for the number of abscissas required in the respective numerical integrations to achieve 1%, 0.1%, and 0.01% accuracy in the field calculations. Next, algorithms are described for accelerated computation of beam patterns for two different ultrasound transducer arrays: regular 1-D linear arrays and regular 2-D linear arrays. For the array types considered, the algorithm is split into two parts: 1) the computation of the field from one piston, and 2) the computation of a piston-array beam pattern based on a pre-computed field from one piston. It is shown that the process of calculating an array beam pattern is equivalent to the convolution of the single-piston field with the complex weights associated with an array of pistons. Our results show that the algorithms for computing monochromatic fields from linear and regularly spaced arrays can benefit greatly from GPU computing hardware, exceeding the performance of an expensive CPU by more than 100 times using an inexpensive GPU board. For a single rectangular piston, the FNM method facilitates volumetric computations with 0.01% accuracy at rates better than 30 ns per field point. Furthermore, we demonstrate array calculation speeds of up to 11.5 X 10(9) field-points per piston per second (0.087 ns per field point per piston) for a 512-piston linear array. Beam volumes containing 256(3) field points are calculated within 1 s for 1-D and 2-D arrays containing 512 and 20(2) pistons, respectively, thus facilitating future real-time thermal dose predictions.     

3D非均匀直线网格GPU体绘制方法研究

计算机图形硬件技术的快速发展可以用来加速可视化过程,为此针对非均匀直线网格,给出了基于均匀辅助网格的CPU光线投射算法、基于辅助纹理的GPU光线投射算法,以及基于切片的3D纹理体绘制算法,并在Nvidia Geforce 6800GT图形卡上对这些算法进行了测试。结果表明,GPU算法远远快于CPU算法,而基于切片的3D纹理体绘制算法则快于GPU光线投射算法。     

Hough transform‐based approach for estimating 3D rotation angles of vertebrae from biplanar radiographs using GPU‐acceleration

For scoliosis assessment, a system was developed to estimate the three‐dimensional (3D) rotation angles of vertebrae from biplanar radiographs. The proposed approach was based on the generalized Hough transform (GHT) technique to match the projected contours of the standard 3D primitive with vertebral edges detected in biplanar radiographs. A deformation tolerant matching strategy was proposed to extend the GHT for an inexact contour matching. The system was implemented on a graphics processing unit (GPU). Seventeen dry vertebral specimens were used to evaluate accuracy. Precision was tested by three operators on 181 vertebrae from radiographs of 15 patients. With GPU computing, the average estimation time was 10 s for a vertebra. Results showed that the 3D estimation error was less than 2.5° with the mean value of 1.6°. The intraoperator variability was within 1.6° and the interoperator variability was within 2.2°. These promising results indicate that the proposed system can help orthopedic surgeons measure the 3D vertebral rotation angles from two‐dimensional radiographs for better assessment of scoliosis. © 2013 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 23, 272–279, 2013     

Non-Local DWI Image Super-Resolution with Joint Information Based on GPU Implementation

Since the spatial resolution of diffusion weighted magnetic resonance imaging (DWI) is subject to scanning time and other constraints, its spatial resolution is relatively limited. In view of this, a new non-local DWI image super-resolution with joint information method was proposed to improve the spatial resolution. Based on the non-local strategy, we use the joint information of adjacent scan directions to implement a new weighting scheme. The quantitative and qualitative comparison of the datasets of synthesized DWI and real DWI show that this method can significantly improve the resolution of DWI. However, the algorithm ran slowly because of the joint information. In order to apply the algorithm to the actual scene, we compare the proposed algorithm on CPU and GPU respectively. It is found that the processing time on GPU is much less than on CPU, and that the highest speedup ratio to the traditional algorithm is more than 26 times. It raises the possibility of applying reconstruction algorithms in actual workplaces.     

On semi‐analytical probabilistic finite element method for homogenization of the periodic fiber‐reinforced composites

The main aim of this paper is a development of the semi‐analytical probabilistic version of the finite element method (FEM) related to the homogenization problem. This approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method. It originates from the generalized stochastic perturbation‐based FEM, where Taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions. The hybrid computational implementation of the system MAPLE with homogenization‐oriented FEM code MCCEFF is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber‐reinforced composites. Although numerical illustration deals with a homogenization of a composite with material properties defined as Gaussian random variables, other composite parameters as well as other probabilistic distributions may be taken into account. The methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements, finite differences or volumes as well as for meshless numerical strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems

Recently, graphics processing units (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector (SPMV) multiplication operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis and also show that the proposed algorithms can yield speedup factors up to 12‐fold for real finite element applications. Copyright © 2015 John Wiley & Sons, Ltd.     

GPU‐accelerated boundary element method for Helmholtz' equation in three dimensions

Recently, the application of graphics processing units (GPUs) to scientific computations is attracting a great deal of attention, because GPUs are getting faster and more programmable. In particular, NVIDIA's GPUs called compute unified device architecture enable highly mutlithreaded parallel computing for non‐graphic applications. This paper proposes a novel way to accelerate the boundary element method (BEM) for three‐dimensional Helmholtz' equation using CUDA. Adopting the techniques for the data caching and the double–single precision floating‐point arithmetic, we implemented a GPU‐accelerated BEM program for GeForce 8‐series GPUs. The program performed 6–23 times faster than a normal BEM program, which was optimized for an Intel's quad‐core CPU, for a series of boundary value problems with 8000–128000 unknowns, and it sustained a performance of 167 Gflop/s for the largest problem (1 058 000 unknowns). The accuracy of our BEM program was almost the same as that of the regular BEM program using the double precision floating‐point arithmetic. In addition, our BEM was applicable to solve realistic problems. In conclusion, the present GPU‐accelerated BEM works rapidly and precisely for solving large‐scale boundary value problems for Helmholtz' equation. Copyright © 2009 John Wiley & Sons, Ltd.     

On general isotropic tensor functions of one tensor

This paper discusses general isotropic real symmetric tensor‐valued functions of one real symmetric tensor. By exploiting the eigenprojection‐based spectral representation of such functions, eigenprojection‐based closed formulae for the function derivatives are derived. The derived formulae provide an alternative to the eigenvector‐based derivative expressions proposed by Chadwick and Ogden (Arch. Rat. Mech. Anal. 1971; 44 :54–68) for the same class of functions and are an extension of the eigenprojection‐based derivative expressions obtained by Carlson and Hoger (Quart. Appl. Math. 1986; 44 (3):409–423) for a subset of the present class of functions. The material presented here is restricted to two‐ and three‐dimensional spaces, which are of particular relevance to continuum mechanics. For completeness, algorithms for closed form computation of the isotropic tensor functions as well as their derivatives, based on the eigenprojection representation, are also presented. These should be of interest to computational mechanics researchers dealing with functions of the present type. Copyright © 2004 John Wiley & Sons, Ltd.