cuda n vector arrays documentclass  (Vector Laboratories)

Journal: Magma (New York, N.y.)

Article Title: Gpu-accelerated JEMRIS for extensive MRI simulations

doi: 10.1007/s10334-025-01281-z

Figure Lengend Snippet: JEMRIS simulations of motion artifacts: input parameters are a numerical phantom with set magnetic properties ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_1$$\end{document} T 1 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_2$$\end{document} T 2 , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_2^*$$\end{document} T 2 ∗ , PD , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \omega$$\end{document} Δ ω , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi$$\end{document} χ ), a motion trajectory as a function of time, an acquisition sequence, transmit/receive coil sensitivity maps. The output of the simulator is the bulk magnetization vector at the acquisition timepoints, which can be converted to k-space matrix by taking the transverse magnetization part, provided the phase encoding order in time

Article Snippet: Second, the classes World , Model and Bloch_CV_Model are modified to initialize the GPU solver and the CUDA N_Vector arrays \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{{\textbf{M}}}({\textbf{r}},t)$$\end{document} M ~ ( r , t ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\tilde{{\textbf{M}}}}({\textbf{r}},t)$$\end{document} M ~ ̇ ( r , t ) for magnetization and its derivatives for all spins.

Techniques: Sequencing, Plasmid Preparation

Journal: Magma (New York, N.y.)

Article Title: Gpu-accelerated JEMRIS for extensive MRI simulations

doi: 10.1007/s10334-025-01281-z

Figure Lengend Snippet: Geometrical phantom simulations setup: ( a ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_1 = 1 / T_1$$\end{document} R = / T and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_2 = 1 / T_2$$\end{document} R 2 = / T 2 maps (units [1/s]) of the constructed numerical phantom containing geometrical shapes enumerated 1–7 with MR properties as depicted in table ( b ). ( c ) Magnitude and phase maps of the simulated 4-channel reception coil array. ( d ) Simulated 2D multi-shot TSE sequence exported from the clinical scanner, sequence parameters are provided in Table

Article Snippet: Second, the classes World , Model and Bloch_CV_Model are modified to initialize the GPU solver and the CUDA N_Vector arrays \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{{\textbf{M}}}({\textbf{r}},t)$$\end{document} M ~ ( r , t ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\tilde{{\textbf{M}}}}({\textbf{r}},t)$$\end{document} M ~ ̇ ( r , t ) for magnetization and its derivatives for all spins.

Techniques: Construct, Sequencing

Journal: Magma (New York, N.y.)

Article Title: Gpu-accelerated JEMRIS for extensive MRI simulations

doi: 10.1007/s10334-025-01281-z

Figure Lengend Snippet: Double and single precision GPU simulations compared to double precision MPI for a geometrical phantom with 2,250,000 spins and a 2D TSE sequence. ( a ) Received signals for the first two spin echoes in coil channel 1. GPU and CPU results closely match with the total signal NRMSE of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.11\%$$\end{document} 0.11 % (double precision) and 0.10% (single precision). IFFT-reconstructed images from receive coil channel 1: ( b ) double precision MPI, ( c ) double precision GPU, and ( e ) single precision GPU. Difference images: ( d ) double precision GPU vs. MPI (NRMSE \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=7e^{-5}\%$$\end{document} = 7 e - 5 % ), ( f ) single precision GPU vs. MPI (NRMSE \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=0.8\%$$\end{document} = 0.8 % ). Computation times reduced from 8.5 h (double precision MPI) to 3.5 h (double precision GPU) and 1.25 h (single precision GPU)

Article Snippet: Second, the classes World , Model and Bloch_CV_Model are modified to initialize the GPU solver and the CUDA N_Vector arrays \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{{\textbf{M}}}({\textbf{r}},t)$$\end{document} M ~ ( r , t ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\tilde{{\textbf{M}}}}({\textbf{r}},t)$$\end{document} M ~ ̇ ( r , t ) for magnetization and its derivatives for all spins.

Techniques: Sequencing

Journal: Magma (New York, N.y.)

Article Title: Gpu-accelerated JEMRIS for extensive MRI simulations

doi: 10.1007/s10334-025-01281-z

Figure Lengend Snippet: Acceleration and accuracy analysis of GPU simulations with increasing number of spins in a geometrical phantom. ( a ) Simulation times as a function of the total number of spins (in a logarithmic scale) for double precision MPI ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$MPI\_DP$$\end{document} M P I _ D P ), double and single precision GPU ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GPU\_DP$$\end{document} G P U _ D P and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$GPU\_SP$$\end{document} G P U _ S P ) simulations. Speed-up factors of 3–12 were achieved for double precision and 7–65 for single precision GPU simulations vs. double precision MPI simulations. ( b ) K-space signal normalized root-mean-square error (NRMSE) for double and single precision GPU simulations compared to the MPI reference. The NRMSE was below \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.08\%$$\end{document} 0.08 % for double precision and between 0.2–0.8% for single precision GPU simulations

Article Snippet: Second, the classes World , Model and Bloch_CV_Model are modified to initialize the GPU solver and the CUDA N_Vector arrays \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{{\textbf{M}}}({\textbf{r}},t)$$\end{document} M ~ ( r , t ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\tilde{{\textbf{M}}}}({\textbf{r}},t)$$\end{document} M ~ ̇ ( r , t ) for magnetization and its derivatives for all spins.

Techniques:

Journal: Magma (New York, N.y.)

Article Title: Gpu-accelerated JEMRIS for extensive MRI simulations

doi: 10.1007/s10334-025-01281-z

Figure Lengend Snippet: Fat fraction quantification errors induced by motion. Separated water and fat proton density, as well as PDFF maps for simulations with ( a ) static phantom and ( b ) moving phantom. ( c ) Histogram of estimated PDFF values in the liver region for static and moving phantom simulations. The ground truth liver PDFF was 10%. For the static phantom, the distribution of PDFF is narrow with mean value at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\%$$\end{document} 8 % and standard deviation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\%$$\end{document} 2 % . In the presence of motion, the estimated PDFF values are distributed with mean \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$14\%$$\end{document} 14 % and standard deviation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\%$$\end{document} 3 %

Article Snippet: Second, the classes World , Model and Bloch_CV_Model are modified to initialize the GPU solver and the CUDA N_Vector arrays \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{{\textbf{M}}}({\textbf{r}},t)$$\end{document} M ~ ( r , t ) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\tilde{{\textbf{M}}}}({\textbf{r}},t)$$\end{document} M ~ ̇ ( r , t ) for magnetization and its derivatives for all spins.

Techniques: Standard Deviation