- Published 2010

Introduction: A general-purpose graphics processing unit (GPU) is a dedicated graphics rendering device with the capability to perform trillion of instructions per second. It offers a powerful processing platform for both graphics and non-graphics applications. Many computer vision and medical imaging algorithms such as advanced MRI reconstruction [1] and Diffusion Tensor Imaging (DTI) connectivity mapping [2] have been paralleled using the GPU architecture. The introduction of the CUDA (Compute Unified Device Architecture) and Tesla technologies [3] from NVIDIA provides an easy way to take advantage of the high performance GPUs for parallel computing on a personal computer or a workstation. DTI is a non-invasive magnetic resonance technique that produces in vivo images of biological tissues with local microstructural characteristics such as water diffusion [4, 5]. Diffusion tensor maps are computed by fitting the signal intensities of diffusion weighted images (DWIs) as a function of their corresponding b-matrices through a multivariate least-squares regression model [4]. This diffusion tensor computation is typically performed on a voxel-by-voxel basis through the entire 3D volume which makes it an ideal application for GPU parallelization. The purpose of this work is to apply GPU hardware in the diffusion tensor map estimation by accelerating the weighted multivariate linear least-squares regression. Unlike solving large matrix problems in linear regression by GPU [6], our aim is to perform thousands of independent multivariate linear regressions in parallel on the GPU. We propose a hybrid approach to accelerate the diffusion tensor estimation: compute the weighted multivariate linear regression on the GPU, and perform the logarithm transform and other tensor derived quantities on the CPU. This hybrid approach takes performance advantage of the GPU to speedup vector and matrix operations in a bulk computation. Methods: In a diffusion tensor model, a signal intensity vector y = {ln(S1), ... , ln(SN)}, where Si represents the i DWI magnitude signal intensity in a DTI acquisition. There are several parameters in a DTI model: = α {Dxx, Dyy, Dzz, Dxy, Dxz, Dyz, ln(A0)}, where Dij are elements of the diffusion tensor, and A0 is the echo intensity with no applied gradients [4]. A log linear model can be written as a first order equation e Bα y + = , where the j row of B contains b-matrix entries of the j DWI acquisition −{ } 1 , 2 , 2 , 2 , , , − j j j j j j yz xz xy zz yy xx b b b b b b , and e is the error vector. The weighted least squares solution using the linear model is given by

@inproceedings{Chang2010AcceleratingDT,
title={Accelerating Diffusion Tensor Estimation Using General-Purpose Graphics Processing Unit},
author={L. C. Chang and Mikhail Gorbachev},
year={2010}
}