Sakoglu Unal, Sood Rohit
Department of Neurology, BRaIN Imaging Center, University of New Mexico, Albuquerque, NM 87131, USA.
Magn Reson Imaging. 2008 Apr;26(3):313-22. doi: 10.1016/j.mri.2007.08.007. Epub 2007 Dec 26.
Perfusion-weighted MRI can be used for estimating blood flow parameters using bolus tracking technique based on dynamic susceptibility contrast MRI. In order to extract flow parameters, several deconvolution techniques have been proposed, of which the singular value decomposition (SVD) and Fourier transform (FT)-based techniques are more popular and widely used. In this work, an FT-based method has been proposed that involves derivation of an optimal shaped filter (defined as a filter function) estimated using minimum mean-squared error (MMSE) technique in the frequency domain. The proposed technique has been compared with the well-established SVD technique using simulation experiments.
Simulation was performed in multiple steps. An arterial input function (AIF) was first defined based on a certain blood flow value. The T2* signal change was then derived from this AIF, and noise was added to the signal. Then, a unique and optimal shaped filter function Phi(f) was derived in order to obtain the best estimate of scaled residue function. One way is by minimizing the mean-squared error between the noiseless and noisy scaled residue function, i.e., using an MMSE method. The effect of low and moderate noise and distorted AIF on cerebral blood flow (CBF) estimates was obtained by using FT-based MMSE method. Results were compared with the SVD technique. In this work, SVD technique was assumed to be the standard reference deconvolution technique.
For low-noise condition, the FT-based technique was more stable than the SVD technique, while for moderate noise, both techniques consistently underestimated CBF. SVD technique was found to be more stable in presence of AIF distortions. However, SVD technique was found to be unstable due to AIF delay compared to the FT-based MMSE method. The shaped filter function was found to be sensitive to effect of AIF distortions.
灌注加权磁共振成像（MRI）可用于基于动态磁敏感对比MRI的团注追踪技术来估计血流参数。为了提取血流参数，已经提出了几种反卷积技术，其中基于奇异值分解（SVD）和傅里叶变换（FT）的技术更受欢迎且应用广泛。在这项工作中，提出了一种基于FT的方法，该方法涉及在频域中使用最小均方误差（MMSE）技术推导估计的最优形状滤波器（定义为滤波函数）。使用模拟实验将所提出的技术与成熟的SVD技术进行了比较。
模拟分多个步骤进行。首先基于一定的血流值定义动脉输入函数（AIF）。然后从该AIF导出T2*信号变化，并向信号中添加噪声。接着，为了获得缩放残差函数的最佳估计，推导了一个独特的最优形状滤波函数Phi(f)。一种方法是通过最小化无噪声和有噪声的缩放残差函数之间的均方误差，即使用MMSE方法。使用基于FT的MMSE方法获得低噪声和中等噪声以及扭曲的AIF对脑血流量（CBF）估计的影响。结果与SVD技术进行了比较。在这项工作中，SVD技术被假定为标准参考反卷积技术。
在低噪声条件下，基于FT的技术比SVD技术更稳定，而在中等噪声条件下，两种技术都持续低估了CBF。发现SVD技术在存在AIF失真时更稳定。然而，与基于FT的MMSE方法相比，发现SVD技术由于AIF延迟而不稳定。发现形状滤波函数对AIF失真的影响敏感。
