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Magn Reson Imaging. 2008 Apr;26(3):313-22. Epub 2007 Dec 26.

Cerebral blood flow estimation from perfusion-weighted MRI using FT-based MMSE filtering method.

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Department of Neurology, BRaIN Imaging Center, University of New Mexico, Albuquerque, NM 87131, USA.



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.

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