Mathematical Framework of Deconvolution Algorithms for Quantification of Perfusion Parameters

MR perfusion weighted imaging (PWI) has been used as sensitive indicator of tissue at risk for infarction. Quantitative perfusion parameters such as cerebral blood flow (CBF), mean transit time (MTT) and cerebral blood volume (CBV) can be obtained from post processing of PWI data using standard singular value decomposition algorithm (SVD). Assumption regarding absence of arterial - tissue delay (ATD) used in SVD algorithm results in underestimation of perfusion parameters. To estimate accurate values for perfusion parameters it is important to understand the mathematical framework behind SVD and improved SVD algorithms (bSVD and rSVD).

This study explains the mathematical framework of SVD and improved SVD algorithms and uses computational techniques that use bSVD algorithm to obtain perfusion parameters maps of CBF, CBV and MTT for acute stroke patient.

Computational techniques based on mathematical deconvolution algorithms are used to post process CBV, CBF and MTT maps where decrease in CBF and CBV were seen in left hemisphere.

The bSVD algorithm is found to be sensitive to ATD and provides more accurate estimates of perfusion parameters than the SVD algorithm, however CBF estimates from bSVD and rSVD still remain influenced by other artifacts Keywords: PWI = perfusion weighted imaging, CBF= cerebral blood flow, MTT = mean transit time, CBV= cerebral blood volume, SVD = singular value decomposition algorithm.