A simulation study on singular value decomposition to estimate the cerebral blood flow in MR perfusion imaging

MR perfusion imaging provides the unique approach to measure the metabolic capacity of brain, which is important in diagnosing the disease as well as assessing the treatment. The retrieve of perfusion parameters from MR perfusion imaging of brain is typically a process of inverse problem. In this paper, singular value decomposition (SVD) is advocated as a solver for the inverse problem, and the SVD technique for estimating the cerebral blood flow (CBF) is elaborated in short. Simulation schemes are designed towards revealing the properties of the inverse problem, namely the effects of signal-noise ratio, arterial input function (AIF) delay and distortion. Our simulation experiments show that the SVD technique is able to precisely reproduce flows when SNR equals to 150 or 10 respectively. The solution of SVD technique is found to be stable in the presence of the AIF distortion. However, the SVD technique is sensitive to the effect of AIF delay, where the high CBFs are underestimated about 20%-30%. Hence therefore a delay correction method is developed and the simulation results show that the corrected CBFs are less suffered from the underestimation which is reduced to a value between ±5%. The simulation results show that SVD method is an effective method to estimate the cerebral blood flow in MR perfusion imaging.