Non-parametric deconvolution using Bézier curves for quantification of cerebral perfusion in dynamic susceptibility contrast MRI

Abstract

Objective: Deconvolution is an ill-posed inverse problem that tends to yield non-physiological residue functions R(t) in dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI). In this study, the use of Bézier curves is proposed for obtaining physiologically reasonable residue functions in perfusion MRI. Materials and methods: Cubic Bézier curves were employed, ensuring R(0) = 1, bounded-input, bounded-output stability and a non-negative monotonically decreasing solution, resulting in 5 parameters to be optimized. Bézier deconvolution (BzD), implemented in a Bayesian framework, was tested by simulation under realistic conditions, including effects of arterial delay and dispersion. BzD was also applied to DSC-MRI data from a healthy volunteer. Results: Bézier deconvolution showed robustness to different underlying residue function shapes. Accurate perfusion estimates were observed, except for boxcar residue functions at low signal-to-noise ratio. BzD involving corrections for delay, dispersion, and delay with dispersion generally returned accurate results, except for some degree of cerebral blood flow (CBF) overestimation at low levels of each effect. Maps of mean transit time and delay were markedly different between BzD and block-circulant singular value decomposition (oSVD) deconvolution. Discussion: A novel DSC-MRI deconvolution method based on Bézier curves was implemented and evaluated. BzD produced physiologically plausible impulse response, without spurious oscillations, with generally less CBF underestimation than oSVD.