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

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 efects of arterial delay
and dispersion. BzD was also applied to DSC-MRI data from a healthy volunteer.
Results Bézier deconvolution showed robustness to diferent 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 fow
(CBF) overestimation at low levels of each efect. Maps of mean transit time and delay were markedly diferent 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.