Deconvolution of bolus-tracking data: a comparison of discretization methods

Model-free measurement of perfusion from bolus-tracking data requires a discretization of the tracer kinetic model. In this study a classification is provided of existing approaches to discretization, and the accuracy of these methods is compared. Two methods are included which are delay invariant (circulant and time shift) and three methods which are not (volterra, singular and hybrid). Simulations of magnetic resonance imaging (MRI) in the brain are performed for two tissue types (plug flow and compartment) with variable delay and dispersion times, temporal resolution and signal to noise. Simulations were compared to measurements in a patient data set. Both delay-invariant methods are equally accurate, but the circulant method is sensitive to data truncation. Overall volterra produces highest estimates of perfusion, followed by hybrid, singular and delay-invariant methods. Volterra is most accurate except in plug-flow without delay or dispersion, which represents an unrealistic tissue type. Differences between methods vanish when delay or dispersion times increase above the temporal resolution. It is concluded that when negative delays cannot be avoided or when an accurate estimate of left-right perfusion ratios is required, the time shift is the method of choice. When delays are certain to be positive and absolute accuracy is the objective, the volterra method is to be preferred.