Pixel-by-pixel deconvolution of bolus-tracking data: optimization and implementation

Quantification of hemodynamic parameters with a deconvolution
analysis of bolus-tracking data is an ill-posed problem which requires
regularization. In a previous study, simulated data without structural errors
were used to validate two methods for a pixel-by-pixel analysis: Standard-Form
Tikhonov Regularization (SFTR) with either the L-Curve Criterion (LCC) or
Generalized Cross Validation (GCV) for selecting the regularization parameter.
However, problems of image artefacts were reported when the methods were
applied to patient data. The aim of this study was to investigate the nature
of these problems in more detail and evaluate strategies of optimization for
routine application in the clinic. In addition we investigated to which extent
the calculation time of the algorithm can be minimized. In order to ensure that
the conclusions are relevant for a larger range of clinical applications, we relied on
patient data for evaluation of the algorithms. Simulated data were used to validate
the conclusions in a more quantitative manner. We conclude that the reported
problems with image quality can be removed by appropriate optimization of either
LCC or GCV. In all examples this could be achieved with LCC without significant
perturbation of the values in pixels where the regularization parameter was
originally selected accurately. GCV could not be optimized for the renal data, and
in the CT data only at the cost of image resolution. Using the implementations
given, calculation times were sufficiently short for routine application in the clinic.