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

Abstract

Quantification of haemodynamic 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 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.