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.

UMMPerfusion: an Open Source Software Tool Towards Quantitative MRI Perfusion Analysis in Clinical Routine

“…The software sets a default value of 0.15 max (S), but allows the user to select a different value if required. A more detailed discussion of selecting the regularization parameter can be found in [30,54]. To parameterize the results, the plasma flow F k of each pixel k is calculated as…”

“…However, we implemented an interface within the plug-in to allow for extensions or to integrate other computations of the perfusion. Since the only difference in calculating perfusion parameters from T1-and T2*-weighted dynamic MRI is the signal to concentration conversion [30], such an extension will be easily to implement in a future version of our plug-in. Also, when using the plug-in for perfusion analysis of moving organs like the heart or the kidneys, motion artifacts have to be corrected for independently, using image registration [21] or breathing, triggering, or navigation techniques during image acquisition [22,53].…”

“…For applications where high accuracy is less important, it offers a suitable alternative to more accurate, but slower and less robust algorithms for model-free deconvolution on the pixel level [30]. Calculating the perfusion parameters by deconvolution is given in the Appendix.…”

“…Since the deconvolution operation can be performed independently for each pixel [30], the calculations can be processed in parallel. The operating system platform (MacOS X) provides native support for parallel processing [39]; therefore, we incorporated support for multi-core/ threaded processing to speed-up the calculation.…”

Quantification of cerebral blood flow, cerebral blood volume, and blood–brain‐barrier leakage with DCE‐MRI

“…[31] was determined by model-free deconvolution with generalized cross-validation (46) and integrated to produce the partialvolume correction factor P A . An R 10 map was calculated by fitting the saturation-recovery data with variable delay times to a monoexponential.…”