Aaron Oliver-Taylor^{1}, Thomas Hampshire^{1}, Nadia A S Smith^{2}, Michael Stritt^{3}, Jan Petr^{4}, Johannes Gregori^{3}, Matthias Günther^{3,5}, Henk J Mutsaerts^{6}, and Xavier Golay^{1,7}

^{1}Gold Standard Phantoms Limited, London, United Kingdom, ^{2}National Physical Laboratory, Teddington, United Kingdom, ^{3}mediri GmbH, Heidelberg, Germany, ^{4}Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany, ^{5}Fraunhofer MEVIS, Bremen, Germany, ^{6}Amsterdam University Medical Center, Amsterdam, Netherlands, ^{7}Institute of Neurology, University College London, London, United Kingdom

ASLDRO is digital reference object software for Arterial Spin Labelling. Here we present the development and demonstration of the DRO software, and its use in a sensitivity and uncertainty analysis of the single-subtraction equation for ASL perfusion quantification.The DRO software was written in python, and can generate synthetic ASL control, label and M0 data in ASL BIDS format. Pulsed and continuous labelling are supported, and patient motion and instrument noise are accurately simulated. It can be used both for testing and validation of image processing software, and for investigating ASL quantification models.

Here, we present ASLDRO, an open-source software package that generates DRO data that more closely represents an ASL experiment, and can thus be used to test pipelines. We demonstrate this software by performing sensitivity and uncertainty analyses of the Whitepaper model.

We conducted sensitivity and uncertainty analyses (also Python 3.7) using the ASLDRO (v2.2.0) output on CBF values calculated using the Whitepaper equation (Figure 2.d) with quantification parameters kept as recommended

Most parameters’ sensitivities are larger for grey matter, which has higher CBF, however the effect size for Transit Time Scale is similar, resulting in the contribution being much larger for white matter. The largest contributing parameter was the tissue T1 scaling factor.

Estimates of mean grey and white matter CBF are significantly lower than the ground truth (60 and 20 mL/min/100g, respectively) due to the first-order bias between the ground truth and calculated CBF, of which a small fraction is partial volume averaging, and the remainder due to the simplified Whitepaper quantification model. The associated standard uncertainties account for the between-subject variability that might be expected. Estimating or measuring these parameters on a per-subject basis with sufficient precision could lower this uncertainty and improve the bias.

We have assumed that all chosen input parameters are independent. However, there is evidence to suggest a correlation between the T1 of tissue and M0

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DRO Pipeline: For label images, the $$$\Delta M$$$ signal generated using the GKM is encoded into the longitudinal magnetisation before either the gradient echo or spin echo signal is calculated (control and M0 no magnetisation is encoded). Rigid rotations and translations simulate patient motion, and an image is formed at the acquisition resolution. Instrument noise is modelled by adding gaussian noise to the real and imaginary channels in k-space, resulting in a Rician noise distribution^{9} in magnitude images.

Tables of a. DRO parameters and their sensitivity/uncertainty analysis values/distributions, b. DRO parameters that are fixed when the model is run, c. Table of quantification parameters that are used in the Whitepaper equation. d. Complete model pipeline: input parameter distributions, random sampling of parameters from these distributions, running the DRO with these parameters, quantification of the control, label and M0 volumes, and then calculation of the mean grey and white matter CBF.

a. Tissue segmentation volume from the input ground truth obtained from the ICBM 2009a Nonlinear Symmetric atlas^{12}. Values in the table in b. are assigned to each of the regions for each quantity volume, relaxation times are for 3 Tesla. c. Example DRO output control, label and corresponding difference images. d. Four transversal MRI slices output from ExploreASL for two DROs with same perfusion but with and without motion. tSNR = temporal signal-to-noise ratio.

Box-whisker plots of the grey matter CBF for each high/low value of each of the input parameters (a-e), f. table with the effect size for the mean grey and mean white matter CBF, and pie charts showing the contributions of each of the primary effects, plus the combined two-way interactions for grey matter (g) and white matter (h).

Histograms (200 bins) of the randomly sampled input parameters (a-e). Labelling efficiency values were limited to a maximum of 1, resulting in an excess of samples with value 1.0. Histograms (200 bins) and fitted gaussians of the output mean CBF for grey matter (f) and white matter (g). Input-output graph showing the values of the mean CBF in each ROI for both the resampled ground truth, and the results form the Whitepaper equation calculation (h), error bars show one standard deviation.