Michael A Chappell^{1}, Martin Craig^{1}, James R Larkin^{2}, Manon A Simard^{2}, Nicola R Sibson^{2}, and Thomas W Okell^{3}

Multi-phase pcASL has been proposed as a means to achieve accurate perfusion quantification that is robust to imperfect shim in the labelling plane. There exists a previously unrecognised bias in the estimation process that is a function of noise on the data. In this work this boas is addressed, exploiting information common to voxels containing tissue fed by the same artery, identified using clustering methods.

^{}A potential short-coming for pseudo-continous ASL (pcASL) perfusion imaging is the sensitivity of the labelling to phase mismatch due to off-resonance fields and arterial flow velocity. One solution is to acquire so-called multi-phase pcASL data (MPpcASL), where labelling is performed at a range of phase offsets and subsequent model fitting used to extract the magnitude associated with the delivery of labeled blood^{1} and hence calculate perfusion. Alternatively the information gained from a multi-phase prescan can be used to adjust the labelling for a subsequent pcASL acquisition^{2}.

A previously unrecognised issue for multi-phase approaches to pcASL is that the model-fitting process is biased by the appearance of noise on the data. In practice, the SNR of ASL data is insufficient to generate unbiased measurements of phase-offset in the labeled arteries and thus of perfusion on a voxelwise basis. The purpose of this study was to address this issue, exploiting the fact that in reality we only need to determine phase offset for each labeled artery and thus can exploit common information found in multiple voxels within a whole region of the brain, offering superior SNR and thus overcoming the bias.

**Simulation study:** Data were simulated according to the modified Fermi function^{1} at 8 phase offsets equally spaced across the full 360 degrees, adding white noise at varying SNR (defined relative to the offset, i.e. static tissue, magnitude) generating 40 instances at each SNR, and then fitted to the same modified Fermi function with three variables (magnitude, phase and offset) using a variational Bayesian model fitting routine^{3,4,5}.

**Multi-stage analysis solution: **Figure 1 illustrates the multi-stage procedure proposed to overcome the bias observed in the model-fitting procedure for MPpcASL data. The main features are: (1) an initial voxelwise fit to produce biased maps of the parameters, (2,3) a supervoxel based clustering procedure^{6} on the (biased) phase map to indetify regions of common phase, (4) model-fitting of the average series in each cluster, (5) additional voxelwise model-fitting with the phase parameter fixed by the appropriate value from the cluster analysis. The key concept is that the phase parameter is specific to the feeding arteries and thus is common across a large number of voxels, appropriate regions of interest can be identified using the initial (biased) phase maps to separate regions with different phase (and thus potentially different feeding artery), and averaging of data within an ROI results in data with a higher SNR, and thus reduced bias when estimating the phase parameter. The multi-stage procedure was implemented in Quantiphyse^{7}.

**Data: **MPpcASL was acquired in isoflurane
anaesthetised female Wistar, Sprague Dawley rats (n=3) at 9.4 T (Agilent). The sequence used eight phase angles, with optimal label duration of 1.4 s and post-label delay of 0.55 s and labeling plane positioning following^{8}. A multislice single-shot spin echo EPI sequence was used for the imaging readout, with a 32x32 mm FOV (64x64 matrix, thickness=1 mm, 10 slices), TE=28.7 ms. For validation perfusion was also determined using autoradiography as in^{8}.

**Evaluation and validation: **Perfusion was quantified using both conventional MPpcASL modified-Fermi fitting and the multi-stage procedure proposed. Kinetic model inversion was performed using BASIL from FSL^{5}. Absolute perfusion values were derived by estimating the equilibrium magnetisation in striatum and converting to the equivalent value in blood based on the partition co-efficient^{8}. These values were compared to the equivalent measure derived from autoradiography.

[1] Jung, Y., Wong, E. C., & Liu, T. T. (2010). Multiphase pseudocontinuous arterial spin labeling (MP-PCASL) for robust quantification of cerebral blood flow. Magnetic Resonance in Medicine, 64(3), 799–810. http://doi.org/10.1002/mrm.22465

[2] Hirschler, L., Debacker, C. S., Voiron, J., Köhler, S., Warnking, J. M., & Barbier, E. L. (2017). Interpulse phase corrections for unbalanced pseudo‐continuous arterial spin labeling at high magnetic field. Magnetic Resonance in Medicine, 60, 1488. http://doi.org/10.1002/mrm.26767.

[3] Chappell, M. A., Groves, A., Whitcher, B., & Woolrich, M. (2009). Variational Bayesian Inference for a Nonlinear Forward Model. IEEE Transactions on Signal Processing, 57(1), 223–236.

[4] Shin, D. D., Chappell, M. A., & Liu, T. T. (2014). Robust and Fast Quantification of CBF measures for Multiphase PCASL using Bayesian Nonlinear Model Fitting (p. 2176). Presented at the Proc. Int. Soc. Magn. Reson. Med., Milan.

[5] www.fmrib.ox.ac.uk/fsl/basil

[6] Irving, B., Popescu, I. A., Bates, R., Allen, P. D., Gomes, A. L., Kannan, P., et al. maskSLIC: Regional Superpixel Generation withApplication to Local Pathology Characterisation inMedical Images. arXiv.org. http://doi.org/arXiv:1606.09518

[7] www.quantiphyse.org

[8] Simard, M. A., Larkin, J. R., Khrapitchev, A. A., Meakin, J. A., Okell, T. W., Jezzard, P., et al. (2016). Validation of quantitative pre-clinical pseudo-continuous ASL in rat brain (p. 1891). Presented at the International Society for Magnetic Resonance in Medicine, Honolulu, USA.

[9] Chappell, M. A., Okell, T. W., Payne, S. J., Jezzard, P., & Woolrich, M. W. (2012). A fast analysis method for non-invasive imaging of blood flow in individual cerebral arteries using vessel-encoded arterial spin labelling angiography. Medical Image Analysis, 16(4), 831–839. http://doi.org/10.1016/j.media.2011.12.004

Schematic of the multi-stage procedure for the analysis of MPpcASL data. Bias in the voxel fitting in (1) is overcome in the final voxelwsie fitting (5) by an intermediate stage of analysis within ROI defined from the original phase map that groups ROIs with common feeding artery.

a) Example of simulated multiphase data including the underlying true function, a noisy realisation, the model fit and the function estimated when taking the mean over 40 realisations; b) the effect of SNR on magnitude (and hence perfusion) estimation, here magnitude is relative to the offset (static tissue) parameter. The bias seen in (a) occurs across a range of SNR and magnitude values in (b) and is particular acute at typical SNR values (>40) and magnitudes (1-5% of offset, approx.equivalent to perfusion in the range 60-300 ml/100g/min).

Images of perfusion from the original biased Ferm-function fitting (top row), corrected analysis using phase derived from ROIs identified during the multi-stage process (middle row), and from autoradiography (bottom row).