Joint Total Variation ESTATICS for Robust Multi-parameter Mapping

Abstract

Quantitative magnetic resonance imaging (qMRI) derives tissue-specific parameters -such as the apparent transverse relaxation rate R 2 , the longitudinal relaxation rate R1 and the magnetisation transfer saturation -that can be compared across sites and scanners and carry important information about the underlying microstructure. The multiparameter mapping (MPM) protocol takes advantage of multi-echo acquisitions with variable flip angles to extract these parameters in a clinically acceptable scan time. In this context, ESTATICS performs a joint loglinear fit of multiple echo series to extract R 2 and multiple extrapolated intercepts, thereby improving robustness to motion and decreasing the variance of the estimators. In this paper, we extend this model in two ways: (1) by introducing a joint total variation (JTV) prior on the intercepts and decay, and (2) by deriving a nonlinear maximum a posteriori estimate. We evaluated the proposed algorithm by predicting left-out echoes in a rich single-subject dataset. In this validation, we outperformed other state-of-the-art methods and additionally showed that the proposed approach greatly reduces the variance of the estimated maps, without introducing bias.

Model-based multi-parameter mapping

“…We tried values and respectively and found an optimal combination with and . For LOGLIN+AONLM, we used the optimal value found in Balbastre et al. (2020) .…”

“… NONLIN performs a non-linear fit or instead of a log-linear fit, but does not use any regularisation. This method was not used in Balbastre et al. (2020) , because Gauss-Newton was not stable enough without regularisation.…”

“…The new Hessian used in this work makes its optimisation possible. NONLIN+JTV adds JTV-regularisation to NONLIN ( Balbastre et al., 2020 ). SPGR-ML performs a non-linear maximum-likelihood fit of the log-parameters , , and logit MT sat .…”

“…In Balbastre et al. (2020) , we introduced a non-linear, spatially regularised version of ESTATICS that was fit using Gauss-Newton optimisation.…”

“…We validated our method on a unique dataset – five repeats of the MPM protocol acquired, within a single session, on a healthy subject – by leave-one-out cross-validation: maps were estimated on one repeat and used to predict the weighted images from the other repeats. Our methods (SPGR+JTV and SPGR-ML) were compared to algorithms that rely on different flavours of the ESTATICS model: LOGLIN uses a log-linear fit to recover the intercepts and decay ( Weiskopf et al., 2014 ), whereas NONLIN, and NONLIN+JTV use a (regularised) non-linear fit ( Balbastre et al., 2020 ). We also applied ESTATICS to echoes that had been previously denoised using the adaptive optimized nonlocal means (AONLM) method ( Manjón et al., 2010 ), as a baseline for the denoising component of our method.…”