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Evaluating T2* bias impact and correction strategies in quantitative proton density mapping
Evelyne Balteau1, Tobias Leutritz2, Nikolaus Weiskopf2, Enrico Reimer2, Antoine Lutti3, Martina F Callaghan4, Siawoosh Mohammadi5, and Karsten Tabelow6

1Cyclotron Research Centre - GIGA-CRC in vivo imaging, University of Liege, Liege, Belgium, 2Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, 3Laboratoire de Recherche en Neuroimagerie, CHUV, University of Lausanne, Lausanne, Switzerland, 4Wellcome Trust Centre for Neuroimaging, University College London, London, United Kingdom, 5Institut für Systemische Neurowissenschaften, Universitätsklinikum Hamburg-Eppendorf, Hamburg, Germany, 6Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

Synopsis

Bias correction is an important step for achieving accurate and precise parameter quantification in MRI. Residual T2*-weighting in quantitative proton density maps estimated from short echo time FLASH images is often considered negligible, despite the potential bias. Using the hMRI toolbox, we analyse simulated FLASH-based multiparameter mapping datasets with variable noise levels. Using the quantitative maps on which the simulations are based as a gold standard, we quantified the bias caused by residual T2*-weighting. Furthermore, we evaluated a number of estimation methods in terms of their sensitivity and/or effectiveness at correcting this T2*-weighting bias, and in terms of their robustness to background noise.

Introduction

Quantitative magnetic resonance imaging (qMRI) helps reveal the biophysical properties governing MRI contrast. By eliminating instrumental biases and other contrast mechanisms influencing the signal amplitude, quantitative parameter maps can be derived and ultimately serve as in vivo biomarkers1. Biases in proton density (PD) map estimation include radio-frequency transmit (B1+) and receive (B1-) fields and T2*-weighting2-5. We focus on the T2* bias in multi-echo fast low angle shot (FLASH) protocols, where the T2* signal dependence is often neglected5,6. Although often pointed out as a potential limitation especially in high iron content areas5,7,8, the extent and severity of this bias and the evaluation of correction strategies have not yet been fully reported.

Methods

Multi-echo FLASH images were simulated according to the multiparameter mapping protocol described previously7. For PD map evaluation, simulations were limited to PD-weighted (FA=6deg) and T1-weighted (FA=21deg) images with TR=25ms and 8 TE values equally spaced between 2.34 and 18.72ms. The FLASH images were simulated using the Ernst equation (assuming perfect RF spoiling9) and sum-of-square combination of the individual receiver coil signals. Gaussian noise was added to the individual coil images resulting in spatially variable signal-to-noise ratios (SNR).

R2*, R1, PD and B1+ maps generated using the hMRI toolbox10 (single subject dataset) were adaptively denoised11,12 and masked to serve as noise-free inputs to the simulation and as references to evaluate deviations of the PD and R2* map estimates. For example, the relative error in PD estimates was evaluated as follows:

$$RelError(\%)=200*\frac{PD_{est}-PD_{ref}}{PD_{est}+PD_{ref}}$$

Synthetic coil sensitivities were generated using the Biot-Savart law13,14 for 48 coil elements distributed on a 24cm-diameter sphere (excluding the area around the inferior pole corresponding to the neck aperture in the head coil).

Simulated data were processed using the hMRI toolbox10, with the ESTATICS model15 to estimate R2* maps and the rational approximation of the Ernst equation6 to estimate R1 and A (biased PD) maps. A maps accounted for B1+ bias only (based on the B1+ map input to data simulation). T2* correction factor 2 (optional), UNICORT-like B1- bias correction7,16 and calibration (setting the average white matter (WM) PD value to 69%17) were then applied to generate quantitative PD maps.

The A maps were derived either from:

(1) the first 6 echoes of the PD-weighted images, averaged to increase SNR,

(2) the first PD-weighted echo only (to reduce T2* bias),

(3) extrapolation (TE=0) of the signal decay in the PD-weighted images18.

An optional T2* correction factor was applied voxel-wise to the A map before B1- bias correction:

$$CorrFac=\frac{1}{mean(exp(-TE_i·R_2^*))}$$

where R2* was estimated using ESTATICS and the mean was calculated across TE1-6 for (1) and TE1 alone for (2). No additional correction factor was required for (3).

All the above methods are implemented in the hMRI toolbox10. The additional T2* correction factor, although sensibly used by some authors3 and easily derived from R2* estimates, is often neglected.

Results

When data were simulated without any additional noise (Fig.1a), the R2* map was perfectly estimated (Fig.2a) and the additional T2* correction factor was successful at correcting for T2* bias in the calculated PD maps (Fig.3b,d). Without T2*-weighting correction, the T2* bias is stronger with method (1) than method (2) due to the longer effective TE in (1) (Fig.3a,c). The bias is especially severe in areas with high R2* values, leading to strongly underestimated PD values in high iron content nuclei. Extrapolation to TE=0 is effective at correcting for T2* bias (Fig.3e). Residual error in the PD estimate can be explained by the approximation5 made to estimate R1 and A and by the imperfect B1- bias correction achieved by the UNICORT procedure.

When SNR decreases (Fig.1b-e) and in the absence of appropriate correction19, the R2* map becomes increasingly biased due to the central chi-distribution of the noise (Fig.2b-e) impairing the effectiveness of the T2* correction factor in both methods (1) and (2). The TE=0 extrapolation method (3) also loses effectiveness and accuracy at lower SNR. These effects are shown in details in Figures 4&5.

Discussion and conclusion

Simulated FLASH multiparameter mapping datasets with increasing noise levels were analysed with the hMRI toolbox and various processing strategies for PD estimation. Without T2* bias correction and with calibration to PD=69% in the WM, PD values were overestimated in the cortex (T2*GM>T2*WM) and strongly underestimated in high iron content areas (globus pallidus, red nuclei, substantia nigra). Our results strongly suggest the necessity for T2* bias correction to increase the sensitivity and specificity of qMRI in these areas. All three methods taking T2*-weighting bias into account are effective. However, method(2) shows lower SNR since it relies on a single echo to estimate PD, while methods (1) (with T2* correction) and (3) perform similarly.

Acknowledgements

EB received funding from the European Structural and Investment Fund / European Regional Development Fund & the Belgian Walloon Government, project BIOMED-HUB (programme 2014-2020). SM received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 658589. NW and SM received funding from the BMBF (01EW1711A and B) in the framework of ERA-NET NEURON. The research leading to these results has also received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 616905. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the grant agreement No 681094, and is supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number 15.0137. MFC is supported by the MRC and Spinal Research Charity through the ERA-NET Neuron joint call (MR/R000050/1). The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome [203147/Z/16/Z].

References

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Figures

Figure 1 - Simulated PD-weighted images (TE=11.70ms) with increasing noise levels. (a) σG = 0%, (b) σG = 1.8%, (c) σG = 3.6%, (d) σG = 5.4%, (e) σG = 18%. The standard deviation of the added Gaussian noise σG is expressed in percent units (%) of the average signal measured in the white matter across all (PD-weighted and T1-weighted) simulated echoes.

Figure 2 - R2* ESTATICS estimation. R2* reference image used for simulations and R2* ESTATICS estimates derived from images with increasing noise levels: (a) σG = 0%, (b) σG = 1.8%, (c) σG = 3.6%, (d) σG = 5.4%, (e) σG = 18%. All maps are equally scaled between 0 and 70 s-1. As expected, the increasing noise level leads to increasingly underestimated R2* values (noise floor effect due to the central chi-distributed noise in the Sum-of-Square combined images)18.

Figure 3 - PD map estimation in the absence of noise. PD reference image (% water content) used for simulations (top right) and PD estimation error (200*(PDest-PDref)/(PDest+PDref) in p.u.) for each method (a-e). All methods taking the T2*-weighting bias into account (b,d,e) provide good and almost identical results. Residual error is mostly related to the B1- bias field imperfect correction (smooth variation across the volume). Errors outlined by anatomical details are likely related to the approximation of the Ernst equation used to estimate the quantitative maps5. Values (Y) within the globus pallidus (blue cross intersection) are reported under each sagittal view for comparison.

Figure 4 - PD map estimation in the presence of increasing noise levels. PD reference map, PD maps estimated with method (3) (top row) and corresponding PD error relative to the PD reference map (bottom row). Noise levels: (a) σG = 0%, (b) σG = 1.8%, (c) σG = 3.6%, (d) σG = 5.4%, (e) σG = 18%. The results for methods (1) & (2) with T2* correction were very close to method (3) (data not shown), except for the lower SNR observed for method (2) (calculation relying on a single echo).

Figure 5 - Standard deviation of the PD error (200*(PDest-PDref)/(PDest+PDref) in p.u.) in the WM for each method and increasing noise levels. Due to the calibration procedure, the average error in the WM is 0. With T2* correction, method (1) achieves better than method (2) due to the higher SNR of the input PD-weighted images (average over 6 echoes versus single echo). The T2* correction reduces the error in the PD estimate as long as the noise added by the R2* estimate is smaller than the variations due to T2* bias. TE=0 extrapolation (method (3)) performs similarly to method (1) with T2* correction.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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