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QUIQI – using a QUality Index for the analysis of Quantitative Imaging data
Giulia Di Domenicantonio1, Nadège Corbin2, John Ashburner2, Martina Callaghan2, and Antoine Lutti1
1Department for Clinical Neuroscience, Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland, 2Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, UCL, London, London, United Kingdom

Synopsis

Image degradation due to head motion is ubiquitous in MRI, reduces sensitivity, hinders clinical diagnosis and increases the risk of spurious findings. The few existing objective measures of degradation are often used sub-optimally, to remove the most degraded datasets from analysis. Using a large dataset (N~1400) we show how to incorporate an validated index of degradation into the analysis of group studies. The benefit is demonstrated for the case of healthy age-related difference in brain relaxometry data using the SPM software. However, the proposed framework is flexible with broad potential, including the analysis of other metrics and body regions.

Introduction

Head movement leads to degradation of MRI data that hampers clinical diagnosis and increases the risk of spurious findings1–3. Quantitative measures of motion degradation4–10 allow the exclusion of affected datasets from analysis3,5. However, the calculation of a threshold for exclusion pertains to the specifics of each study (e.g. demographics, data type, etc.), precluding generalisation. Also, even subtle head motions, reported in ~40-50% of study participants, have an observable impact on MRI-based brain measures3,11,12. A preferable solution would be a data analysis framework that assigns weights to each dataset, calculated from a measure of motion degradation to achieve optimal sensitivity to brain change. We introduce such a framework here, using the motion degradation index (MDI) described in10. In a standard General Linear Model (GLM) analysis, we show the relationship between this MDI and the residual errors after model fitting, which invalidates the assumption of uniform variance (‘homoscedasticity’) of standard GLM approaches. To address this, we use this relationship to compute weights for each dataset using the restricted maximum likelihood (ReML) algorithm of the SPM software, designed for the analysis of functional MRI data (pre-whitening and group-level analysis)13. This approach restores the validity of the homoscedasticity assumption. We compare the statistical efficiency of the proposed framework with a standard approach where the most degraded datasets are excluded from analysis.

Methods

MRI data was acquired on 1398 healthy participants recruited from the population of Lausanne, Switzerland (mean age: 56y.o; SD: 14y.o.; BrainLaus/PsyCoLaus study14, full protocol described in15,16). Here we consider the data acquired using a multi-echo FLASH readout with proton density-weighted contrast, used to compute maps of the effective transverse relaxation rate R2*. As an MDI, we used the standard deviation of the R2* maps in white matter10. This index has been validated against the history of head motion during data acquisition (figure 1) and allows the quantification of motion degradation even when the actual motion history is unknown. The R2* maps were spatially normalized to group space as in17,18. A study of healthy age-related differences in R2* was conducted in grey and white matter, using a 2nd-order polynomial model of age embedded in the GLM framework of SPM12. Additional regressors controlling for gender and total intracranial volume were also included in the analysis. The proposed framework was compared against an analysis that excluded datasets with an MDI value above 4.5s-1. This threshold accounts for the systematic increase in the MDI at 1mm3 resolution compared to 1.5mm3 10,20 and led to the exclusion of 17% of the cohort from analysis, in-line with previous studies3,5.

Results

In a standard analysis, significant age-associated differences in R2* were found in grey matter. These were particularly pronounced in sub-cortical areas due to age-related iron accumulation in these regions17,19 (see figure 2A). Figure 2B shows a map of the mean-square residuals (‘ResMS’), obtained from the fit of the ageing model to the R2* maps. Regions of highest residuals included sub-cortical and basal areas (i.e. cerebellum, brainstem). The variance of the residual maps, calculated across voxels for each dataset, closely follows a 2nd-order polynomial dependence on the MDI value (R2=0.71, see figure 2C; white matter: R2=0.82, data not shown). From figure 2C, the set of basis functions required by ReML to compute the noise covariance matrix V included an offset term, as well as linear and quadratic terms of MDI values in their diagonals (figure 3A). The hyper-parameters l estimated by ReML (figure 3B) closely matched the polynomial estimates of figure 2C. From the estimate of V, dataset-specific weights W were computed turning a standard (ordinary-least squares, OLS) analysis into a weighted-least square (WLS) analysis. This removed the dependence of the residual errors on the MDI (R2=0.01, see figure 3B; white matter: R2=0.16, data not shown). Figure 4 shows maps and histograms of F-scores of age-associated differences in R2* for the proposed WLS analysis (A) and from a standard OLS analysis after removal of the datasets with an MDI above 4.5s-1 (B). A significant age-associated change in R2* was found in 84% and 80% of grey-matter voxels respectively. The proposed WLS approach led to an average increase of 17% in F-scores compared to removal of the most degraded datasets.

Discussion

In a GLM analysis, motion degradation invalidates the fundamental assumption of uniform variance in standard ordinary-least squares approaches (‘homoscedasticity’). To address this issue, we propose a framework that incorporates measures of motion degradation into the analysis of MRI data. From these measures, weights are computed for each dataset to restore the validity of the homoscedasticity assumption. This framework circumvents the need to remove the datasets most affected by motion degradation and leads to optimal sensitivity to brain change. The framework was assessed by conducting a study of age-related brain changes using relaxometry data computed from one multi-echo dataset. However, it is broad and flexible: it can accommodate other metrics of motion degradation and is applicable to other brain metrics. In future work we will show its applicability to relaxometry data computed from multiple contrasts (e.g. T1 or MT maps21,22).

Acknowledgements

AL is supported by the Swiss National Science Foundation (project grant Nr. 320030_184784) and the ROGER DE SPOELBERCH foundation. 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

Validation of the Motion Degradation Index. The standard deviation of R2* in white matter follows a linear relationship with the history of head motion during data acquisition. In Castella et al.10, head motion was calculated in real-time, allowing the suspension of data acquisition to preserve image quality (green arrow). Here, we use this index to quantify motion degradation although the actual motion history is unknown (red arrow). Taken from Castella et al.10.

Standard analysis results. Statistical maps of the strength of R2* change with age (A). Residual mean-square errors, obtained from the fit of the ageing model to the R2* maps (B). The variance of the residual maps, calculated across voxels for each dataset, closely follows a 2nd-order polynomial dependence on the Motion Degradation Index (R2=0.71, C; the polynomial coefficients are shown in the bar plot).

Using the Motion Degradation Index (MDI) to model the noise covariance in the data. Following figure 2C, the estimation of the noise covariance V used a set of basis functions with an offset term, as well as linear and quadratic terms of MDI values in their diagonals (A). The hyper-parameters λ estimated by ReML closely matched the polynomial estimates of figure 2C (B). Using the weights computed from V in the analysis removed the dependence of the residual errors on the MDI (C).

Sensitivity to brain change. Statistical F-scores of age-associated differences obtained from the proposed WLS analysis (A) and by removing the datasets with the highest Motion Degradation Index (MDI) from the analysis (B). The left-hand plots depict the weights used in the analysis - computed from the MDI (A) or 1 for MDI<4.5 and 0 elsewhere (B). In the histograms, the dashed lines indicate the significance threshold (p<0.05 FWE; respectively 13.58 and 13.57 in A and B).

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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