Robust resting state fMRI processing for studies on typical brain development based on multi-echo EPI acquisition

Abstract

Several methodological challenges affect the study of typical brain development based on resting state blood oxygenation level dependent (BOLD) functional MRI (fMRI). One such challenge is mitigating artifacts such as those from head motion, known to be more substantial in younger subjects than older subjects. Other challenges include controlling for potential age-dependence in cerebrospinal fluid (CSF) volume affecting anatomical-functional coregistration; in vascular density affecting BOLD contrast-to-noise; and in CSF pulsation creating time series artifacts. Historically, these confounds have been approached through incorporating artifact-specific temporal and/or spatial filtering into preprocessing pipelines. However, such paths often come with new confounds or limitations. In this study we take the approach of a bottom-up revision of fMRI methodology based on acquisition of multi-echo fMRI and comprehensive utilization of the information in the TE-domain to enhance several aspects of fMRI analysis in the context of a developmental study. We show in a cohort of 25 healthy subjects, aged 9 to 43 years, that the analysis of multi-echo fMRI data eliminates a number of arbitrary processing steps such as bandpass filtering and spatial smoothing, while enabling procedures such as $T_{2}^{*}$ mapping, BOLD contrast normalization and signal dropout recovery, precise anatomical-functional coregistration based on $T_{2}^{*}$ measurements, automatic denoising through removing subject motion, scanner-related signal drifts and physiology, as well as statistical inference for seed-based connectivity. These enhancements are of both theoretical significance and practical benefit in the study of typical brain development.

Appendix

A.1 Multi-echo independent components analysis and denoising

The central step of the ME-ICA procedure was decomposition of optimally combined ME data into approximately spatially independent components, then denoising by removing remove non-BOLD components. This procedure is summarized here in 4 steps based on (Kundu et al. 2013):

• 1. For dimensionality estimation and reduction, multi-echo principal components analysis (ME-PCA) was applied to the optimally combined dataset. This first involved principal components analysis (PCA) of the optimally combined time series dataset. Time series were masked, mean-centered and variance normalized, creating a voxel × time data matrix. PCA was then implemented as singular value decomposition (SVD, Eq. 4) with partial matrices

  $$ X=USV $$

  (4)

  where X is the variance-normalized data, U and V are left and right singular vectors, and S is the vector of singular values. The amplitude of each principal component at each voxel for each TE was computed by multiple least squares fit of the PCA time courses (V, the right singular matrix) to the preprocessed signal-unit time series of each TE.

• 2. Component-level TE-dependence analysis was applied to PCA components in order to detect data dimensionality, as the second step of the ME-PCA procedure. For each component at each voxel, the principal component signal amplitudes at different TEs were fit to linear TE-dependence and TE-independence models, and corresponding F-statistics for goodness of fit were computed. The TE-dependence and TE-independence models are Eqs. 5a and b

  $$ {\Delta} S_{TE} / S_{TE} = {\Delta} S_{0} /S_{0} $$

  (5a)
  $$ {\Delta} S_{TE} / S_{TE} = - {\Delta} R_{2}^{*}TE $$

  (5b)

  where ΔS _{T E} is signal change from mean for a fluctuation at a TE (i.e. its β weight from least squares fit), and S _{T E} is the signal mean at a TE, ${\Delta } R_{2}^{*}$ is change in susceptibility-weighted transverse relaxation time that is solved for in the TE-dependence BOLD model, S ₀ is initial signal intensity (i.e at TE=0), and ΔS ₀ is the change in initial signal intensity that is solved for in the TE-independence non-BOLD model. The respective F-statistics are then determined (6a and b):

  $$ F_{R_{2}^{*}}=\frac{\frac{\alpha_{0}-\alpha_{R_{2}^{*}}}{\alpha_{R_{2}^{*}}}}{\frac{\text{d.f.}_{0}-\text{d.f.}_{R_{2}^{*}}}{\text{d.f.}_{R_{2}^{*}}}} $$

  (6a)
  $$ F_{S_{0}}=\frac{\frac{\alpha_{0}-\alpha_{S_{0}}}{\alpha_{S_{0}}}}{\frac{\text{d.f.}_{0}-\text{d.f.}_{S_{0}}}{\text{d.f.}_{S_{0}}}} $$

  (6b)

  where α ₀ is the null variance ($\sum {\beta ^{2}_{c,v,TE}}$), $\alpha _{R_{2}^{*}}$ is the variance explained by the fit to the TE-dependence model, $\alpha _{S_{0}}$ is the variance explained by the fit to the TE-independence model, d.f.₀ is total number of degrees of freedom for TE-dependence models (equal to number of echoes, 3), and $\text {d.f.}_{R_{2}^{*}}$ and $\text {d.f.}_{S_{0}}$ are the degrees of freedom used in the respective fits (1 each). The statistics κ and ρ were computed to indicate overall component-level weighting of TE-dependence and TE-independence, as an intensity-weighted average of the respective F values for each component:

  $$ \kappa_{c} = \frac{{\sum\limits_{v}^{V}}{z_{c,v}^{p} F_{c,v,R_{2}^{*}}}}{\sum{z_{c,v}^{p} }} $$

  (7a)
  $$ \rho_{c} = \frac{{\sum\limits_{v}^{V}}{z_{c,v}^{p} F_{c,v,S_{0}}}}{\sum{z_{c,v}^{p} }} $$

  (7b)

  where c is component index, v is voxel index, V is the total number of voxels, z is normalized signal power,p is a power factor (default 2). Dimensionality reduction was based on thresholds for κ, ρ, and eigenvalue as determined after sorting respective values from the inflection points of the respective Scree plots (i.e. using an elbow-finding routine). Optimally combined time series were dimensionally reduced to the principal components with above-threshold κ, or ρ, or eigenvalue (i.e. isolating any correlated signal associated with MR contrast), followed by re-centering and re-normalizing the time series, then the full data matrix.

• 3. FastICA of dimensionally reduced data using the tanh contrast function produced a time-domain independent component mixing matrix (variance normalized). The mixing matrix was fit using multiple least squares to the separate TE time series data, in order to compute per-voxel TE-dependence and TE-independence model fits for ICA components, in addition to respective F-statistics and component-level κ and ρ values that indicated BOLD and non-BOLD weighting, respectively. This involved application of Eqs. 5–7 for ICA component β weights.

• 4. After computation of component-level TE-dependence and independence statistics, components were classified into BOLD and non-BOLD categories. TE-dependence and TE-independence are robust assessments of the physical mechanism of signal generation, such that artifactual components could be definitively identified in having any one of the following signatures, which indicate that artifactual ρ or $F_{S_{0}}$ weighting is more substantial than the κ or $F_{R_{2}^{*}}$ weightings :

  (a) ρ > κ

  (b) number of significant (F > F(n _e ,1) _{p < 0.05}) S ₀-weighted voxels greater than the number of significant $R_{2}^{*}$-weighted voxels

  (c) greater overlap of p<0.05 thresholded $F_{S_{0}}$ maps and rank-thresholded signal change maps than of thresholded $F_{R_{2}^{*}}$ maps

  (d) greater $F_{R_{2}^{*}}$ in component spatial noise versus clustered voxels, based on a two-sample T-test ($T_{R_{2}^{*}\text {-clustering}}$) after F−Z transformation.

  (e) After ranking above metrics (κ, ρ, Dice for $F_{R_{2}^{*}}$ and $F_{S_{0}}$ maps, $T_{R_{2}^{*}\text {-clustering}}$, and significant $F_{R_{2}^{*}}$ and $F_{S_{0}}$ voxel counts) in ascending order towards greater artifact weighting or lesser BOLD weighting, a rank-sum test was used to identify and reject components that approached several of the above rejection criteria. Data were denoised by projecting the spatial ICA components that were classified as non-BOLD out of the data. This produced separated volumetric time series datasets for “isolated” non-BOLD fluctuations on the one hand, and BOLD denoised time series on the other.

A.2 ME-ICR seed-based functional connectivity analysis

For individual datasets, ME-ICR seed-based functional connectivity maps were computed for a given subject-dataset using the BOLD component basis extracted from ME-ICA decomposition and component selection. After selecting a seed voxel a, the vector of BOLD independent coefficients from that voxel was extracted and used to compute Pearson correlation with BOLD independent coefficient vectors from every other voxel, each represented as b. This produced a map of correlation values based on the computation:

$$ R_{a,b} = \frac{I_{a}}{|I_{a}|} \cdot \frac{I_{b}}{|I_{b}|} $$

(8)

where R _a,b is the Pearson correlation of coefficient vectors I _a and I _b . Next, each correlation value was converted to a standard score (Z) using the canonical Fisher R − Z transform, using the standard error term for normalization:

$$ Z_{a,b} = \text{arctanh}(R_{a,b}) \cdot \sqrt{N_{c} - 3} $$

(9)

The DOF for standard error was the number of BOLD independent components (N _c ). The significance (p) value for this standard score (Z) was computed from the standard normal cumulative distribution function, and statistically significant Z-values were anatomically mapped.

A.3 Reference $T_{2}^{*}$ values

Table 1 shows $T_{2}^{*}$ values for tissue types as computed from means of multi-echo EPI time courses of a 31.5 year old subject. These values satisfy Eq. 3 towards the creation of a $T_{2}^{*}$-based weight map for anatomical-functional coregistration. Note for gray and white matter compartments, the expected trend (${T_{2}^{*}}_{\text {gray}} > {T_{2}^{*}}_{\text {white}}$ ) is reversed and variance of gray matter $T_{2}^{*}$ is increased, in part due to inclusion of orbitofrontal “dropout” area in calculation. The 75 ^th percentile $T_{2}^{*}$ values reflect the expected trend.

Table 1 Reference $T_{2}^{*}$ values (ms) for representative healthy adult of age 31.5y