Synopsis

This work introduces an extension of sparse paradigm free mapping (SPFM) for multiecho (ME) fMRI: ME-SPFM. Based on the ME-fMRI signal model and L1-norm regularized estimators, ME-SPFM produces voxel-wise estimates of time-varying changes in the transverse relaxation ($$$R_2^*$$$) and the net magnetization ($$$S_0$$$) without prior information about experimental paradigms. Our evaluations demonstrate that ME-SPFM significantly outperforms its SE counterpart in terms of sensitivity and specificity, nearly matching that of traditional model-based analyses. ME-SPFM’s ability to blindly detect individual events at the single-subject level makes it an ideal candidate to explore the time-varying nature of brain activity in experimentally unconstrained paradigms (naturalistic, resting-state) or clinical applications (detection of inter-ictal epileptic events).

Introduction

Multi-echo (ME) fMRI result in $$$K$$$ time-series per voxel; each acquired at different TEs. Optimal combination of echoes (OC^[1,2]) or automatic ME-based denoising (MEICA^[3]) improves the sensitivity of BOLD-fMRI for GLM-based analyses that require information about the timing of experimental events^[4]. An alternative analytic approach is “blind event-detection” methods, which try detecting BOLD-events based solely on a hemodynamic response model (e.g., gamma variate function) and do not need event-timing information. These methods output event-wise spatial maps which can be used to decode their cognitive nature^[5].

One such “blind event-detection” method is Sparse Free Paradigm Mapping (SPFM)^[6]. SPFM successfully detects events, yet it lacks the sensitivity of GLM. To address this, we propose an ME-based SPFM formulation that exploits the linear dependence of neuronally-driven BOLD events with TE^[3]. Using a multi-task, event-related dataset we demonstrate how ME-SPFM can reliably detect individual events—namely single-trials at the subject level—with significantly better specificity and sensitivity than its single-echo (SE) counterpart; and nearly matching traditional GLM results. This suggests that ME-SPFM can help confidently decipher the dynamic nature of brain activity in naturalistic paradigms, resting-state or clinical applications with unknown event-timing.

Methods

DATA: 9 healthy adults. Anatomicals were preceded by one (3 subjects) or two ME functional scans (3T, EPI, FA=70°, $$$TE$$$=16.3/32.2/48.1ms, TR=2s, Res=3x3x4mm, $$$N$$$=220 volumes, #Slices=30, ASSET=2). Each run had 30 trials of each of 6 different tasks (4s each; Figure 1.A).

PREPROCESSING: Three different pre-processing pipelines were used. They are depicted in Figures 1.B-C.

GLM: For each subject and task, two activation maps were computed with AFNI 3dREMLfit: 1) modeling all trials together (TASK-BASED), or 2) modeling trials individually (TRIAL-BASED). Maps obtained with both models were used as gold standard for computation of sensitivity, specificity and dice coefficients ($$$q=p_{FDR}\leq$$$0.05 for TASK-BASED, and $$$p_{UNC}\leq$$$0.05 for TRIAL-BASED).

SE-SPFM: SPFM performs the deconvolution of voxel times series ($$$\mathbf{y}\in\mathbb{R}^{N}$$$) based on a linear haemodynamic model ($$$\mathbf{H}\in \mathbb{R}^{N \times N}$$$) using a regularized L1-norm estimator so that the neuronal-related time-series generating the BOLD response ($$$\mathbf{s}\in\mathbb{R}^N$$$) is estimated by solving $$$\mathbf{\widehat{s}}=\min_{\mathbf{s}}\|\mathbf{y}-\mathbf{H}\mathbf{s}\|_2^2 + \lambda \|\mathbf{s}\|_1$$$ ^[6]. SPFM was applied on the E02, OC and MEICA pipelines (AFNI 3dPFM).

ME-SPFM: Voxel-wise SPC time-series acquired at $$$TE_k$$$ are defined as $$$\mathbf{y}_k = \frac{\bf{\Delta S}_0}{S_0} - TE_k \bf{\Delta R}_2^*$$$ ^[7]. As in SE-SPFM, a haemodynamic model for the neuronal-related $$$\bf{\Delta R}_2^*$$$ time-series can be defined as $$$\bf{\Delta R}_2^* = \mathbf{H}\mathbf{s}$$$. With $$$N_e$$$, it can be shown that $$\underbrace{\left[ \begin{array}{c} \mathbf{y}_1 \\ \vdots \\ \mathbf{y}_K \end{array} \right]}_{\widetilde{\mathbf{y}}} = \underbrace{\left[ \begin{array}{c} \mathbf{I} \\ \vdots \\ \mathbf{I} \\ \end{array}\right]}_{\widetilde{\mathbf{I}}} \bf{\Delta}\bf{\rho} - \underbrace{ \left[ \begin{array}{c} TE_1 \mathbf{H} \\ \vdots \\ TE_K \mathbf{H}\\ \end{array}\right]}_{\widetilde{\mathbf{H}}} \bf{\Delta s}.$$ The ME-SPFM method estimates $$$\mathbf{s}$$$ and $$$\bf{\Delta\rho}=\frac{\bf{\Delta S}_0}{S_0}$$$ by solving $$$\mathbf{\widehat{x}}=\min_{\mathbf{x}}\|\mathbf{\widetilde{y}}-\mathbf{T}\mathbf{x}\|_2^2 + \lambda \|\mathbf{x}\|_1$$$, where $$$\mathbf{x}^T=\left[\bf{\Delta}\bf{\rho}^T,\bf{\Delta s}^T\right]$$$ and $$$\mathbf{T}=\left[\widetilde{\mathbf{I}} \ \widetilde{\mathbf{H}}\right]$$$.

For both SE-SPFM and ME-SPFM, we used the SPM canonical HRF to generate the convolution matrices $$$\mathbf{H}$$$, and the Bayesian Information Criterion (BIC) to select the regularization parameter $$$\lambda$$$. Furthermore, their activation maps were computed for each trial considering the volumes of the deconvolved coefficients ($$$\mathbf{\widehat{s}}$$$) when each trial occurs (i.e. 3 TRs).

Results

Figure 2.A depicts inputs to the three methods. Both SPFM variants lack a design matrix with event timing information. SE-SPFM uses a single time series per voxel (either middle echo, OC or MEICA); ME-SPFM uses all three echoes.

Figure 2.B shows representative activation maps for individual events in one subject. The $$$\Delta R_2^*$$$ maps from ME-SPFM more clearly resemble those from the event-based GLM approach. While SE-SPFM maps normally include the same locations as the GLM maps (i.e. high spatial specificity), they exhibit reduced sensitivity.

Figure 3 illustrate fits for GLM and ME-SPFM results in five representative voxels from one dataset located in areas relevant to each task. ME-SPFM reliably detected (deflection of blue trace) all experimental events (dark-grey bands). The figure also shows how ME-SPFM detects additional BOLD events that take place as scanning progresses (black arrows) but that could not be revealed by any conventional GLM approach.

Figures 4 and 5 plot the sensitivity, specificity and dice coefficient values for the different methods using as gold standard for comparison both the task-specific (Figure 4) and trial-specific (Figure 5) GLM maps. In both instances, the ME version of the SPFM algorithm significantly outperforms its SE counterpart.

Conslusions

Acknowledgements

References

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