Hemodynamic Deconvolution Demystified: Sparsity-Driven Regularization at Work

Abstract

Deconvolution of the hemodynamic response is an important step to access short timescales of brain activity recorded by functional magnetic resonance imaging (fMRI). Albeit conventional deconvolution algorithms have been around for a long time (e.g., Wiener deconvolution), recent stateof-the-art methods based on sparsity-pursuing regularization are attracting increasing interest to investigate brain dynamics and connectivity. This technical note revisits the main concepts underlying two main methods, Paradigm Free Mapping and Total Activation, in the most accessible way. Despite their apparent differences, these methods are theoretically equivalent as they represent the synthesis and analysis sides of the same problem. We demonstrate this equivalence in practice with their best-available implementations using both simulations, with different signal-to-noise ratios, and experimental data of motor task and resting-state fMRI. We evaluate the parameter settings that lead to equivalent results, and showcase the potential of these algorithms compared to other widely-used approaches. This note is useful for practitioners interested in gaining a better understanding of state-of-the-art hemodynamic deconvolution, and who want to make use of them with the most efficient implementation.

Visualization of the Dynamic Brain Activation Pattern During a Decision Making Task

“…Some effects of the regularization constant for the closed form solution have been tested and described in the appendix section. Some of the earlier studies have shown SNR based regularized constant value selection techniques, mainly targeted for iterative L1 regularization [Uruñuela et al, 2021].…”

“…Moreover, deconvolution models have also been used to identify underlying neural events from the observed BOLD time series [23,24,25]. Commonly, hemodynamic deconvolution models use lasso regularization (L1 regularization) which results in temporally sparse neuronal activity [26,27,28]. One of the main goals was to obtain a obtain a continuous visualization of the decision-making process while the output of L1 regularization was sparse.…”

Whole-brain multivariate hemodynamic deconvolution for multi-echo fMRI with stability selection

“…In any case, extending the proposed stability selection technique to other formulations of the hemodynamic deconvolution problem, such as the voxel-wise (i.e., univariate) single-echo (Gaudes et al, 2013; Uruñuela et al, 2020), univariate multi-echo (Caballero-Gaudes et al, 2019), or low-rank and sparse formulations (Uruñuela et al, 2021b; Cherkaoui et al, 2021), is relatively straightforward. Moreover, considering that synthesis-based models, such as Paradigm Free Mapping (Gaudes et al, 2013), and analysis-based models, such as Total Activation (Karahanoğlu et al, 2013), for temporal hemodynamic deconvolution yield identical results (Uruñuela et al, 2021a), and the fact that a multi-echo formulation provides higher accuracy for deconvolution (Caballero-Gaudes et al, 2019), we argue that the proposed MvME-SPFM method with stability selection should result in more reliable estimates of the activity-inducing signal.…”

“…Moreover, the multivariate formulation could exploit complimentary multimodal information such as structural connectvity from diffusion-based MRI data (Bolton et al, 2019b). In addition, the proposed formulation can be easily adapted to model the changes in neuronal activty in terms of its innovations, which can be more appropiate to capture sustained BOLD events (Uruñuela et al, 2021a).…”

Deconvolution of the Functional Ultrasound Response in the Mouse Visual Pathway Using Block-Term Decomposition

“…This issue has been addressed by (Karahanoglu et al, 2013;Karahanolu and Van De Ville, 2015;Uruuela et al, 2021), where the authors have defined the term activity-inducing signal, which, as the name suggests, comprises any input signal that induces hemodynamic activity. We will refer to activity-inducing signals as source signals in the rest of this paper, which steers the reader to broader terminology not only used in biomedical signal processing, but also in acoustics and telecommunications (Naik and Wang, 2014), and emphasizes that recorded output data are sourced by such signals.…”