Functional magnetic resonance imaging data analysis is often directed to identify and disentangle the neural processes that occur in different brain regions during task or at rest, and employs the blood oxygen level dependent (BOLD) signal of fMRI as a proxy for neuronal activity mediated through neurovascular coupling. The goal of this thesis is to enhance and expand techniques for identifying and analyzing individual trial event-related BOLD responses based on the Paradigm Free Mapping (PFM) algorithm, which utilizes a linear hemodynamic response model and relies on regularized least squares estimators to deconvolve the neuronal-related signal that drives the BOLD effect. Notably, these techniques estimate neuronal-related activity without relying on prior paradigm information.
First of all, this work aims to establish the equivalence between the synthesis-based PFM and analysis-based Total Activation (TA) algorithms. Then, the thesis addresses the challenge of selecting the regularization parameter. This was accomplished by employing the stability selection procedure, which provides a measure of the likelihood that the estimated neuronal-related events are accurate. Building upon this, the next goal of this work is to extend the original univariate PFM formulation to a multivariate context, enabling the incorporation of spatial information through regularization terms such as the mixed-norm regularization. Expanding further, the third objective of this thesis is to extend the multivariate PFM formulation to a multi-subject framework, facilitating the estimation of shared and individualized neuronal-related activity across subjects. This approach proved particularly suitable for naturalistic fMRI experiments. Lastly, the fourth and last goal of this work is to introduce an additional regularization term, the nuclear norm, into the multivariate PFM formulation. This term was employed to estimate global fluctuations during the deconvolution process and mitigate their impact on the estimation of neuronal-related activity, thereby reducing bias.
The techniques presented in this thesis were thoroughly evaluated using simulations and experimental fMRI datasets. Comparisons were made with established fMRI analysis methods, including the single-trial general linear model, previous PFM algorithms, and other state-of-the-art techniques. Notably, the developed methods demonstrated the ability to accurately detect single trial BOLD responses in resting-state and naturalistic fMRI data, without relying on prior event information. Additionally, the potential application of multi-subject PFM in identifying both shared and individualized neuronal-related activity in more ecological datasets was explored, yielding promising results. Moreover, the utilization of low-rank and sparse PFM facilitated the extraction of global fluctuations, such as the global signal, physiological fluctuations, and motion artifacts, thereby reducing their influence on the analysis. In summary, this work demonstrates that PFM techniques can be used to reliably retrieve the neuronal-related activity from fMRI data without any prior information about the experimental paradigm, and that there now exists a formulation of PFM that is suitable for potentially any experimental setting and research question.