Sparse coupled logistic regression to estimate co-activation and modulatory influences of brain regions

Accurate mapping of the functional interactions between remote brain areas with resting-state functional magnetic resonance imaging requires the quantification of their underlying dynamics. In conventional methodological pipelines, a spatial scale of interest is first selected and dynamic analysis then proceeds at this hypothesised level of complexity. If large-scale functional networks or states are studied, more local regional rearrangements are then not described, potentially missing important neurobiological information. Here, we propose a novel mathematical framework that jointly estimates resting-state functional networks and spatially more localised cross-regional modulations. To do so, the changes in activity of each brain region are modelled by a logistic regression including co-activation coefficients (reflective of network assignment, as they highlight simultaneous activations across areas) and causal interplays (denoting finer regional cross-talks, when one region active at time t modulates the t to t + 1 transition likelihood of another area). A two-parameter ℓ1 regularisation scheme is used to make these two sets of coefficients sparse: one controls overall sparsity, while the other governs the trade-off between co-activations and causal interplays, enabling to properly fit the data despite the yet unknown balance between both types of couplings. Across a range of simulation settings, we show that the framework successfully retrieves the two types of cross-regional interactions at once. Performance across noise and sample size settings was globally on par with that of other existing methods, with the potential to reveal more precise information missed by alternative approaches. Preliminary application to experimental data revealed that in the resting brain, co-activations and causal modulations co-exist with a varying balance across regions. Our methodological pipeline offers a conceptually elegant alternative for the assessment of functional brain dynamics and can be downloaded at https://c4science.ch/source/Sparse_logistic_regression.git.