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 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.

使用静息状态功能磁共振成像准确映射远程大脑区域之间的功能相互作用需要量化它们的潜在动力学。在传统的方法学管道中，首先选择感兴趣的空间尺度，然后在这个假设的复杂性水平上进行动态分析。如果研究大规模的功能网络或状态，则不会描述更多的局部区域重排，可能会丢失重要的神经生物学信息。在这里，我们提出了一个新的数学框架，该框架联合估计静息状态功能网络和空间上更局部的跨区域调制。为此，每个大脑区域的活动变化通过逻辑回归建模，包括共激活系数（反映网络分配，t调制另一个区域的t到t  + 1 过渡可能性）。两参数正则化方案用于使这两组系数稀疏：一组控制整体稀疏性，而另一组控制共激活和因果相互作用之间的权衡，尽管这两种耦合类型之间的平衡尚不清楚，但仍能正确拟合数据. 在一系列模拟设置中，我们表明该框架一次成功地检索了两种类型的跨区域交互。噪声和样本大小设置的性能在全球范围内与其他现有方法相当，有可能揭示替代方法遗漏的更精确信息。对实验数据的初步应用表明，在静止的大脑中，共激活和因果调制以不同区域的不同平衡共存。