Large-scale dynamic modeling of task-fMRI signals via subspace system identification

Abstract

Objective. We analyze task-based fMRI time series to produce large-scale dynamical models that are capable of approximating the observed signal with good accuracy. Approach. We extend subspace system identification methods for deterministic and stochastic state-space models with external inputs. The dynamic behavior of the generated models is characterized using control-theoretic analysis tools. To validate their effectiveness, we perform a probabilistic inversion of the identified input–output relationships via joint state-input maximum likelihood estimation. Our experimental setup explores a large dataset generated using state-of-the-art acquisition and pre-processing methods from the Human Connectome Project. Main results. We analyze both anatomically parcellated and spatially dense time series, and propose an efficient algorithm to address the high-dimensional optimization problem resulting from the latter. Our results enable the quantification of input–output transfer functions between each task condition and each region of the cortex, as exemplified by a motor task. Further, the identified models produce impulse response functions between task conditions and cortical regions that are compatible with typical hemodynamic response functions. We then extend subspace methods to account for multi-subject experimental configurations, identifying models that capture common dynamical characteristics across subjects. Finally, we show that system inversion via maximum-likelihood allows the time-of-occurrence of the task stimuli to be estimated from the observed outputs. Significance. The ability to produce dynamical input–output models might have an impact in the expanding field of neurofeedback. In particular, the models we produce allow the partial quantification of the effect of external task-related inputs on the metabolic response of the brain, conditioned on its current state. Such a notion provides a basis for leveraging control-theoretic approaches to neuromodulation and self-regulation in therapeutic applications.