How to Probe Dynamics of Brain Function: A Narrative Review

The brain is the quintessential complex dynamic system. Static analytic approaches, such as time-averaged connectivity or correlations, remain widely used but cannot characterize dynamic processes that are central to brain function and dysfunction. Fluctuations in state are central to psychiatric illness, so constraining analysis to time-averaged, static techniques fundamentally limits insight. Dynamic modeling approaches address this gap by quantifying temporal complexity, identifying causal influences, compressing activity into latent trajectories in abstract representational spaces, and simulating whether hypothesized principles can reproduce observed data. Early methods such as sliding-window correlations and temporal independent component analysis have progressed to more advanced frameworks such as dynamic causal modeling, recurrent neural networks, and neural differential equations. This review organizes current dynamic analytic approaches with respect to 4 broad research goals: 1) describing patterns of brain activity over time, 2) inferring causal mechanisms, 3) decoding latent dynamics, and 4) simulating complex neural processes. For each of these broad goals, we highlight representative methods, their assumptions, clinical applications, and limitations. In each case, we provide links to available open access tools. Together, these approaches provide a framework for testing theories of brain function directly in clinical populations. By aligning analytic tools with systems-level theories, dynamic modeling approaches represent more than technical progress; they reflect a conceptual shift from static, data-driven descriptions to theory-informed tests of brain processes as they unfold over time.