  Demystifying effective connectivity among neuronal populations has become the
trend to understand the brain mechanisms of Parkinson's disease, schizophrenia,
mild traumatic brain injury, and many other unlisted neurological diseases.
Dynamic modeling is a state-of-the-art approach to explore various
connectivities among neuronal populations corresponding to different
electrophysiological responses. Through estimating the parameters in the
dynamic models, including the strengths and propagation delays of the
electrophysiological signals, the discovery of the underlying connectivities
can lead to the elucidation of functional brain mechanisms. In this report, we
survey six dynamic models that describe the intrinsic function of a single
neuronal/subneuronal population and three effective network estimation methods
that can trace the connections among the neuronal/subneuronal populations. The
six dynamic models are event related potential, local field potential,
conductance-based neural mass model, mean field model, neural field model, and
canonical micro-circuits; the three effective network estimation approaches are
dynamic causal modeling, structural causal model, and vector autoregression.
Subsequently, we discuss dynamic parameter estimation methods including
variational Bayesian, particle filtering, Metropolis-Hastings algorithm,
Gauss-Newton algorithm, collocation method, and constrained optimization. We
summarize the merits and drawbacks of each model, network estimation approach,
and parameter estimation method. In addition, we demonstrate an exemplary
effective network estimation problem statement. Last, we identify possible
future work and challenges to develop an elevated package.
