Efficient estimation of time-dependent functional connectivity using Structural Connectivity constraints
Multivariate autoregressive models [MAR] allows estimating effective brain connectivity by considering both power and phase fluctuations of the signals involved. A MAR models brain activity in one region as a linear combination of past activations in all other regions. A Hidden Markov model, HMM, whose states emisions are drawn from state-specific MARs, can then be used to model fast switching of effective brain connectivity over time. However, the large number of MAR parameters, impede the accurate and efficient estimation of such models from neuroimaging timeseries with limited length. We propose a new model for inferring time-dependent effective brain connectivity by using a sparse MAR parameterisation to model the states emisions of a Hidden Semi-Markov Model, HsMM-MAR-AC. The sparse MAR model parameters are restricted by Anatomical Connectivity information in two ways: direct effective connectivity between two regions is only considered if the corresponding structural link/connection exists; and the time-lag associated with each direct connection is computed based on the average fibre length between the two regions, such that only one lag per connection is estimated. We simulated ground truth time-dependent brain connectivity states by generating time-series of 4 to 10 minutes sampled at 5ms, from switching Resting State Networks with a reference structural connectivity, and evaluated the accuracy of the new model in recovering the simulated Brain connectivity States against different levels of connectivity thresholding above and below the reference. We show that even when restricting the MAR to half of the reference connections, the model was able to recover the number of brain states, the associated connectivity features and their dynamics, with as little data as 4 mins. More relaxed structural connectivity thresholds required longer data to estimate the model accurately, and became computationally unfeasible without anatomical restrictions. HsMM-MAR-AC offers an efficient algorithm for estimating time-depend Effective Connectivity (tdEC) from neuroimaging data, that exploits the advantages of MAR without identifiability problems, excessive demand on data collection, or unnecessary computational complexity.