A model selection method for nonlinear system identification based FMRI effective connectivity analysis

Identifying Brain Network Structure for an fMRI Effective Connectivity Study Using the Least Absolute Shrinkage and Selection Operator (LASSO) Method

Background: Studying causality relationships between different brain regions using the fMRI method has attracted great attention. To investigate causality relationships between different brain regions, we need to identify both the brain network structure and the influence magnitude. Most current methods concentrate on magnitude estimation, but not on identifying the connection or structure of the network. To address this problem, we proposed a nonlinear system identification method, in which a polynomial kernel was adopted to approximate the relation between the system inputs and outputs. However, this method has an overfitting problem for modelling the input-output relation if we apply the method to model the brain network directly. Methods: To overcome this limitation, this study applied the least absolute shrinkage and selection operator (LASSO) model selection method to identify both brain region networks and the connection strength (system coefficients). From these coefficients, the causality influence is derived from the identified structure. The method was verified based on the human visual cortex with phase-encoded designs. The functional data were pre-processed with motion correction. The visual cortex brain regions were defined based on a retinotopic mapping method. An eight-connection visual system network was adopted to validate the method. The proposed method was able to identify both the connected visual networks and associated coefficients from the LASSO model selection. Results: The result showed that this method can be applied to identify both network structures and associated causalities between different brain regions. Conclusions: System identification with LASSO model selection algorithm is a powerful approach for fMRI effective connectivity study.

A new transfer entropy method for measuring directed connectivity from complex-valued fMRI data

BACKGROUND

Inferring directional connectivity of brain regions from functional magnetic resonance imaging (fMRI) data has been shown to provide additional insights into predicting mental disorders such as schizophrenia. However, existing research has focused on the magnitude data from complex-valued fMRI data without considering the informative phase data, thus ignoring potentially important information.

METHODS

We propose a new complex-valued transfer entropy (CTE) method to measure causal links among brain regions in complex-valued fMRI data. We use the transfer entropy to model a general non-linear magnitude-magnitude and phase-phase directed connectivity and utilize partial transfer entropy to measure the complementary phase and magnitude effects on magnitude-phase and phase-magnitude causality. We also define the significance of the causality based on a statistical test and the shuffling strategy of the two complex-valued signals.

RESULTS

Simulated results verified higher accuracy of CTE than four causal analysis methods, including a simplified complex-valued approach and three real-valued approaches. Using experimental fMRI data from schizophrenia and controls, CTE yields results consistent with previous findings but with more significant group differences. The proposed method detects new directed connectivity related to the right frontal parietal regions and achieves 10.2-20.9% higher SVM classification accuracy when inferring directed connectivity using anatomical automatic labeling (AAL) regions as features.

CONCLUSION

The proposed CTE provides a new general method for fully detecting highly predictive directed connectivity from complex-valued fMRI data, with magnitude-only fMRI data as a specific case.

Macroscopic resting-state brain dynamics are best described by linear models

It is typically assumed that large networks of neurons exhibit a large repertoire of nonlinear behaviours. Here we challenge this assumption by leveraging mathematical models derived from measurements of local field potentials via intracranial electroencephalography and of whole-brain blood-oxygen-level-dependent brain activity via functional magnetic resonance imaging. We used state-of-the-art linear and nonlinear families of models to describe spontaneous resting-state activity of 700 participants in the Human Connectome Project and 122 participants in the Restoring Active Memory project. We found that linear autoregressive models provide the best fit across both data types and three performance metrics: predictive power, computational complexity and the extent of the residual dynamics unexplained by the model. To explain this observation, we show that microscopic nonlinear dynamics can be counteracted or masked by four factors associated with macroscopic dynamics: averaging over space and over time, which are inherent to aggregated macroscopic brain activity, and observation noise and limited data samples, which stem from technological limitations. We therefore argue that easier-to-interpret linear models can faithfully describe macroscopic brain dynamics during resting-state conditions.

Nonlinear estimation of BOLD signals with the aid of cerebral blood volume imaging

BACKGROUND

The hemodynamic balloon model describes the change in coupling from underlying neural activity to observed blood oxygen level dependent (BOLD) response. It plays an increasing important role in brain research using magnetic resonance imaging (MRI) techniques. However, changes in the BOLD signal are sensitive to the resting blood volume fraction (i.e., [Formula: see text]) associated with the regional vasculature. In previous studies the value was arbitrarily set to a physiologically plausible value to circumvent the ill-posedness of the inverse problem. These approaches fail to explore actual [Formula: see text] value and could yield inaccurate model estimation.

METHODS

The present study represents the first empiric attempt to derive the actual [Formula: see text] from data obtained using cerebral blood volume imaging, with the aim of augmenting the existing estimation schemes. Bimanual finger tapping experiments were performed to determine how [Formula: see text] influences the model estimation of BOLD signals within a single-region and multiple-regions (i.e., dynamic causal modeling). In order to show the significance of applying the true [Formula: see text], we have presented the different results obtained when using the real [Formula: see text] and assumed [Formula: see text] in terms of single-region model estimation and dynamic causal modeling.

RESULTS

The results show that [Formula: see text] significantly influences the estimation results within a single-region and multiple-regions. Using the actual [Formula: see text] might yield more realistic and physiologically meaningful model estimation results.

CONCLUSION

Incorporating regional venous information in the analysis of the hemodynamic model can provide more reliable and accurate parameter estimations and model predictions, and improve the inference about brain connectivity based on fMRI data.

Sparse multivariate autoregressive modeling for mild cognitive impairment classification

Brain connectivity network derived from functional magnetic resonance imaging (fMRI) is becoming increasingly prevalent in the researches related to cognitive and perceptual processes. The capability to detect causal or effective connectivity is highly desirable for understanding the cooperative nature of brain network, particularly when the ultimate goal is to obtain good performance of control-patient classification with biological meaningful interpretations. Understanding directed functional interactions between brain regions via brain connectivity network is a challenging task. Since many genetic and biomedical networks are intrinsically sparse, incorporating sparsity property into connectivity modeling can make the derived models more biologically plausible. Accordingly, we propose an effective connectivity modeling of resting-state fMRI data based on the multivariate autoregressive (MAR) modeling technique, which is widely used to characterize temporal information of dynamic systems. This MAR modeling technique allows for the identification of effective connectivity using the Granger causality concept and reducing the spurious causality connectivity in assessment of directed functional interaction from fMRI data. A forward orthogonal least squares (OLS) regression algorithm is further used to construct a sparse MAR model. By applying the proposed modeling to mild cognitive impairment (MCI) classification, we identify several most discriminative regions, including middle cingulate gyrus, posterior cingulate gyrus, lingual gyrus and caudate regions, in line with results reported in previous findings. A relatively high classification accuracy of 91.89 % is also achieved, with an increment of 5.4 % compared to the fully-connected, non-directional Pearson-correlation-based functional connectivity approach.

Modulation of effective connectivity in the default mode network at rest and during a memory task

It is known that the default mode network (DMN) may be modulated by a cognitive task and by performance level. Changes in the DMN have been examined by investigating resting-state activation levels, but there have been very few studies examining the modulation of effective connectivity of the DMN during a task in healthy older subjects. In this study, the authors examined how effective connectivity changed in the DMN between rest and during a memory task. The authors also investigated whether there was any relationship between effective connectivity modulation in the DMN and memory performance, to establish whether variations in cognitive performance are related to neural network effective connectivity, either at rest or during task performance. Twenty-eight healthy older participants underwent a resting-state functional magnetic resonance imaging scan and an emotional face-name encoding task. Effective connectivity analyses were performed on the DMN to examine the effective connectivity modulation in these two different conditions. During the resting state, there was strong self-influence in the regions of the DMN, while the main regions with statistically significant cross-regional effective connectivity were the posterior cingulate cortex (PCC) and the hippocampus (HP). During the memory task, the self-influence effective connectivities remained statistically significant across the DMN, and there were statistically significant effective connectivities from the PCC, HP, amygdala (AM), and parahippocampal region to other DMN regions. The authors found that effective connectivities from PCC, HP, and AM (in both resting state and during task) were linearly correlated to memory performance. The results suggest that superior memory ability in this older cohort was associated with effective connectivity both at rest and during the memory task of three DMN regions, which are also known to be important for memory function.

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg-Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.