Martin Havlíček

Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.

Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data

Increasing interest in understanding dynamic interactions of brain neural networks leads to formulation of sophisticated connectivity analysis methods. Recent studies have applied Granger causality based on standard multivariate autoregressive (MAR) modeling to assess the brain connectivity. Nevertheless, one important flaw of this commonly proposed method is that it requires the analyzed time series to be stationary, whereas such assumption is mostly violated due to the weakly nonstationary nature of functional magnetic resonance imaging (fMRI) time series. Therefore, we propose an approach to dynamic Granger causality in the frequency domain for evaluating functional network connectivity in fMRI data. The effectiveness and robustness of the dynamic approach was significantly improved by combining a forward and backward Kalman filter that improved estimates compared to the standard time-invariant MAR modeling. In our method, the functional networks were first detected by independent component analysis (ICA), a computational method for separating a multivariate signal into maximally independent components. Then the measure of Granger causality was evaluated using generalized partial directed coherence that is suitable for bivariate as well as multivariate data. Moreover, this metric provides identification of causal relation in frequency domain, which allows one to distinguish the frequency components related to the experimental paradigm. The procedure of evaluating Granger causality via dynamic MAR was demonstrated on simulated time series as well as on two sets of group fMRI data collected during an auditory sensorimotor (SM) or auditory oddball discrimination (AOD) tasks. Finally, a comparison with the results obtained from a standard time-invariant MAR model was provided.

Evaluation of functional network connectivity in event-related FMRI data based on ICA and time-frequency granger causality

In this article we show that Adaptive Multivariate Autoregressive (AMVAR) modeling accompanied by proper preprocessing is an effective technique for evaluation of spectral Granger causality among functional brain networks identified by independent component analysis from eventrelated fMRI data.

11. Is ica of fmri data able to find haemodynamic fluctuations related to epilepsy without help of EEG

Traditional approach to epilepsy localization using functional magnetic resonance imaging (fMRI) technique utilizes timings of spike EEG events in so called spike-informed general linear model. Simultaneous fMRI-EEG examination represents a challenging problem in terms of both technical equipment and signal processing. Main goals of our work were to show that haemodynamic changes related to epilepsy can be detected in the blood oxygen level dependent (BOLD) signal without using EEG, and to find optimal settings for the used independent component analysis (ICA) decomposition. In our retrospective study, we compared spatial maps of independent components (IC) derived from preoperative BOLD recordings (24 sessions) with a spatial masks of surgically removed tissue from patients with focal epilepsy. At each patient, there was one component selected as epilepsy-related (ER-) candidate based on spatial similarity criteria. Each ER-candidate IC was visually inspected by a neurologist and either classified as being epilepsy-related or marked as artifact. A dataset of 17 healthy controls was used to evaluate ER-candidate selection process (for each resection mask we tested belonging patient’s data against healthy controls using Wilcoxon test). In the patient group, we found a significantly better fit with the respective resection masks than the healthy control group, in 15 of 24 cases. The cases, where ER-candidate IC was classified as artifact (related to motion or large blood vessel), corresponds with cases of statistically insignificant results, which indicates validity of our approach. Several data decomposition/reduction methods were tested. Best fit between the ER-candidate IC and resection mask was obtained when performing ICA decomposition based on 98% of variability contained in the original data. After identifying possible typical properties of the ER-candidate component, ICA of fMRI data may become a suitable method for improving epilepsy localization, thus becoming a potentially valuable tool with future application in clinics.

Deconvolution of neuronal signal from hemodynamic response

In this paper we describe a deconvolution technique for obtaining an approximation of the neuronal signal from an observed hemodynamic response in fMRI data. Our approach, based on the Rauch-Tung-Striebel smoother for square-root cubature Kalman filter, enables us to accurately infer the hidden states, parameters, and the input of the dynamic system. Using a series of simulations we show in this paper that we are able to move beyond the limitation of a poorly sampled observation signal and estimate the true structure of underlying neuronal signal with significantly improved temporal resolution.

Estimation of neuronal responses from fMRI data

In this paper we describe a deconvolution technique for estimation of the neuronal signal from an observed hemodynamic responses in fMRI data. Our approach, based on the Rauch-Tung-Striebel smoother for square-root cubature Kalman filter, enables us to accurately infer the hidden states, parameters, and the input of the dynamic system. Additionally, we enhance the cubature Kalman filter with a variational Bayesian approach for adaptive estimation of the measurement noise covariance.