Multiscale adaptive smoothing models for the hemodynamic response function in fMRI

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and frequency information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-the-art methods, such as the smooth finite impulse response (sFIR) model.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS609 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Simultaneous EEG-fMRI Analysis with Application to Detection of Seizure Signal Sources

Non

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Bayesian multi-modal model comparison: a case study on the generators of the spike and the wave in generalized spike–wave complexes

We present a novel approach to assess the networks involved in the generation of spontaneous pathological brain activity based on multi-modal imaging data. We propose to use probabilistic fMRI-constrained EEG source reconstruction as a complement to EEG-correlated fMRI analysis to disambiguate between networks that co-occur at the fMRI time resolution. The method is based on Bayesian model comparison, where the different models correspond to different combinations of fMRI-activated (or deactivated) cortical clusters. By computing the model evidence (or marginal likelihood) of each and every candidate source space partition, we can infer the most probable set of fMRI regions that has generated a given EEG scalp data window. We illustrate the method using EEG-correlated fMRI data acquired in a patient with ictal generalized spike–wave (GSW) discharges, to examine whether different networks are involved in the generation of the spike and the wave components, respectively. To this effect, we compared a family of 128 EEG source models, based on the combinations of seven regions haemodynamically involved (deactivated) during a prolonged ictal GSW discharge, namely: bilateral precuneus, bilateral medial frontal gyrus, bilateral middle temporal gyrus, and right cuneus. Bayesian model comparison has revealed the most likely model associated with the spike component to consist of a prefrontal region and bilateral temporal–parietal regions and the most likely model associated with the wave component to comprise the same temporal–parietal regions only. The result supports the hypothesis of different neurophysiological mechanisms underlying the generation of the spike versus wave components of GSW discharges

Finding Nonlinear Relationships in Functional Magnetic Resonance Imaging Data with Genetic Programming

The human brain is a complex, nonlinear dynamic chaotic system that is poorly understood. When faced with these difficult to understand systems, it is common to observe the system and develop models such that the underlying system might be deciphered. When observing neurological activity within the brain with functional magnetic resonance imaging (fMRI), it is common to develop linear models of functional connectivity; however, these models are incapable of describing the nonlinearities we know to exist within the system. A genetic programming (GP) system was developed to perform symbolic regression on recorded fMRI data. Symbolic regression makes fewer assumptions than traditional linear tools and can describe nonlinearities within the system. Although GP is a powerful form of machine learning that has many drawbacks (computational cost, overfitting, stochastic), it may provide new insights into the underlying system being studied. The contents of this thesis are presented in an integrated article format. For all articles, data from the Human Connectome Project were used. In the first article, nonlinear models for 507 subjects performing a motor task were created. These nonlinear models generated by GP contained fewer ROI than what would be found with traditional, linear tools. It was found that the generated nonlinear models would not fit the data as well as the linear models; however, when compared to linear models containing a similar number of ROI, the nonlinear models performed better. Ten subjects performing 7 tasks were studied in article two. After improvements to the GP system, the generated nonlinear models outperformed the linear models in many cases and were never significantly worse than the linear models. Forty subjects performing 7 tasks were studied in article three. Newly generated nonlinear models were applied to unseen data from the same subject performing the same task (intrasubject generalization) and many nonlinear models generalized to unseen data better than the linear models. The nonlinear models were applied to unseen data from other subjects performing the same task (intersubject generalization) and were not capable of generalizing as well as the linear

Semiparametric detection of significant activation for brain fMRI

Functional magnetic resonance imaging (fMRI) aims to locate activated regions in human brains when specific tasks are performed. The conventional tool for analyzing fMRI data applies some variant of the linear model, which is restrictive in modeling assumptions. To yield more accurate prediction of the time-course behavior of neuronal responses, the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels. Under mild regularity conditions, we demonstrate that a class of the proposed semiparametric test statistics, based on the local linear estimation technique, follow $\chi^2$ distributions under null hypotheses for a number of useful hypotheses. Furthermore, the asymptotic power functions of the constructed tests are derived under the fixed and contiguous alternatives. Simulation evaluations and real fMRI data application suggest that the semiparametric inference procedure provides more efficient detection of activated brain areas than the popular imaging analysis tools AFNI and FSL.Comment: Published in at http://dx.doi.org/10.1214/07-AOS519 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Approaches based on nonlinear Kalman filtering to deal with physiological noise in the estimation of the hemodynamic response from functional near-infrared spectroscopy data

This thesis proposes a novel algorithm based on nonlinear Kalman filtering to reduce physiological noise that contaminates functional near-infrared spectroscopy (fNIRS) signals and improve the estimation of the hemodynamic response. fNIRS is a recent neuroimaging technique which can monitor brain activity non invasively by using near-infrared light. In particular, comparisons with other literature methods will be carried out, highlighting the strength of the model-based method propose