Nonstationary noise estimation in functional MRI

Cannulation Skill Assessment Using Functional Data Analysis

OBJECTIVE

A clinician's operative skill-the ability to safely and effectively perform a procedure-directly impacts patient outcomes and well-being. Therefore, it is necessary to accurately assess skill progression during medical training as well as develop methods to most efficiently train healthcare professionals.

METHODS

In this study, we explore whether time-series needle angle data recorded during cannulation on a simulator can be analyzed using functional data analysis methods to (1) identify skilled versus unskilled performance and (2) relate angle profiles to degree of success of the procedure.

RESULTS

Our methods successfully differentiated between types of needle angle profiles. In addition, the identified profile types were associated with degrees of skilled and unskilled behavior of subjects. Furthermore, the types of variability in the dataset were analyzed, providing particular insight into the overall range of needle angles used as well as the rate of change of angle as cannulation progressed in time. Finally, cannulation angle profiles also demonstrated an observable correlation with degree of cannulation success, a metric that is closely related to clinical outcome.

CONCLUSION

In summary, the methods presented here enable rich assessment of clinical skill since the functional (i.e., dynamic) nature of the data is duly considered.

Correcting for Non-stationarity in BOLD-fMRI Connectivity Analyses

In this work fMRI BOLD datasets are shown to contain slice-dependent non-stationarities. A model containing slice-dependent, non-stationary signal power is proposed to address time-varying signal power during BOLD data acquisition. The impact of non-stationary power on functional MRI connectivity is analytically derived, establishing that pairwise connectivity estimates are scaled by a function of the time-varying signal power, with magnitude upper bound by 1, and that the variance of sample correlation is increased, thereby inducing spurious connectivity. Consequently, we make the observation that time-varying power during acquisition of BOLD timeseries has the propensity to diminish connectivity estimates. To ameliorate the impact of non-stationary signal power, a simple correction for slice-dependent non-stationarity is proposed. Our correction is analytically shown to restore both signal stationarity and, subsequently, the integrity of connectivity estimates. Theoretical results are corroborated with empirical evidence demonstrating the utility of our correction. In addition, slice-dependent non-stationary variance is experimentally determined to be optimally characterized by an inverse Gamma distribution. The resulting distribution of a voxel's signal intensity is analytically derived to be a generalized Student's-t distribution, providing support for the Gaussianity assumption typically imposed by fMRI connectivity methods.

An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters

Single Particle Tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Most existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work, we propose an estimation algorithm to determine time-varying parameters of systems that discretely switch between different linear models of motion with Gaussian noise statistics, covering dynamics such as diffusion, directed motion, and Ornstein-Uhlenbeck dynamics. Our algorithm consists of three stages. In the first stage, we use a sliding window approach, combined with Expectation Maximization (EM) to determine maximum likelihood estimates of the parameters as a function of time. These results are only used to roughly estimate the number of model switches that occur in the data to guide the selection of algorithm parameters in the second stage. In the second stage, we use Change Detection (CD) techniques to identify where the models switch, taking advantage of the off-line nature of the analysis of SPT data to create non-causal algorithms with better precision than a purely causal approach. Finally, we apply EM to each set of data between the change points to determine final parameter estimates. We demonstrate our approach using experimental data generated in the lab under controlled conditions.

A time-varying approach to single particle tracking with a nonlinear observation model

Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop a local time-varying estimation algorithm for estimating motion model parameters from the data considering nonlinear observations. Our approach uses several well-known existing tools, namely the Expectation Maximization (EM) algorithm combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), and applies them to the time-varying case through a sliding window methodology. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply our time-varying approach to the UKF, we first need to transform the measurements into a model with additive Gaussian noise. This is carried out using a variance stabilizing transform. Results from simulations show that our approach is successful in tracing time-varying diffusion constants at a range of physically relevant signal levels. We also discuss the initialization for the EM algorithm based on the available data.

Risk related brain regions detection and individual risk classification with 3D image FPCA

Understanding how people make decisions from risky choices has attracted increasing attention of researchers in economics, psychology and neuroscience. While economists try to evaluate individual’s risk preference through mathematical modeling, neuroscientists answer the question by exploring the neural activities of the brain. We propose a model-free method, 3-dimensional image functional principal component analysis (3DIF), to provide a connection between active risk related brain region detection and individual’s risk preference. The 3DIF methodology is directly applicable to 3-dimensional image data without artificial vectorization or mapping and simultaneously guarantees the contiguity of risk related brain regions rather than discrete voxels. Simulation study evidences an accurate and reasonable region detection using the 3DIF method. In real data analysis, five important risk related brain regions are detected, including parietal cortex (PC), ventrolateral prefrontal cortex (VLPFC), lateral orbifrontal cortex (lOFC), anterior insula (aINS) and dorsolateral prefrontal cortex (DLPFC), while the alternative methods only identify limited risk related regions. Moreover, the 3DIF method is useful for extraction of subjective specific signature scores that carry explanatory power for individual’s risk attitude. In particular, the 3DIF method perfectly classifies both strongly and weakly risk averse subjects for in-sample analysis. In out-of-sample experiment, it achieves 73 -88  overall accuracy, among which 90 -100  strongly risk averse subjects and 49 -71  weakly risk averse subjects are correctly classified with leave-k-out cross validations.

Time, frequency, and time-varying Granger-causality measures in neuroscience

This article proposes a systematic methodological review and an objective criticism of existing methods enabling the derivation of time, frequency, and time-varying Granger-causality statistics in neuroscience. The capacity to describe the causal links between signals recorded at different brain locations during a neuroscience experiment is indeed of primary interest for neuroscientists, who often have very precise prior hypotheses about the relationships between recorded brain signals. The increasing interest and the huge number of publications related to this topic calls for this systematic review, which describes the very complex methodological aspects underlying the derivation of these statistics. In this article, we first present a general framework that allows us to review and compare Granger-causality statistics in the time domain, and the link with transfer entropy. Then, the spectral and the time-varying extensions are exposed and discussed together with their estimation and distributional properties. Although not the focus of this article, partial and conditional Granger causality, dynamical causal modelling, directed transfer function, directed coherence, partial directed coherence, and their variant are also mentioned.

On the Reliability of Individual Brain Activity Networks

There is intense interest in fMRI research on whole-brain functional connectivity, and however, two fundamental issues are still unresolved: the impact of spatiotemporal data resolution (spatial parcellation and temporal sampling) and the impact of the network construction method on the reliability of functional brain networks. In particular, the impact of spatiotemporal data resolution on the resulting connectivity findings has not been sufficiently investigated. In fact, a number of studies have already observed that functional networks often give different conclusions across different parcellation scales. If the interpretations from functional networks are inconsistent across spatiotemporal scales, then the whole validity of the functional network paradigm is called into question. This paper investigates the consistency of resting state network structure when using different temporal sampling or spatial parcellation, or different methods for constructing the networks. To pursue this, we develop a novel network comparison framework based on persistent homology from a topological data analysis. We use the new network comparison tools to characterize the spatial and temporal scales under which consistent functional networks can be constructed. The methods are illustrated on Human Connectome Project data, showing that the DISCOH₂ network construction method outperforms other approaches at most data spatiotemporal resolutions.

Scanning fast and slow: current limitations of 3 Tesla functional MRI and future potential

Functional MRI at 3T has become a workhorse for the neurosciences, e.g., neurology, psychology, and psychiatry, enabling non-invasive investigation of brain function and connectivity. However, BOLD-based fMRI is a rather indirect measure of brain function, confounded by physiology related signals, e.g., head or brain motion, brain pulsation, blood flow, intermixed with susceptibility differences close or distant to the region of neuronal activity. Even though a plethora of preprocessing strategies have been published to address these confounds, their efficiency is still under discussion. In particular, physiological signal fluctuations closely related to brain supply may mask BOLD signal changes related to "true" neuronal activation. Here we explore recent technical and methodological advancements aimed at disentangling the various components, employing fast multiband vs. standard EPI, in combination with fast temporal ICA. Our preliminary results indicate that fast (TR <0.5 s) scanning may help to identify and eliminate physiologic components, increasing tSNR and functional contrast. In addition, biological variability can be studied and task performance better correlated to other measures. This should increase specificity and reliability in fMRI studies. Furthermore, physiological signal changes during scanning may then be recognized as a source of information rather than a nuisance. As we are currently still undersampling the complexity of the brain, even at a rather coarse macroscopic level, we should be very cautious in the interpretation of neuroscientific findings, in particular when comparing different groups (e.g., age, sex, medication, pathology, etc.). From a technical point of view our goal should be to sample brain activity at layer specific resolution with low TR, covering as much of the brain as possible without violating SAR limits. We hope to stimulate discussion toward a better understanding and a more quantitative use of fMRI.

Applications of functional data analysis: A systematic review

BACKGROUND

Functional data analysis (FDA) is increasingly being used to better analyze, model and predict time series data. Key aspects of FDA include the choice of smoothing technique, data reduction, adjustment for clustering, functional linear modeling and forecasting methods.

METHODS

A systematic review using 11 electronic databases was conducted to identify FDA application studies published in the peer-review literature during 1995-2010. Papers reporting methodological considerations only were excluded, as were non-English articles.

RESULTS

In total, 84 FDA application articles were identified; 75.0% of the reviewed articles have been published since 2005. Application of FDA has appeared in a large number of publications across various fields of sciences; the majority is related to biomedicine applications (21.4%). Overall, 72 studies (85.7%) provided information about the type of smoothing techniques used, with B-spline smoothing (29.8%) being the most popular. Functional principal component analysis (FPCA) for extracting information from functional data was reported in 51 (60.7%) studies. One-quarter (25.0%) of the published studies used functional linear models to describe relationships between explanatory and outcome variables and only 8.3% used FDA for forecasting time series data.

CONCLUSIONS

Despite its clear benefits for analyzing time series data, full appreciation of the key features and value of FDA have been limited to date, though the applications show its relevance to many public health and biomedical problems. Wider application of FDA to all studies involving correlated measurements should allow better modeling of, and predictions from, such data in the future especially as FDA makes no a priori age and time effects assumptions.

A wavelet-based Bayesian approach to regression models with long memory errors and its application to FMRI data

This article considers linear regression models with long memory errors. These models have been proven useful for application in many areas, such as medical imaging, signal processing, and econometrics. Wavelets, being self-similar, have a strong connection to long memory data. Here we employ discrete wavelet transforms as whitening filters to simplify the dense variance-covariance matrix of the data. We then adopt a Bayesian approach for the estimation of the model parameters. Our inferential procedure uses exact wavelet coefficients variances and leads to accurate estimates of the model parameters. We explore performances on simulated data and present an application to an fMRI data set. In the application we produce posterior probability maps (PPMs) that aid interpretation by identifying voxels that are likely activated with a given confidence.

Detection and characterization of single-trial fMRI bold responses: paradigm free mapping

This work presents a novel method of mapping the brain's response to single stimuli in space and time without prior knowledge of the paradigm timing: paradigm free mapping (PFM). This method is based on deconvolution of the hemodynamic response from the voxel time series assuming a linear response and using a ridge-regression algorithm. Statistical inference is performed by defining a spatio-temporal t-statistic and by controlling for multiple comparisons using the false discovery rate procedure. The methodology was validated on five subjects who performed self-paced and visually cued finger tapping at 7 Tesla, with moderate (TR = 2 s) and high (TR = 0.4 s) temporal resolution. The results demonstrate that detection of single-trial BOLD events is feasible without a priori information on the stimulus paradigm. The proposed method opens up the possibility of designing temporally unconstrained paradigms to study the cortical response to unpredictable mental events.

Functional data analysis in brain imaging studies

Functional data analysis (FDA) considers the continuity of the curves or functions, and is a topic of increasing interest in the statistics community. FDA is commonly applied to time-series and spatial-series studies. The development of functional brain imaging techniques in recent years made it possible to study the relationship between brain and mind over time. Consequently, an enormous amount of functional data is collected and needs to be analyzed. Functional techniques designed for these data are in strong demand. This paper discusses three statistically challenging problems utilizing FDA techniques in functional brain imaging analysis. These problems are dimension reduction (or feature extraction), spatial classification in functional magnetic resonance imaging studies, and the inverse problem in magneto-encephalography studies. The application of FDA to these issues is relatively new but has been shown to be considerably effective. Future efforts can further explore the potential of FDA in functional brain imaging studies.

A multiscale analysis of the temporal characteristics of resting-state fMRI data

In this paper, we conduct an investigation of the null hypothesis distribution for functional magnetic resonance imaging (fMRI) time series using multiscale analysis tools, SiZer (significance of zero crossings of the derivative) and wavelets. Most current approaches to the analysis of fMRI data assume simple models for temporal (short term or long term) dependence structure. Such simplifications are to some extent necessary due to the complex, high-dimensional nature of the data, but to date there have been few systematic studies of the dependence structures under a range of possible null hypotheses, using data sets gathered specifically for that purpose. We aim to address some of these issues by analyzing the detrended data with a long enough time horizon to study possible long-range temporal dependence. Our multiscale approach shows that even for resting-state data, data, i.e. "null" or ambient thought, some voxel time series cannot be modeled by white noise and need long-range dependent type error structure. This finding suggests the use of different time series models in different parts of the brain in fMRI studies.

Dynamic Granger-Geweke causality modeling with application to interictal spike propagation

A persistent problem in developing plausible neurophysiological models of perception, cognition, and action is the difficulty of characterizing the interactions between different neural systems. Previous studies have approached this problem by estimating causal influences across brain areas activated during cognitive processing using structural equation modeling (SEM) and, more recently, with Granger-Geweke causality. While SEM is complicated by the need for a priori directional connectivity information, the temporal resolution of dynamic Granger-Geweke estimates is limited because the underlying autoregressive (AR) models assume stationarity over the period of analysis. We have developed a novel optimal method for obtaining data-driven directional causality estimates with high temporal resolution in both time and frequency domains. This is achieved by simultaneously optimizing the length of the analysis window and the chosen AR model order using the SURE criterion. Dynamic Granger-Geweke causality in time and frequency domains is subsequently calculated within a moving analysis window. We tested our algorithm by calculating the Granger-Geweke causality of epileptic spike propagation from the right frontal lobe to the left frontal lobe. The results quantitatively suggested that the epileptic activity at the left frontal lobe was propagated from the right frontal lobe, in agreement with the clinical diagnosis. Our novel computational tool can be used to help elucidate complex directional interactions in the human brain.

Smoothing dynamic positron emission tomography time courses using functional principal components

A functional smoothing approach to the analysis of PET time course data is presented. By borrowing information across space and accounting for this pooling through the use of a nonparametric covariate adjustment, it is possible to smooth the PET time course data thus reducing the noise. A new model for functional data analysis, the Multiplicative Nonparametric Random Effects Model, is introduced to more accurately account for the variation in the data. A locally adaptive bandwidth choice helps to determine the correct amount of smoothing at each time point. This preprocessing step to smooth the data then allows subsequent analysis by methods such as Spectral Analysis to be substantially improved in terms of their mean squared error.

Real-time 3T fMRI data of brain tumour patients for intra-operative localization of primary motor areas

INTRODUCTION

In patients with tumours in or near the motor cortex reliable intra-operative identification of the precentral gyrus can be difficult due to anatomical dislocation. Maps of functional magnetic resonance imaging (fMRI) based on the blood oxygen level dependent (BOLD) effect are used to localize eloquent functional areas of the brain but require postprocessing for reduction of false positive activations. We set the focus of this study on the evaluation of feasibility and clinical usefulness of using real-time fMRI t-maps without postprocessing for pre-operative planning and intra-operative localization of functional motor areas.

METHODS

Real-time fMRI t-maps from a 3-T MRI scanner were co-registered with MRI data. Ten patients were operated under general anaesthesia using 3D neuronavigation with integrated real-time fMRI t-maps. Surgical and functional outcome was compared to results of 12 patients who previously underwent wake surgeries.

RESULTS

Good neurological outcome was achieved in all treated patients. Main activation clusters on fMRI real-time maps were easily identified. Co-registered real-time fMRI data without additional postprocessing were useful in planning the surgical approach. However, due to brain shift and large voxel size of BOLD contrast signals on t-maps exact localization of borders between tumours and functional areas was not possible intra-operatively.

CONCLUSION

Our method is very simple to use and effective in guiding the neurosurgeon safely through minimally invasive craniotomies to tumours in eloquent areas without setting lesions to functional areas. Furthermore, the neurosurgeon is more independent when tumour location requires acquisition of fMRI data for pre-operative planning and intra-operative navigation.

fMRI data analysis with nonstationary noise models: a Bayesian approach

The assumption of noise stationarity in the functional magnetic resonance imaging (fMRI) data analysis may lead to the loss of crucial dynamic features of the data and thus result in inaccurate activation detection. In this paper, a Bayesian approach is proposed to analyze the fMRI data with two nonstationary noise models (the time-varying variance noise model and the fractional noise model). The covariance matrices of the time-varying variance noise and the fractional noise after wavelet transform are diagonal matrices. This property is investigated under the Bayesian framework. The Bayesian estimator not only gives an accurate estimate of the weights in general linear model, but also provides posterior probability of activation in a voxel and, hence, avoids the limitations (i.e., using only hypothesis testing) in the classical methods. The performance of the proposed Bayesian methods (under the assumption of different noise models) are compared with the ordinary least squares (OLS) and the weighted least squares (WLS) methods. Results from the simulation studies validate the superiority of the proposed approach to the OLS and WLS methods considering the complex noise structures in the fMRI data.

MR-Encephalography: Fast multi-channel monitoring of brain physiology with magnetic resonance

A new approach to measure activation-related changes in the brain by magnetic resonance is described offering high temporal resolution of 10-100 measurements per second. This is achieved by simultaneous multi-channel reception where the spatial resolution during continuous observation is determined by the sensitive volume of each coil alone without any additional spatial encoding gradients. Experimental results demonstrate the very high sensitivity of this approach, which allows to directly measure and monitor the stimulus-dependent hemodynamic response as well as ECG- and breathing-related signal fluctuations. One-dimensional spatial encoding either parallel or orthogonal to the cortex demonstrates that vascular signals can be identified by the pronounced signal variation at the ECG-frequency. Noise analysis at different frequencies reveals regional signal fluctuations in the frequency range between 2 and 10 Hz. Furthermore, initial results show that frequency changes in the order of <0.03 Hz corresponding to <1 nano Tesla can be detected. In addition to its potential use in neuroscientific studies, this new method opens a wide range of applications for fast physiological monitoring and can be easily combined with conventional high-resolution imaging.