Erik Barry Erhardt, PhD

Tracking Whole-Brain Connectivity Dynamics in the Resting State
Elena A. Allen, Eswar Damaraju, Sergey M. Plis, Erik B. Erhardt, Tom Eichele, and Vince D. Calhoun
Cerebral Cortex
Received: July 24, 2012
Accepted: October 15, 2012
Online: November 11, 2012
http://cercor.oxfordjournals.org/content/early/2012/11/09/cercor.bhs352.abstract
doi: 10.1093/cercor/bhs352

Abstract
Spontaneous fluctuations are a hallmark of recordings of neural signals, emergent over time scales spanning milliseconds and tens of minutes. However, investigations of intrinsic brain organization based on resting-state functional magnetic resonance imaging have largely not taken into account the presence and potential of temporal variability, as most current approaches to examine functional connectivity (FC) implicitly assume that relationships are constant throughout the length of the recording. In this work, we describe an approach to assess whole-brain FC dynamics based on spatial independent component analysis, sliding time window correlation, and k-means clustering of windowed correlation matrices. The method is applied to resting-state data from a large sample (n = 405) of young adults. Our analysis of FC variability highlights particularly flexible connections between regions in lateral parietal and cingulate cortex, and argues against a labeling scheme where such regions are treated as separate and antagonistic entities. Additionally, clustering analysis reveals unanticipated FC states that in part diverge strongly from stationary connectivity patterns and challenge current descriptions of interactions between large-scale networks. Temporal trends in the occurrence of different FC states motivate theories regarding their functional roles and relationships with vigilance/arousal. Overall, we suggest that the study of time-varying aspects of FC can unveil flexibility in the functional coordination between different neural systems, and that the exploitation of these dynamics in further investigations may improve our understanding of behavioral shifts and adaptive processes.

MIND, Research

I just returned from a fun event-filled couple days at Wright State Univeristy in Dayton, Ohio, visiting statistician Harry Khamis.  Harry invited me to give two talks on Friday, November 2nd, 2012: one in Statistics and a second in Neuroscience, arranged by Thomas N. Hangartner.  Harry was the model host; I always felt taken care of, my needs met.

I was excited to meet two people from my talks who could use the methods I presented. Prof Nasser H Kashou develops models for HRF functions, which the SimTB might be helpful for. Prof Yvonne Vadeboncoeur uses stable isotopes to study freshwater ecosystems, and we had some exciting discussion about collaborative opportunities.

The links to the papers the talks draw on are at the bottom.

My morning neuroimaging talk (10:15) in the Department of Biomedical, Industrial & Human Factors Engineering (BIE) included two-and-one-half topics: SimTB, subject variability with GICA, and a little data visualization.

Title
Capturing inter-subject variability with group independent component analysis of fMRI data: a simulation study

Abstract
A key challenge in functional neuroimaging is the meaningful combination of results across subjects. Even in a sample of healthy participants, brain morphology and functional organization exhibit considerable variability, such that no two individuals have the same neural activation at the same location in response to the same stimulus. This inter-subject variability limits inferences at the group-level as average activation patterns may fail to represent the patterns seen in individuals. A promising approach to multi-subject analysis is group independent component analysis (GICA), which identifies group components and reconstructs activations at the individual level. GICA has gained considerable popularity, particularly in studies where temporal response models cannot be specified. However, a comprehensive understanding of the performance of GICA under realistic conditions of inter-subject variability is lacking. In this study we use simulated functional magnetic resonance imaging (fMRI) data to determine the capabilities and limitations of GICA under conditions of spatial, temporal, and amplitude variability. Simulations, generated with the SimTB toolbox, address questions that commonly arise in GICA studies, such as: (1) How well can individual subject activations be estimated and when will spatial variability preclude estimation? (2) Why does component splitting occur and how is it affected by model order? (3) How should we analyze component features to maximize sensitivity to intersubject differences? Overall, our results indicate an excellent capability of GICA to capture between-subject differences and we make a number of recommendations regarding analytic choices for application to functional imaging data. mialab.mrn.org/software/simtb

My afternoon statistics talk (3:00) in the Department of Mathematics and Statistics to a packed room (they had to bring in additional chairs!) included work that extends my published stable isotope sourcing work.

Title
An extended Bayesian stable isotope mixing model for trophic level inference

Abstract
You are what and where you eat on the food web. We developed an extended Bayesian mixing model to jointly infer organic matter utilization and isotopic enrichment of organic matter sources in order to infer the trophic levels of several numerically abundant fish species (consumers) present in Apalachicola Bay, FL, USA. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation is estimated without error or that isotope ratios are uncorrelated. The model uses stable isotope ratios of carbon, nitrogen, and sulfur, isotopic fractionations, elemental concentrations, elemental assimilation efficiencies, as well as prior information (expert opinion) to inform the diet and trophic level parameters. The model appropriately accounts for uncertainly and prior information at all levels of the analysis.

Neuroscience talk
Summary of both SimTB papers.

SimTB, a simulation toolbox for fMRI data under a model of spatiotemporal separability
Erik B. Erhardt, Elena A. Allen, Yonghua Wei, Tom Eichele, Vince D. Calhoun
NeuroImage 59 (2012), pp. 4160-4167
http://www.sciencedirect.com/science/article/pii/S105381191101370X

Capturing inter-subject variability with group independent component analysis of fMRI data: A simulation study
Elena A. Allen, Erik B. Erhardt, Yonghua Wei, Tom Eichele, Vince D. Calhoun
NeuroImage
http://www.sciencedirect.com/science/article/pii/S1053811911011712

Data visualization in the neurosciences: overcoming the curse of dimensionality
Elena A. Allen, Erik B. Erhardt, Vince D. Calhoun
Neuron
www.cell.com/neuron/retrieve/pii/S089662731200428X

Statistics talk
A Bayesian framework for stable isotope mixing models
Erik B. Erhardt and Edward J. Bedrick
Environmental and Ecological Statistics
http://www.springerlink.com/content/vg4v62j8717671p3/

Bio
Erik Barry Erhardt, PhD, is an Assistant Professor of Statistics at the University of New Mexico Department of Mathematics and Statistics, where he serves as Director of the statistics consulting clinic. His research interests include Bayesian and frequentist statistical methods for stable isotope sourcing and brain imaging. Erik is a Howard Hughes Medical Institute Interfaces Scholar collaborating in interdisciplinary research and consulting. StatAcumen.com

MIND, Research, stable isotopes, Statistics

Elena A. Allen, Erik B. Erhardt, Vince D. Calhoun
Neuron
Accepted 7 May 2012
Online 24 May 2012
doi:10.1016/j.neuron.2012.05.001
www.cell.com/neuron/retrieve/pii/S089662731200428X

Abstract:
In publications, presentations, and popular media, scientific results are predominantly communicated through graphs. But are these figures clear and honest, or misleading? We examine current practices in data visualization and discuss improvements, advocating design choices which reveal data rather than hide it.

MIND, Research, Statistics

Correspondence between Structure and Function in the Human Brain at Rest
Judith Maxine Segall, Elena A Allen, Rex E Jung, Erik B Erhardt, Sunil Kumar Arja, Kent A Kiehl, Vince D Calhoun
Frontiers in Neuroinformatics
Accepted 12 Mar 2012, 6:10
www.frontiersin.org/neuroinformatics/10.3389/fninf.2012.00010/abstract

Abstract:
To further the understanding of basic and complex cognitive functions of the human brain, multidisciplinary neuroimaging research has explored both functional and structural connectivity. For structural connectivity, the most prevalent method has been diffusion weighted imaging, which measures the connections of large white matter bundles. Recently, functional connectivity has been measured using resting-state fMRI (rs-fMRI). Surprisingly, few studies have examined structural gray matter, which supports the BOLD response. The overall aim of this study is to explore how gray matter (GM) structure corresponds to function. A cohort of 603 healthy participants was scanned on the same 3T scanner at the Mind Research Network to investigate the spatial correlations between structure and function. This was done by applying spatial independent component analysis (ICA) to GMD maps, to delineate structural components based on the covariation of GMD between regions, and to rs-fMRIdata, to discover spatial patterns with common temporal features. Decomposed structural and functional components were then compared by spatial correlation. The basal ganglia network showed the highest structural to rs-functional component correlation (r=0.59). Our remaining results generally show correspondence between one structural network and several functional networks. We also studied relationships between the weights of different structural components and found networks in frontal and parietal regions showing covariation across subjects. We also identified the precuneus as a hub for in structural network correlations. In addition, we analyzed relationships between component weights and age, concluding that age has an effect on structural components.

MIND, Research

Modular organization of functional network connectivity in healthy controls and patients with schizophrenia during the resting state
Qingbao Yu, Sergey M Plis, Erik B Erhardt, Elena A Allen, Jing Sui, Kent A Kiehl, Godfrey Pearlson, Vince D Calhoun
2011 Frontiers in Systems Neuroscience

Abstract
Neuroimaging studies have shown that functional brain networks composed from select regions of interest (ROIs) have a modular community structure. However, the organization of functional network connectivity (FNC), comprising a purely data-driven network built from spatially independent brain components, is not yet clear. The aim of this study is to explore the modular organization of FNC in both healthy controls (HCs) and patients with schizophrenia (SZs). Resting state functional magnetic resonance imaging (R-fMRI) data of HCs and SZs were decomposed into independent components (ICs) by group independent component analysis (ICA). Then weighted brain networks (in which nodes are brain components) were built based on correlations between ICA time courses. Clustering coefficients and connectivity strength of the networks were computed. A dynamic branch cutting algorithm was used to identify modules of the FNC in HCs and SZs. Results show stronger connectivity strength and higher clustering coefficient in HCs with more and smaller modules in SZs. In addition, HCs and SZs had some different hubs. Our findings demonstrate altered modular architecture of the FNC in schizophrenia and provide insights into abnormal topological organization of intrinsic brain networks in this mental illness.

MIND, Research

Our paper detailing our simulation toolbox (SimTB) has been published in NeuroImage.

SimTB, a simulation toolbox for fMRI data under a model of spatiotemporal separability
Erik B. Erhardt, Elena A. Allen, Yonghua Wei, Tom Eichele, Vince D. Calhoun
NeuroImage 59 (2012), pp. 4160-4167
Received at Elsevier: 29 Nov 2011, Available online 8 Dec 2011, published online 5 Jan 2012
ISSN 1053-8119, 10.1016/j.neuroimage.2011.11.088
(http://dx.doi.org/10.1016/j.neuroimage.2011.11.088)
http://www.sciencedirect.com/science/article/pii/S105381191101370X
Keywords: simulation; fMRI; group analysis

SimTB flowchart for simulation of fMRI data

Abstract
We introduce SimTB, a MATLAB toolbox designed to simulate functional magnetic resonance imaging (fMRI) datasets under a model of spatiotemporal separability. The toolbox meets the increasing need of the fMRI community to more comprehensively understand the effects of complex processing strategies by providing a ground truth that estimation methods may be compared against. SimTB captures the fundamental structure of real data, but data generation is fully parameterized and fully controlled by the user, allowing for accurate and precise comparisons. The toolbox offers a wealth of options regarding the number and configuration of spatial sources, implementation of experimental paradigms, inclusion of tissue-specific properties, addition of noise and head movement, and much more. A straightforward data generation method and short computation time (3–10 seconds for each dataset) allow a practitioner to simulate and analyze many datasets to potentially understand a problem from many angles. Beginning MATLAB users can use the SimTB graphical user interface (GUI) to design and execute simulations while experienced users can write batch scripts to automate and customize this process. The toolbox is freely available at http://mialab.mrn.org/software together with sample scripts and tutorials.

Keyword: simulation; fMRI; group analysis

MIND, Research

Our paper using our simulation toolbox (SimTB) detailing what can be learned about multi-subject ICA on fMRI data has been published in NeuroImage.

Capturing inter-subject variability with group independent component analysis of fMRI data: A simulation study
Elena A. Allen, Erik B. Erhardt, Yonghua Wei, Tom Eichele, Vince D. Calhoun
NeuroImage, Available online 14 October 2011, ISSN 1053-8119, 10.1016/j.neuroimage.2011.10.010.
Volume 59, Issue 4, 15 February 2012, Pages 4141–4159
(http://www.sciencedirect.com/science/article/pii/S1053811911011712)
Keywords: fMRI; Inter-subject variability; Group ICA; Multi-subject; Model order; Simulations

Abstract
A key challenge in functional neuroimaging is the meaningful combination of results across subjects. Even in a sample of healthy participants, brain morphology and functional organization exhibit considerable variability, such that no two individuals have the same neural activation at the same location in response to the same stimulus. This inter-subject variability limits inferences at the group-level as average activation patterns may fail to represent the patterns seen in individuals. A promising approach to multi-subject analysis is group independent component analysis (GICA), which identifies group components and reconstructs activations at the individual level. GICA has gained considerable popularity, particularly in studies where temporal response models cannot be specified. However, a comprehensive understanding of the performance of GICA under realistic conditions of inter-subject variability is lacking. In this study we use simulated functional magnetic resonance imaging (fMRI) data to determine the capabilities and limitations of GICA under conditions of spatial, temporal, and amplitude variability. Simulations, generated with the SimTB toolbox, address questions that commonly arise in GICA studies, such as: (1) How well can individual subject activations be estimated and when will spatial variability preclude estimation? (2) Why does component splitting occur and how is it affected by model order? (3) How should we analyze component features to maximize sensitivity to intersubject differences? Overall, our results indicate an excellent capability of GICA to capture between-subject differences and we make a number of recommendations regarding analytic choices for application to functional imaging data.

MIND, Research

For the second issue of Brain Connectivity, a new journal, we were invited to provide a response to a “controversial article” about issues of analysis and interpretation in fMRI.  In a fun paper, Elena, Eswar, Vince, and I provide our perspective and some better practices to continue the dialogue.

On network derivation, classification, and visualization: a response to Habeck and Moeller
Erik B. Erhardt, Elena A. Allen, Eswar Damaraju, Vince D. Calhoun.
Brain Connectivity 1(2), 2011.

Abstract
In the decade and a half since Biswal’s fortuitous discovery of spontaneous correlations in functional imaging data, the field of functional connectivity (FC) has seen exponential growth resulting in the identification of widely-replicated intrinsic networks and the innovation of novel analytic methods with the promise of diagnostic application.  As such a young field undergoing rapid change, we have yet to converge upon a desired and needed set of standards.  In this issue, Habeck and Moeller begin a dialogue for developing best practices by providing four criticisms with respect to FC estimation methods, interpretation of FC networks, assessment of FC network features in classifying sub-populations, and network visualization.  Here, we respond to Habeck and Moeller and provide our own perspective on the concerns raised in the hope that the neuroimaging field will benefit from this discussion.

MIND, Research

Update: both papers have been published, simulation toolbox and inter-subject variability.

Elena Allen and I recently submitted two papers that detail a simulation toolbox for fMRI data (SimTB) and capturing inter-subject variability with group independent component analysis (ICA) using simulations. It’s been an exciting and interesting project because we can at last generate interesting and complex datasets to use as a “ground truth” to compare estimation and processing techniques.  We’ve learned a lot about the limits of some methods, as well as their robustness.  The papers will be submitted next week.  For those with MATLAB, it’s available at http://mialab.mrn.org/software.

SimTB, a simulation toolbox for fMRI data under a model of spatiotemporal separability
EB Erhardt, EA Allen, Y Wei, T Eichele, VD Calhoun. (2011)

We introduce SimTB, a MATLAB toolbox designed to simulate functional magnetic resonance imaging (fMRI) datasets under a model of spatiotemporal separability. The toolbox meets the increasing need of the fMRI community to more comprehensively understand the effects of complex processing strategies by providing a ground truth that estimation methods may be compared against. SimTB captures the fundamental structure of real data, but data generation is fully parameterized and fully controlled by the user, allowing for accurate and precise comparisons. The toolbox offers a wealth of options regarding the number and configuration of spatial sources, implementation of experimental paradigms, inclusion of tissue-specific properties, addition of noise and head movement, and much more. A straightforward data generation method and short computation time (3-10 seconds for each dataset) allow a practitioner to simulate and analyze many datasets to potentially understand a problem from many angles. Beginning MATLAB users can use the SimTB graphical user interface (GUI) to design and execute simulations while experienced users can write batch scripts to automate and customize this process. The toolbox is freely available at http://mialab.mrn.org/software together with sample scripts and tutorials.

Capturing inter-subject variability with group independent component analysis of fMRI data: a simulation study
EA Allen, EB Erhardt, Y Wei, T Eichele, VD Calhoun. (2011)

A key challenge in functional neuroimaging is the meaningful combination of results across subjects. Even in a sample of healthy participants, brain morphology and functional organization exhibit considerable variability, such that no two individuals have the same neural activation at the same location in response to the same stimulus. This inter-subject variability limits inferences at the group-level as average activation patterns may fail to represent the patterns seen in individuals. A promising approach to multi-subject analysis is group independent components analysis (GICA), which identities group components and reconstructs activations at the individual level. GICA has gained considerable popularity, particularly in studies where temporal response models cannot be specied. However, a comprehensive understanding of the performance of GICA under realistic conditions of inter-subject variability is lacking. In this study we use simulated functional magnetic resonance imaging (fMRI) data to determine the capabilities and limitations of GICA under conditions of spatial, temporal, and amplitude variability. Simulations, generated with the SimTB toolbox, address questions that commonly arise in GICA studies, such as: (1) How well can individual subject activations be estimated and when will spatial variability preclude estimation? (2) Why does component splitting occur and how is it aected by model order? (3) How should we analyze component features to maximize sensitivity to intersubject differences? Overall, our results indicate an excellent capability of GICA to capture between-subject differences and we make a number of recommendations regarding analytic choices for application to functional imaging data.

SimTB flowchart for simulation of fMRI data

MIND, Research

In this paper we’ve put together a cohort of so-called “healthy normal controls” in the largest single group independent component analysis (ICA) forward model. Included in our analysis approach is a statistical methodology for performing mancova when the number of fMRI brain voxels (roughly V=60K) to test for activation differences over demographic variables is much larger than the number of subjects (N=603).  This massive project involved researchers nearly spanning our Medical Image Analysis Laboratory (MIALab), but many other investigators at the Mind Research Network (MRN).  It is a great example of what makes collaboration fun, challenging, and productive (thank you Elena, Eswar, Bill, Judith, Martin, and Srinivas).

A baseline for the multivariate comparison of resting state networks

http://www.frontiersin.org/systems_neuroscience/10.3389/fnsys.2011.00002/abstract

Read more…

MIND, Research