Data Thresholding and Fitting Personalized Ising Models as Networks of Heterogeneous Brain Regions
Poster No:
1475
Submission Type:
Abstract Submission
Authors:
Adam Craig1, Sida Chen2, Qianyuan Tang3, Changsong Zhou4
Institutions:
1Hong Kong Baptist University, Kowloon Tong, Kowloon, 2Hong Kong Baptist University, Kowloon City, Hong Kong, 3Hong Kong Baptist University, Kowloon, Hong Kong, 4Hong Kong Baptist University, Hong Kong, Hong Kong
First Author:
Co-Author(s):
Introduction:
Prior studies have used Ising models to study functional integration and segregation in the brain, including [1], [2], and [3], but they fit models to pooled functional data, ignoring individual differences. Furthermore, fitting requires binarizing the data to create an achievable target, but no study has shown how choice of threshold affects properties of the data or model. Finally, while [3] compares the coupling parameters of the model to the structural connectivity (SC) of the brain, the relationship between the external field parameter and structural heterogeneity of brain regions remains unexplored.
We use Boltzmann learning [4] with new refinements that allow it to fit a large model to limited individual data. We find the range of thresholds at which original and binarized data functional connectivity (FC) remain correlated. We then show that, for the fitted models, coupling and SC remain correlated across this range, but external field influences behavior of the model and correlates with region structural features more at higher thresholds. This increased role better reflects the reality of the brain as a network of nodes with heterogeneous properties.
We use Boltzmann learning [4] with new refinements that allow it to fit a large model to limited individual data. We find the range of thresholds at which original and binarized data functional connectivity (FC) remain correlated. We then show that, for the fitted models, coupling and SC remain correlated across this range, but external field influences behavior of the model and correlates with region structural features more at higher thresholds. This increased role better reflects the reality of the brain as a network of nodes with heterogeneous properties.
Methods:
Human brain data
We use young adult resting-state fMRI data from the Human Connectome Project S1200 data release [5], preprocessed with the pipeline from [6] and parcellated according to a 360-region Atlas [7]. We z-score each region time series, then binarize it at a threshold θ. We use the algorithm from [8] to estimate the SC from diffusion tensor imaging data and the structural MRI pipeline from [9] to measure the average thickness, myelination, curvature, and sulcus depth of each region.
Ising model fitting
Each brain region in the model has an external field, h_i, and each pair of regions has a coupling, J_ij. We initialize h_i to the mean state of the region and J_ij to the uncentered covariance of the pair, find the simulation temperature that maximizes correlation between data and model FC, and then fit using Boltzmann learning [4], sampling model states with the Metropolis algorithm [10].
Parameter-structure correlations
We calculate Pearson correlations of individual model h_i with region structural MRI features. We also compute the correlation of J_ij with SC.
We use young adult resting-state fMRI data from the Human Connectome Project S1200 data release [5], preprocessed with the pipeline from [6] and parcellated according to a 360-region Atlas [7]. We z-score each region time series, then binarize it at a threshold θ. We use the algorithm from [8] to estimate the SC from diffusion tensor imaging data and the structural MRI pipeline from [9] to measure the average thickness, myelination, curvature, and sulcus depth of each region.
Ising model fitting
Each brain region in the model has an external field, h_i, and each pair of regions has a coupling, J_ij. We initialize h_i to the mean state of the region and J_ij to the uncentered covariance of the pair, find the simulation temperature that maximizes correlation between data and model FC, and then fit using Boltzmann learning [4], sampling model states with the Metropolis algorithm [10].
Parameter-structure correlations
We calculate Pearson correlations of individual model h_i with region structural MRI features. We also compute the correlation of J_ij with SC.
·Workflow for fitting Ising model to fMRI data
Results:
Choices of θ in the range [0, 1] preserve correlations between original and binarized data FC. In this range, our workflow produces correlations between data and model FC greater than 90% in over 95% of cases. Furthermore, correlation between individual-level J_ij and SC is consistently above 31%. For comparison, correlation between individual data FC and SC is 16.9%.
Binarizing at θ=0 generates models in which zeroing h_i does not influence FC correlation, implying that only J_ij determine model behavior, whereas binarizing at θ =1 instead gives models in which removing h_i does decrease FC correlation. Furthermore, increasing the threshold increases correlations between h_i and local features. Of these, myelination has the strongest correlation (20.1% for threshold 1 SD), exceeding any with spatial coordinates and having a significant component that disappears when we shuffle parameter-feature pairs by individual within a region.
Binarizing at θ=0 generates models in which zeroing h_i does not influence FC correlation, implying that only J_ij determine model behavior, whereas binarizing at θ =1 instead gives models in which removing h_i does decrease FC correlation. Furthermore, increasing the threshold increases correlations between h_i and local features. Of these, myelination has the strongest correlation (20.1% for threshold 1 SD), exceeding any with spatial coordinates and having a significant component that disappears when we shuffle parameter-feature pairs by individual within a region.
·Summary of key results
Conclusions:
We present a new workflow for creating fMRI data-driven Ising model representations of individual differences in coactivation and excitability of brain regions and show that such a model can capture individual differences in both brain connectivity and regional heterogeneity that correlate with differences in brain structure. Going forward, we hope to use this improved linkage between brain structure and brain function to identify the networks of regions and connections that have the greatest influence on functional integration and segregation. Focusing on such core networks may lead to new models with greater explanatory power and new therapies that target such networks to achieve stronger effects with less extreme interventions.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 2
fMRI Connectivity and Network Modeling 1
Task-Independent and Resting-State Analysis
Keywords:
Computational Neuroscience
Data analysis
FUNCTIONAL MRI
Machine Learning
Modeling
NORMAL HUMAN
STRUCTURAL MRI
WHITE MATTER IMAGING - DTI, HARDI, DSI, ETC
Workflows
Other - Ising model
1|2Indicates the priority used for review
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