Transforming Structural Networks into Functional Networks: A Physics-Guided Deep Learning Approach

1549 

Abstract Submission 

Ayush Kanyal¹, Vince Calhoun², Dong Hye Ye¹

¹Georgia State University, ATLANTA, GA, ²GSU/GATech/Emory, Decatur, GA

Ayush Kanyal  
Georgia State University
ATLANTA, GA

Vince Calhoun  
GSU/GATech/Emory
Decatur, GA

Dong Hye Ye  
Georgia State University
ATLANTA, GA

Schizophrenia (SZ) is a severe mental condition that has an impact on an individual's thoughts, feelings, and behavior. The use of deep learning in MRIs and medical imaging has opened new avenues for research into techniques to detect SZ. SZ patients have been shown to have changes in their brain morphology and often exhibit unusual functional connectivity [2]. This validates the use of deep learning approaches on fractional anisotropy (FA) maps and functional MRI data. A variety of strategies, particularly those based on computational models, have been developed to better understand the link between structural connectivity (SC) and functional connectivity (FC). In this work, we use a physics-guided dynamical model that is based on the Kuramoto model of synchronization along with a deep learning architecture to better understand the relationship between SC and FC.

Fig. 1 depicts our overall approach. FA, or fractional anisotropy maps, are a type of output from diffusion tensor imaging (DTI) scans [4]. Diffusion tensor imaging (DTI) provides quantitative information about the directional organization, integrity, and structural properties of white matter tracts in the brain. High FA values indicate highly organized fiber bundle orientations, while low FA values suggest disorganized or damaged fibers [6].
Once we have the structural connectivity from the FA maps, we apply the Kuramoto simulation to get the estimated FC matrices. Kuramoto simulation [7] refers to a physics model that simulates the synchronization of many interacting oscillators, such as groups of neurons in the brain. With a dynamic model derived from the Kuramoto model, our approach treats each brain region as an individual oscillator with distinct dynamics. Li et al. [8] used the Kuramoto dynamic model to calculate the phase information. (See the equation in Fig. 1, where Θ_i is the i-th brain region's phase state. ω_i is the intrinsic frequency of the i-th brain region. λ is the global coupling strength. A_ij is the coupling strength from the j-th to the i-th region, and α denotes the phase shift.) We then use the Balloon-Windkessel hemodynamics model to get the simulated FC matrices. We then use a U-Net to predict FC matrices from physics-guided input.

We used a subset of the FBIRN [9] dataset, consisting of 278 patients, of whom 137 are SZ and 141 are healthy. We performed five-fold cross-validation to gauge the performance of our methods, and the results are summarized in Fig 2 b. We used correlation and mean square error as our metrics. Also, we ran the U-Net with an identical architecture with the same 150 epochs and a learning rate of 0.001 directly on the structural connectivity matrix to have a baseline for our comparison. The U-Net consists of a downsampling and an upsampling path. In downsampling, there are a series of convolutional layers followed by ReLU activation functions. Similarly, in the upsampling path, we use transposed convolution.
The empirical FNC is derived from fMRI. fMRI measures blood oxygenation to determine connections between various brain regions. Spatial Independent Component Analysis (ICA) studies functional connections between brain regions at the network level. These connections are referred to as functional network connectivity [9]. The physics-guided model achieved a lower mean square error (0.0490) and higher correlation (0.748) than the SC-only model (0.1106 and 0.4253).

We propose a physics-guided approach for predicting FCs from SCs. We performed a comparative study between the Kuramoto model with the U-Net and just using the U-Net on SC. The experimental results on clinical datasets demonstrated enhanced predictions in the case of using a physics-guided model with higher correlation and lower mean square error when the predicted outputs are compared to the empirical FC matrices.

Psychiatric (eg. Depression, Anxiety, Schizophrenia)

Connectivity (eg. functional, effective, structural) ¹

Diffusion MRI Modeling and Analysis

fMRI Connectivity and Network Modeling

Methods Development ²

Data analysis

FUNCTIONAL MRI

Machine Learning

Psychiatric Disorders

Schizophrenia