Speed-up pFIC: Deep learning accelerated inversion of parametric feedback inhibition control model

1913 

Abstract Submission 

Tianchu Zeng¹, Shaoshi Zhang¹, Fang Tian², B. T. Thomas Yeo¹

¹National University of Singapore, Singapore, Singapore, ²National University of Singapore, National University of Singapore, Singapore

Tianchu Zeng  
National University of Singapore
Singapore, Singapore

Shaoshi Zhang  
National University of Singapore
Singapore, Singapore

Fang Tian  
National University of Singapore
National University of Singapore, Singapore

B. T. Thomas Yeo  
National University of Singapore
Singapore, Singapore

The efficacy of neural mass models in capturing the neural dynamics is well-established[8]. Prior works[5,8] optimized model parameters by using Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm[4] with forward simulation via Euler integration, referred to as parametric feedback inhibition control model (pFIC). However, pFIC requires solving ordinary differential equations (ODE) for each cortical region simultaneously and each time step sequentially, posing a computational hurdle for model inversion.
To tackle this, we propose speed-up pFIC (supFIC) by integrating deep learning to neural mass model framework, leading to a 1500% speed-up of parameter optimization process.

We use CMA-ES to iteratively optimize local circuit parameters. It starts with sampling several candidate parameters from a Gaussian distribution. Simulated fMRI data are generated by running forward simulations with candidate parameters and structural connectivity (SC) matrices[1]. Evaluation of candidate parameters depends on the agreement between the empirical and simulated static functional connectivity (FC) and FC dynamics (FCD)[3]. We quantify the agreement between empirical and simulated FC using Pearson's correlation (r) and absolute difference between the means (d), as well as empirical and simulated FCD using KS statistics (KS). Parameters with the minimum loss, defined as (1-r)+d+KS, are used to initialize candidate parameters for the next iteration.
Our supFIC addresses the computational bottleneck associated with slow forward simulation by utilizing deep learning. To this end, 2 deep networks are trained, including a classifier and a predictor. Only the predictor(Fig 1A) is shown due to their similar network architectures. The classifier determines whether the inputs generate fMRI data within the firing rate range constraints, while the predictor directly generates the loss between simulated and empirical matrices bypassing the process of solving the system ODE, thus speeding up the parameter optimization process.
The pFIC was used to generate the ground-truth parameters to train the deep networks and evaluate their performance. After training, we adopt a hybrid procedure to optimize local circuit parameters, which consists of ~67% iterations of deep learning optimization followed by ~33% iterations of forward simulation via Euler integration. The deep learning process speeds up the optimization procedure by 300% while the Euler integration improves the stability of the optimized parameters.
To further validate supFIC, we compared its model performance with pFIC using HCP dataset[2,7] and replicated our prior findings on excitation/inhibition ratio (E/I ratio) using a developmental dataset[6].

The loss predicted by supFIC is close to ground-truth loss (r>0.8)(Fig 1B). Furthermore, we compare the 10 sets of parameters with the lowest loss in HCP dataset to that of pFIC. We show supFIC can numerically perform better than pFIC while only using 1 random initialization instead of 5, as originally proposed by pFIC(Fig 2A). This is equivalent to a 1500% (300% x 5) speed-up of parameter optimization process.
We then validate supFIC by replicating our previous findings on excitation/inhibition ratio (E/I ratio)[8] using the Philadelphia Neurodevelopment Cohort (PNC) dataset[6]. Like our previous results, E/I ratio decreases during development(Fig 2B) with sensory regions displaying a faster reduction compared to association regions(Fig 2C). After matching the age(Fig 2D left), E/I ratio is significantly lower for high-performance groups compared to low-performance groups(Fig 2D right). E/I ratio differences are more pronounced in association regions than in sensory regions(Fig 2E).

Overall, supFIC substantially accelerates model inversion without sacrificing performance. More importantly, our model replicates prior findings regarding E/I ratio. This opens the possibility to study neural mass model with higher spatial and temporal resolutions.

Connectivity (eg. functional, effective, structural)

fMRI Connectivity and Network Modeling ²

Methods Development ¹

Multivariate Approaches

Task-Independent and Resting-State Analysis

Computational Neuroscience

Computing

Design and Analysis

FUNCTIONAL MRI

Modeling

Multivariate

Other - Deep learning