Increasing spectral DCM flexibility and speed by leveraging Julia's ModelingToolkit and automated differentiation

Area of Science:

• Computational Neuroscience
• Neuroimaging Analysis
• Systems Neuroscience

Background:

• Inferring neural parameters from neuroimaging and electrophysiological data involves solving the complex inverse problem.
• Existing methods may lack efficiency and flexibility in composing dynamical models and parameter fitting.

Purpose of the Study:

• To introduce a novel Julia package for enhanced neural parameter estimation.
• To provide a modular and efficient framework for building dynamical models and performing spectral dynamic causal modeling (sDCM).
• To improve the accuracy and speed of inverse problem solving in computational neuroscience.

Main Methods:

• Development of a Julia package utilizing ModelingToolkit.jl for modular model composition.
• Implementation of parameter fitting using spectral dynamic causal modeling (sDCM) with Laplace approximation.
• Leveraging Automatic Differentiation for increased computational efficiency and accuracy.

Main Results:

• The package enables the composition of complex dynamical models in a simple, modular fashion.
• Parameter fitting via sDCM is implemented, analogous to established MATLAB toolboxes.
• Demonstrated improvement in correcting for fMRI scanner field strengths (1.5T, 3T, 7T) in model fitting.

Conclusions:

• The new Julia package offers a flexible and powerful approach to neural modeling and parameter estimation.
• The use of Automatic Differentiation significantly enhances the speed and accuracy of the fitting procedure.
• The developed method provides a practical solution for improving fMRI data analysis across various scanner configurations.