Leveraging Julia's automated differentiation and symbolic computation to increase spectral DCM flexibility and speed

David Hofmann; Anthony G Chesebro; Chris Rackauckas; Lilianne R Mujica-Parodi; Karl J Friston; Alan Edelman; Helmut H Strey

doi:10.1101/2023.10.27.564407

Leveraging Julia's automated differentiation and symbolic computation to increase spectral DCM flexibility and speed

bioRxiv [Preprint]. 2023 Nov 1:2023.10.27.564407. doi: 10.1101/2023.10.27.564407.

Authors

David Hofmann^{1

2}, Anthony G Chesebro^{1

3}, Chris Rackauckas², Lilianne R Mujica-Parodi^{1

4

3

5}, Karl J Friston⁶, Alan Edelman², Helmut H Strey^{1

4

3}

Affiliations

¹ Laufer Center for Physical and Quantitative Biology, State University of New York at Stony Brook, NY.
² Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, MA.
³ Department of Biomedical Engineering, State University of New York at Stony Brook, NY.
⁴ Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, MA.
⁵ Baszucki Endowed Chair for Metabolic Neuroscience, Stony Brook University, NY.
⁶ Wellcome Trust Centre for Neuroimaging, University College London, London UK.

Abstract

Using neuroimaging and electrophysiological data to infer neural parameter estimations from theoretical circuits requires solving the inverse problem. Here, we provide a new Julia language package designed to i) compose complex dynamical models in a simple and modular way with ModelingToolkit.jl, ii) implement parameter fitting based on spectral dynamic causal modeling (sDCM) using the Laplace approximation, analogous to MATLAB implementation in SPM12, and iii) leverage Julia's unique strengths to increase accuracy and speed by employing Automatic Differentiation during the fitting procedure. To illustrate the utility of our flexible modular approach, we provide a method to improve correction for fMRI scanner field strengths (1.5T, 3T, 7T) when fitting models to real data.

Keywords: DCM; Julia; LFP; Neuroblox; SPM; causal; circuit; fMRI; model; neural; neuroimaging.

Publication types

Preprint

Abstract

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