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Conductance-based dynamic causal modeling: A mathematical review of its application to cross-power spectral densities


Pereira, Inês; Frässle, Stefan; Heinzle, Jakob; Schöbi, Dario; Do, Cao Tri; Gruber, Moritz; Stephan, Klaas Enno (2021). Conductance-based dynamic causal modeling: A mathematical review of its application to cross-power spectral densities. NeuroImage, 245:118662.

Abstract

Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been extended to electrophysiological data, and several variants have been developed. Their biophysically motivated formulations make these models promising candidates for providing a mechanistic understanding of human brain dynamics, both in health and disease. However, due to their complexity and reliance on concepts from several fields, fully understanding the mathematical and conceptual basis behind certain variants of DCM can be challenging. At the same time, a solid theoretical knowledge of the models is crucial to avoid pitfalls in the application of these models and interpretation of their results. In this paper, we focus on one of the most advanced formulations of DCM, i.e. conductance-based DCM for cross-spectral densities, whose components are described across multiple technical papers. The aim of the present article is to provide an accessible exposition of the mathematical background, together with an illustration of the model's behavior. To this end, we include step-by-step derivations of the model equations, point to important aspects in the software implementation of those models, and use simulations to provide an intuitive understanding of the type of responses that can be generated and the role that specific parameters play in the model. Furthermore, all code utilized for our simulations is made publicly available alongside the manuscript to allow readers an easy hands-on experience with conductance-based DCM.

Abstract

Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been extended to electrophysiological data, and several variants have been developed. Their biophysically motivated formulations make these models promising candidates for providing a mechanistic understanding of human brain dynamics, both in health and disease. However, due to their complexity and reliance on concepts from several fields, fully understanding the mathematical and conceptual basis behind certain variants of DCM can be challenging. At the same time, a solid theoretical knowledge of the models is crucial to avoid pitfalls in the application of these models and interpretation of their results. In this paper, we focus on one of the most advanced formulations of DCM, i.e. conductance-based DCM for cross-spectral densities, whose components are described across multiple technical papers. The aim of the present article is to provide an accessible exposition of the mathematical background, together with an illustration of the model's behavior. To this end, we include step-by-step derivations of the model equations, point to important aspects in the software implementation of those models, and use simulations to provide an intuitive understanding of the type of responses that can be generated and the role that specific parameters play in the model. Furthermore, all code utilized for our simulations is made publicly available alongside the manuscript to allow readers an easy hands-on experience with conductance-based DCM.

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Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:04 Faculty of Medicine > Institute of Biomedical Engineering
Dewey Decimal Classification:170 Ethics
610 Medicine & health
Scopus Subject Areas:Life Sciences > Neurology
Life Sciences > Cognitive Neuroscience
Uncontrolled Keywords:Cognitive Neuroscience, Neurology
Language:English
Date:1 December 2021
Deposited On:07 Jan 2022 14:41
Last Modified:26 Apr 2024 01:38
Publisher:Elsevier
ISSN:1053-8119
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.neuroimage.2021.118662
PubMed ID:34687862
Project Information:
  • : FunderRené und Susanne Braginsky Stiftung
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  • : Project Title
  • : FunderEidgenössische Technische Hochschule Zürich
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  • : FunderUniversität Zürich
  • : Grant ID
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  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)