Neuronal Transfer Entropy: a Biophysical Model of Information Flow Based on Dynamic Causal Modelling
Poster No:
1479
Submission Type:
Abstract Submission
Authors:
Leonardo Novelli1, Adeel Razi2
Institutions:
1Monash University, Melbourne, Victoria, 2Monash University, Melbourne, VIC
First Author:
Co-Author:
Introduction:
Transfer entropy and Dynamic Causal Modelling (DCM) are widely adopted methods to infer large-scale brain connectivity from neuroimaging time series. Here, we combine their strengths by deriving Transfer Entropy mathematically under the spectral DCM model for resting-state fMRI.
Transfer Entropy is an information-theoretic measure that can quantify how information is transferred between brain regions, shedding light on the computations performed by the brain [1,2,3]. One problem is that non-invasive neuroimaging techniques don't measure brain activity directly but via proxies, like blood oxygenation in fMRI or scalp electrical signals in EEG. These may distort the Transfer Entropy estimates.
We can mitigate this issue by leveraging DCM, a widely used method to fit biophysical models to data, which explicitly separates neuronal activity from measurements [4,5]. So, even though neuroimaging signals are indirect proxies of neuronal activity, DCM can infer the directed (effective) connectivity among brain regions. DCM has been validated using optogenetics [6], and the effective connectivity values are interpretable as directed excitatory and inhibitory effects.
Transfer Entropy is an information-theoretic measure that can quantify how information is transferred between brain regions, shedding light on the computations performed by the brain [1,2,3]. One problem is that non-invasive neuroimaging techniques don't measure brain activity directly but via proxies, like blood oxygenation in fMRI or scalp electrical signals in EEG. These may distort the Transfer Entropy estimates.
We can mitigate this issue by leveraging DCM, a widely used method to fit biophysical models to data, which explicitly separates neuronal activity from measurements [4,5]. So, even though neuroimaging signals are indirect proxies of neuronal activity, DCM can infer the directed (effective) connectivity among brain regions. DCM has been validated using optogenetics [6], and the effective connectivity values are interpretable as directed excitatory and inhibitory effects.
Methods:
We derived Neuronal Transfer Entropy for fMRI, a DCM-based version of Transfer Entropy that combines the strengths of these two methods: it leverages Transfer Entropy's ability to quantify information flow and DCM's ability to infer neuronal interactions from indirect neuroimaging measurements.
The main idea is illustrated in Fig. 1. First, we use DCM to fit a model to the observed data and infer the requisite parameters, including the effective connectivity matrix that describes the directed (excitatory or inhibitory) effects between brain regions. Then, we use these parameters to derive a DCM-based parametric estimator of Transfer Entropy. This function takes the DCM effective connectivity as input and estimates the Neuronal Transfer Entropy, i.e., the amount of information (in bits) transferred between brain regions. The mathematical derivations are based on the theory of stochastic processes [7,8] and spectral factorisation [9,10].
The main idea is illustrated in Fig. 1. First, we use DCM to fit a model to the observed data and infer the requisite parameters, including the effective connectivity matrix that describes the directed (excitatory or inhibitory) effects between brain regions. Then, we use these parameters to derive a DCM-based parametric estimator of Transfer Entropy. This function takes the DCM effective connectivity as input and estimates the Neuronal Transfer Entropy, i.e., the amount of information (in bits) transferred between brain regions. The mathematical derivations are based on the theory of stochastic processes [7,8] and spectral factorisation [9,10].
Results:
We analytically derived the Neuronal Transfer Entropy in a toy system with two brain regions connected by a single directional link (X→Y). In Fig. 2, the Neuronal Transfer Entropy plotted on the vertical axis is a function of the effective connectivity (directed link strength) and time horizon, the two horizontal axes. The information transfer peaks at a finite horizon and eventually decays to zero. The peak's timing and value depend on the strength of the effective connectivity. In future work, will will extend these Neuronal Transfer Entropy derivations to multiple brain regions using numerical spectral factorisation.
Conclusions:
This novel Neuronal Transfer Entropy based on spectral DCM offers several significant benefits and innovations:
- It quantifies context-sensitive changes in the information flow between the neuronal populations. This solves the issues faced by current transfer entropy methods that estimate information flow directly from the neuroimaging time series.
- It quantifies how Transfer Entropy depends upon neuronal effective connectivity (Fig. 1).
- It renders Neuronal Transfer Entropy robust to measurement noise [11] and other confounding factors, e.g. the hemodynamic response in the case of fMRI.
- It quantifies the uncertainty of the Neuronal Transfer Entropy estimates via Bayesian inference.
- It could improve the identification and understanding of different brain states and their transitions.
- It advances the application of Transfer Entropy to state-space models.
This new Neuronal Transfer Entropy is a mechanistic, neuro-physiologically grounded model of information transfer that links synaptic physiology to information processing-in a formal and empirically testable fashion. It allows us to precisely measure when, where, and how much information flows in the brain.
- It quantifies context-sensitive changes in the information flow between the neuronal populations. This solves the issues faced by current transfer entropy methods that estimate information flow directly from the neuroimaging time series.
- It quantifies how Transfer Entropy depends upon neuronal effective connectivity (Fig. 1).
- It renders Neuronal Transfer Entropy robust to measurement noise [11] and other confounding factors, e.g. the hemodynamic response in the case of fMRI.
- It quantifies the uncertainty of the Neuronal Transfer Entropy estimates via Bayesian inference.
- It could improve the identification and understanding of different brain states and their transitions.
- It advances the application of Transfer Entropy to state-space models.
This new Neuronal Transfer Entropy is a mechanistic, neuro-physiologically grounded model of information transfer that links synaptic physiology to information processing-in a formal and empirically testable fashion. It allows us to precisely measure when, where, and how much information flows in the brain.
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural)
fMRI Connectivity and Network Modeling 1
Methods Development 2
Keywords:
Computational Neuroscience
FUNCTIONAL MRI
Modeling
Other - Connectivity
1|2Indicates the priority used for review
Abstract Information
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