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Disentangling causal webs in brain using functional magnetic
resonance imaging
By: Natalia Z. Bielczyk, Sebo Uithol, Tim van Mourik, Paul Anderson, Jeffrey C. Glennon
and Jan K. Buitelaar
Presented By - Tarun Khajuria
An overview of current approaches
Topics Covered
• Causality
• Basics of functional Magnetic Resonance Imaging
• Problems with fMRI data
• Parameters of Comparison
• Computational Methods for inferring Causality using fMRI
• Discussion
Causality
• When process A is the cause of process B, A is necessarily in the past of B, and without A, B would not occur.
A
B
A causes B
Causality in Neuroscience
• Behaviour depends on many neural processes
• And on other factors (availability of blood and sugar)
• Interest in lead specific factors
• Can depend on experimental conditions
Image Source: https://blogs.plos.org/neuro/2018/01/08/can-we-trust-statistics-in-fmri-studies/
Causality in Neuroscience• Causation can never be observed
directly, just correlation.
• High correlation indicates a causal link
• Type of correlates used in fMRI link neuronal activity to
• Mental and Behavioural Phenomenon
• Physiological States
• Neuronal Activity in other parts of brain
Image Source: Pujol, J & Harrison, Ben & Ortiz, H & Deus, Juan & Soriano-Mas, Carles & López-Solà, Marina & Yucel, Murat & Perich, X & Cardoner, Narcis. (2009). Influence of the fusiform gyrus on amygdala response to emotional faces in the non-clinical range of social anxiety. Psychological medicine. 39. 1177-87. 10.1017/S003329170800500X.
Limitations of fMRI data
• Temporal Resolution (<1Hz)
• Signal to Noise Ratio
• Region Definition
Image Source : https://en.wikipedia.org/wiki/Haemodynamic_response
Limitations of fMRI data : Region Definition
• Definition of Network Nodes
• Based on Brain Anatomy
• Known functional ROIs
• Data Driven
Image Source :https://www.brown.edu/research/facilities/mri/resting-state-fmri
Causal Inference in fMRI• The challenge in finding causal web of dynamic changes in
the brain and the limitations of fMRI data
• The inference techniques can be divided on the basis of
• The complexity of Model
• Approach towards samples:
• Use temporal sequences
• Rely only on state-space equations
• Rely only on statistical properties of time series.
Criteria for Evaluation• Characteristics of Model to study causality
• Sign of Connections
• Strength of Connections
• Confidence Intervals
• Bi-directionality
• Immediacy
• Resilience to confounds
• Type of Inference
• Computational Cost
• Size of Network
Criteria for Evaluation
• Sign of Connection
• Strength of Connection
• Confidence Interval
A
B
A excites B / A inhibits B
Criteria for Evaluation
• Bi- directionality
• Immediacy
• Resilience to confounds
A
B
Bi - directionality
A
B
C
Immediacy
A
B
C
Confounds
Criteria for Evaluation
• Type of inference
• Hypothesis testing
• Model Comparison
• Computational Cost
• Size of Network
Inferencing Methods
Network Wise Methods
• Granger Causality
• Structural Equation Modelling
• Dynamic Causal Modelling
• Transfer Entropy
Granger Causality (GC)
• Originated in Economics
• Causality based on dependence of signal A on the past values of signal B
• Each signal can be explained by its past values and a Gaussian Noise
Granger Causality (GC)
• Does not impose any contains on Network Model
• Deconvolution is performed to model data more faithfully
• Requires signal Stationarity
• Informative about directionality of causal link
Transfer Entropy (TE)
• Data Driven technique
• The decrease in entropy signal Y causes in the entropy of signal X
Transfer Entropy (TE)
• Requires no assumptions about the properties of data, not even signal stationarity
• It can measure signal strength, sign of connections
• Bidirectional Connections
• Computationally cheap
• Did not perform well on synthetic data experiments
Structural Equation Modelling (SEM)
• Simplified version of GC
• Express every ROI time series as a linear combination of all other time series, hence regressing coefficients for maximal likelihood.
Structural Equation Modelling (SEM)
• It can retrieve both excretory and inhibitory connections
• The connection coefficients indicate the strength of the connections
• Resilient to confounds only under the assumption that the network is isolated.
Dynamic Causal Modelling (DCM)
• Developed specifically for fMRI signal
• Most popular method in use
• Build a two level model
• Neuronal Level
• Hemodynamic Level
Dynamic Causal Modelling (DCM)
• Model is fit by reducing cost function Negative free energy which is a trade off between model accuracy and complexity
• Creating the models with initial weights is highly dependent on the previous knowledge of the biological and physiological constraints
• Computational very costly and cannot be effectively used on large networks
• In practice works very well and has been used to produce highly reproducible results.
Hierarchical Methods
• LiNGAM (Linear Non -Gaussian Acyclic Models)
• Bayesian Models
LiNGAM
• Data driven approach with the assumption of acyclicity
• Infers connections based on residual noise and regressors from the model
• It can detect both excitatory and inhibitory connections
Bayesian Networks (BN)
• Model free/Model Based technique: No assumption on model
• The co-occurance between nodes indicates a causal link and the strengths of conditional probability decides the direction.
Pair Wise Methods
• Patel’s tau
• Pairwise Likelihood ratio
Patel’s tau (PT)
• Find correlation between nodes to final valid connections
• Uses the bayesian statistics to infer the causality between two nodes.
• Model Free inference
• P(Y|X) > P P(X|Y)
• P(Y|X) < P P(X|Y)
Pairwise Likelihood Ratio
• Find correlation between nodes to find valid connections
• Uses analysis based on LinGAM to find the causality direction between two nodes
• Model Free inference
Comparison
Upcoming Advances
• Leminar Analysis
• Whole Brain Effective Connectivity using Covariance Matrices
• Neural Network Models
Image Source: Laminar analysis of 7 T BOLD using an imposed spatial activation pattern in human V1. Jonathan R.PolimeniaBruceFischlabDouglas N.GreveaLawrence L.Waldac
Discussion
• DCM is the most popular approach for causal inference, but has concerns about scalability for large networks.
• Use of pair-wise approaches is promising as they can describe causal web for large networks
• With more use of techniques like Transcranial Magnetic Stimulation and Optogenetics a rigid validation of these method has become feasible.
Thank You
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