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