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Peter Zeidman

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15 papers

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YNIMG Journal 2023 Journal Article

A primer on Variational Laplace (VL)

Peter Zeidman
Karl Friston
Thomas Parr

This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations.

YNIMG Journal 2022 Journal Article

Directed coupling in multi-brain networks underlies generalized synchrony during social exchange

Edda Bilek
Peter Zeidman
Peter Kirsch
Heike Tost
Andreas Meyer-Lindenberg
Karl Friston

Advances in social neuroscience have made neural signatures of social exchange measurable simultaneously across people. This has identified brain regions differentially active during social interaction between human dyads, but the underlying systems-level mechanisms are incompletely understood. This paper introduces dynamic causal modeling and Bayesian model comparison to assess the causal and directed connectivity between two brains in the context of hyperscanning (h-DCM). In this setting, correlated neuronal responses become the data features that have to be explained by models with and without between-brain (effective) connections. Connections between brains can be understood in the context of generalized synchrony, which explains how dynamical systems become synchronized when they are coupled to each another. Under generalized synchrony, each brain state can be predicted by the other brain or a mixture of both. Our results show that effective connectivity between brains is not a feature within dyads per se but emerges selectively during social exchange. We demonstrate a causal impact of the sender's brain activity on the receiver of information, which explains previous reports of two-brain synchrony. We discuss the implications of this work; in particular, how characterizing generalized synchrony enables the discovery of between-brain connections in any social contact, and the advantage of h-DCM in studying brain function on the subject level, dyadic level, and group level within a directed model of (between) brain function.

YNIMG Journal 2022 Journal Article

Effects of face repetition on ventral visual stream connectivity using dynamic causal modelling of fMRI data

Sung-Mu Lee
Roni Tibon
Peter Zeidman
Pranay S. Yadav
Richard Henson

Stimulus repetition normally causes reduced neural activity in brain regions that process that stimulus. Some theories claim that this "repetition suppression" reflects local mechanisms such as neuronal fatigue or sharpening within a region, whereas other theories claim that it results from changed connectivity between regions, following changes in synchrony or top-down predictions. In this study, we applied dynamic causal modeling (DCM) on a public fMRI dataset involving repeated presentations of faces and scrambled faces to test whether repetition affected local (self-connections) and/or between-region connectivity in left and right early visual cortex (EVC), occipital face area (OFA) and fusiform face area (FFA). Face "perception" (faces versus scrambled faces) modulated nearly all connections, within and between regions, including direct connections from EVC to FFA, supporting a non-hierarchical view of face processing. Face "recognition" (familiar versus unfamiliar faces) modulated connections between EVC and OFA/FFA, particularly in the left hemisphere. Most importantly, immediate and delayed repetition of stimuli were also best captured by modulations of connections between EVC and OFA/FFA, but not self-connections of OFA/FFA, consistent with synchronization or predictive coding theories, though also possibly reflecting local mechanisms like synaptic depression.

YNIMG Journal 2021 Journal Article

Adiabatic dynamic causal modelling

Amirhossein Jafarian
Peter Zeidman
Rob. C Wykes
Matthew Walker
Karl J. Friston

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity.

YNIMG Journal 2020 Journal Article

Bayesian fusion and multimodal DCM for EEG and fMRI

Huilin Wei
Amirhossein Jafarian
Peter Zeidman
Vladimir Litvak
Adeel Razi
Dewen Hu
Karl J. Friston

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors - derived from dynamic causal modelling (DCM) of EEG data - for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters - as measured by the Kullback-Leibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proof-of-principle that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation.

YNIMG Journal 2020 Journal Article

Comparing dynamic causal models of neurovascular coupling with fMRI and EEG/MEG

Amirhossein Jafarian
Vladimir Litvak
Hayriye Cagnan
Karl J. Friston
Peter Zeidman

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain - using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison - asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software.

YNIMG Journal 2019 Journal Article

A guide to group effective connectivity analysis, part 1: First level analysis with DCM for fMRI

Peter Zeidman
Amirhossein Jafarian
Nadège Corbin
Mohamed L. Seghier
Adeel Razi
Cathy J. Price
Karl J. Friston

Dynamic Causal Modelling (DCM) is the predominant method for inferring effective connectivity from neuroimaging data. In the 15 years since its introduction, the neural models and statistical routines in DCM have developed in parallel, driven by the needs of researchers in cognitive and clinical neuroscience. In this guide, we step through an exemplar fMRI analysis in detail, reviewing the current implementation of DCM and demonstrating recent developments in group-level connectivity analysis. In the appendices, we detail the theory underlying DCM and the assumptions (i. e. , priors) in the models. In the first part of the guide (current paper), we focus on issues specific to DCM for fMRI. This is accompanied by all the necessary data and instructions to reproduce the analyses using the SPM software. In the second part (in a companion paper), we move from subject-level to group-level modelling using the Parametric Empirical Bayes framework, and illustrate how to test for commonalities and differences in effective connectivity across subjects, based on imaging data from any modality.

YNIMG Journal 2019 Journal Article

A guide to group effective connectivity analysis, part 2: Second level analysis with PEB

Peter Zeidman
Amirhossein Jafarian
Mohamed L. Seghier
Vladimir Litvak
Hayriye Cagnan
Cathy J. Price
Karl J. Friston

This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i. e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e. g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i. e. , posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. The preliminary first level (subject specific) DCM for fMRI analysis is covered in a companion paper. Here, we detail group-level analysis procedures that are suitable for use with data from any neuroimaging modality. This paper is accompanied by an example dataset, together with step-by-step instructions demonstrating how to reproduce the analyses.

YNIMG Journal 2019 Journal Article

Dynamic causal modelling revisited

K.J. Friston
Katrin H. Preller
Chris Mathys
Hayriye Cagnan
Jakob Heinzle
Adeel Razi
Peter Zeidman

This paper revisits the dynamic causal modelling of fMRI timeseries by replacing the usual (Taylor) approximation to neuronal dynamics with a neural mass model of the canonical microcircuit. This provides a generative or dynamic causal model of laminar specific responses that can generate haemodynamic and electrophysiological measurements. In principle, this allows the fusion of haemodynamic and (event related or induced) electrophysiological responses. Furthermore, it enables Bayesian model comparison of competing hypotheses about physiologically plausible synaptic effects; for example, does attentional modulation act on superficial or deep pyramidal cells – or both? In this technical note, we describe the resulting dynamic causal model and provide an illustrative application to the attention to visual motion dataset used in previous papers. Our focus here is on how to answer long-standing questions in fMRI; for example, do haemodynamic responses reflect extrinsic (afferent) input from distant cortical regions, or do they reflect intrinsic (recurrent) neuronal activity? To what extent do inhibitory interneurons contribute to neurovascular coupling? What is the relationship between haemodynamic responses and the frequency of induced neuronal activity? This paper does not pretend to answer these questions; rather it shows how they can be addressed using neural mass models of fMRI timeseries.

YNIMG Journal 2019 Journal Article

Thalamocortical dynamics underlying spontaneous transitions in beta power in Parkinsonism

Carolina Reis
Andrew Sharott
Peter J. Magill
Bernadette C.M. van Wijk
Thomas Parr
Peter Zeidman
Karl J. Friston
Hayriye Cagnan

Parkinson's disease (PD) is a neurodegenerative condition in which aberrant oscillatory synchronization of neuronal activity at beta frequencies (15–35 Hz) across the cortico-basal ganglia-thalamocortical circuit is associated with debilitating motor symptoms, such as bradykinesia and rigidity. Mounting evidence suggests that the magnitude of beta synchrony in the parkinsonian state fluctuates over time, but the mechanisms by which thalamocortical circuitry regulates the dynamic properties of cortical beta in PD are poorly understood. Using the recently developed generic Dynamic Causal Modelling (DCM) framework, we recursively optimized a set of plausible models of the thalamocortical circuit (n = 144) to infer the neural mechanisms that best explain the transitions between low and high beta power states observed in recordings of field potentials made in the motor cortex of anesthetized Parkinsonian rats. Bayesian model comparison suggests that upregulation of cortical rhythmic activity in the beta-frequency band results from changes in the coupling strength both between and within the thalamus and motor cortex. Specifically, our model indicates that high levels of cortical beta synchrony are mainly achieved by a delayed (extrinsic) input from thalamic relay cells to deep pyramidal cells and a fast (intrinsic) input from middle pyramidal cells to superficial pyramidal cells. From a clinical perspective, our study provides insights into potential therapeutic strategies that could be utilized to modulate the network mechanisms responsible for the enhancement of cortical beta in PD. Specifically, we speculate that cortical stimulation aimed to reduce the enhanced excitatory inputs to either the superficial or deep pyramidal cells could be a potential non-invasive therapeutic strategy for PD.

YNIMG Journal 2019 Journal Article

Variational representational similarity analysis

Karl J. Friston
Jörn Diedrichsen
Emma Holmes
Peter Zeidman

This technical note describes a variational or Bayesian implementation of representational similarity analysis (RSA) and pattern component modelling (PCM). It considers RSA and PCM as Bayesian model comparison procedures that assess the evidence for stimulus or condition-specific patterns of responses distributed over voxels or channels. On this view, one can use standard variational inference procedures to quantify the contributions of particular patterns to the data, by evaluating second-order parameters or hyperparameters. Crucially, this allows one to use parametric empirical Bayes (PEB) to infer which patterns are consistent among subjects. At the between-subject level, one can then assess the evidence for different (combinations of) hypotheses about condition-specific effects using Bayesian model comparison. Alternatively, one can select a single hypothesis that best explains the pattern of responses using Bayesian model selection. This note rehearses the technical aspects of within and between-subject RSA using a worked example, as implemented in the Statistical Parametric Mapping (SPM) software. En route, we highlight the connection between univariate and multivariate analyses of neuroimaging data and the sorts of analyses that are possible using component modelling and representational similarity analysis.

YNICL Journal 2018 Journal Article

Altered intrinsic and extrinsic connectivity in schizophrenia

Yuan Zhou
Peter Zeidman
Shihao Wu
Adeel Razi
Cheng Chen
Liuqing Yang
Jilin Zou
Gaohua Wang

Schizophrenia is a disorder characterized by functional dysconnectivity among distributed brain regions. However, it is unclear how causal influences among large-scale brain networks are disrupted in schizophrenia. In this study, we used dynamic causal modeling (DCM) to assess the hypothesis that there is aberrant directed (effective) connectivity within and between three key large-scale brain networks (the dorsal attention network, the salience network and the default mode network) in schizophrenia during a working memory task. Functional MRI data during an n-back task from 40 patients with schizophrenia and 62 healthy controls were analyzed. Using hierarchical modeling of between-subject effects in DCM with Parametric Empirical Bayes, we found that intrinsic (within-region) and extrinsic (between-region) effective connectivity involving prefrontal regions were abnormal in schizophrenia. Specifically, in patients (i) inhibitory self-connections in prefrontal regions of the dorsal attention network were decreased across task conditions; (ii) extrinsic connectivity between regions of the default mode network was increased; specifically, from posterior cingulate cortex to the medial prefrontal cortex; (iii) between-network extrinsic connections involving the prefrontal cortex were altered; (iv) connections within networks and between networks were correlated with the severity of clinical symptoms and impaired cognition beyond working memory. In short, this study revealed the predominance of reduced synaptic efficacy of prefrontal efferents and afferents in the pathophysiology of schizophrenia.

YNIMG Journal 2018 Journal Article

Bayesian population receptive field modelling

Peter Zeidman
Edward Harry Silson
Dietrich Samuel Schwarzkopf
Chris Ian Baker
Will Penny

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain.

YNIMG Journal 2017 Journal Article

OpenNFT: An open-source Python/Matlab framework for real-time fMRI neurofeedback training based on activity, connectivity and multivariate pattern analysis

Yury Koush
John Ashburner
Evgeny Prilepin
Ronald Sladky
Peter Zeidman
Sergei Bibikov
Frank Scharnowski
Artem Nikonorov

Neurofeedback based on real-time functional magnetic resonance imaging (rt-fMRI) is a novel and rapidly developing research field. It allows for training of voluntary control over localized brain activity and connectivity and has demonstrated promising clinical applications. Because of the rapid technical developments of MRI techniques and the availability of high-performance computing, new methodological advances in rt-fMRI neurofeedback become possible. Here we outline the core components of a novel open-source neurofeedback framework, termed Open NeuroFeedback Training (OpenNFT), which efficiently integrates these new developments. This framework is implemented using Python and Matlab source code to allow for diverse functionality, high modularity, and rapid extendibility of the software depending on the user’s needs. In addition, it provides an easy interface to the functionality of Statistical Parametric Mapping (SPM) that is also open-source and one of the most widely used fMRI data analysis software. We demonstrate the functionality of our new framework by describing case studies that include neurofeedback protocols based on brain activity levels, effective connectivity models, and pattern classification approaches. This open-source initiative provides a suitable framework to actively engage in the development of novel neurofeedback approaches, so that local methodological developments can be easily made accessible to a wider range of users.

YNIMG Journal 2016 Journal Article

Bayesian model reduction and empirical Bayes for group (DCM) studies

Karl J. Friston
Vladimir Litvak
Ashwini Oswal
Adeel Razi
Klaas E. Stephan
Bernadette C.M. van Wijk
Gabriel Ziegler
Peter Zeidman

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e. g. , dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.