Author name cluster

Will Penny

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

9 papers

1 author row

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.

Details DOI

YNIMG Journal 2017 Journal Article

Multivariate dynamical modelling of structural change during development

Gabriel Ziegler
Gerard R. Ridgway
Sarah-Jayne Blakemore
John Ashburner
Will Penny

Here we introduce a multivariate framework for characterising longitudinal changes in structural MRI using dynamical systems. The general approach enables modelling changes of states in multiple imaging biomarkers typically observed during brain development, plasticity, ageing and degeneration, e. g. regional gray matter volume of multiple regions of interest (ROIs). Structural brain states follow intrinsic dynamics according to a linear system with additional inputs accounting for potential driving forces of brain development. In particular, the inputs to the system are specified to account for known or latent developmental growth/decline factors, e. g. due to effects of growth hormones, puberty, or sudden behavioural changes etc. Because effects of developmental factors might be region-specific, the sensitivity of each ROI to contributions of each factor is explicitly modelled. In addition to the external effects of developmental factors on regional change, the framework enables modelling and inference about directed (potentially reciprocal) interactions between brain regions, due to competition for space, or structural connectivity, and suchlike. This approach accounts for repeated measures in typical MRI studies of development and aging. Model inversion and posterior distributions are obtained using earlier established variational methods enabling Bayesian evidence-based comparisons between various models of structural change. Using this approach we demonstrate dynamic cortical changes during brain maturation between 6 and 22 years of age using a large openly available longitudinal paediatric dataset with 637 scans from 289 individuals. In particular, we model volumetric changes in 26 bilateral ROIs, which cover large portions of cortical and subcortical gray matter. We account for (1) puberty-related effects on gray matter regions; (2) effects of an early transient growth process with additional time-lag parameter; (3) sexual dimorphism by modelling parameter differences between boys and girls. There is evidence that the regional pattern of sensitivity to dynamic hidden growth factors in late childhood is similar across genders and shows a consistent anterior-posterior gradient with strongest impact to prefrontal cortex (PFC) brain changes. Finally, we demonstrate the potential of the framework to explore the coupling of structural changes across a priori defined subnetworks using an example of previously established resting state functional connectivity.

Details DOI

YNIMG Journal 2016 Journal Article

Causal evidence that intrinsic beta-frequency is relevant for enhanced signal propagation in the motor system as shown through rhythmic TMS

Vincenzo Romei
Markus Bauer
Joseph L. Brooks
Marcos Economides
Will Penny
Gregor Thut
Jon Driver
Sven Bestmann

Correlative evidence provides support for the idea that brain oscillations underpin neural computations. Recent work using rhythmic stimulation techniques in humans provide causal evidence but the interactions of these external signals with intrinsic rhythmicity remain unclear. Here, we show that sensorimotor cortex follows externally applied rhythmic TMS (rTMS) stimulation in the beta-band but that the elicited responses are strongest at the intrinsic individual beta peak frequency. While these entrainment effects are of short duration, even subthreshold rTMS pulses propagate through the network and elicit significant cortico-spinal coupling, particularly when stimulated at the individual beta-frequency. Our results show that externally enforced rhythmicity interacts with intrinsic brain rhythms such that the individual peak frequency determines the effect of rTMS. The observed downstream spinal effect at the resonance frequency provides evidence for the causal role of brain rhythms for signal propagation.

Details DOI

RLDM Conference 2013 Conference Abstract

Decoding future state representations during planning

Zeb Kurth-Nelson
Will Penny
Quentin Huys
ETH Zurich
Marc Guitart-Masip
Anna Jafarpour
Gareth Barnes
Raymond Dolan

Planning enables humans and animals to use their knowledge of the structure of the world to anticipate the consequences of their actions, even when these consequences have never been experienced. Yet little is known about the algorithm used by the brain for planning. A possible neural basis for planning is hinted at in recordings in rodents that have revealed “preplay”, or explicit sequential neural representation of future states, at decision points. In humans, neuroimaging studies have also identified neural correlates of future state values, but a direct observation of a neural representation of future states during planning has re- mained elusive. Directly observing these representations would allow us to disambiguate different possible planning algorithms. In the present study, we asked subjects to perform a 5-step planning task in a complex maze. To prevent habitization, one unavailable transition was cued to subjects at the beginning of each trial. Fitting computational models with different maximum search depths to behavioral data suggested a wide range of depth between subjects, with some maximizing only immediate rewards, and others taking into ac- count deep future contingencies. We took advantage of the fast time resolution of magnetoencephalography (MEG), along with multivariate pattern classification, to study neural representations of future states during planning. Dimensionality of MEG time-frequency data was reduced with principal components analysis, and a linear classifier was applied to the low-dimensional data. The classifier was trained by recording MEG activity while presenting stimuli in random order before the task began. In leave-one-out cross-validation on the training data, this classifier performed significantly above chance for all subjects. We then applied this classifier to neural data acquired at choice points during the task, and using this approach we seek to identify future states represented during planning.

PDF Details

YNIMG Journal 2011 Journal Article

Generalised filtering and stochastic DCM for fMRI

Baojuan Li
Jean Daunizeau
Klaas E. Stephan
Will Penny
Dewen Hu
Karl Friston

This paper is about the fitting or inversion of dynamic causal models (DCMs) of fMRI time series. It tries to establish the validity of stochastic DCMs that accommodate random fluctuations in hidden neuronal and physiological states. We compare and contrast deterministic and stochastic DCMs, which do and do not ignore random fluctuations or noise on hidden states. We then compare stochastic DCMs, which do and do not ignore conditional dependence between hidden states and model parameters (generalised filtering and dynamic expectation maximisation, respectively). We first characterise state-noise by comparing the log evidence of models with different a priori assumptions about its amplitude, form and smoothness. Face validity of the inversion scheme is then established using data simulated with and without state-noise to ensure that DCM can identify the parameters and model that generated the data. Finally, we address construct validity using real data from an fMRI study of internet addiction. Our analyses suggest the following. (i) The inversion of stochastic causal models is feasible, given typical fMRI data. (ii) State-noise has nontrivial amplitude and smoothness. (iii) Stochastic DCM has face validity, in the sense that Bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity. (iv) Relaxing conditional independence assumptions can have greater construct validity, in terms of revealing group differences not disclosed by variational schemes. Finally, we note that the ability to model endogenous or random fluctuations on hidden neuronal (and physiological) states provides a new and possibly more plausible perspective on how regionally specific signals in fMRI are generated.

Details DOI

YNIMG Journal 2011 Journal Article

Post hoc Bayesian model selection

Karl Friston
Will Penny

This note describes a Bayesian model selection or optimization procedure for post hoc inferences about reduced versions of a full model. The scheme provides the evidence (marginal likelihood) for any reduced model as a function of the posterior density over the parameters of the full model. It rests upon specifying models through priors on their parameters, under the assumption that the likelihood remains the same for all models considered. This provides a quick and efficient scheme for scoring arbitrarily large numbers of models, after inverting a single (full) model. In turn, this enables the selection among discrete models that are distinguished by the presence or absence of free parameters, where free parameters are effectively removed from the model using very precise shrinkage priors. An alternative application of this post hoc model selection considers continuous model spaces, defined in terms of hyperparameters (sufficient statistics) of the prior density over model parameters. In this instance, the prior (model) can be optimized with respect to its evidence. The expressions for model evidence become remarkably simple under the Laplace (Gaussian) approximation to the posterior density. Special cases of this scheme include Savage–Dickey density ratio tests for reduced models and automatic relevance determination in model optimization. We illustrate the approach using general linear models and a more complicated nonlinear state-space model.

Details DOI

YNIMG Journal 2008 Journal Article

Bayesian decoding of brain images

Karl Friston
Carlton Chu
Janaina Mourão-Miranda
Oliver Hulme
Geraint Rees
Will Penny
John Ashburner

This paper introduces a multivariate Bayesian (MVB) scheme to decode or recognise brain states from neuroimages. It resolves the ill-posed many-to-one mapping, from voxel values or data features to a target variable, using a parametric empirical or hierarchical Bayesian model. This model is inverted using standard variational techniques, in this case expectation maximisation, to furnish the model evidence and the conditional density of the model’s parameters. This allows one to compare different models or hypotheses about the mapping from functional or structural anatomy to perceptual and behavioural consequences (or their deficits). We frame this approach in terms of decoding measured brain states to predict or classify outcomes using the rhetoric established in pattern classification of neuroimaging data. However, the aim of MVB is not to predict (because the outcomes are known) but to enable inference on different models of structure–function mappings; such as distributed and sparse representations. This allows one to optimise the model itself and produce predictions that outperform standard pattern classification approaches, like support vector machines. Technically, the model inversion and inference uses the same empirical Bayesian procedures developed for ill-posed inverse problems (e. g. , source reconstruction in EEG). However, the MVB scheme used here extends this approach to include a greedy search for sparse solutions. It reduces the problem to the same form used in Gaussian process modelling, which affords a generic and efficient scheme for model optimisation and evaluating model evidence. We illustrate MVB using simulated and real data, with a special focus on model comparison; where models can differ in the form of the mapping (i. e. , neuronal representation) within one region, or in the (combination of) regions per se.

Details DOI

YNIMG Journal 2007 Journal Article

Variational free energy and the Laplace approximation

Karl Friston
Jérémie Mattout
Nelson Trujillo-Barreto
John Ashburner
Will Penny

This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of variational learning and expectation maximisation (EM), we show how the ReML objective function can be adjusted to provide an approximation to the log-evidence for a particular model. This means ReML can be used for model selection, specifically to select or compare models with different covariance components. This is useful in the context of hierarchical models because it enables a principled selection of priors that, under simple hyperpriors, can be used for automatic model selection and relevance determination (ARD). Deriving the ReML objective function, from basic variational principles, discloses the simple relationships among Variational Bayes, EM and ReML. Furthermore, we show that EM is formally identical to a full variational treatment when the precisions are linear in the hyperparameters. Finally, we also consider, briefly, dynamic models and how these inform the regularisation of free energy ascent schemes, like EM and ReML.

Details DOI

YNIMG Journal 2003 Journal Article

Variational Bayesian inference for fMRI time series

Will Penny
Stefan Kiebel
Karl Friston

We describe a Bayesian estimation and inference procedure for fMRI time series based on the use of General Linear Models with Autoregressive (AR) error processes. We make use of the Variational Bayesian (VB) framework which approximates the true posterior density with a factorised density. The fidelity of this approximation is verified via Gibbs sampling. The VB approach provides a natural extension to previous Bayesian analyses which have used Empirical Bayes. VB has the advantage of taking into account the variability of hyperparameter estimates with little additional computational effort. Further, VB allows for automatic selection of the order of the AR process. Results are shown on simulated data and on data from an event-related fMRI experiment.

Details DOI