Christopher J. Long

Pharmacological differentiation of opioid receptor antagonists by molecular and functional imaging of target occupancy and food reward-related brain activation in humans

Opioid neurotransmission has a key role in mediating reward-related behaviours. Opioid receptor (OR) antagonists, such as naltrexone (NTX), can attenuate the behaviour-reinforcing effects of primary (food) and secondary rewards. GSK1521498 is a novel OR ligand, which behaves as an inverse agonist at the μ-OR sub-type. In a sample of healthy volunteers, we used [11C]-carfentanil positron emission tomography to measure the OR occupancy and functional magnetic resonance imaging (fMRI) to measure activation of brain reward centres by palatable food stimuli before and after single oral doses of GSK1521498 (range, 0.4–100 mg) or NTX (range, 2–50 mg). GSK1521498 had high affinity for human brain ORs (GSK1521498 effective concentration 50=7.10 ng ml−1) and there was a direct relationship between receptor occupancy (RO) and plasma concentrations of GSK1521498. However, for both NTX and its principal active metabolite in humans, 6-β-NTX, this relationship was indirect. GSK1521498, but not NTX, significantly attenuated the fMRI activation of the amygdala by a palatable food stimulus. We thus have shown how the pharmacological properties of OR antagonists can be characterised directly in humans by a novel integration of molecular and functional neuroimaging techniques. GSK1521498 was differentiated from NTX in terms of its pharmacokinetics, target affinity, plasma concentration–RO relationships and pharmacodynamic effects on food reward processing in the brain. Pharmacological differentiation of these molecules suggests that they may have different therapeutic profiles for treatment of overeating and other disorders of compulsive consumption.

Nonstationary noise estimation in functional MRI.

An important issue in functional MRI analysis is accurate characterisation of the noise processes present in the data. Whilst conventional fMRI noise representations often assume stationarity (or time-invariance) in the noise generating sources, such approaches may serve to suppress important dynamic information about brain function. As an alternative to these fixed temporal assumptions, we present in this paper two time-varying procedures for examining nonstationary noise structure in fMRI data. In the first procedure, we approximate nonstationary behaviour by means of a collection of simple but numerous time-varying parametric models. This is accomplished through the derivation of a locally parametric AutoRegressive (AR) plus drift model which tracks temporal covariance by allowing the model parameters to evolve over time. Before exploring time variation in these parameters, window-widths (bandwidths) that are well suited to the latent time-varying noise structure must be determined. To do this, we employ a bandwidth selection mechanism based on Steins Unbiased Risk Estimator (SURE) criterion. In the second procedure, we describe the fMRI noise using a nonparametric method based on Functional Data Analysis (FDA). This process generates well-conditioned nonstationary covariance estimates that reflect temporal continuity in the underlying data structure whilst penalizing effective model dimension. We demonstrate both methods on simulated data and investigate the presence of nonstationary noise in resting fMRI data using the whitening capabilities of the locally parametric procedure. We evaluate the comparative behaviour of the stationary and nonstationary AR-based methods on data acquired at 1.5, 3 and 7 T magnetic field strengths and show that incorporation of time variation in the AR parameters leads to an overall decrease in the level of residual structure in the data. The FDA noise modelling technique is formulated within an activation mapping procedure and compared to the SPM (Statistical Parametric Mapping) toolbox on a cognitive face recognition task. Both the SPM and FDA methods show good sensitivity on this task, but we find that inclusion of the nonstationary FDA noise model seems to improve detection power in important task-related medial temporal regions.

Spatiotemporal wavelet analysis for functional MRI

Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulus-convolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximum-likelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give well-identified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower mean-squared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies.

Large Scale Kalman Filtering Solutions to the Electrophysiological Source Localization Problem- A MEG Case Study

Computational solutions to the high-dimensional Kalman filtering problem are described in the setting of the MEG inverse problem. The overall objective of the described work is to localize and estimate dynamic brain activity from observed extraneous magnetic fields recorded at an array of sensor positions on the scalp and to do so in a manner that takes advantage of the true underlying statistical continuity in the current sources. To this end, we outline inverse mapping procedures that combine models of current dipoles with dynamic state-space estimation algorithms. While these algorithms are eminently well-suited to this class of dynamic inverse problems, they possess computational limitations that need to be addressed either by approximation or through the use of high performance computational resources. In this work we describe such a high performance computing (HPC) solution to the Kalman filter and demonstrate its applicability to the magnetoencephalography (MEG) inverse problem

STATE-SPACE SOLUTIONS TO THE DYNAMIC MAGNETOENCEPHALOGRAPHY INVERSE PROBLEM USING HIGH PERFORMANCE COMPUTING.

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an L(2) regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intra-cortical sources. In our model, the observation model is derived from the steady-state solution to Maxwells equations while the latent model representing neural dynamics is given by a random walk process. We show that the Kalman filter (KF) and the Kalman smoother [also known as the fixed-interval smoother (FIS)] may be used to solve the ensuing high-dimensional state-estimation problem. Using a well-known relationship between Bayesian estimation and Kalman filtering, we show that the MNE estimates carry a significant zero bias. Calculating these high-dimensional state estimates is a computationally challenging task that requires High Performance Computing (HPC) resources. To this end, we employ the NSF Teragrid Supercomputing Network to compute the source estimates. We demonstrate improvement in performance of the state-space algorithm relative to MNE in analyses of simulated and actual somatosensory MEG experiments. Our findings establish the benefits of high-dimensional state-space modeling as an effective means to solve the MEG source localization problem.

fMRI signal modeling using Laguerre polynomials

In order to construct spatial activation plots from functional magnetic resonance imaging (fMRI) data, a complex spatio-temporal modeling problem must be solved. A crucial part of this process is the estimation of the hemodynamic response (HR) function, an impulse response relating the stimulus signal to the measured noisy response. The estimation of the HR is complicated by the presence of low frequency colored noise. The standard approach to modeling the HR is to use simple parametric models, although FIR models have been used. We pursue a nonparametric approach using orthonormal causal Laguerre polynomials which have become popular in the system identification literature. It also happens that the shape of the basis elements is similar to that of a typical HR. We thus expect to achieve a compact and so bias reduced and low noise representation of the HR. This is not the case in FIR modeling, because a low FIR order is unable to cover the whole length of the HR over its region of support while a high FIR order results in overestimation of signal and underestimation of noise leading to misleading interpretations.

PARAMETER ESTIMATION AND DYNAMIC SOURCE LOCALIZATION FOR THE MAGNETOENCEPHALOGRAPHY (MEG) INVERSE PROBLEM

Dynamic estimation methods based on linear state-space models have been applied to the inverse problem of magnetoencephalography (MEG), and can improve source localization compared with static methods by incorporating temporal continuity as a constraint. The efficacy of these methods is influenced by how well the state-space model approximates the dynamics of the underlying brain current sources. While some components of the state-space model can be inferred from brain anatomy and knowledge of the MEG instrument noise structure, parameters governing the temporal evolution of underlying current sources are unknown and must be selected on an ad-hoc basis or estimated from data. In this work, we apply the expectation-maximization (EM) algorithm to estimate parameters and sources in an MEG state-space model and demonstrate in simulation studies that the resulting source estimates are superior to those provided by static methods or dynamic methods employing ad hoc parameter selection.

Hemodynamic transfer function estimation with Laguerre polynomials and confidence intervals construction, from functional magnetic resonance imaging (fMRI) data

In order to construct spatial activation plots from functional magnetic resonance imaging (fMRI) data, a complex spatio-temporal modeling problem must be solved. A crucial part of this process is the estimation of the hemodynamic response (HR) function, an impulse response relating the stimulus signal to the measured noisy response. The estimation of the HR is complicated by the presence of low frequency colored noise. The standard approach to modeling the HR is to use simple parametric models, although FIR models have been used. We offer two contributions. First, we pursue a nonparametric approach using orthonormal causal Laguerre polynomials which have become popular in the system identification literature. It also happens that the shape of the basis elements is similar to that of a typical HR. We thus expect to achieve a compact, and so bias reduced, and low noise representation of the HR. Additionally, we develop a procedure for providing confidence intervals for the whole HR function. This feature is completely lacking in all previous work.

Identifying fMRI Model Violations With Lagrange Multiplier Tests

The standard modeling framework in functional magnetic resonance imaging (fMRI) is predicated on assumptions of linearity, time invariance and stationarity. These assumptions are rarely checked because doing so requires specialized software, although failure to do so can lead to bias and mistaken inference. Identifying model violations is an essential but largely neglected step in standard fMRI data analysis. Using Lagrange multiplier testing methods we have developed simple and efficient procedures for detecting model violations such as nonlinearity, nonstationarity and validity of the common double gamma specification for hemodynamic response. These procedures are computationally cheap and can easily be added to a conventional analysis. The test statistic is calculated at each voxel and displayed as a spatial anomaly map which shows regions where a model is violated. The methodology is illustrated with a large number of real data examples.

A dynamic solution to the ill-conditioned magnetoencephalography (MEG) source localization problem

Dynamic inverse solutions are described that localize dynamic brain activity measured from extraneous magnetic fields at an array of sensor positions on the scalp. The measured spatiotemporal magnetic fields are produced by small but coherent neuronal currents and are recorded using arrays of multichannel SQUID (superconducting quantum interference devices) gradiometers. We outline inverse mapping procedures that combine models of current dipoles with dynamic state-space estimation algorithms. These algorithms are based on a series of hierarchical mathematical relationships that employ principles from electrical and electromagnetic field theory to relate the observed MEG measurements to the current source dipoles. As we show, one solution that is naturally suited to this type of problem is the well-known Kalman filter and smoother