A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.     

A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal evolution of the distributed generators of the EEG can be reconstructed at each voxel of a discretisation of the gray matter of brain. By fitting linear autoregressive models with neighbourhood interactions to EEG time series, new classes of inverse solutions with improved resolution and localisation ability can be explored. For the purposes of model comparison and parameter estimation from given data, we employ a likelihood maximisation approach. Both for instantaneous and dynamical inverse solutions, we derive estimators of the time-dependent estimation error at each voxel. The performance of the algorithm is demonstrated by application to simulated and clinical EEG recordings. It is shown that by choosing appropriate dynamical models, it becomes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions.     

A distributed spatio-temporal EEG/MEG inverse solver

We propose a novel l(1)l(2)-norm inverse solver for estimating the sources of EEG/MEG signals. Based on the standard l(1)-norm inverse solvers, this sparse distributed inverse solver integrates the l(1)-norm spatial model with a temporal model of the source signals in order to avoid unstable activation patterns and "spiky" reconstructed signals often produced by the currently used sparse solvers. The joint spatio-temporal model leads to a cost function with an l(1)l(2)-norm regularizer whose minimization can be reduced to a convex second-order cone programming (SOCP) problem and efficiently solved using the interior-point method. The efficient computation of the SOCP problem allows us to implement permutation tests for estimating statistical significance of the inverse solution. Validation with simulated and human MEG data shows that the proposed solver yields source time course estimates qualitatively similar to those obtained through dipole fitting, but without the need to specify the number of dipole sources in advance. Furthermore, the l(1)l(2)-norm solver achieves fewer false positives and a better representation of the source locations than the conventional l(2) minimum-norm estimates.     

Hierarchical Bayesian estimation for MEG inverse problem

Source current estimation from MEG measurement is an ill-posed problem that requires prior assumptions about brain activity and an efficient estimation algorithm. In this article, we propose a new hierarchical Bayesian method introducing a hierarchical prior that can effectively incorporate both structural and functional MRI data. In our method, the variance of the source current at each source location is considered an unknown parameter and estimated from the observed MEG data and prior information by using the Variational Bayesian method. The fMRI information can be imposed as prior information on the variance distribution rather than the variance itself so that it gives a soft constraint on the variance. A spatial smoothness constraint, that the neural activity within a few millimeter radius tends to be similar due to the neural connections, can also be implemented as a hierarchical prior. The proposed method provides a unified theory to deal with the following three situations: (1) MEG with no other data, (2) MEG with structural MRI data on cortical surfaces, and (3) MEG with both structural MRI and fMRI data. We investigated the performance of our method and conventional linear inverse methods under these three conditions. Simulation results indicate that our method has better accuracy and spatial resolution than the conventional linear inverse methods under all three conditions. It is also shown that accuracy of our method improves as MRI and fMRI information becomes available. Simulation results demonstrate that our method appropriately resolves the inverse problem even if fMRI data convey inaccurate information, while the Wiener filter method is seriously deteriorated by inaccurate fMRI information.     

A simpler solution to the old problem of frozen leads

Pacemaker generator replacement is usually a straightforward and simple procedure. However, it is occasionally complicated by entrapment of the lead in the header. Solutions to this problem have been described previously. We describe a simpler and safer technique to solve this old problem.     

A dielectric inverse problem applied to human skin measurements during glucose excursions

A fringing field capacitive sensor has been used to measure the dielectric properties of human skin and underlying tissue in the MHz frequency range. It has recently been shown in clinical experimental studies that these dielectric properties can be related to the effects of in vivo glucose variations of the test subject. Previously, the relationship between electrical impedance and the glucose level has been established via statistical methods, such as the regression method. In this work, we explored a different approach, namely the resolution of the so-called inverse problem. First we applied the method on an artificial two-layer lossy system in order to test the sensitivity of the solution to forced changes in the layer properties and its stability to a constant setting. After validation of this method on artificial systems, a similar inverse problem was set and solved for dielectric measurements on human skin during an induced glucose excursion, where the skin is also modelled as a double-layer system. The changes of the measured permittivity and conductivity of the second layer versus the glucose changes are calculated for 22 study days. The statistical distribution shows that the median slopes of both dielectric properties are negative. These results can be used to test our hypothesis and to continue building potential explanations for the phenomena induced by the glucose changes on the skin layer dielectric parameters.     

Population-level inferences for distributed MEG source localization under multiple constraints: application to face-evoked fields

We address some key issues entailed by population inference about responses evoked in distributed brain systems using magnetoencephalography (MEG). In particular, we look at model selection issues at the within-subject level and feature selection issues at the between-subject level, using responses evoked by intact and scrambled faces around 170 ms (M170). We compared the face validity of subject-specific forward models and their summary statistics in terms of how estimated responses reproduced over subjects. At the within-subject level, we focused on the use of multiple constraints, or priors, for inverting distributed source models. We used restricted maximum likelihood (ReML) estimates of prior covariance components (in both sensor and source space) and show that their relative importance is conserved over subjects. At the between-subject level, we used standard anatomical normalization methods to create posterior probability maps that furnish inference about regionally specific population responses. We used these to compare different summary statistics, namely; (i) whether to test for differences between condition-specific source estimates, or whether to test the source estimate of differences between conditions, and (ii) whether to accommodate differences in source orientation by using signed or unsigned (absolute) estimates of source activity.     

Simple solution to problem of biostator-induced insulin aggregation

It has recently been reported that there is a significant loss of insulin immunoreactivity and bioavailability secondary to heat-induced insulin aggregation during prolonged insulin delivery by the Biostator. This artifact of Biostator insulin delivery system makes data generated by studies that use prolonged, continuous insulin infusions performed with the Biostator uninterpretable. We report the prevention of this problem by the addition of 20 ml heparinized whole blood to a 500-ml reservoir containing the insulin to be infused. The proposed solution is simple, economical, and without risk to the subject since his or her own blood can be used.     

Learn-Morph-Infer: A new way of solving the inverse problem for brain tumor modeling

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer, the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction–diffusion and reaction–advection–diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.     

An empirical Bayesian solution to the source reconstruction problem in EEG

Distributed linear solutions of the EEG source localisation problem are used routinely. In contrast to discrete dipole equivalent models, distributed linear solutions do not assume a fixed number of active sources and rest on a discretised fully 3D representation of the electrical activity of the brain. The ensuing inverse problem is underdetermined and constraints or priors are required to ensure the uniqueness of the solution. In a Bayesian framework, the conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimisation of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to various constraints. Here we formulate the conventional "Weighted Minimum Norm" (WMN) solution in terms of hierarchical linear models. An "Expectation-Maximisation" (EM) algorithm is used to obtain a "Restricted Maximum Likelihood" (ReML) estimate of the hyperparameters, before estimating the "Maximum a Posteriori" solution itself. This procedure can be considered a generalisation of previous work that encompasses multiple constraints. Our approach was compared with the "classic" WMN and Maximum Smoothness solutions, using a simplified 2D source model with synthetic noisy data. The ReML solution was assessed with four types of source location priors: no priors, accurate priors, inaccurate priors, and both accurate and inaccurate priors. The ReML approach proved useful as: (1) The regularisation (or influence of the a priori source covariance) increased as the noise level increased. (2) The localisation error (LE) was negligible when accurate location priors were used. (3) When accurate and inaccurate location priors were used simultaneously, the solution was not influenced by the inaccurate priors. The ReML solution was then applied to real somatosensory-evoked responses to illustrate the application in an empirical setting.