脑源定位技术的精度评估及其在实际中的应用

脑源定位技术旨在通过头皮表面的脑电、脑磁信号来识别大脑内的神经活动源，是研究大脑皮层神经活动、认知过程和病理功能的基础。其毫秒级的时间分辨率可以有效弥补功能核磁共振在低时间分辨率方面的不足。然而，理论分析层面中逆问题的不适定性，以及实践操作层面上不同的记录方式、电极数量和头模型构建等过程带来的误差，给脑源定位的准确性带来极大挑战，也在一定程度上限制了脑源定位方法在神经科学和心理学研究以及临床诊断治疗中的实际应用。因此，理论分析和实践操作层面中的精度评估在脑源定位方法的实际使用中至关重要。针对以上问题，本文在对现有脑源定位方法介绍的基础上，着重分析了脑源定位技术的精度评估方法以及其在基础研究和临床诊断治疗中的实际应用。具体地，本文在理论分析中总结了基于空间分辨率、基于点扩散以及串扰函数的评估方法对于不同脑源定位方法中源的重叠程度和其他源对目标源的影响；在实践操作中介绍了记录方式、电极数量和密度、头部容积传导模型等因素对源定位精度的影响；进一步介绍了脑源定位技术在时频分析、连通性分析中的应用，以及其在临床中的应用，包括癫痫、注意缺陷与多动障碍等脑部疾病。     

基于模拟退火法由脑磁图推测电流偶极子参数

利用模拟退火（Ｓｉｍｕｌａｔｅｄ Ａｎｎｅａｌｉｎｇ） 算法,由脑磁图（ ＭＥＧ） 数据反演脑内作为磁源的单电流偶极子参数,可以得到理想的结果。在上述工作的基础上,对脑内多电流偶极子参数的反演,则呈现如下状况：即以少于实际源数目的偶极子为源假设反演,目标函数得不到极小优化。反之,目标函数可以得到极小优化, 但出现多余的伪偶极子, 且这些伪偶极子在多次不同条件的反演结果中,处于不稳定状态。若将多次反演结果中处于不稳定状态的偶极子作为伪偶极子的判据而将其排除,则可以得到一种判断磁源偶极子数目的方法     

Real-Time Localization of Moving Dipole Sources for Tracking Multiple Free-Swimming Weakly Electric Fish

In order to survive, animals must quickly and accurately locate prey, predators, and conspecifics using the signals they generate. The signal source location can be estimated using multiple detectors and the inverse relationship between the received signal intensity (RSI) and the distance, but difficulty of the source localization increases if there is an additional dependence on the orientation of a signal source. In such cases, the signal source could be approximated as an ideal dipole for simplification. Based on a theoretical model, the RSI can be directly predicted from a known dipole location; but estimating a dipole location from RSIs has no direct analytical solution. Here, we propose an efficient solution to the dipole localization problem by using a lookup table (LUT) to store RSIs predicted by our theoretically derived dipole model at many possible dipole positions and orientations. For a given set of RSIs measured at multiple detectors, our algorithm found a dipole location having the closest matching normalized RSIs from the LUT, and further refined the location at higher resolution. Studying the natural behavior of weakly electric fish (WEF) requires efficiently computing their location and the temporal pattern of their electric signals over extended periods. Our dipole localization method was successfully applied to track single or multiple freely swimming WEF in shallow water in real-time, as each fish could be closely approximated by an ideal current dipole in two dimensions. Our optimized search algorithm found the animal’s positions, orientations, and tail-bending angles quickly and accurately under various conditions, without the need for calibrating individual-specific parameters. Our dipole localization method is directly applicable to studying the role of active sensing during spatial navigation, or social interactions between multiple WEF. Furthermore, our method could be extended to other application areas involving dipole source localization.     

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Magneto- and electroencephalography (MEG/EEG) are neuroimaging techniques that provide a high temporal resolution particularly suitable to investigate the cortical networks involved in dynamical perceptual and cognitive tasks, such as attending to different sounds in a cocktail party. Many past studies have employed data recorded at the sensor level only, i.e., the magnetic fields or the electric potentials recorded outside and on the scalp, and have usually focused on activity that is time-locked to the stimulus presentation. This type of event-related field / potential analysis is particularly useful when there are only a small number of distinct dipolar patterns that can be isolated and identified in space and time. Alternatively, by utilizing anatomical information, these distinct field patterns can be localized as current sources on the cortex. However, for a more sustained response that may not be time-locked to a specific stimulus (e.g., in preparation for listening to one of the two simultaneously presented spoken digits based on the cued auditory feature) or may be distributed across multiple spatial locations unknown a priori, the recruitment of a distributed cortical network may not be adequately captured by using a limited number of focal sources.Here, we describe a procedure that employs individual anatomical MRI data to establish a relationship between the sensor information and the dipole activation on the cortex through the use of minimum-norm estimates (MNE). This inverse imaging approach provides us a tool for distributed source analysis. For illustrative purposes, we will describe all procedures using FreeSurfer and MNE software, both freely available. We will summarize the MRI sequences and analysis steps required to produce a forward model that enables us to relate the expected field pattern caused by the dipoles distributed on the cortex onto the M/EEG sensors. Next, we will step through the necessary processes that facilitate us in denoising the sensor data from environmental and physiological contaminants. We will then outline the procedure for combining and mapping MEG/EEG sensor data onto the cortical space, thereby producing a family of time-series of cortical dipole activation on the brain surface (or "brain movies") related to each experimental condition. Finally, we will highlight a few statistical techniques that enable us to make scientific inference across a subject population (i.e., perform group-level analysis) based on a common cortical coordinate space.     

Effects of cavities on EEG dipole localization and their relations with surface electrode positions

Effects of cavities in the human head on EEG dipole localization have been investigated by computer simulation. The human head is represented by a homogeneous spherical conductor including an eccentric spherical cavity which approximates effects of actual cavities inside the head. The homogeneous sphere model is used for assessing the effects caused by neglecting the cavity in the volume conductor model in the inverse dipole fitting procedure. Four electrode configurations have been examined to investigate their relation to the EEG inverse dipole solution. After examination of 2520 dipoles in the brain, the effects of cavities in the human head are found to be negligible when the dipole is located in the cortex or in the subcortex. When the dipole is located in the brain stem, the EEG inverse dipole solution is strongly affected by the cavity and is sensitive to the electrode configuration on the scalp. The EEG inverse dipole solution in the deep brain is sensitive to inhomogeneity in the lower part of the head when a single positive or negative potential pole is observed by the electrodes on the scalp, and at the same time is sensitive to the extent of the scalp covered by the electrodes. In conclusion, the electrodes should cover as much of the upper scalp as possible for deep source localization.     

Theoretical and Computational Multiple Regression Study of Gastric Electrical Activity Using Dipole Tracing from Magnetic Field Measurements

The biomagnetic inverse problem has captured the interest of both mathematicians and physicists due to its important applications in the medical field. As a result of our experience in analyzing the electrical activity of the gastric smooth muscle, we present here a theoretical model of the magnetic field in the stomach and a computational implementation whereby we demonstrate its realism and usefulness. The computational algorithm developed for this purpose consists of dividing the magnetic field signal input surface into centroid-based grids that allow recursive least-squares approximations to be applied, followed by comparison tests in which the locations of the best-fitting current dipoles are determined. In the second part of the article, we develop a multiple-regression analysis of experimental gastric magnetic data collected using Superconducting QUantum Interference Device (SQUID) magnetometers and successfully processed using our algorithm. As a result of our analysis, we conclude on statistical grounds that it is sufficient to model the electrical activity of the GI tract using only two electric current dipoles in order to account for the magnetic data recorded non-invasively with SQUID magnetometers above the human abdomen.     

Harmony: EEG/MEG Linear Inverse Source Reconstruction in the Anatomical Basis of Spherical Harmonics

EEG/MEG source localization based on a “distributed solution” is severely underdetermined, because the number of sources is much larger than the number of measurements. In particular, this makes the solution strongly affected by sensor noise. A new way to constrain the problem is presented. By using the anatomical basis of spherical harmonics (or spherical splines) instead of single dipoles the dimensionality of the inverse solution is greatly reduced without sacrificing the quality of the data fit. The smoothness of the resulting solution reduces the surface bias and scatter of the sources (incoherency) compared to the popular minimum-norm algorithms where single-dipole basis is used (MNE, depth-weighted MNE, dSPM, sLORETA, LORETA, IBF) and allows to efficiently reduce the effect of sensor noise. This approach, termed Harmony, performed well when applied to experimental data (two exemplars of early evoked potentials) and showed better localization precision and solution coherence than the other tested algorithms when applied to realistically simulated data.     

A method for solution of the multi-objective inverse problems under uncertainty

We describe a method to solve multi-objective inverse problems under uncertainty. The method was tested on non-linear models of dynamic series and population dynamics, as well as on the spatiotemporal model of gene expression in terms of non-linear differential equations. We consider how to identify model parameters when experimental data contain additive noise and measurements are performed in discrete time points. We formulate the multi-objective problem of optimization under uncertainty. In addition to a criterion of least squares difference we applied a criterion which is based on the integral of trajectories of the system spatiotemporal dynamics, as well as a heuristic criterion CHAOS based on the decision tree method. The optimization problem is formulated using a fuzzy statement and is constrained by penalty functions based on the normalized membership functions of a fuzzy set of model solutions. This allows us to reconstruct the expression pattern of hairy gene in Drosophila even-skipped mutants that is in good agreement with experimental data. The reproducibility of obtained results is confirmed by solution of inverse problems using different global optimization methods with heuristic strategies.     

The Influence of Wavelets on Multiscale Analysis and Parametrization of Midlatency Auditory Evoked Potentials

This work shows methodological aspects of heuristic pattern recognition in auditory evoked potentials. A linear and a nonlinear transformation based on wavelet transform are presented. They result in a statistical error model and an entropy function related to the Gibbs function and describe changes in midlatency auditory evoked potentials induced by general anaesthesia. The same transformations were calculated using 12 common wavelets. We present a method to compare the two defined parametrizations with respect to their ability to discriminate two defined states which is responsive and unresponsive depending on the wavelet used for the analysis. Auditory evoked potentials of 60 patients undergoing general anaesthesia were analysed. We propose the defined statistical error model and the entropy function as a very robust measure of changes in auditory evoked potentials. The influence of the wavelets suggest that for each parametrization the goodness of the wavelet should be validated.     

The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns

In this paper, we compare the relationship between scale and period in ecological pattern analysis and wavelet analysis. We also adapt a commonly used wavelet, the Morlet, to ecological pattern analysis. Using Monte Carlo assessments, we apply methods of statistical significance test to wavelet analysis for pattern analysis. In order to understand the inherent strength and weakness of the Morlet and the Mexican Hat wavelets, we also investigate and compare the properties of two frequently used wavelets by testing with field data and four artificial transects of different typical patterns which is often encountered in ecological research. It is shown that the Mexican Hat provides better detection and localization of patch and gap events over the Morlet, whereas the Morlet offers improved detection and localization of scale over the Mexican Hat. There is always a trade-off between the detection and localization of scale versus patch and gap events. Therefore, the best composite analysis is the combination of their advantages. The properties of wavelet in dealing with ecological data may be affected by characteristics intrinsic to wavelet itself. The peaks of different scales in isograms of wavelet power spectrum from the Mexican Hat may overlap with each other. Alternatively, these peaks of different scales in isograms of wavelet power spectrum may combine with each other unless the size of the analyzed scales is significantly different. These overlapping or combining lead to combining of peaks for different scales, or the masking of trough between peaks of different scales in the scalogram. Ecologists should combine all the information in scalogram and isograms of wavelet coefficient and wavelet power spectrum from different wavelets, which can provide us a broader view and precise pattern information.     

Maximum decoding abilities of temporal patterns and synchronized firings: application to auditory neurons responding to click trains and amplitude modulated white noise

Simultaneous recordings of an increasing number of neurons have recently become available, but few methods have been proposed to handle this activity. Here, we extract and investigate all the possible temporal neural activity patterns based on synchronized firings of neurons recorded on multiple electrodes, or based on bursts of single-electrode activity in cat primary auditory cortex. We apply this to responses to periodic click trains or sinusoïdal amplitude modulated noise by obtaining for each pattern its temporal modulation transfer function. An algorithm that maximizes the mutual information between all patterns and stimuli subsequently leads to the identification of patterns that optimally decode modulation frequency (MF). We show that stimulus information contained in multi-electrode synchronized firing is not redundant with single-electrode firings and leads to improved efficiency of MF decoding. We also show that the combined use of firing rate and temporal codes leads to a better discrimination of the MF.     

A spike-based model of binaural sound localization

This paper describes a spike-based model of binaural sound localization using interaural time differences (ITDs). To handle the problem of temporal coding and to facilitate a hardware implementation all neurons are simulated by a spike response model, which includes postsynaptic potentials (PSPs) and a refractory period. A winner-take-all (WTA) network selects the dominant source from the representation of the sound's angles of incidences, and can be biased by a multisensory support. We use simulations on real audio data to investigate the function and the practical application of the system.     

The estimation of time varying dipoles on the basis of evoked potentials

When a stimulus is presented to a subject, different cortical areas are activated simultaneously. These cortical sources are the generators of evoked potentials. The geometry parameters and the amplitude time course of each source can be estimated on the basis of EP data and the appropriate mathematical model. In the present paper, a model is proposed which describes EPs as the result of a set of stagnant dipoles, with time varying amplitude. It is shown how the parameter estimation problem can be solved efficiently. The method automatically solves the problem of separating overlapping components. A lower limit for the residual is derived, which can be used to determine the minimum number of sources required to describe observed responses adequately.     

High-resolution magnetoencephalography--studies with a small-volume phantom]

To investigate the spatiotemporal organisation of neuronal processes in an animal model using magnetoencephalography (MEG), a high temporal resolution (ms) and an appropriate spatial resolution of about 1 mm is necessary. With the aim of determining the localization error and the resolution power of high-resolution MEG systems, we developed a phantom capable of simulating the characteristics of animal models. The phantom enables us to variably position at least two magnetic field sources to within 0.1 mm. For source localization on the basis of the magnetic field data, a spatial filtering algorithm was used. The investigation of a 16-channel micro SQUID-MEG system with a current dipole orientated tangentially to the phantom surface produced the following localization data (min ... max, x, y--horizontal plane, z--depth); systematic localization error e(x) = 1.16 ... 1.67 mm, e(y) = -1.01 ... -1.28 mm, e(z) = -5.22 ... -7.64 mm, standard deviation of the individual measurements perpendicular to the dipole axis s(perp) = 0.05 ... 0.22 mm, along this axis s(long) = 0.20 ... 1.73 mm, in the depths sz = 0.17 ... 3.17 mm. The "goodness of fit" was > 95%. Separation of two dipoles was still possible for parallel dipoles at a distance apart of d(parallel) = 0.03 mm and for those oriented perpendicularly to each other at a distance apart of d(perp) = 0.10 mm. On the basis of these results we conclude that the MEG system can achieve a resolution sufficient to permit the investigation of neuronal microstructures. The spatial errors detected were related to sensor position in the cryostatic vessel as well as to external low-frequency noise.     

A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment

The success of hyperthermia in the treatment of cancer depends on the precise prediction and control of temperature. It was absolutely a necessity for hyperthermia treatment planning to understand the temperature distribution within living biological tissues. In this paper, dual-phase-lag model of bio-heat transfer has been studied using Gaussian distribution source term under most generalized boundary condition during hyperthermia treatment. An approximate analytical solution of the present problem has been done by Finite element wavelet Galerkin method which uses Legendre wavelet as a basis function. Multi-resolution analysis of Legendre wavelet in the present case localizes small scale variations of solution and fast switching of functional bases. The whole analysis is presented in dimensionless form. The dual-phase-lag model of bio-heat transfer has compared with Pennes and Thermal wave model of bio-heat transfer and it has been found that large differences in the temperature at the hyperthermia position and time to achieve the hyperthermia temperature exist, when we increase the value of τ_T. Particular cases when surface subjected to boundary condition of 1st, 2nd and 3rd kind are discussed in detail. The use of dual-phase-lag model of bio-heat transfer and finite element wavelet Galerkin method as a solution method helps in precise prediction of temperature. Gaussian distribution source term helps in control of temperature during hyperthermia treatment. So, it makes this study more useful for clinical applications.     

Dipole source analysis of auditory P300 response in depressive and anxiety disorders

This paper is to study auditory event-related potential P300 in patients with anxiety and depressive disorders using dipole source analysis. Auditory P300 using 2-stimulus oddball paradigm was collected from 35 patients with anxiety disorder, 32 patients with depressive disorder, and 30 healthy controls. P300 dipole sources and peak amplitude of dipole activities were analyzed. The source analysis resulted in a 4-dipole configuration, where temporal dipoles displayed greater P300 amplitude than that of frontal dipoles. In addition, a right-greater-than-left hemispheric asymmetry of dipole magnitude was found in patients with anxiety disorder, whereas a left-greater-than-right hemispheric asymmetry of dipole magnitude was observed in depressed patients. Results indicated that the asymmetry was more prominent over the temporal dipole than that of frontal dipoles in patients. Patients with anxiety disorder may increase their efforts to enhance temporal dipole activity to compensate for a deficit in frontal cortex processing, while depressed patients show dominating reduction of right temporal activity. The opposite nature of results observed with hemispheric asymmetry in depressive and anxiety disorders could serve to be valuable information for psychiatric studies.     

Source Reconstruction Accuracy of MEG and EEG Bayesian Inversion Approaches

Electro- and magnetoencephalography allow for non-invasive investigation of human brain activation and corresponding networks with high temporal resolution. Still, no correct network detection is possible without reliable source localization. In this paper, we examine four different source localization schemes under a common Variational Bayesian framework. A Bayesian approach to the Minimum Norm Model (MNM), an Empirical Bayesian Beamformer (EBB) and two iterative Bayesian schemes (Automatic Relevance Determination (ARD) and Greedy Search (GS)) are quantitatively compared. While EBB and MNM each use a single empirical prior, ARD and GS employ a library of anatomical priors that define possible source configurations. The localization performance was investigated as a function of (i) the number of sources (one vs. two vs. three), (ii) the signal to noise ratio (SNR; 5 levels) and (iii) the temporal correlation of source time courses (for the cases of two or three sources). We also tested whether the use of additional bilateral priors specifying source covariance for ARD and GS algorithms improved performance. Our results show that MNM proves effective only with single source configurations. EBB shows a spatial accuracy of few millimeters with high SNRs and low correlation between sources. In contrast, ARD and GS are more robust to noise and less affected by temporal correlations between sources. However, the spatial accuracy of ARD and GS is generally limited to the order of one centimeter. We found that the use of correlated covariance priors made no difference to ARD/GS performance.     

A Computational Model of Aging and Calcification in the Aortic Heart Valve

The aortic heart valve undergoes geometric and mechanical changes over time. The cusps of a normal, healthy valve thicken and become less extensible over time. In the disease calcific aortic stenosis (CAS), calcified nodules progressively stiffen the cusps. The local mechanical changes in the cusps, due to either normal aging or pathological processes, affect overall function of the valve. In this paper, we propose a computational model for the aging aortic valve that connects local changes to overall valve function. We extend a previous model for the healthy valve to describe aging. To model normal/uncomplicated aging, leaflet thickness and extensibility are varied versus age according to experimental data. To model calcification, initial sites are defined and a simple growth law is assumed. The nodules then grow over time, so that the area of calcification increases from one model to the next model representing greater age. Overall valve function is recorded for each individual model to yield a single simulation of valve function over time. This simulation is the first theoretical tool to describe the temporal behavior of aortic valve calcification. The ability to better understand and predict disease progression will aid in design and timing of patient treatments for CAS.     

Location coding by opponent neural populations in the auditory cortex

Although the auditory cortex plays a necessary role in sound localization, physiological investigations in the cortex reveal inhomogeneous sampling of auditory space that is difficult to reconcile with localization behavior under the assumption of local spatial coding. Most neurons respond maximally to sounds located far to the left or right side, with few neurons tuned to the frontal midline. Paradoxically, psychophysical studies show optimal spatial acuity across the frontal midline. In this paper, we revisit the problem of inhomogeneous spatial sampling in three fields of cat auditory cortex. In each field, we confirm that neural responses tend to be greatest for lateral positions, but show the greatest modulation for near-midline source locations. Moreover, identification of source locations based on cortical responses shows sharp discrimination of left from right but relatively inaccurate discrimination of locations within each half of space. Motivated by these findings, we explore an opponent-process theory in which sound-source locations are represented by differences in the activity of two broadly tuned channels formed by contra- and ipsilaterally preferring neurons. Finally, we demonstrate a simple model, based on spike-count differences across cortical populations, that provides bias-free, level-invariant localization—and thus also a solution to the “binding problem” of associating spatial information with other nonspatial attributes of sounds.     

Ultrafast,accurate, and robust localization of anisotropic dipoles

The resolution of single molecule localization imaging techniques largely depends on the precision of localization algorithms. However, the commonly used Gaussian function is not appropriate for anisotropic dipoles because it is not the true point spread function. We derived the theoretical point spread function of tilted dipoles with restricted mobility and developed an algorithm based on an artificial neural network for estimating the localization, orientation and mobility of individual dipoles. Compared with fitting-based methods, our algorithm demonstrated ultrafast speed and higher accuracy, reduced sensitivity to defocusing, strong robustness and adaptability, making it an optimal choice for both two-dimensional and threedimensional super-resolution imaging analysis.