Regional analysis of volumes and reproducibilities of automatic and manual hippocampal segmentations.

PURPOSE: Precise and reproducible hippocampus outlining is important to quantify hippocampal atrophy caused by neurodegenerative diseases and to spare the hippocampus in whole brain radiation therapy when performing prophylactic cranial irradiation or treating brain metastases. This study aimed to quantify systematic differences between methods by comparing regional volume and outline reproducibility of manual, FSL-FIRST and FreeSurfer hippocampus segmentations. MATERIALS AND METHODS: This study used a dataset from ADNI (Alzheimer's Disease Neuroimaging Initiative), including 20 healthy controls, 40 patients with mild cognitive impairment (MCI), and 20 patients with Alzheimer's disease (AD). For each subject back-to-back (BTB) T1-weighted 3D MPRAGE images were acquired at time-point baseline (BL) and 12 months later (M12). Hippocampi segmentations of all methods were converted into triangulated meshes, regional volumes were extracted and regional Jaccard indices were computed between the hippocampi meshes of paired BTB scans to evaluate reproducibility. Regional volumes and Jaccard indices were modelled as a function of group (G), method (M), hemisphere (H), time-point (T), region (R) and interactions. RESULTS: For the volume data the model selection procedure yielded the following significant main effects G, M, H, T and R and interaction effects G-R and M-R. The same model was found for the BTB scans. For all methods volumes reduces with the severity of disease. Significant fixed effects for the regional Jaccard index data were M, R and the interaction M-R. For all methods the middle region was most reproducible, independent of diagnostic group. FSL-FIRST was most and FreeSurfer least reproducible. DISCUSSION/CONCLUSION: A novel method to perform detailed analysis of subtle differences in hippocampus segmentation is proposed. The method showed that hippocampal segmentation reproducibility was best for FSL-FIRST and worst for Freesurfer. We also found systematic regional differences in hippocampal segmentation between different methods reinforcing the need of adopting harmonized protocols.

A three domain covariance framework for EEG/MEG data.

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets.

A morpho-density approach to estimating neural connectivity.

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.

Independently outgrowing neurons and geometry-based synapse formation produce networks with realistic synaptic connectivity.

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.

Data-driven modeling of phase interactions between spontaneous MEG oscillations.

OBJECTIVE: Synchronization between distributed rhythms in the brain is commonly assessed by estimating the synchronization strength from simultaneous measurements. This approach, however, does not elucidate the phase dynamics that underlies synchronization. For this, an explicit dynamical model is required. Based on the assumption that the recorded rhythms can be described as weakly coupled oscillators, we propose a method for characterizing their phase-interaction dynamics. METHODS: We propose to model ongoing magnetoencephalographic (MEG) oscillations as weakly coupled oscillators. Based on this model, the phase interactions between simultaneously recorded signals are characterized by estimating the modulation in instantaneous frequency as a function of their phase difference. Furthermore, we mathematically derive the effect of volume conduction on the model and show how indices for strength and direction of coupling can be derived. RESULTS: The methodology is tested using simulations and is applied to ongoing occipital-frontal MEG oscillations of healthy subjects in the alpha and beta bands during rest. The simulations show that the model is robust against the presence of noise, short observation times, and model violations. The application to MEG data shows that the model can reconstruct the observed occipital-frontal phase difference distributions. Furthermore, it suggests that phase locking in the alpha and beta band is established by qualitatively different mechanisms. CONCLUSION: When the recorded rhythms are assumed to be weakly coupled oscillators, a dynamical model for the phase interactions can be fitted to data. The model is able to reconstruct the observed phase difference distribution, and hence, provides a dynamical explanation for observed phase locking.

A space-frequency analysis of MEG background processes.

In MEG source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account. Since this covariance is in general too large to estimate based on the data and to invert efficiently, different parametrizations have been proposed in the literature. These models can be seen as special cases of the general decomposition of the covariance into a sum of Kronecker products of spatial matrices X(n) and temporal matrices T(n) (Van Loan, 2000). In this study we investigate the assumption of the matrices T(n) being Toeplitz. If so, the covariance matrix in the space-frequency domain will have an approximate block-diagonal structure, facilitating inversion, which is a prerequisite for source localization. In this study we address the question whether the Toeplitz approximation is valid for data sets obtained in visual evoked field, auditory evoked field, somatosensory evoked field experiments and data sets containing spontaneous activity. It turns out that on average 87% is in the block-diagonal of the sample covariance, which is close to the values obtained for real Toeplitz matrices T(n). This implies that the space-frequency domain is very interesting for source localization since the major part of the entire covariance can be incorporated in that domain straightforwardly. Finally, the two major processes in the background activity are characterized in terms of their spatial and frequency patterns, yielding a focal and a non-focal pattern in 8 of 10 data sets analyzed in this study. The focal pattern represents the alpha frequency at parieto-occipital areas, whereas the non-focal pattern is more widespread both in space and in frequency.

The spatiotemporal MEG covariance matrix modeled as a sum of Kronecker products.

The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for describing multiple, independent phenomena in the ongoing background activity. Whereas the single KP model can be interpreted by assuming that background activity is generated by randomly distributed dipoles with certain spatial and temporal characteristics, the sum model can be physiologically interpreted by assuming a composite of such processes. Taking enough terms into account, the spatiotemporal sample covariance matrix can be described exactly by this extended model. In the estimation of the sum of KP model, it appears that the sum of the first 2 KP describes between 67% and 93%. Moreover, these first two terms describe two physiological processes in the background activity: focal, frequency-specific alpha activity, and more widespread non-frequency-specific activity. Furthermore, temporal nonstationarities due to trial-to-trial variations are not clearly visible in the first two terms, and, hence, play only a minor role in the sample covariance matrix in terms of matrix power. Considering the dipole localization, the single KP model appears to describe around 80% of the noise and seems therefore adequate. The emphasis of further improvement of localization accuracy should be on improving the source model rather than the covariance model.

A maximum-likelihood estimator for trial-to-trial variations in noisy MEG/EEG data sets.

The standard procedure to determine the brain response from a multitrial evoked magnetoencephalography (MEG) or electroencephalography (EEG) data set is to average the individual trials of these data, time locked to the stimulus onset. When the brain responses vary from trial-to-trial this approach is false. In this paper, a maximum-likelihood estimator is derived for the case that the recorded data contain amplitude variations. The estimator accounts for spatially and temporally correlated background noise that is superimposed on the brain response. The model is applied to a series of 17 MEG data sets of normal subjects, obtained during median nerve stimulation. It appears that the amplitude of late component (30-120 ms) shows a systematic negative trend indicating a weakening response during stimulation time. For the early components (20-35 ms) no such a systematic effect was found. The model is furthermore applied on a MEG data set consisting of epileptic spikes of constant spatial distribution but varying polarity. For these data, the advantage of applying the model is that positive and negative spikes can be processed with a single model, thereby reducing the number of degrees of freedom and increasing the signal-to-noise ratio.

The coupled dipole model: an integrated model for multiple MEG/EEG data sets.

Often MEG/EEG is measured in a few slightly different conditions to investigate the functionality of the human brain. This kind of data sets show similarities, though are different for each condition. When solving the inverse problem (IP), performing the source localization, one encounters the problem that this IP is ill-posed: constraints are necessary to solve and stabilize the solution to the IP. Moreover, a substantial amount of data is needed to avoid a signal to noise ratio (SNR) that is too poor for source localizations. In the case of similar conditions, this common information can be exploited by analyzing the data sets simultaneously. The here proposed coupled dipole model (CDM) provides an integrated method in which these similarities between conditions are used to solve and stabilize the inverse problem. The coupled dipole model is applicable when data sets contain common sources or common source time functions. The coupled dipole model uses a set of common sources and a set of common source time functions (STFs) to model all conditions in one single model. The data of each condition are mathematically described as a linear combination of these common spatial and common temporal components. This linear combination is specified in a coupling matrix for each data set. The coupled dipole model was applied in two simulation studies and in one experimental study. The simulations show that the errors in the estimated spatial and temporal parameters decrease compared to the standard separate analyses. A decrease in position error of a factor of 10 was shown for the localization of two nearby sources. In the experimental application, the coupled dipole model was shown to be necessary to obtain a plausible solution in at least 3 of 15 conditions investigated. Moreover, using the CDM, a direct comparison between parameters in different conditions is possible, whereas in separate models, the scaling of the amplitude parameters varies in general from data set to data set.

A mathematical approach to the temporal stationarity of background noise in MEG/EEG measurements.

The general spatiotemporal covariance matrix of the background noise in MEG/EEG signals is huge. To reduce the dimensionality of this matrix it is modeled as a Kronecker product of a spatial and a temporal covariance matrix. When the number of time samples is larger than, say, J = 500, the iterative Maximum Likelihood estimation of these two matrices is still too time-consuming to be useful on a routine basis. In this study we looked for methods to circumvent this computationally expensive procedure by using a parametric model with subject-dependent parameters. Such a model would additionally help with interpreting MEG/EEG signals. For the spatial covariance, models have been derived already and it has been shown that measured MEG/EEG signals can be understood spatially as random processes, generated by random dipoles. The temporal covariance, however, has not been modeled yet, therefore we studied the temporal covariance matrix in several subjects. For all subjects the temporal covariance shows an alpha oscillation and vanishes for large time lag. This gives rise to a temporal noise model consisting of two components: alpha activity and additional random noise. The alpha activity is modeled as randomly occurring waves with random phase and the covariance of the additional noise decreases exponentially with lag. This model requires only six parameters instead of 12 J(J + 1). Theoretically, this model is stationary but in practice the stationarity of the matrix is highly influenced by the baseline correction. It appears that very good agreement between the data and the parametric model can be obtained when the baseline correction window is taken into account properly. This finding implies that the background noise is in principle a stationary process and that nonstationarities are mainly caused by the nature of the preprocessing method. When analyzing events at a fixed sample after the stimulus (e.g., the SEF N20 response) one can take advantage of this nonstationarity by optimizing the baseline window to obtain a low noise variance at this particular sample.

In vivo measurement of the brain and skull resistivities using an EIT-based method and realistic models for the head.

In vivo measurements of equivalent resistivities of skull (rho(skull)) and brain (rho(brain)) are performed for six subjects using an electric impedance tomography (EIT)-based method and realistic models for the head. The classical boundary element method (BEM) formulation for EIT is very time consuming. However, the application of the Sherman-Morrison formula reduces the computation time by a factor of 5. Using an optimal point distribution in the BEM model to optimize its accuracy, decreasing systematic errors of numerical origin, is important because cost functions are shallow. Results demonstrate that rho(skull)/rho(brain) is more likely to be within 20 and 50 rather than equal to the commonly accepted value of 80. The variation in rho(brain)(average = 301 omega x cm, SD = 13%) and rho(skull)(average = 12230 omega x cm, SD = 18%) is decreased by half, when compared with the results using the sphere model, showing that the correction for geometry errors is essential to obtain realistic estimations. However, a factor of 2.4 may still exist between values of rho(skull)/rho(brain) corresponding to different subjects. Earlier results show the necessity of calibrating rho(brain) and rho(skull) by measuring them in vivo for each subject, in order to decrease errors associated with the electroencephalogram inverse problem. We show that the proposed method is suited to this goal.