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How reliable are fMRI-EEG studies of epilepsy? A nonparametric approach to analysis validation and optimization.

Simultaneously acquired functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) data hold great promise for localizing the spatial source of epileptiform events detected in the EEG trace. Despite a number of studies applying this method, there has been no independent and systematic validation of the approach. The present study uses a nonparametric method to show that interictal discharges lead to a blood oxygen level dependent (BOLD) response that is significantly different to that obtained by examining random 'events'. We also use this approach to examine the optimization of analysis strategy for detecting these BOLD responses. Two patients with frequent epileptiform events and a healthy control were studied. The fMRI data for each patient were analyzed using a model derived from the timings of the epileptiform events detected on EEG during fMRI scanning. Twenty sets of random pseudoevents were used to generate a null distribution representing the level of chance correlation between the EEG events and fMRI data. The same pseudoevents were applied to control data. We demonstrate that it is possible to detect blood oxygen level-dependent (BOLD) changes related to interictal discharges with specific and independent knowledge about the reliability of this activation. Biologically generated events complicate the fMRI-EEG experiment. Our proposed validation examines whether identified events have an associated BOLD response beyond chance and allows optimization of analysis strategies. This is an important step beyond standard analysis. It informs clinical interpretation because it permits assessment of the reliability of the connection between interictal EEG events and the BOLD response to those events.

Analysis of Variance↗

A critique of functional localisers.

In this critique, we review the usefulness of functional localising scans in functional MRI studies. We consider their conceptual motivations and the implications for experimental design and inference. Functional localisers can often be viewed as acquiring data from cells that have been removed from an implicit factorial design. This perspective reveals their potentially restrictive nature. We deconstruct two examples from the recent literature to highlight the key issues. We conclude that localiser scans can be unnecessary and, in some instances, lead to a biased and inappropriately constrained characterisation of functional anatomy.

Brain Mapping↗

On rotational invariance in adaptive spatial filtering of fMRI data.

Canonical correlation analysis (CCA) has previously been shown to work well for detecting neural activity in fMRI data. The reason is that CCA enables simultaneous temporal modeling and adaptive spatial filtering of the data. This article introduces a novel method for adaptive anisotropic filtering using the CCA framework and compares it to a previously proposed method. Isotropic adaptive filtering, which is only able to form isotropic filters of different sizes, is also presented and evaluated. It is shown that a new feature of the proposed method is invariance to the orientation of activated regions, and that the detection performance is superior to both that of the previous method and to isotropic filtering.

Artifacts↗

A multivariate approach for processing magnetization effects in triggered event-related functional magnetic resonance imaging time series.

Triggered event-related functional magnetic resonance imaging requires sparse intervals of temporally resolved functional data acquisitions, whose initiation corresponds to the occurrence of an event, typically an epileptic spike in the electroencephalographic trace. However, conventional fMRI time series are greatly affected by non-steady-state magnetization effects, which obscure initial blood oxygen level-dependent (BOLD) signals. Here, conventional echo-planar imaging and a post-processing solution based on principal component analysis were employed to remove the dominant eigenimages of the time series, to filter out the global signal changes induced by magnetization decay and to recover BOLD signals starting with the first functional volume. This approach was compared with a physical solution using radiofrequency preparation, which nullifies magnetization effects. As an application of the method, the detectability of the initial transient BOLD response in the auditory cortex, which is elicited by the onset of acoustic scanner noise, was used to demonstrate that post-processing-based removal of magnetization effects allows to detect brain activity patterns identical with those obtained using the radiofrequency preparation. Using the auditory responses as an ideal experimental model of triggered brain activity, our results suggest that reducing the initial magnetization effects by removing a few principal components from fMRI data may be potentially useful in the analysis of triggered event-related echo-planar time series. The implications of this study are discussed with special caution to remaining technical limitations and the additional neurophysiological issues of the triggered acquisition.

Artifacts↗

Large-scale neural models and dynamic causal modelling.

Dynamic causal modelling (DCM) is a method for estimating and making inferences about the coupling among small numbers of brain areas, and the influence of experimental manipulations on that coupling [Friston, K.J., Harrison, L., Penny, W., 2003 Dynamic causal modelling. Neuroimage 19, 1273-1302]. Large-scale neural modelling aims to construct neurobiologically grounded computational models with emergent behaviours that inform our understanding of neuronal systems. One such model has been used to simulate region-specific BOLD time-series [Horwitz, B., Friston, K.J., Taylor, J.G., 2000. Neural modeling and functional brain imaging: an overview. Neural Netw. 13, 829-846]. DCM was used to make inferences about effective connectivity using data generated by a model implementing a visual delayed match-to-sample task [Tagamets, M.A., Horwitz, B., 1998. Integrating electrophysiological and anatomical experimental data to create a large-scale model that simulates a delayed match-to-sample human brain imaging study. Cereb. Cortex 8, 310-320]. The aim was to explore the validity of inferences made using DCM about the connectivity structure and task-dependent modulatory effects, in a system with a known connectivity structure. We also examined the effects of misspecifying regions of interest. Models with hierarchical connectivity and reciprocal connections were examined using DCM and Bayesian Model Comparison [Penny, W.D., Stephan, K.E., Mechelli, A., Friston, K.J., 2004. Comparing dynamic causal models. Neuroimage 22, 1157-1172]. This approach revealed strong evidence for those models with correctly specified anatomical connectivity. Furthermore, Bayesian model comparison favoured those models when bilinear effects corresponded to their implementation in the neural model. These findings generalised to an extended model with two additional areas and reentrant circuits. The conditional uncertainty of coupling parameter estimates increased in proportion to the number of incorrectly specified regions. These results highlight the role of neural models in establishing the validity of estimation and inference schemes. Specifically, Bayesian model comparison confirms the validity of DCM in relation to a well-characterised and comprehensive neuronal model.

Bayes Theorem↗

Cortical layer-dependent BOLD and CBV responses measured by spin-echo and gradient-echo fMRI: insights into hemodynamic regulation.

Spatial specificity of functional magnetic resonance imaging (fMRI) signals to sub-millimeter functional architecture remains controversial. To investigate this issue, high-resolution fMRI in response to visual stimulus was obtained in isoflurane-anesthetized cats at 9.4 T using conventional gradient-echo (GE) and spin-echo (SE) techniques; blood oxygenation-level dependent (BOLD) and cerebral blood volume (CBV)-weighted data were acquired without and with injection of 10 mg Fe/kg monocrystalline iron oxide nanoparticles (MION), respectively. Studies after MION injection at two SE times show that the T2' contribution to SE fMRI is minimal. GE and SE BOLD changes were spread across the cortical layers. GE and SE CBV-weighted fMRI responses peaked at the middle cortical layer, which has the highest experimentally-determined microvascular volume; full-width at half-maximum was <1.0 mm. Parenchymal sensitivity of GE CBV-weighted fMRI was approximately 3 times higher than that of SE CBV-weighted fMRI and approximately 1.5 times higher than that of BOLD fMRI. It is well known that GE CBV-weighted fMRI detects a volume change in vessels of all sizes, while SE CBV-weighted fMRI is heavily weighted toward microvascular changes. Peak CBV change of 10% at the middle of the cortex in GE measurements was 1.8 times higher than that in SE measurements, indicating that CBV changes occur predominantly for vasculature connecting the intracortical vessels and capillaries. Our data supports the notion of laminar-dependent CBV regulation at a sub-millimeter scale.

Animals↗

Divide and conquer: a defense of functional localizers.

Numerous functionally distinct regions of cortex (e.g., V1, MT, the fusiform face area) can be easily identified in any normal human subject in just a few minutes of fMRI scanning. However, the locations of these regions vary across subjects. Investigations of these regions have therefore often used a functional region of interest (fROI) approach in which the region is first identified functionally in each subject individually, before subsequent scans in the same subjects test specific hypotheses concerning that region. This fROI method, which resembled long-established practice in visual neurophysiology, has methodological, statistical, and theoretical advantages over standard alternatives (such as whole-brain analyses of group data): (i) because functional properties are more consistently and robustly associated with fROIs than with locations in stereotaxic space, functional hypotheses concerning fROIs are often the most straightforward to frame, motivate, and test, (ii) because hypotheses are tested in only a handful of fROIs (instead of in tens of thousands of voxels), advance specification of fROIs provides a massive increase in statistical power over whole-brain analyses, and (iii) some fROIs may serve as candidate distinct components of the mind/brain worth investigation as such. Of course fROIs can be productively used in conjunction with other complementary methods. Here, we explain the motivation for and advantages of the fROI approach, and we rebut the criticism of this method offered by Friston et al. (Friston, K., Rotshtein, P., Geng, J., Sterzer, P., Henson, R., in press. A critique of functional localizers. NeuroImage).

Brain Mapping↗

A new method for fast quantitative mapping of absolute water content in vivo.

The presence of brain edema, in its various forms, is an accompanying feature of many diseased states. Although the localized occurrence of brain edema may be demonstrated with MRI, the quantitative determination of absolute water content, an aspect that could play an important role in the objective evaluation of the dynamics of brain edema and the monitoring of the efficiency of treatment, is much more demanding. We present a method for the localized and quantitative measurement of absolute water content based on the combination of two fast multi-slice and multi-time point sequences QUTE and TAPIR for mapping the T(2)* and T(1) relaxation times, respectively. Incorporation of corrections for local B(1) field miscalibrations, temperature differences between the subject and a reference probe placed in the FOV, receiver profile inhomogeneities and T(1) saturation effects are included and allow the determination of water content with anatomical resolution and a precision >98%. The method was validated in phantom studies and was applied to the localized in vivo measurement of water content in a group of normal individuals and a patient with brain tumor. The results demonstrate that in vivo measurement of regional absolute water content is possible in clinically relevant measurement times with a statistical and systematic measurement error of <2%.

Adult↗

Handedness, dichotic-listening ear advantage, and gender effects on planum temporale asymmetry--a volumetric investigation using structural magnetic resonance imaging.

Previous research has often examined whether the asymmetrical structure of the planum temporale (PT) represents an anatomical correlate of lateralized language-processing functions, gathering diverging empirical evidence by comparing PT asymmetry in subjects with differing handedness, gender, or speech lateralization. Apart from other methodological problems, direct comparisons between studies are hampered by insufficient assessment and consideration of all three potential determinants of structural cerebral asymmetry. Based on volumetric assessment of structural Magnetic Resonance Imaging (MRI) scans of 104 healthy subjects, the present study replicated earlier observations of an overall leftward PT asymmetry, which was found to prevail irrespective of handedness, gender, or dichotic-listening ear advantage. However, the mean magnitude of this leftward asymmetry was not determined by either one of these factors in itself, but varied depending on their specific combination. A clear correspondence between structural and functional asymmetry was only observed among right-handed males. In this particular subgroup, more pronounced structural asymmetry was associated with an enlarged PT on the left side, while the enhanced leftward asymmetry of female sinistrals resulted from smaller adjusted volumes of their right PT. The existence of such complex interactions suggests that future research in this area can only be expected to overcome past inconsistencies by adequately considering handedness, gender, and speech lateralization.

Auditory Cortex↗

Volumes of the caudate nuclei in women with somatization disorder and healthy women.

Very little is known about the pathophysiology of somatization disorder. This study was designed to analyze the volumes of some brain structures possibly involved in somatization based on the observation of glucose metabolism of the brain in these patients. We studied 10 female patients with a diagnosis of somatization disorder or undifferentiated somatoform disorder with no comorbid current DSM-IV Axis I disorder and compared them to 16 healthy female volunteers using brain MRI (1.5 T instrument). The patients had bilateral enlargement of caudate nuclei volumes compared with healthy volunteers. These volume differences in the caudate nuclei could be associated with the pathophysiology of somatization.

Adult↗

Computer simulation of the inverse problem of electrocardiography: use of properties of harmonic functions.

The problem of reconstructing the pattern of heart excitation from body surface potentials is simulated. The problem is well known as the inverse problem of electrocardiography and in a general case this problem has a non-unique solution. The relationship of the problem with the inverse problem of potential theory is shown. From this relationship a new excitation propagation model for the heart ventricles is developed. The model is based on a classical multidipole cardiogenerator, but is stable, flexible, and provides a unique solution for the inverse problem of electrocardiography.

Body Surface Potential Mapping↗

A system for computing neuromorphometry from magnetic resonance images.

A new technique for the automated measurement of a variety of gross neuroanatomical structures (such as cerebral ventricles) is described. The system exploits the local statistical properties of dual-echo magnetic resonance images of the brain to produce a fully unsupervised classification of these images into a variety of tissue types. Following this, a simple region agglomeration procedure aggregates the segmented regions by class, and submits these regions to a computational-geometric analysis from which a wide variety of measures are derived.

Brain↗

Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.

The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

Computer Simulation↗

Solutions to the Behrens-Fisher problem.

When testing the equality of the means from two independent normally distributed populations given that the variances of the two populations are unknown but assumed equal the classical Student's two sample t-test is recommended. If the underlying population distributions are normal with unequal and unknown variances, either Welch's t-statistic or Satterthwaite's Approximate F test is suggested. However, Welch's procedure is non-robust under most non-normal distributions. There is a variable tolerance level around the strict assumptions of data independence, homogeneity of variances, identically and normal distributions. Few textbooks offer alternatives when one or more of the underlying assumptions are not defensible. We have developed an executable FORTRAN code for producing the statistics suggested by Cressie and Whitford, Yuen and Dixon, and Yuen. An executable FORTRAN is available from the author on request (e-mail only).

Animals↗

TRI2SOLID: an application of reverse engineering methods to the creation of CAD models of bone segments.

For many biomechanical engineering activities it would be useful to have the three dimensional (3D) geometry of bone segments available in form of vectorial models within computer aided design (CAD) environments. In this paper a new method for the semi-automatic conversion of a stack of CT images of a femur into a CAD solid model is described. This method is relatively simple, accurate, and requires only a 3D CAD plus a few additional programs available in the public domain. The proposed method was used to convert the CT scan data set of a human femur into a valid CAD model; the resulting solid was two times more accurate than that obtained using the commonly used procedure based on 2D segmentation.

Algorithms↗

Very fast approximate reconstruction of MR images.

The ultra fast Fourier transform (UFFT) provides the means for a very fast computation of a magnetic resonance (MR) image, because it is implemented using only additions and no multiplications at all. It achieves this by approximating the complex exponential functions involved in the Fourier transform (FT) sum with computationally simpler periodic functions. This approximation introduces erroneous spectrum peaks of small magnitude. We examine the performance of this transform in some typical MRI signals. The results show that this transform can very quickly provide an MR image. It is proposed to be used as a replacement of the classically used FFT whenever a fast general overview of an image is required.

Algorithms↗

On the behavior of approaches to simulate reactive transport.

Two families of approaches exist to simulate reactive transport in groundwater: The Direct Substitution Approach (DSA), based on Newton-Raphson and the Picard or Sequential Iteration Approach (SIA). We applied basic versions of both methods to several test cases and compared both computational demands and quality of the solution for varying grid size. Results showed that the behavior of the two approaches is sensitive to both grid size and chemistry. As a general rule, the DSA is more robust than the SIA, in the sense that its convergence is less sensitive to time step size (any approach will converge given a sufficiently small time step). Moreover, the DSA leads to a better simulation of sharp fronts, which can only be reproduced with fine grids after many iterations when the SIA is used. As a consequence, the DSA runs faster than SIA in chemically difficult cases (i.e., highly non-linear and/or very retarded), because the SIA may require very small time steps to converge. On the other hand, the size of the system of equations is much larger for the DSA than for the SIA, so that its CPU time and memory requirements tend to be less favorable with increasing grid size. As a result, the SIA may become faster than the DSA for very large, chemically simple problems. The use of an iterative linear solver for the DSA makes its CPU time less sensitive to grid size.

Calcium Carbonate↗

Graphical display of fMRI data: visualizing multidimensional space.

Visualization of multidimensional data is an integral part of computational statistics and exploratory data analysis (EDA). We show how visualization of fMRI time-courses may be used to reveal the fMRI data structure. We consider fMRI time-courses (TCs) as points in multidimensional space. In simulated and in vivo data, we show that minimum spanning tree (MST)-based sequencing of multivariate time-courses, in combination with a homogeneity map visualization, allows for effective and useful graphical display of the groups of coactivated time-courses obtained by temporal clustering. This display may serve as a tool for investigation of brain connectivity. We also suggest a simple overall display of the entire fMRI data set.

Artifacts↗