Reducing the unwanted draining vein BOLD contribution in fMRI with statistical post-processing methods

Recent BOLD fMRI data analysis methods show promise in reducing contributions from draining veins. The phase regressor method developed by [Menon, R.S., 2002. Post-acquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn. Reson. Med., 47, 1-9] creates phase and magnitude images, regresses magnitude as a function of phase, and subtracts phase-estimated magnitudes from the observed magnitudes. The corrected magnitude images are used to compute cortical activations. The complex constant phase method, developed by [Rowe, D.B., Logan, B.R., 2004. A complex way to compute fMRI activation. NeuroImage, 23, 1078-1092], uses complex-valued reconstructed images and a nonlinear regressor model to compute magnitude cortical activations assuming temporally constant phase. In both methods, the usage of the phase information is claimed to bias against voxels with task-related phase changes caused by some draining veins. The behavior of the statistical methods in data with several task-related magnitude and phase changes is compared. The power of the statistical methods for determining voxels with specific task-related magnitude and phase change combinations are determined in ideal simulated data. The phase regressor and complex constant phase activation determination techniques are examined to characterize the responses of the models to select task-related phase and magnitude change combinations in representative simulated time series. Possible draining veins in human preliminary data are discussed and analyzed with the models and the current challenges which prevent these methods from being reliably implemented are discussed.     

A complex way to compute fMRI activation

In functional magnetic resonance imaging, voxel time courses after Fourier or non-Fourier "image reconstruction" are complex valued as a result of phase imperfections due to magnetic field inhomogeneities. Nearly all fMRI studies derive functional "activation" based on magnitude voxel time courses [Bandettini, P., Jesmanowicz, A., Wong, E., Hyde, J.S., 1993. Processing strategies for time-course data sets in functional MRI of the human brain. Magn. Reson. Med. 30 (2): 161-173 and Cox, R.W., Jesmanowicz, A., Hyde, J.S., 1995. Real-time functional magnetic resonance imaging. Magn. Reson. Med. 33 (2): 230-236]. Here, we propose to directly model the entire complex or bivariate data rather than just the magnitude-only data. A nonlinear multiple regression model is used to model activation of the complex signal, and a likelihood ratio test is derived to determine activation in each voxel. We investigate the performance of the model on a real dataset, then compare the magnitude-only and complex models under varying signal-to-noise ratios in a simulation study with varying activation contrast effects.     

Parameter estimation in the magnitude-only and complex-valued fMRI data models

In functional magnetic resonance imaging, voxel time courses are complex-valued data but are traditionally converted to real magnitude-only data ones. At a large signal-to-noise ratio (SNR), the magnitude-only data Ricean distribution is approximated by a normal distribution that has been suggested as reasonable in magnitude-only data magnetic resonance images for an SNR of 5 and potentially as low as 3. A complex activation model has been recently introduced by Rowe and Logan [Rowe, D.B., and Logan, B.R. (2004). A complex way to compute fMRI activation. NeuroImage, 23 (3):1078-1092] that is valid for all SNRs. The properties of the parameter estimators and activation statistic for these two models and a more accurate Ricean approximation based on a Taylor series expansion are characterized in terms of bias, variance, and Cramer-Rao lower bound. It was found that the unbiased estimators in the complex model continued to be unbiased for lower SNRs while those of the normal magnitude-only data model became biased as the SNR decreased and at differing levels for the regression coefficients. The unbiased parameter estimators from the approximate magnitude-only Ricean Taylor model were unbiased to lower SNRs than the magnitude-only normal ones. Further, the variances of the parameter estimators achieved their minimum value in the complex data model regardless of SNR while the magnitude-only data normal model and Ricean approximation using a Taylor series did not as the SNR decreased. Finally, the mean activation statistic for the complex data model was higher and not SNR dependent while it decreased with SNR in the magnitude-only data models but less so for the approximate Ricean model. These results indicate that using the complex data model and not approximations to the true magnitude-only Ricean data model is more appropriate at lower SNRs. Therefore, since the computational cost is relatively low for the complex data model and since the SNR is not inherently known a priori for all voxels, the complex data model is recommended at all SNRs.     

Complex fMRI analysis with unrestricted phase is equivalent to a magnitude-only model

Due to phase imperfections, voxel time course measurements are complex valued. However, most fMRI studies measure activation using magnitude-only time courses. We show that magnitude-only analyses are equivalent to a complex fMRI activation model in which the phase is unrestricted, or allowed to dynamically change over time. This suggests that improvements to the magnitude-only model are possible by modeling the phase in each voxel over time.     

Using nonlinear models in fMRI data analysis: model selection and activation detection

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uluda?, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.     

Overt naming in aphasia studied with a functional MRI hemodynamic delay design

The purpose of this study was to develop a functional MRI method to examine overt speech in stroke patients with aphasia. An fMRI block design for overt picture naming was utilized which took advantage of the hemodynamic response delay where increased blood flow remains for 4-8 s after the task [(Friston, K.J., Jezzard, P., Turner, R., 1994. Analysis of functional MRI time-series. Hum. Brain Mapp. 1, 153-171)]. This allowed task-related information to be obtained after the task, minimizing motion artifact from overt speech (Eden, G.F., Joseph, J., Brown, H.E., Brown, C.P., Zeffiro, T.A., 1999. Utilizing hemodynamic delay and dispersion to detect fMRI signal change without auditory interference: the behavior interleaved gradients technique. Magn. Reson. Med. 41, 13-20; Birn, RM., Bandettini, P.A., Cox, R.W., Shaker, R., 1999. Event-related fMRI of tasks involving brief motion. Hum. Brain Mapp. 7, 106-114; Birn, R.M., Cox, R.W., Bandettini, P.A., 2004. Experimental designs and processing strategies for fMRI studies involving overt verbal responses. NeuroImage 23, 1046-1058). Five chronic aphasia patients participated (4 mild-moderate and 1 severe nonfluent/global). The four mild-moderate patients who correctly named 88-100% of the pictures during fMRI, had a greater number of suprathreshold voxels in L supplementary motor area (SMA) than R SMA (P < 0.07). Three of these four mild-moderate patients showed activation in R BA 45 and/or 44; along with L temporal and/or parietal regions. The severe patient, who named no pictures, activated almost twice as many voxels in R SMA than L SMA. He also showed activation in R BA 44, but had remarkably extensive L and R temporal activation. His poor naming and widespread temporal activation may reflect poor modulation of the bi-hemispheric neural network for naming. Results indicate that this fMRI block design utilizing hemodynamic response delay can be used to study overt naming in aphasia patients, including those with mild-moderate or severe aphasia. This method permitted verification that the patients were cooperating with the task during fMRI. It has application for future fMRI studies of overt speech in aphasia.     

Changes in fMRI magnitude data and phase data observed in block-design and event-related tasks

Functional magnetic resonance imaging (fMRI) data are acquired as a complex image pair including magnitude and phase information. The vast majority of fMRI experiments do not attempt to take advantage of the time varying phase information. The phase of the MRI signal is related to the local magnetic field changes, suggesting it may contain useful information about the source of hemodynamic activity. Analysis of phase data acquired from different fMRI experiments has shown the presence of activity in response to various stimuli. However, there have been no studies that have examined phase data in a larger group of subjects for multiple types of fMRI tasks nor have studies examined phase changes due to event-related stimuli. In this paper, we evaluate the correspondence between the magnitude and phase changes at a group level in a block-design motor tapping task and in an event-related auditory oddball task. The results for both block-design and event-related tasks indicate the presence of task-related information in the phase data with phase-only and magnitude-only approaches showing signal changes in the expected brain regions. Although there is more overall activity detected with magnitude data, the phase-only analysis also reveals activity in regions expected to be involved in the task, some of which were not significantly activated in the magnitude-only analysis, suggesting that the phase might provide some unique information. In addition, the phase can potentially increase sensitivity within regions also showing magnitude changes. Future work should focus on additional methods for combining the magnitude and phase data.     

Comparing hemodynamic models with DCM

The classical model of blood oxygen level-dependent (BOLD) responses by Buxton et al. [Buxton, R.B., Wong, E.C., Frank, L.R., 1998. Dynamics of blood flow and oxygenation changes during brain activation: the Balloon model. Magn. Reson. Med. 39, 855-864] has been very important in providing a biophysically plausible framework for explaining different aspects of hemodynamic responses. It also plays an important role in the hemodynamic forward model for dynamic causal modeling (DCM) of fMRI data. A recent study by Obata et al. [Obata, T., Liu, T.T., Miller, K.L., Luh, W.M., Wong, E.C., Frank, L.R., Buxton, R.B., 2004. Discrepancies between BOLD and flow dynamics in primary and supplementary motor areas: application of the Balloon model to the interpretation of BOLD transients. NeuroImage 21, 144-153] linearized the BOLD signal equation and suggested a revised form for the model coefficients. In this paper, we show that the classical and revised models are special cases of a generalized model. The BOLD signal equation of this generalized model can be reduced to that of the classical Buxton model by simplifying the coefficients or can be linearized to give the Obata model. Given the importance of hemodynamic models for investigating BOLD responses and analyses of effective connectivity with DCM, the question arises which formulation is the best model for empirically measured BOLD responses. In this article, we address this question by embedding different variants of the BOLD signal equation in a well-established DCM of functional interactions among visual areas. This allows us to compare the ensuing models using Bayesian model selection. Our model comparison approach had a factorial structure, comparing eight different hemodynamic models based on (i) classical vs. revised forms for the coefficients, (ii) linear vs. non-linear output equations, and (iii) fixed vs. free parameters, epsilon, for region-specific ratios of intra- and extravascular signals. Using fMRI data from a group of twelve subjects, we demonstrate that the best model is a non-linear model with a revised form for the coefficients, in which epsilon is treated as a free parameter.     

Low-frequency fluctuations in the cardiac rate as a source of variance in the resting-state fMRI BOLD signal

Heart rate fluctuations occur in the low-frequency range (<0.1 Hz) probed in functional magnetic resonance imaging (fMRI) studies of resting-state functional connectivity and most fMRI block paradigms and may be related to low-frequency blood-oxygenation-level-dependent (BOLD) signal fluctuations. To investigate this hypothesis, temporal correlations between cardiac rate and resting-state fMRI signal timecourses were assessed at 3 T. Resting-state BOLD fMRI and accompanying physiological data were acquired and analyzed using cross-correlation and regression. Time-shifted cardiac rate timecourses were included as regressors in addition to established physiological regressors (RETROICOR (Glover, G.H., Li, T.Q., Ress, D., 2000. Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR. Magn Reson Med 44, 162-167) and respiration volume per unit time (Birn, R.M., Diamond, J.B., Smith, M.A., Bandettini, P.A., 2006b. Separating respiratory-variation-related fluctuations from neuronal-activity-related fluctuations in fMRI. NeuroImage 31, 1536-1548). Significant correlations between the cardiac rate and BOLD signal timecourses were revealed, particularly negative correlations in gray matter at time shifts of 6-12 s and positive correlations at time shifts of 30-42 s (TR=6 s). Regressors consisting of cardiac rate timecourses shifted by delays of between 0 and 24 s explained an additional 1% of the BOLD signal variance on average over the whole brain across 9 subjects, a similar additional variance to that explained by respiration volume per unit time and RETROICOR regressors, even when used in combination with these other physiological regressors. This suggests that including such time-shifted cardiac rate regressors will be beneficial for explaining physiological noise variance and will thereby improve the statistical power in future task-based and resting-state fMRI studies.     

Cross-correlation: an fMRI signal-processing strategy

The discovery of functional MRI (fMRI), with the first papers appearing in 1992, gave rise to new categories of data that drove the development of new signal-processing strategies. Workers in the field were confronted with image time courses, which could be reshuffled to form pixel time courses. The waveform in an active pixel time-course was determined not only by the task sequence but also by the hemodynamic response function. Reference waveforms could be cross-correlated with pixel time courses to form an array of cross-correlation coefficients. From this array of numbers, colorized images could be created and overlaid on anatomical images. An early paper from the authors' laboratory is extensively reviewed here (Bandettini et al., 1993. Magn. Reson. Med. 30:161-173). That work was carried out using the vocabulary of vector algebra. Cross-correlation methodology was central to the discovery of functional connectivity MRI (fcMRI) by Biswal et al. (1995. Magn. Reson. Med. 34:537-541). In this method, a whole volume time course of images is collected while the brain is nominally at rest and connectivity is studied by cross-correlation of pixel time courses.     

High spatial resolution increases the specificity of block-design BOLD fMRI studies of overt vowel production

Functional MRI (fMRI) studies of tasks involving orofacial motion, such as speech, are prone to problems related to motion-induced magnetic field variations. Orofacial motion perturbs the static magnetic field, leading to signal changes that correlate with the task and corrupt activation maps with false positives or signal loss. These motion-induced signal changes represent a contraindication for the implementation of fMRI to study the neurophysiology of orofacial motion. An fMRI experiment of a structured, non-semantic vowel production task was performed using four different voxel volumes and three different slice orientations in an attempt to find a set of acquisition parameters leading to activation maps with maximum specificity. Results indicate that the use of small voxel volumes (2 x 2 x 3 mm(3)) yielded a significantly higher percentage of true positive activation compared to the use of larger voxel volumes. Slice orientation did not have as great an impact as spatial resolution, although coronal slices appeared superior at high spatial resolutions. Furthermore, it was found that combining the strategy of high spatial resolution with an optimum task duration and post-processing methods for separating true and false positives greatly improved the specificity of single-subject, block-design fMRI studies of structured, overt vowel production.     

A temporal comparison of BOLD, ASL, and NIRS hemodynamic responses to motor stimuli in adult humans

In this study, we have preformed simultaneous near-infrared spectroscopy (NIRS) along with BOLD (blood oxygen level dependent) and ASL (arterial spin labeling)-based fMRI during an event-related motor activity in human subjects in order to compare the temporal dynamics of the hemodynamic responses recorded in each method. These measurements have allowed us to examine the validity of the biophysical models underlying each modality and, as a result, gain greater insight into the hemodynamic responses to neuronal activation. Although prior studies have examined the relationships between these two methodologies through similar experiments, they have produced conflicting results in the literature for a variety of reasons. Here, by employing a short-duration, event-related motor task, we have been able to emphasize the subtle temporal differences between the hemodynamic parameters with a high contrast-to-noise ratio. As a result of this improved experimental design, we are able to report that the fMRI measured BOLD response is more correlated with the NIRS measure of deoxy-hemoglobin (R = 0.98; P < 10(-20)) than with oxy-hemoglobin (R = 0.71), or total hemoglobin (R = 0.53). This result was predicted from the theoretical grounds of the BOLD response and is in agreement with several previous works [Toronov, V.A.W., Choi, J.H., Wolf, M., Michalos, A., Gratton, E., Hueber, D., 2001. "Investigation of human brain hemodynamics by simultaneous near-infrared spectroscopy and functional magnetic resonance imaging." Med. Phys. 28 (4) 521-527.; MacIntosh, B.J., Klassen, L.M., Menon, R.S., 2003. "Transient hemodynamics during a breath hold challenge in a two part functional imaging study with simultaneous near-infrared spectroscopy in adult humans". NeuroImage 20 1246-1252.; Toronov, V.A.W., Walker, S., Gupta, R., Choi, J.H., Gratton, E., Hueber, D., Webb, A., 2003. "The roles of changes in deoxyhemoglobin concentration and regional cerebral blood volume in the fMRI BOLD signal" Neuroimage 19 (4) 1521-1531]. These data have also allowed us to examine more detailed measurement models of the fMRI signal and comment on the roles of the oxygen saturation and blood volume contributions to the BOLD response. In addition, we found high correlation between the NIRS measured total hemoglobin and ASL measured cerebral blood flow (R = 0.91; P < 10(-10)) and oxy-hemoglobin with flow (R = 0.83; P < 10(-05)) as predicted by the biophysical models. Finally, we note a significant amount of cross-modality, correlated, inter-subject variability in amplitude change and time-to-peak of the hemodynamic response. The observed co-variance in these parameters between subjects is in agreement with hemodynamic models and provides further support that fMRI and NIRS have similar vascular sensitivity.     

SSPNet: An interpretable 3D-CNN for classification of schizophrenia using phase maps of resting-state complex-valued fMRI data

Convolutional neural networks (CNNs) have shown promising results in classifying individuals with mental disorders such as schizophrenia using resting-state fMRI data. However, complex-valued fMRI data is rarely used since additional phase data introduces high-level noise though it is potentially useful information for the context of classification. As such, we propose to use spatial source phase (SSP) maps derived from complex-valued fMRI data as the CNN input. The SSP maps are not only less noisy, but also more sensitive to spatial activation changes caused by mental disorders than magnitude maps. We build a 3D-CNN framework with two convolutional layers (named SSPNet) to fully explore the 3D structure and voxel-level relationships from the SSP maps. Two interpretability modules, consisting of saliency map generation and gradient-weighted class activation mapping (Grad-CAM), are incorporated into the well-trained SSPNet to provide additional information helpful for understanding the output. Experimental results from classifying schizophrenia patients (SZs) and healthy controls (HCs) show that the proposed SSPNet significantly improved accuracy and AUC compared to CNN using magnitude maps extracted from either magnitude-only (by 23.4 and 23.6% for DMN) or complex-valued fMRI data (by 10.6 and 5.8% for DMN). SSPNet captured more prominent HC-SZ differences in saliency maps, and Grad-CAM localized all contributing brain regions with opposite strengths for HCs and SZs within SSP maps. These results indicate the potential of SSPNet as a sensitive tool that may be useful for the development of brain-based biomarkers of mental disorders.     

Support vector machines for temporal classification of block design fMRI data

This paper treats support vector machine (SVM) classification applied to block design fMRI, extending our previous work with linear discriminant analysis [LaConte, S., Anderson, J., Muley, S., Ashe, J., Frutiger, S., Rehm, K., Hansen, L.K., Yacoub, E., Hu, X., Rottenberg, D., Strother S., 2003a. The evaluation of preprocessing choices in single-subject BOLD fMRI using NPAIRS performance metrics. NeuroImage 18, 10-27; Strother, S.C., Anderson, J., Hansen, L.K., Kjems, U., Kustra, R., Siditis, J., Frutiger, S., Muley, S., LaConte, S., Rottenberg, D. 2002. The quantitative evaluation of functional neuroimaging experiments: the NPAIRS data analysis framework. NeuroImage 15, 747-771]. We compare SVM to canonical variates analysis (CVA) by examining the relative sensitivity of each method to ten combinations of preprocessing choices consisting of spatial smoothing, temporal detrending, and motion correction. Important to the discussion are the issues of classification performance, model interpretation, and validation in the context of fMRI. As the SVM has many unique properties, we examine the interpretation of support vector models with respect to neuroimaging data. We propose four methods for extracting activation maps from SVM models, and we examine one of these in detail. For both CVA and SVM, we have classified individual time samples of whole brain data, with TRs of roughly 4 s, thirty slices, and nearly 30,000 brain voxels, with no averaging of scans or prior feature selection.     

Mapping the orientation of intravoxel crossing fibers based on the phase information of diffusion circular spectrum

A new method is presented to map the orientation of intravoxel crossing fibers by using the phase of the diffusion circular spectrum harmonics. In a previous study [Zhan, W., Gu, H., Xu, S., Silbersweig, D.A., Stern, E., Yang, Y., 2003. Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients. Magn. Reson. Med. 49, 1077-1088], we demonstrated that the magnitude of the 4th-order harmonic of the diffusion circular spectrum can be used to identify the existence of fiber crossings. However, the orientation of the intravoxel crossing fibers remained unknown. This study extends the diffusion circular spectrum mapping method so that it is able to identify the orientation of the intravoxel crossing fibers by utilizing the phase information of the circular spectrum. In general, the phase of the circular harmonic determines the rotation of the apparent diffusion coefficient (ADC) profile on the sampling circle that is spanned by the major and medium eigenvector of the diffusion tensor and thus can be used to determine the orientation of the crossing fibers. Simulation results show that the regular tensor-based major eigenvector maps have obvious artifacts in the fiber-crossing area, whereas the estimated crossing fibers by the proposed method are much more consistent with the orientation of the actual intravoxel fibers. Diffusion MRI experiments were performed on five healthy human brains using a 3T scanner. The brain regions with fiber crossings were selected by thresholding the magnitudes of the 4th-order circular spectrum map. Intravoxel crossing fibers were estimated by the phase of the 4th-order harmonic for each voxel within these areas. The estimated intravoxel crossing fibers demonstrated a clear consistency with the orientations of fiber tracks in the surrounding tissues, reducing the fiber orientation discontinuity of the regular major eigenvector map.     

A BOLD search for baseline

While we occasionally observe negative BOLD signals, its physiological basis has remained uncertain. This is in part due to the qualitative use of fMRI where the baseline is conveniently differenced away to reveal focal area(s) of interest. Recently, however, there has been a noticeable trend towards quantitative neuroimaging where changes in oxidative energetics (CMR(O2)) are quantified by calibrated fMRI. Pasley et al. [Pasley, B.N., Inglis, B.A., Freeman, R.D., 2007. Analysis of oxygen metabolism implies a neural origin for the negative BOLD response in human visual cortex. NeuroImage] used calibrated fMRI in conjunction with a novel stimulus paradigm to investigate the neural basis of the negative BOLD signal in awake humans. They hypothesized - based on prior results - that if the baseline was lowered then DeltaCMR(O2) would have to be larger. While their main findings point to an energetic basis for the negative BOLD signal, their results have far reaching implications for the present definition of baseline as well as for future research investigating the neural and/or energetic basis of baseline.     

Functional imaging of the human superior colliculus: An optimised approach

Effective functional imaging of the human Superior Colliculus (SC) has often been regarded as difficult because of the small size of the SC and its proximity to sources of pulsatile (cardiac) noise. An optimised approach to functional imaging of the SC with fMRI is presented, based upon the novel finding that visually-induced BOLD responses in the SC are qualitatively different from responses in both cortical (V1) and sub-cortical (LGN) comparison areas. An optimised model with a Haemodynamic Response Function (HRF) which peaks early (4–5 s) and then falls rapidly is shown to be best suited for revealing SC responses, while a model peaking at 6 s and falling more slowly was most sensitive in the two comparison areas. Additionally, a method of correcting for the noise characteristics of fMRI responses proposed recently by de Zwart et al. (de Zwart, J. A., van Gelderen, P., Fukunaga, M., & Duyn, J. H. (2008). Reducing correlated noise in fMRI data. Magn Reson Med, 59, 939–945) is modified for use in the SC, and shown to be highly effective at further improving the statistical detectability of responses by modelling out noise. Together these methods represent a significant advance over previous approaches to functional imaging of the human SC. They permit the routine detection of strong SC activity in single subjects at standard spatial resolutions.     

Valid conjunction inference with the minimum statistic

In logic a conjunction is defined as an AND between truth statements. In neuroimaging, investigators may look for brain areas activated by task A AND by task B, or a conjunction of tasks (Price, C.J., Friston, K.J., 1997. Cognitive conjunction: a new approach to brain activation experiments. NeuroImage 5, 261-270). Friston et al. (Friston, K., Holmes, A., Price, C., Buchel, C., Worsley, K., 1999. Multisubject fMRI studies and conjunction analyses. NeuroImage 10, 85-396) introduced a minimum statistic test for conjunction. We refer to this method as the minimum statistic compared to the global null (MS/GN). The MS/GN is implemented in SPM2 and SPM99 software, and has been widely used as a test of conjunction. However, we assert that it does not have the correct null hypothesis for a test of logical AND, and further, this has led to confusion in the neuroimaging community. In this paper, we define a conjunction and explain the problem with the MS/GN test as a conjunction method. We present a survey of recent practice in neuroimaging which reveals that the MS/GN test is very often misinterpreted as evidence of a logical AND. We show that a correct test for a logical AND requires that all the comparisons in the conjunction are individually significant. This result holds even if the comparisons are not independent. We suggest that the revised test proposed here is the appropriate means for conjunction inference in neuroimaging.     

Delayed hemodynamic responses in schizophrenia

While there are many reports of reduced amplitude of hemodynamic responses in schizophrenia, there are no reports of delayed hemodynamic responses, in spite of event-related brain potential (ERP) evidence of slowed neural responses. Recently, Henson et al. (2002) [Henson, R., Price, C., Rugg, M., Turner, R., Friston, K., 2002. Detecting latency differences in event-related BOLD responses: application to words versus nonwords and initial versus repeated face presentations. NeuroImage, 15:83-97] proposed a new method for testing small latency effects (<2 s) in hemodynamic responses. fMRI data were collected during a visual oddball task with infrequent (12%) targets (K) and frequent (88%) standards (X), presented every 1-3 s pseudorandomly, with 7-24 s between targets. SPM99 yielded parameter estimates for the hemodynamic response and its temporal derivative (TD). Beta images reflecting hemodynamic response magnitude to target stimuli were minimally thresholded (P < 0.05, uncorrected), and latencies were estimated for surviving voxels using TD and hemodynamic response beta values. DSM-IV schizophrenia patients (n = 12) and sex- and age-matched healthy control subjects (n = 12) were recruited from the community. Although groups differed only minimally in activation height, hemodynamic responses were significantly delayed in basal ganglia, thalamus, and anterior cingulate in patients with schizophrenia. Psychomotor slowing reflected in reaction times to targets recorded outside the magnet was related to hemodynamic slowing in basal ganglia, anterior cingulate, thalamus, as well as left cerebellum in controls. Delays in the hemodynamic response have far-reaching implications for understanding the pathophysiology of schizophrenia from slowed neural responses to slowed substrate delivery, and depending of the degree of delay, may raise methodological issues regarding modeling hemodynamic responses in patients and controls.     

Approaching ultimate intrinsic SNR in a uniform spherical sample with finite arrays of loop coils

We investigated to what degree and at what rate the ultimate intrinsic (UI) signal‐to‐noise ratio (SNR) may be approached using finite radiofrequency detector arrays. We used full‐wave electromagnetic field simulations based on dyadic Green's functions to compare the SNR of arrays of loops surrounding a uniform sphere with the ultimate intrinsic SNR (UISNR), for increasing numbers of elements over a range of magnetic field strengths, voxel positions, sphere sizes, and acceleration factors. We evaluated the effect of coil conductor losses and the performance of a variety of distinct geometrical arrangements such as “helmet” and “open‐pole” configurations in multiple imaging planes. Our results indicate that UISNR at the center is rapidly approached with encircling arrays and performance is substantially lower near the surface, where a quadrature detection configuration tailored to voxel position is optimal. Coil noise is negligible at high field, where sample noise dominates. Central SNR for practical array configurations such as the helmet is similar to that of close‐packed arrangements. The observed trends can provide physical insights to improve coil design. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 44B: 53–65, 2015