Bayesian source separation of fMRI signals

In analyzing the results of functional magnetic resonance imaging, the identification of significant activation in voxels is a crucial task. In computing the activation level, a standard method is to select an assumed to be known reference function and perform a multiple regression of the time courses on it and a linear trend. Once the linear trend is found, the correlation between the assumed to be known reference function and the detrended observed time-course in each voxel is computed and voxels colored according to their correlation. But the most important question is: How do we choose the reference function? This paper develops a Bayesian statistical approach to determining the underlying source reference function based on Bayesian source separation, and uses it on both simulated and real fMRI data. This underlying reference function is the unobserved response due the presentation of the experimental stimulus

Signal Processing Spreads a Voxel’s Temporal Frequency Task-Activated Peak and Induces Spatial Correlations in Dual-Task Complex-Valued fMRI

Roll 213. Barth's Counsel Schedule / Bannon's History Copies. Image 7 of 21. (13 October, 1955) [PHO 1.213.7]The Boleslaus Lukaszewski (Father Luke) Photographs contain more than 28,000 images of Saint Louis University people, activities, and events between 1951 and 1970. The photographs were taken by Boleslaus Lukaszewski (Father Luke), a Jesuit priest and member of the University's Philosophy Department faculty

Quantifying the Statistical Impact of GRAPPA in fcMRI Data with a Real-Valued Isomorphism

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed on the effects that the GRAPPA operation has on reconstructed voxel means and correlations. The interpolation of missing spatial frequencies with the GRAPPA model is shown to result in an artificial correlation induced between voxels in the reconstructed images, and these artificial correlations are shown to reside in the low temporal frequency spectrum commonly associated with functional connectivity. Through a real-valued isomorphism, such as the one outlined in this manuscript, the exact artificial correlations induced by the GRAPPA model are not simply estimated, as they would be with simulations, but are precisely quantified. If these correlations are unaccounted for, they can incur an increase in false positives in functional connectivity studies

Complex-Valued Time-Series Correlation Increases Sensitivity in FMRI Analysis

Purpose To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis. Materials and Methods The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel\u27s temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex. Results The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing. Conclusions Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation

Impacts of Simultaneous Multislice Acquisition on Sensitivity and Specificity in fMRI

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal “leakage” between aliased locations, i.e., slice “leakage,” and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) reconstruction algorithmand acceleration factor (AF = 8) used in the fMRI data in the young adult Human Connectome Project (HCP). We also evaluate split slice-GRAPPA (leak block), which can reduce slice leakage. We use simulations to disentangle higher test statistics into true positives (sensitivity) and false positives (decreased specificity). Slice leakage was greatly decreased by split slice-GRAPPA. Noise amplification was decreased by using moderate acceleration factors (AF = 4). We examined slice leakage in unprocessed fMRI motor task data from the HCP. When data were smoothed, we found evidence of slice leakage in some, but not all, subjects. We also found evidence of SMS noise amplification in unprocessed task and processed resting-state HCP data

Complex-valued Time Series Modeling for Improved Activation Detection in fMRI Studies

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we develop magnitude and phase detrending procedures for complex-valued time series and examine the effect of spatial smoothing. These methods improve the power of complex-valued data-based activation statistics. Our results advocate for the use of the complex-valued data and the modeling of its dependence structures as a more efficient and reliable tool in fMRI experiments over the current practice of using only magnitude-valued datasets

Incorporating Relaxivities to More Accurately Reconstruct MR Images

Purpose To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step. Materials and methods In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2⁎, T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2⁎, ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2⁎, T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects. Result Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations. Conclusion With the use of the proposed method, the effects of T2⁎ and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration

The SENSE-Isomorphism Theoretical Image Voxel Estimation (SENSE-ITIVE) Model for Reconstruction and Observing Statistical Properties of Reconstruction Operators

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show that not only is the skew-symmetric coil covariance unlike that of real data, but the estimated covariance structure between voxels over a time series of experimental data is not an identity matrix. As such, a new model, entitled SENSE-ITIVE, is described with both revised coil and voxel covariance structures. Both the SENSE and SENSE-ITIVE models are represented in terms of real-valued isomorphisms, allowing for a statistical analysis of reconstructed voxel means, variances, and correlations resulting from the use of different coil and voxel covariance structures used in the reconstruction processes to be conducted. It is shown through both theoretical and experimental illustrations that the miss-specification of the coil and voxel covariance structures in the SENSE model results in a lower standard deviation in each voxel of the reconstructed images, and thus an artificial increase in SNR, compared to the standard deviation and SNR of the SENSE-ITIVE model where both the coil and voxel covariances are appropriately accounted for. It is also shown that there are differences in the correlations induced by the reconstruction operations of both models, and consequently there are differences in the correlations estimated throughout the course of reconstructed time series. These differences in correlations could result in meaningful differences in interpretation of results

A scale-model room as a practical teaching experiment

A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham&rsquo;s p-theorem.<br /