Generalized likelihood ratio tests for complex fMRI data: a simulation study

Bayesian estimation of changes in transverse relaxation rates

Although the biasing of R(2)* estimates by assuming magnitude MR data to be normally distributed has been described, the effect on changes in R(2)* (DeltaR(2)*), such as induced by a paramagnetic contrast agent, has not been reported. In this study, two versions of a novel Bayesian maximum a posteriori approach for estimating DeltaR(2)* are described and evaluated: one that assumes normally distributed data and the other, Rice-distributed data. The approach enables the robust, voxelwise determination of the uncertainty in DeltaR(2)* estimates and provides a useful statistical framework for quantifying the probability that a pixel has been significantly enhanced. This technique was evaluated in vivo, using ultrasmall superparamagnetic iron oxide particles in orthotopic murine prostate tumors. It is shown that assuming magnitude data to be normally distributed causes DeltaR(2)* to be underestimated when signal-to-noise ratio is modest. However, the biasing effect is less than is found in R(2)* estimates, implying that the simplifying assumption of normally distributed noise is more justifiable when evaluating DeltaR(2)* compared with when evaluating precontrast R(2)* values.

Lesion detection in dynamic FDG-PET using matched subspace detection

We describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumors from background using the time activity curves (TACs) that characterize the uptake of PET tracers. TACs are modeled using linear subspaces with additive Gaussian noise. Using TACs from a primary tumor region of interest (ROI) and one or more background ROIs, each identified by a human observer, two linear subspaces are identified. Applying a matched subspace detector to these identified subspaces on a voxel-by-voxel basis throughout the dynamic image produces a test statistic at each voxel which on thresholding indicates potential locations of secondary or metastatic tumors. The detector is derived for three cases: using a single TAC with white noise of unknown variance, using a single TAC with known noise covariance, and detection using multiple TACs within a small ROI with known noise covariance. The noise covariance is estimated for the reconstructed image from the observed sinogram data. To evaluate the proposed method, a simulation-based receiver operating characteristic (ROC) study for dynamic PET tumor detection is designed. The detector uses a dynamic sequence of frame-by-frame 2-D reconstructions as input. We compare the performance of the subspace detectors with that of a Hotelling observer applied to a single frame image and of the Patlak method applied to the dynamic data. We also show examples of the application of each detection approach to clinical PET data from a breast cancer patient with metastatic disease.

Bayesian kernel methods for analysis of functional neuroimages

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.

Complex data analysis in high-resolution SSFP fMRI

In transition-band steady-state free precession (SSFP) functional MRI (fMRI), functional contrast originates from a bulk frequency shift induced by a deoxygenated hemoglobin concentration change in the activated brain regions. This frequency shift causes a magnitude and/or phase-signal change depending on the off-resonance distribution of a voxel in the balanced-SSFP (bSSFP) profile. However, in early low-resolution studies, only the magnitude signal activations were shown. In this paper the task-correlated phase-signal change is presented in a high-resolution (1 x 1 x 1 mm3) study. To include this phase activation in a functional analysis, a new complex domain data analysis method is proposed. The results show statistically significant phase-signal changes in a large number of voxels comparable to that of the magnitude-activated voxels. The complex-data analysis method successfully includes these phase activations in the activation map and thus provides wider coverage compared to magnitude-data analysis results.

Implications of the Rician distribution for fMRI generalized likelihood ratio tests

In functional magnetic resonance imaging (fMRI), the general linear model test (GLMT) is widely used for brain activation detection. However, the GLMT relies on the assumption that the noise corrupting the data is Gaussian distributed. Because the majority of fMRI studies employ magnitude image reconstructions, which are Rician distributed, this assumption is invalid and has significant consequences in case the signal-to-noise ratio (SNR) is low. In this study, we show that the GLMT should not be used at low SNR. Furthermore, we propose a generalized likelihood ratio test for magnitude MR data that has the same performance compared to the GLMT for high SNR, but performs significantly better than the GLMT for low SNR.