Kirt A. Schaper

Magnetic Resonance Image Tissue Classification Using a Partial Volume Model

We describe a sequence of low-level operations to isolate and classify brain tissue within T1-weighted magnetic resonance images (MRI). Our method first removes nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. We compensate for image nonuniformities due to magnetic field inhomogeneities by fitting a tricubic B-spline gain field to local estimates of the image nonuniformity spaced throughout the MRI volume. The local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. The measurement model uses mean tissue intensity and noise variance values computed from the global image and a multiplicative bias parameter that is estimated for each region during the histogram fit. Voxels in the intensity-normalized image are then classified into six tissue types using a maximum a posteriori classifier. This classifier combines the partial volume tissue measurement model with a Gibbs prior that models the spatial properties of the brain. We validate each stage of our algorithm on real and phantom data. Using data from the 20 normal MRI brain data sets of the Internet Brain Segmentation Repository, our method achieved average kappa indices of kappa = 0.746 +/- 0.114 for gray matter (GM) and kappa = 0.798 +/- 0.089 for white matter (WM) compared to expert labeled data. Our method achieved average kappa indices kappa = 0.893 +/- 0.041 for GM and kappa = 0.928 +/- 0.039 for WM compared to the ground truth labeling on 12 volumes from the Montreal Neurological Institutes BrainWeb phantom.

Qualitative and quantitative evaluation of six algorithms for correcting intensity nonuniformity effects.

The desire to correct intensity nonuniformity in magnetic resonance images has led to the proliferation of nonuniformity-correction (NUC) algorithms with different theoretical underpinnings. In order to provide end users with a rational basis for selecting a given algorithm for a specific neuroscientific application, we evaluated the performance of six NUC algorithms. We used simulated and real MRI data volumes, including six repeat scans of the same subject, in order to rank the accuracy, precision, and stability of the nonuniformity corrections. We also compared algorithms using data volumes from different subjects and different (1.5T and 3.0T) MRI scanners in order to relate differences in algorithmic performance to intersubject variability and/or differences in scanner performance. In phantom studies, the correlation of the extracted with the applied nonuniformity was highest in the transaxial (left-to-right) direction and lowest in the axial (top-to-bottom) direction. Two of the six algorithms demonstrated a high degree of stability, as measured by the iterative application of the algorithm to its corrected output. While none of the algorithms performed ideally under all circumstances, locally adaptive methods generally outperformed nonadaptive methods.

Principal Component Analysis and the Scaled Subprofile Model Compared to Intersubject Averaging and Statistical Parametric Mapping: I. “Functional Connectivity” of the Human Motor System Studied with [15O]Water PET

Using [15O]water PET and a previously well studied motor activation task, repetitive finger-to-thumb opposition, we compared the spatial activation patterns produced by (1) global normalization and intersubject averaging of paired-image subtractions, (2) the mean differences of ANCOVA-adjusted voxels in Statistical Parametric Mapping, (3) ANCOVA-adjusted voxels followed by principal component analysis (PCA), (4) ANCOVA-adjustment of mean image volumes (mean over subjects at each time point) followed by F-masking and PCA, and (5) PCA with Scaled Subprofile Model pre- and postprocessing. All data analysis techniques identified large positive focal activations in the contralateral sensorimotor cortex and ipsilateral cerebellar cortex, with varying levels of activation in other parts of the motor system, e.g., supplementary motor area, thalamus, putamen; techniques 1–4 also produced extensive negative areas. The activation signal of interest constitutes a very small fraction of the total nonrandom signal in the original dataset, and the exact choice of data preprocessing steps together with a particular analysis procedure have a significant impact on the identification and relative levels of activated regions. The challenge for the future is to identify those preprocessing algorithms and data analysis models that reproducibly optimize the identification and quantification of higher-order sensorimotor and cognitive responses.

Quasi-Conformally Flat Mapping the Human Cerebellum

We present a novel approach to creating flat maps of the brain. It is impossible to flatten a curved surface in 3D space without metric and areal distortion; however, the Riemann Mapping Theorem implies that it is theoretically possible to preserve conformal (angular) information under flattening. Our approach attempts to preserve the conformal structure between the original cortical surface in 3-space and the flattened surface. We demonstrate this with data from the human cerebellum and we produce maps in the conventional Euclidean plane, as well as in the hyperbolic plane and on a sphere. Conformal mappings are uniquely determined once certain normalizations have been chosen, and this allows one to impose a coordinate system on the surface when flattening in the hyperbolic or spherical setting. Unlike existing methods, our approach does not require that cuts be introduced in the original surface. In addition, hyperbolic and spherical maps allow the map focus to be transformed interactively to correspond to any anatomical landmark.

Putting our heads together: a consensus approach to brain/non-brain segmentation in T1-weighted MR volumes.

We describe an approach to brain extraction from T1-weighted MR volumes that uses a hierarchy of masks created by different models to form a consensus mask. The algorithm (McStrip) incorporates atlas-based extraction via nonlinear warping, intensity-threshold masking with connectivity constraints, and edge-based masking with morphological operations. Volume and boundary metrics were computed to evaluate the reproducibility and accuracy of McStrip against manual brain extraction on 38 scans from normal and ataxic subjects. McStrip masks were reproducible across six repeat scans of a normal subject and were significantly more accurate than the masks produced by any of the individual algorithmic components.

Activation pattern reproducibility: measuring the effects of group size and data analysis models.

The reproducibility of patterns from brain activation experiments has been examined only for suprathreshold spatially localized foci. Scatter plots comparing signal levels across all pairs of Talairach voxels for pairs of functional activation images provide an alternative approach for assessing reproducibility. Image‐wide, signal‐level reproducibility may be quantitatively summarized using pattern similarity measures such as the Pearson product‐moment correlation, ρ. Empirical population distributions of ρ for many pair‐wise image comparisons, generated using statistical resampling techniques, may be used to examine the impact of a wide range of experimental variables. We demonstrate the use of such empirical ρ‐histograms to measure changes in reproducibility for [15O]‐water PET scans of a simple motor task as a function of group size and data analysis model. Hum. Brain Mapping 5:312–316, 1997.

Graphical analysis of MR feature space for measurement of CSF, gray-matter, and white-matter volumes.

The problem of volume averaging in quantitating CSF, gray-matter, and white-matter fractions in the brain is solved using a three-compartment model and a simple graphical analysis of a multispectral MR feature space. Compartmentalization is achieved without the ambiguities of thresholding techniques or the need to assume that the underlying pixel probability distributions have a particular form. A 2D feature space is formed by double SE (proton density-and T2-weighted) MR data with image nonuniformity removed by a novel technique in which the brain itself serves as a uniformity reference. Compartments other than the basic three were rejected by the tailoring of limits in feature space. Phantom scans substantiate this approach, and the importance of the careful selection and standardization of pure tissue reference signals is demonstrated. Compartmental profiles from standardized subvolumes of three normal brains, based on a 3D (Talairach) coordinate system, demonstrate slice-by-slice detail; longitudinal studies confirm reproducibility. Compartmentalization may be described graphically and algebraically, complementing data displays in feature space and images of compartmentalized brain scans. These studies anticipate the application of our compartmentalization technique to patients with neurological disorders.

Quantitative evaluation of three cortical surface flattening methods

During the past decade, several computational approaches have been proposed for the task of mapping highly convoluted surfaces of the human brain to simpler geometric objects such as a sphere or a topological disc. We report the results of a quantitative comparison of FreeSurfer, CirclePack, and LSCM with respect to measurements of geometric distortion and computational speed. Our results indicate that FreeSurfer performs best with respect to a global measurement of metric distortion, whereas LSCM performs best with respect to angular distortion and best in all but one case with a local measurement of metric distortion. FreeSurfer provides more homogeneous distribution of metric distortion across the whole cortex than CirclePack and LSCM. LSCM is the most computationally efficient algorithm for generating spherical maps, while CirclePack is extremely fast for generating planar maps from patches.

Cortical surface flattening using least square conformal mapping with minimal metric distortion

Although flattening a cortical surface necessarily introduces metric distortion due to the non-constant Gaussian curvature of the surface, the Riemann mapping theorem states that continuously differentiable surfaces can be mapped without angular distortion. We apply the so-called least-square conformal mapping approach to flatten a patch of the cortical surface onto planar regions and to produce spherical conformal maps of the entire cortex while minimizing metric distortion within the class of conformal maps. Our method, which preserves angular information and controls metric distortion, only involves the solution of a linear system and a nonlinear minimization problem with three parameters and is a very fast approach.

Measuring Activation Pattern Reproducibility Using Resampling Techniques

This study presents two “similarity measures” of activation pattern reproducibility that do not require a choice of model-dependent noise definitions and thresholds. Both measures are derived from scatter plots that provide a visual comparison of the signal levels across all pairs of Talairach voxels for pairs of activation images. The first measure is the Pearson product-moment correlation of the scatter plot. The second measure is the ratio of the “signal” and “noise” histogram widths for all Talairach voxel signal levels projected onto the major and minor axes, respectively, from a principal components analysis of the scatter plot. Empirical population histograms of these similarity measures for many pair-wise image comparisons of independent groups of subjects were generated using statistical resampling techniques. The resulting “reproducibility histograms” were used to examine the impact of four different data analysis models on groups of 1, 4, 8, and 12 subjects for [15O]water positron emission tomography scans of a simple motor task. For each group size, activation images from models using single voxel noise estimates were less reproducible than images from models using multivoxel noise estimation procedures. This occurs because single voxel noise estimates produce a lower “activation signal-to-noise ratio” compared to multivoxel estimates when measured using the model-independent noise scale of the second similarity measure. These data demonstrate that the number of activated voxels found using thresholding procedures depends strongly on group size and the particular data analysis model used and that models using single voxel noise estimation procedures have suboptimal activation signal-to-noise ratios.