Peter Neelin

A unified statistical approach for determining significant signals in images of cerebral activation

We present a unified statistical theory for assessing the significance of apparent signal observed in noisy difference images. The results are usable in a wide range of applications, including fMRI, but are discussed with particular reference to PET images which represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. Our main result is an estimate of the P‐value for local maxima of Gaussian, t, χ2 and F fields over search regions of any shape or size in any number of dimensions. This unifies the P‐values for large search areas in 2‐D (Friston et al. [1991]: J Cereb Blood Flow Metab 11:690–699) large search regions in 3‐D (Worsley et al. [1992]: J Cereb Blood Flow Metab 12:900–918) and the usual uncorrected P‐value at a single pixel or voxel.

A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain

Many studies of brain function with positron emission tomography (PET) involve the interpretation of a subtracted PET image, usually the difference between two images under baseline and stimulation conditions. The purpose of these studies is to see which areas of the brain are activated by the stimulation condition. In many cognitive studies, the activation is so slight that the experiment must be repeated on several subjects and the subtracted images are averaged to improve the signal-to-noise ratio. The averaged image is then standardized to have unit variance and then searched for local maxima. The main problem facing investigators is which of these local maxima are statistically significant. We describe a simple method for determining an approximate p value for the global maximum based on the theory of Gaussian random fields. The p value is proportional to the volume searched divided by the product of the full widths at half-maximum of the image reconstruction process or number of resolution elements. Rather than working with local maxima, our method focuses on the Euler characteristic of the set of voxels with a value larger than a given threshold. The Euler characteristic depends only on the topology of the regions of high activation, irrespective of their shape. For large threshold values this is approximately the same as the number of isolated regions of activation above the threshold. We can thus not only determine if any activation has taken place, but we can also estimate how many isolated regions of activation are present.

Incorporating Prior Knowledge into Image Registration

The first step in the spatial normalization of brain images is usually to determine the affine transformation that best maps the image to a template image in a standard space. We have developed a rapid and automatic method for performing this registration, which uses a Bayesian scheme to incorporate prior knowledge of the variability in the shape and size of heads. We compared affine registrations with and without incorporating the prior knowledge. We found that the affine transformations derived using the Bayesian scheme are much more robust and that the rate of convergence is greater.

Searching scale space for activation in PET images.

PET images of cerebral blood flow (CBF) in an activation study are usually smoothed to a resolution much poorer than the intrinsic resolution of the PET camera. This is done to reduce noise and to overcome problems caused by neuroanatomic variability among different subjects undertaking the same experimental task. In many studies the choice of this smoothing is arbitrarily fixed at about 20 mm FWHM, and the resulting statistical field or parametric map is searched for local maxima. Poline and Mazoyer [(1994): J Cereb Blood Flow Metab 14:690–699; (1994): IEEE Trans Med Imaging 13(4):702–710] have proposed a 4‐D search over smoothing kernel widths as well as the usual three spatial dimensions. If the peaks are well separated then this makes it possible to estimate the size of regions of activation as well as their location. One of the main problems identified by Poline and Mazoyer is how to assess the significance of scale space peaks. In this paper we provide a solution for the case of pooled‐variance Z‐statistic images (Gaussian fields). Our main result is a unified P value for the 4‐D local maxima that is accurate for searches over regions of any shape or size. Our results apply equally well to any Gaussian statistical field, such as those resulting from fMRI.

Warping of a computerized 3-D atlas to match brain image volumes for quantitative neuroanatomical and functional analysis

We describe the implementation, experience and preliminary results obtained with a 3-D computerized brain atlas for topographical and functional analysis of brain sub-regions. A volume-of-interest (VOI) atlas was produced by manual contouring on 64 adjacent 2 mm-thick MRI slices to yield 60 brain structures in each hemisphere which could be adjusted, originally by global affine transformation or local interactive adjustments, to match individual MRI datasets. We have now added a non-linear deformation (warp) capability (Bookstein, 1989) into the procedure for fitting the atlas to the brain data. Specific target points are identified in both atlas and MRI spaces which define a continuous 3-D warp transformation that maps the atlas on to the individual brain image. The procedure was used to fit MRI brain image volumes from 16 young normal volunteers. Regional volume and positional variability were determined, the latter in such a way as to assess the extent to which previous linear models of brain anatomical variability fail to account for the true variation among normal individuals. Using a linear model for atlas deformation yielded 3-D fits of the MRI data which, when pooled across subjects and brain regions, left a residual mis-match of 6 - 7 mm as compared to the non-linear model. The results indicate a substantial component of morphometric variability is not accounted for by linear scaling. This has profound implications for applications which employ stereotactic coordinate systems which map individual brains into a common reference frame: quantitative neuroradiology, stereotactic neurosurgery and cognitive mapping of normal brain function with PET. In the latter case, the combination of a non-linear deformation algorithm would allow for accurate measurement of individual anatomic variations and the inclusion of such variations in inter-subject averaging methodologies used for cognitive mapping with PET.

Voxel-based morphometry of human brain with age and cerebrovascular risk factors.

The objectives of this study were to evaluate the correlations of the volumes of the gray matter and white matter with age, and the correlations of the tissue probabilities of the gray matter and white matter with age and several cerebrovascular risk factors. We obtained magnetic resonance (MR) images of the brain and clinical information from 769 normal Japanese subjects. We processed the MR images automatically by correcting for inter-individual differences in brain size and shape, and by segmenting the MR images into the gray matter and white matter. Volumetry of the brain revealed a significant negative correlation between the gray matter volume and age, which was not observed between white matter volume and age. Voxel-based morphometry showed that age, systolic blood pressure, and alcohol drinking correlated with the regional tissue probabilities of the gray matter and white matter.

Validation of an mri/pet landmark registration method using 3d simulated pet images and point simulations

Three-dimensional (3D) simulated PET images generated from MRI were used to validate a multimodality registration technique based on the identification of internal anatomical landmarks. In addition, point-based simulations were compared with registration datasets acquired over 3 yr of routine use of the technique. Registration errors were found to range from 1.0 mm at the brain centre to 2.8 mm in each dimension at the brain surface.

CHAPTER 64 – A Unified Statistical Approach for Determining Significant Signals in Location and Scale Space Images of Cerebral Activation

This chapter presents a unified P-value for assessing the significance of peaks in statistical fields searched over regions of any shape or size. This is extended to 4D scale space searches over smoothing filter width as well as location. The results are usable in a wide range of applications, including positron emission tomography (PET) and fMRI, but are discussed with particular reference to PET images that represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. The first result, derived by Worsley, is an estimate of the P-value for local maxima of Gaussian fields over search regions of any shape or size in any number of dimensions. This unifies the P-values for large search areas in 2D, large search regions in 3D, and the usual uncorrected p-value at a single pixel or voxel. This makes it possible to restrict the search to small anatomical regions, such as the cingulate gyrus or caudate nucleus, or two-dimensional regions, such as a slice or the cortical surface, or even single voxels. The results are also generalizable to 4D searches in time as well as space, which may be useful for fMRI. The second result is an extension to searches over smoothing filter width or scale space.

MINC 2.0: A Flexible Format for Multi-Modal Images

It is often useful that an imaging data format can afford rich metadata, be flexible, scale to very large file sizes, support multi-modal data, and have strong inbuilt mechanisms for data provenance. Beginning in 1992, MINC was developed as a system for flexible, self-documenting representation of neuroscientific imaging data with arbitrary orientation and dimensionality. The MINC system incorporates three broad components: a file format specification, a programming library, and a growing set of tools. In the early 2000s the MINC developers created MINC 2.0, which added support for 64-bit file sizes, internal compression, and a number of other modern features. Because of its extensible design, it has been easy to incorporate details of provenance in the header metadata, including an explicit processing history, unique identifiers, and vendor-specific scanner settings. This makes MINC ideal for use in large scale imaging studies and databases. It also makes it easy to adapt to new scanning sequences and modalities.

Validation of a Dynamic PET Simulator in Clinical Brain Studies

This work has been undertaken to evaluate the accuracy of 3-D dynamic simulations in neurological imaging protocols with positron emission tomography (PET). We used [18F] uorodopa PET images from a pair of normal brain and Parkinsonian brain. Spatially correlated MR images were segmented into several tissue types and anatomical structures. Voxels within every structure were assigned with the time activity curves (TACs) derived from clinical studies after correcting for partial volume e ects. Both noisefree and noisy projection data of this brain model were created and reconstructed as in the real scans. TACs were then generated from the dynamic images and compared with the measured data. The results show good agreement between the simulated and observed TACs in the normal brain. However the match is poorer in the Parkinsons brain particularly in striatal structures. This suggests a possible mismatch between the simulated true activity distribution and that in the diseased brain. Both normal and patient data have root-mean-square errors of 2% in cortical gray matter and <10% in striatum without and with noise. This tool can be used to optimize temporal sampling strategy and parameter estimation algorithms. 2