S. Marrett

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.

Anatomical mapping of functional activation in stereotactic coordinate space

Numerous applications have been reported for the stereotactic mapping of focal changes in cerebral blood flow during sensory and cognitive activation as measured with positron emission tomography (PET) subtraction images. Since these images lack significant anatomical information, analysis of these kinds of data has been restricted to an automated search for peaks in the PET subtraction dataset and localization of the peak coordinates within a standardized stereotactic atlas. This method is designed to identify isolated foci with dimensions smaller than the image resolution. Details of activation patterns that may extend over finite distances, following the underlying anatomical structures, will not be apparent. We describe the combined mapping into stereotactic coordinate space of magnetic resonance imaging (MRI) and PET information from each of a set of subjects such that the major features of the activation pattern, particularly extended tracts of increased blood flow, can be immediately assessed within their true anatomical context as opposed to that presumed using a standard atlas alone. Near areas of high anatomical variability, e.g., central sulcus, or of sharp curvature, e.g., frontal and temporal poles, this information can be essential to the localization of a focus to the correct gyrus or for the rejection of extracerebral peaks. It also allows for the removal from further analysis of data from cognitively-normal subjects with abnormal anatomy such as enlarged ventricles. In patients with neuropathology, e.g., Alzheimers disease, arteriovenous malformation, stroke, or neoplasm, the use of correlated MRI is mandatory for correct localization of functional activation.

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.

MRI-PET Correlation in Three Dimensions Using a Volume-of-Interest (VOI) Atlas

Quantitative interpretation of functional images (PET or SPECT) is hampered by poor spatial resolution, low counting statistics, and, for many tracers, low contrast between different brain structures of interest. Furthermore, normal tracer distributions can be severely disrupted by such gross pathologies as stroke, tumor, and dementia. Hence, the complementary anatomical information provided by CT or MRI is essential for accurate and reproducible regional analysis of functional data. We have developed methods for the simultaneous three-dimensional display and analysis of image volumes from MRI and PET. A general algorithm for defining the affine transformation between two equivalent point ensembles has been adapted for the purpose of registering MRI and PET image volumes by means of a simple fiducial arrangement. In addition, we have extended previous MRI-based computerized atlas methodology to three dimensions. The native atlas planes were spaced at 2 mm intervals, sufficient axial sampling to permit the generation of oblique planar sections through the atlas space. This will allow for an infinite number of angulations and axial offsets in two-dimensional region-of-interest (ROI) templates, all derived from the same master three-dimensional volume-of-interest (VOI) atlas and therefore maintaining topographical consistency throughout. These ROI templates may be selected to match the image orientation for conventional two-dimensional segmentation and data extraction.

Anatomical-Functional Correlation Using an Adjustable MRI-Based Region of Interest Atlas with Positron Emission Tomography

A procedure is described for combining anatomical information from magnetic resonance imaging (MRI) or computerized tomography (CT) and functional information from positron emission tomography (PET) in a rapid fashion. MRI data are combined with a procedure for the definition, storage, and recall of anatomically based regions of interest. An atlas of standard regions of interest, defined for a set of 18 parallel planes spaced at 6-mm intervals, provides an initial region of interest template for each patient slice. Global adjustments to scale, orientation, and position are applied to obtain an initial match. Individual regions of interest may then be moved, deleted, or redrawn as needed. The ability to store region of interest templates ensures reproducibility of analysis over long periods and introduces a standardization of analysis technique. In 25 brain structures, the mean coefficient of variation in cerebral glucose utilization rate (CMRGlc) measurements among five neuroanatomically trained observers was reduced from 8.1% for manual region of interest definition to 4.0% using the template approach with MRI. Template analysis for space-occupying lesions such as tumors or infarcts is illustrated with PET data from a stroke study, emphasizing the facility for rapid, reproducible analysis of multifunctional studies. MRI-PET matching for a structurally intact caudate nucleus having reduced CMRGlc in Huntingtons disease emphasizes the accuracy of anatomical localization required to quantify small structures.

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.

The Effect of Nimodipine on the Evolution of Human Cerebral Infarction Studied by PET

Fourteen patients were studied by positron emission tomography (PET) within 48 h of onset of a hemispheric ischemic stroke and again 7 days later. After the first set of PET scans, the patients were randomized to receive either nimodipine (n = 7) or a carrier solution (n = 7) by intravenous infusion. The infusions were maintained until the end of the second PET studies. CBF, cerebral blood volume (CBV), oxygen extraction ratio (OER), CMRO2, and CMRglc were measured each time. These metabolic and perfusion measurements were performed by standard methods. A surface map of each metabolic and perfusion measurement in the cortical mantle was generated by interpolating between the available slices. The various surface maps representing the physiological characteristics determined in the same or subsequent studies were aligned so that all data sets could be analyzed identically using an array of square regions of interest (ROIs). The functional status of each ROI was recorded at the two intervals following the cerebrovascular accident to characterize the evolution of the infarct, penumbra, and normal brain regions. We presumed the ischemic penumbra to be cortical regions in the proximity of the infarct and perfused at CBF values between 12 and 18 ml/100 g/min on the first PET scan, while densely ischemic regions had CBF of <12 nl/100 g/min and normally perfused brain >18 ml/100 g/min. In the densely ischemic zone, CBF increased more in the nimodipine-treated group than in the carrier group. As well, in this region nimodipine reversed the decline in CMRO2 noted in the carrier group, the difference in the changes being significant. In the penumbra zone, comparable trends were noted in OER and CMRO2 but the difference in the changes between the two groups did not reach statistical significance. Changes in CMRglc and CBV were comparable between the two groups in both cortical regions.

Anatomical-Functional Correlative Analysis Of The Human Brain Using Three Dimensional Imaging Systems

Quantitative interpretation of functional images (PET or SPECT) is hampered by poor spatial resolution, low counting statistics and, for many tracers, low contrast between different brain structures of interest. Further, normal tracer distributions can be severely distorted by such gross pathologies as stroke, tumor and dementia. Hence, the complementary anatomical information provided by CT or MRI is essential for accurate and reproducible regional analysis of functional data. We have developed methods for the three-dimensional integration and simultaneous display of image volumes from MRI and PET. PET data was collected from an older Therascan 3-slice scanner with 12 mm resolution and a 15-slice Scanditronix PC-2048 system having 5-6 mm resolution in each dimension. MRI data was obtained from a Philips 1.5 Tesla Gyroscan scanner. The image volumes were loaded into a PIXAR 3-D image computer for simultaneous display. A general algorithm for finding the optimal transformation between two ensembles of equivalent points was implemented and investigated through simulation studies. Using a locally-developed 3-D image/graphics analysis package, equivalent points in the two image volumes were identified, either manually or via an adjustable computerized volume-of-interest (VOI) atlas. The MRI data were then re-sampled along planes parallel to the PET planes and the two volumes overlaid using opacity-weighted composition. Arbitrary oblique planes through the two volumes were obtained in interactive sessions.

Glycolysis in Neurons, Not Astrocytes, Delays Oxidative Metabolism of Human Visual Cortex during Sustained Checkerboard Stimulation in vivo

The regulation of brain energy metabolism during neuronal activation is poorly understood. Specifically, the extent to which oxidative metabolism rather than glycolysis supplies the additional ATP necessary to sustain neuronal activation is in doubt. A recent hypothesis claims that astrocytes generate lactate with the muscle-type lactate dehydrogenase (LDH) isozyme LD5. Lactate from astrocytes then undergoes oxidation in neurons after reconversion to pyruvate by the LDH subtype LD1. On the basis of this hypothesis, the authors predicted that the time course of an excitatory increase of the oxidative metabolism of brain tissue must depend on the degree to which astrocytes provide neurons with pyruvate in the form of lactate. From the known properties of the LDH subtypes, the authors predicted two time courses for the changes of oxygen consumption in response to neuronal stimulation: one reflecting the properties of the neuronal LDH subtype LD1, and the other reflecting the astrocytic LDH subtype LD5. Measuring oxygen consumption (CMR o2) with positron emission tomography, the authors demonstrated increased CMR o2 during sustained stimulation of visual cortex with a complex stimulus. The CMR o2 increased 20.5% after 3 minutes and 27.5% after 8 minutes of stimulation, consistent with a steady-state oxygen–glucose metabolism ratio of 5.3, which is closest to the index predicted for the LD1 subtype. The index is equal to the oxygen–glucose metabolism ratio of 5.5 calculated at baseline, indicating that pyruvate is converted to lactate in a cellular compartment with an LDH reaction closest to that of LD1, whether at rest or during stimulation of the visual cortex with the current stimulus. The findings are consistent with a claim that neurons increase their oxidative metabolism in parallel with an increase of pyruvate, the latter generated by neuronal rather than astrocytic glycolysis.