Journal of Cerebral Blood Flow and Metabolism

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.

An international group of experts in pharmacokinetic modeling recommends a consensus nomenclature to describe in vivo molecular imaging of reversibly binding radioligands.

Statistical parametric maps (SPMs) are potentially powerful ways of localizing differences in regional cerebral activity. This potential is limited by uncertainties in assessing the significance of these maps. In this report, we describe an approach that may partially resolve this issue. A distinction is made between using SPMs as images of change significance and using them to identify foci of significant change. In the first case, the SPM can be reported nonselectively as a single mathematical object with its omnibus significance. Alternatively, the SPM constitutes a large number of repeated measures over the brain. To reject the null hypothesis, that no change has occurred at a specific location, a threshold adjustment must be made that accounts for the large number of comparisons made. This adjustment is shown to depend on the SPM's smoothness. Smoothness can be determined empirically and be used to calculate a threshold required to identify significant foci. The approach models the SPM as a stationary stochastic process. The theory and applications are illustrated using uniform phantom images and data from a verbal fluency activation study of four normal subjects.

An accurate, reproducible method for determining the infarct volumes of gray matter structures is presented for use with presently available image analysis systems. Areas of stained sections with optical densities above that of a threshold value are automatically recognized and measured. This eliminates the potential error and bias inherent in manually delineating infarcted regions. Moreover, the volume of surviving normal gray matter is determined rather than that of the infarct. This approach minimizes the error that is introduced by edema, which distorts and enlarges the infarcted tissue and surrounding white matter.

The method of graphical analysis for the evaluation of sequential data (e.g., tissue and blood concentrations over time) in which the test substance is irreversibly trapped in the system has been expanded. A simpler derivation of the original analysis is presented. General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured. In addition, general equations are derived for situations when trapping of the test substance is incomplete and for a combination of these two conditions. These derivations are independent of the actual configuration of the compartmental system being analyzed and show what information can be obtained for the period when the reversible compartments are in effective steady state with the blood. This approach is also shown to result in equations with at least one less nonlinear term than those derived from direct compartmental analysis. Specific applications of these equations are illustrated for a compartmental system with one reversible region (with or without reversible binding) and one irreversible region.

Reactive oxygen species have been implicated in brain injury after ischemic stroke. These oxidants can react and damage the cellular macromolecules by virtue of the reactivity that leads to cell injury and necrosis. Oxidants are also mediators in signaling involving mitochondria, DNA repair enzymes, and transcription factors that may lead to apoptosis after cerebral ischemia. Transgenic or knockout mice with cell- or site-specific prooxidant and antioxidant enzymes provide useful tools in dissecting the events involving oxidative stress in signaling and damage in ischemic brain injury.

The distribution volume ratio (DVR), which is a linear function of receptor availability, is widely used as a model parameter in imaging studies. The DVR corresponds to the ratio of the DV of a receptor-containing region to a nonreceptor region and generally requires the measurement of an arterial input function. Here we propose a graphical method for determining the DVR that does not require blood sampling. This method uses data from a nonreceptor region with an average tissue-to-plasma efflux constant k₂ to approximate the plasma integral. Data from positron emission tomography studies with [¹⁵C]raclopride (n = 20) and [¹¹C] d-threo-methylphenidate ([¹¹C]dMP) (n = 8) in which plasma data were taken and used to compare results from two graphical methods, one that uses plasma data and one that does not. k₂ was 0.163 and 0.051 min⁻¹ for [¹¹C]raclopride and [¹¹C]dMP, respectively. Results from both methods were very similar, and the average percentage difference between the methods was −0.11% for [¹¹C]raclopride and 0.46% for [¹¹C]dMP for DVR of basal ganglia (BG) to cerebellum (CB). Good agreement between the two methods was also achieved for DVR images created by both methods. This technique provides an alternative method of analysis not requiring blood sampling that gives equivalent results for the two ligands studied. It requires initial studies with blood sampling to determine the average kinetic constant and to test applicability. In some cases, it may be possible to neglect the b̅₂ term if the BG/CB ratio becomes reasonably constant for a sufficiently long period of time over the course of the experiment.

A graphical method of analysis applicable to ligands that bind reversibly to receptors or enzymes requiring the simultaneous measurement of plasma and tissue radioactivities for multiple times after the injection of a radiolabeled tracer is presented. It is shown that there is a time t† after which a plot of f ^t₀ROI( t') dt'/ROI( t) versus f ^t₀ C_p( t') dt'/ROI( t) (where ROI and C_p are functions of time describing the variation of tissue radioactivity and plasma radioactivity, respectively) is linear with a slope that corresponds to the steady-state space of the ligand plus the plasma volume, V_p. For a two-compartment model, the slope is given by λ + V_p, where λ is the partition coefficient and the intercept is −1/[ k₂(1 + V_p/λ)]. For a three-compartment model, the slope is λ(1 + B_max/ K_d) + V_p and the intercept is −{(1 + B_max/ K_d)/ k₂ + [ k_off(1 + K_d/ B_max)]⁻¹} [1 + V_p/λ(1 + B_max/ K_d)]⁻¹ (where B_max represents the concentration of ligand binding sites and K_d the equilibrium dissociation constant of the ligand–binding site complex, k_off ( k₄) the ligand–binding site dissociation constant, and k₂ is the transfer constant from tissue to plasma). This graphical method provides the ratio B_max/ K_d from the slope for comparison with in vitro measures of the same parameter. It also provides an easy, rapid method for comparison of the reproducibility of repeated measures in a single subject, for longitudinal or drug intervention protocols, or for comparing experimental results between subjects. Although the linearity of this plot holds when ROI/ C_p is constant, it can be shown that, for many systems, linearity is effectively reached some time before this. This analysis has been applied to data from [ N-methyl-¹¹C]-(–)-cocaine ([¹¹C]cocaine) studies in normal human volunteers and the results are compared to the standard nonlinear least-squares analysis. The calculated value of B_max/ K_d for the high-affinity binding site for cocaine is 0.62 ± 0.20, in agreement with literature values.