Visual analysis is also used in a number of studies However, more often visual interpretation is supplemented with semiquantitative and quantitative data processing (Medvedev 2008). More accurate information, compared with visual assessment, sufficient for clinical and most scientific studies can be obtained by means of ­semiquantitative analysis. There are several kinds of data processing with use of semiquantitative image analysis. The simplest kind is determining regional radioactivity normalized to an internal zone of reference. The contralateral area or brain activity on the whole may serve as reference. For semiquantitative analysis, the SUV (standardized uptake value) can be also used. However, in some studies it has been shown that the method of calculating SUV is imperfect and in some cases it introduces up to 50% error in assessing brain metabolism (Cremerius 1997).

The so-called spatial normalization is an important aspect of PET image processing. Normalization aims at leveling all the particular anatomic characteristics of the patient’s brain by reducing its parameters (e.g., form, size, spatial situation during data collection) to a certain standard (Senda 2000; Gispert 2003). There are two different approaches to image standardization. First of all, the patient’s scanograms can be transformed by achieving a precise coincidence of the points of reference (internal markers which are brain contours or sulci) in the obtained PET tomograms or standard MRI data available in the data base (anatomic normalization). For that purpose a computer brain atlas is used; for example, HBA (Human Brain Atlas) developed by the Department of Neuroscience of Karolinska Institute, Sweden (Hikima et al. 2004).

Another variant is reducing to standard RP distribution in the patient’s brain; for example, when studying regional glucose metabolism or cerebral blood flow (functional normalization). Currently the SPM software (Statistical Parametric Mapping, Welcome Department of Cognitive Neurology, Institute of Neurology, London, UK) and NEUROSTAT based on 3D SSP (Department of Internal Medicine, University of Michigan, Ann Arbor, MI, USA) improved by Prof. S. Minoshima (University of Washington, Seattle, WA, USA) are used (Minoshima et al. 1995; Gispert 2003; Hikima et al. 2004; Hosaka 2005). It should be noted that this division of standardization methods concerns not only the main principles that underlie them. This does not mean that some elements of anatomical normalization cannot be used in the second group of methods. For example, in NEUROSTAT the method of marker coincidence is used, bicomissural lines serving as markers. Furthermore, in SPM, parameters of PET image deformation can be set by means of MRI scans obtained in the same patient.

In image standardization by means of internal markers such as brain contours or sulci (fissure of Sylvius, central and cingulate gyri, etc.) with use of a computer atlas (e.g., HBA), corresponding image pixels and their averaging are compared. This process is performed in most software packages under the control of an operator. Therefore, this method of image standardization may be useful in the presence of marked anatomic peculiarities of the patient’s brain (Hosaka 2005). In the case when RP uptake is used for standardization, the idea on the real situation of the brain structures is largely conventional. For example, the precentral sulcus of a patient may functionally correspond to the same area of another one, even in the absence of anatomic correspondence. In other words, functional brain normalization between subjects by means of the second method group is objective and reliable but precise anatomic coincidence of corresponding structures cannot be quite guaranteed. In spite of that, there are data confirming in most cases the accuracy of comparing anatomic and functional data after image standardization based on the normalization of RP distribution in the brain (Ishii 2001).

The statistical parametric mapping (SPM) was developed in 1988 and presently is the widest spread method of image standardization. Its creation was conditioned first of all by the rapid development of the methods of functional visualization, especially PET. The main method of finding differences between PET data of patients and those of a control group was then comparison of RP uptake in the regions of interest, which were outlined manually (Friston et al. 1991). For this reason, information on functional activity in pixels and voxels situated outside the chosen region of interest was in fact lost. Then these data were processed with the help of multifactor dispersion analysis. The region of interest was used as the level (degree of impact) of factor. This means that the impact on the region of interest of a given diagnosis or therapy was reflected in the region of interest itself and had a non-additive character. In other words, the effect of therapeutic measures was not allowed for in assessing metabolic and perfusion changes in the region of interest. Meanwhile, treatment is known to have a general impact on functional processes, which shows up in many regions of interest in the brain. This is why in the late 1980s a group of researchers decided to create a way of data processing that permitted the detection of changes on the basis of parametric maps in the absence of information on the precise localization of the pathologic process. This technique was called statistical parametric mapping (SPM) and that was for several reasons. First of all, it completely corresponds to the acronym designating mapping of statistically significant probabilities, the method of processing EEG results (where “SPM” stands for “significant probability mapping”). This technique permits the creation of pseudomaps of P-magnitudes for determining the spatial-temporal organization of the evoked electric response, which makes easier the visual assessment of obtained EEG data. Further, SPM makes it possible to identify and localize differences in EEG images between patient groups and healthy people (Senda 2000). The second reason for this name is related to the history of development of PET. In the 1970s to 1980s, tomograms were obtained out of raw data which reflected a large number of different physiologic processes (oxygen metabolism, oxygen extraction fraction, regional cerebral blood flow). These images were called parametric maps. In fact, these physiologic parameters were a non-linear function of initial data (Huang et al. 1983). A distinction of SPM from these maps consists of the fact that in SPM, distribution is determined on the basis of a null hypothesis (Senda 2000). This means that SPM is based on a statistical data model which permits determination of error and significance of the detected changes (Moustafa and Baron 2008). Thus, SPM converts changes in images into statistical indices. The choice of statistical methods of processing depends on the task set by the researcher. First of all, he should decide on whether to use a T-test, for comparing the averages, or an F-test, to confront the dispersions of the two general sets.

The methodology of SPM was presented in detail in several reports published in the early 1990s (Friston et al. 1990, 1991, 1993). In the first stage, images are reoriented by way of comparing corresponding scan voxels in order to level artifacts induced by movements of the head. The normal brain of adults is known to have roughly the same sizes and form. However, some individual characteristics are always observed in the form of the topographic situation of the gyri and sulci in the cortical sections or, for example, differences in the shape of the corpus callosum. Therefore, the second stage of preparing images is their spatial normalization. One of the advantages of SPM is the possibility to create by means of software algorithms standard patterns which can be obtained out of scans of the control group and then be used together with available patterns for spatial normalization (Senda 2000; Herholz 2003). Each 3D brain image is transformed so that all the superficial structures precisely coincide with analogous regions of the pattern included in the program. This process (the so-called affine transformation) includes turning, parallel transfer, scale change and non-linear image deformation. Then, scan smoothing is done with consequent voxel averaging relative to the neighboring elements of the 3D image, which permits to increase the ratio of signal/noise. For this purpose, a Gauss filter or (rarer) wavelet image is used (Silverman 1999; Frackowiak 2003).

SPM presupposes characteristics by voxels of data variability with the ­introduction of compounded factor (global activity) and residual dispersion determination (Frackowiak 2003). For this purpose the general linear model is used, which can be considered as an extension of linear multiple regression for the case of one dependent variable. So the important advantage of SPM is the possibility to take into account the global brain activity in covariational analysis in order to detect specific changes in the region of interest (Stern 1992).

The last SPM version (SPM 8) allows not only the statistic processing of positron emission tomograms but also the analysis of images obtained by means of other functional methods of examination (fMRI, EEG, EMG) as well as fusion of multimodal data.

In 1995, Minoshima and coworkers suggested a method of projecting functional activity of the cortex (regional glucose metabolism or blood flow) on the surface of the brain in the form of a 3D image (Minoshima et al. 1995). This method was based on the image standardization developed before at Michigan University and has been called SSP (stereotactic surface projection). This analysis was first used for the early diagnosis of Alzheimer’s disease. The advantage of this method consists of the possibility to level the discrepancy between RP uptake in the radial direction which remains after standardization in the 3D images. Due to a partial volume effect, the distribution of functional brain activity along the periphery of the cortex reflects the distribution of the gray matter to a greater degree than radioactivity per millimeter of gray matter (Minoshima et al. 1995, 1997; Cross 2000). Therefore, the use of surface projection permits the avoidance of a misestimation of gray matter distribution in the volume of the brain (Minoshima et al. 1995). This technique is based on the idea that the cortex is essentially a 2D plate of sheet structure, curved and convoluted in the 3D space. Therefore, information obtained in the radial profile is insignificant. However, this is right only as regards the cerebral gyri but not sulci. Consequently, the sulci should be unbent and smoothed with the help of software, which is possible only on the basis of MRI data because of insufficiently high spatial resolution of positron emission tomograms. It should be noted that SSP provokes a slightly bigger loss in spatial resolution than does SPM (Hosaka 2005).

Along with the above-described characteristics of 3D SSP, there are some differences in approach to image standardization in the main software packages. For example in NEUROSTAT, differences in size between the patient’s brain and the standard pattern designed in the database are leveled by way of linear scaling (zooming). Then, in order to adjust the shape of the brain to the stereotaxic Talairach and Tournoux atlases or to that of Monreal Neurological Institute, nonlinear image deformation along nerve fiber bundles is used. As was said above, the first stage of image standardization in SPM is determination of the optimum parameters of affine transformation (three parameters giving the turn, three giving the parallel transfer [these six parameters determine image movement], three parameters setting scaling and three setting the slope angle of coordinate axes to corresponding coordinate planes in transition from the initial rectangular coordinate system to the non-rectangular one).

Then nonlinear deformation of the shape of the patient’s brain is performed ­usually by way of linear combination of the basis function of the 3D discrete cosines transformation. The adjustment of images includes minimization of the square of difference between the image and the pattern (Frackowiak 2003).

Some studies have shown that in spite of differences in data standardization algorithms, the results of image processing by means of the these two main software packages prove to be comparable (Senda 2000; Frackowiak 2003). For example, the difference between them in determining the localization of a point of interest does not exceed 1.5 mm with PET solving capacity of 5–6 mm. However, 3D SSP is used more seldomly than SPM. At the same time, its popularity among researchers is gradually growing; for example, this software package, together with the base of volunteers’ images presented by Prof. S. Minoshima, are set in the workstations of some of modern PET/CT systems.

There are two kinds of statistical design for examining regional glucose metabolism with the use of intersubjective averaging by way of spatial data normalization. At the same time, it should be noted that for ¹⁸F-FDG usually the statistical significance of the influence of the factor affecting the object is studied. The first kind is used in order to determine specific changes in glucose metabolism in patients with different brain diseases. For that purpose the objects of examination are divided into groups (k(i)), images (Y) of every patient (i) are obtained and the presence or absence of significant differences in regional glucose metabolism between groups are determined:

, where μ is the overall mean, δ is the difference of means, ε is the remainder term (the difference between the given function and the function that approximates it), H ₀ is the null hypothesis.

The second kind is used for assessing the differences in glucose metabolism depending on the age. For this purpose, patients of different ages (x(i)) are examined, images (Y) of every patient (i) are obtained and it is determined whether there is significant correlation between the age and regional glucose metabolism:

, where μ is the overall mean, δ is the difference of means, ε is the remainder term and H ₀ is the null hypothesis (Senda 2000).

The quantitative analysis of images is based on biologically grounded mathematical models, which show the radioactivity uptake in the compartments. The latter may reflect both physiological interfaces (vascular space, hematoencephalic barrier and cytoplasm neuron membrane, and others) and biochemical processes (enzyme anabolism and catabolism, transport molecules, receptor proteins). These models should necessarily represent simplified but really existing biological systems or processes.

Initially the quantitative assessment of glucose utilization in the brain was done by the Kety-Schmidt method, developed in 1944, by way of consistent definition of the overall blood flow and difference in glucose content in the arteries and veins of the brain As is known, almost the whole of the glucose (>90%) in the CNS undergoes aerobic decomposition, therefore glucose and oxygen consumption is measured in parallel (Kety 1950, 1956; Kety and Schmidt 1948). The study of regional glucose utilization with ¹⁸F-FDG is based on the method described by Sokoloff (1977). Initially the method was developed for autoradiography with use of ¹⁴C-labeled 2-desoxyglucose. Later on, in 1979 Phelps and coworkers suggested measuring the level of glucose consumption in humans with the help of ¹⁸F-FDG (Phelps et al. 1979). In early works on regional glucose consumption, it was detected that the overall brain metabolism utilizes roughly 5.5 mg glucose/min/100 g. This rate may vary from 3.6 to 5.2 mg glucose/min/100 g in the white matter to 5.8–10.3 mg glucose/min/100 g in the gray matter. It is also accepted in the scientific literature to measure glucose consumption in mmmol/min/100 g. This allows stoichiometric comparison with concentration of other substances consumed by the brain (e.g., oxygen or ketone bodies). Grams may be converted to moles by means of division of glucose concentration rate in grams by the relative molecular mass of glucose. The absolute values of regional glucose metabolism rate in most of the brain structures remain stable for all age groups.

It should be noted that in spite of high accuracy of quantitative analysis in determining the functional activity of the brain structures, it has not received wide use in clinical practice because of the technical complexity of the procedure and difficult mathematical data processing. Initially the quantitative assessment of brain glucose consumption was performed by the Kety-Schmidt method suggested in 1944, by way of consistent definition of overall cerebral blood flow and difference in glucose content in cerebral arteries and veins (Kety and Schmidt 1948). As is known, almost all glucose in the CNS (>90%) undergoes aerobic decomposition, therefore oxygen consumption and glucose consumption change in parallel.

Cerebral blood flow is traditionally characterized by two indices: blood flow velocity per time unit (for example, mL/min) and tissue perfusion level, which is expressed as blood volume flowing through a certain amount of tissue per time unit (for example, mL/min/100 g). In the brain of a healthy person, blood flow is closely related to the metabolic activity of a given brain structure. This relation is realized by autoregulation mechanisms and is crucial for adequate blood supply of the brain.

The main quantitative parameters of assessing cerebral blood circulation are: cerebral blood flow (CBF), mL/min/100 g; blood volume circulating in cerebral vessels (cerebral blood volume, CBV) mL/100 g; fraction of oxygen extracted by the brain from arterial blood (oxygen excretion fraction, OEF), %; oxygen metabolism rate (OMR), mL/min/100 g and glucose metabolism rate (GMR), mL/min/100 g.

In the same vascular blood, flow rate and glucose consumption rate are virtually in linear relationship. Nevertheless, there can be some differences in ratio of perfusion and metabolism between different basins. For example, since most lateral sections of the neocortex are supplied with blood through the medial cerebral artery, the perfusion level in this area determined with help of H₂¹⁵O virtually corresponds to the level of regional brain metabolism measured in the convexital sections. On the other hand, the cerebellum, in spite of low glucose metabolism compared with the neocortex, is characterized by considerably higher perfusion rates.

H₂¹⁵O or ¹⁵O study of cerebral blood flow is widely used for assessing the activity of cerebral areas participating in neurophysiological processes. The short half-life period of the radionuclide ¹⁵O permits the analysis of changes in functional activity of brain structures in the same subject under different experimental conditions (Wieler et al. 1986). This makes it possible to study such states as rest/motion, wakefulness/different sleep phases, comfort/discomfort or pain, emotional calmness/induced grief as well as anxiety, sexual excitement, fear, irritation. This paradigm of studying brain function is used in a large number of studies aimed at specifying the role of brain structures in processes of thought and behavior, both normal and pathologic. Besides that, the influence of medicines on different sections of the cortex and basal nuclei is studied with the help of H₂¹⁵O.

In order to study the dopaminergic system, an [¹⁸F] fluorinated analog of the dopamine precursor 3,4-dioxyphenylalanine – ¹⁸F-DOPA – is used.

DOPA transforms to dopamine with help of the enzyme aromatic amino acid decarboxylase (AAD). Analysis of ¹⁸F-DOPA distribution permits assessment of AAD-catalyzed dopamine synthesis in neurons. The level of ¹⁸F-DOPA uptake is determined by the following factors: penetration of the RP through the blood–brain barrier, decarboxylation to fluorodopamine and uptake in neuronal terminals. At the same time, this RP does not permit to differentiate whether the detected changes are due to a disturbance in dopamine production activity through terminals or to the general decrease in number of terminals (Volkow et al. 1996; Verhoeff 1999).

A number of models with different degrees of complexity have been suggested for the quantitative analysis of AAD activity by means of PET. Usually the three-compartment model is applied, which reflects the reversible competitive transfer of ¹⁸F-DOPA through the blood–brain barrier, its AAD-mediated decarboxylation and uptake, release of fluorodopamine from vesicles, its metabolism and excretion from tissues.

The formation of metabolites beyond the CNS (for example, 3-O-methyl-[¹⁸F] fluoro-l-DOPA) is also allowed for in mathematical models.

In studies on serotonin [¹¹C]α-methyl-l-tryptophan is currently used. Under the effect of the enzyme tryptophanhydroxylase, it is transformed to α-methylhydroxytryptophan, then its decarboxylation (with participation of AAD) and transition to α-methylserotonin take place. Unlike serotonin, α-methylserotonin is not catabolyzed by monoaminoxidase and consequently its accumulation level reflects the activity of the serotonin synthesis. The initial studies carried out with the indicated RP have shown significant difference in intensity of serotonin synthesis among volunteers (for example, depending on the sex, presence of migraine in the anamnesis, etc.) (Chugani et al. 1998). In subsequent studies on animals, it has been demonstrated that [¹¹C]α-methyl-l-tryptophan transport and uptake in the brain largely depend on the concentration of large neutral aminoacids in blood plasma and in cerebral matter (Chugani et al. 1999; Shoaf et al. 2000).

The study of the cholinergic system arouses much interest due to its participation in the pathogenesis of Alzheimer’s disease and, to a lesser extent, of schizophrenia and parkinsonism. ¹¹C-Nicotine was one of the first RPs synthesized for studying the cholinergic system of the brain (Muzic et al. 1998). However, its uptake reflects perfusion and blood–brain barrier penetrability to a greater extent than specific binding with acetylcholine receptors. A more selective pharmaceutical is an analog of the nicotine receptor agonist epibatidin (exo-2-(2′-chloro-5′-pyridil) – azabicyclo [2.2.1] heptanes labeled with ¹⁸F.

An analog of 3-quinuclidinyl benzilate has been suggested for studying muscarinic receptors (Giindisch 2000).

¹¹C-Flumazenil is an RP of much importance for studying the density of benzodiazepine receptors; it is widely used for diagnosing epilepsy (Koepp et al. 2000).

Besides that, PET is used for assessing mu-opiate and kappa-opiate receptors. In order to assess their density, ¹⁸F-cyclofoxy (fluorinated analog of the opiate receptor antagonist naltrexone), ¹¹C-diprenorphine and ¹¹C-carfentanyl are used (Schadrack et al. 1999; Zubieta et al. 2000).