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Fractal analysis - a new approach in brain receptor imaging

Jyrki Kuikka and Jari Tiihonen

Improvements in detector technology and the development of radioligands for brain receptor imaging have introduced exiting new insights into the pathophysiology of various neuropsychiatric disorders and have improved the possibilities of optimizing the treatment for patients suffering from them. Positron emission tomography (PET) and single-photon emission tomography (SPET) with tailored radiopharmaceuticals provide information on the topographic physiological chemistry of the living human brain. The different patterns of brain receptor densities and distribution can be imaged and modelled with PET and SPET. The normal receptor distribution in the brain is broadly heterogeneous with different cortical layers, which show receptor densities varying from very low to high. Further exploration of the data shows that human neurophysiology and neural architectures possess fractal properties that may be altered during activation and in different neuropsychiatric disorders. This review highlights recent findings in SPET receptor imaging and the use of fractal analysis in the interpretation of images representing various neuropsychiatric disorders.

Key words: brain; fractals; positron emission tomography; receptor; single-photon emission tomography.

Ann Med 1998: 30: 242-248.

Introduction

Functional changes usually precede structural changes in neuropsychiatric disorders. These functional changes can be observed with functional magnetic resonance imaging and spectroscopy (fMRI and MRS), serial x-ray computed tomography (cine CT), magneto-encephalography (MEG), positron emission tomography (PET) or single-photon emission tomography (SPET) (1-4). There is no doubt that fMRI will have a major impact as a tool in the imaging of regional blood flow and diffusion. Also, as x-ray CT scanners are readily available in most hospitals, the serial CT method might be useful in monitoring blood flow and volume changes in response to treatment. MEG allows ro localize fast cortical electromagnetic transients in a millisecond scale. Nuclear medicine with modern PET and SPET provides information on the topographic physiological chemistry of the living human brain allowing to trace anatomical and temporal distribution of the given radiolabelled molecules. Each of these techniques has both unique advantages and serious limitations (1, 5). None of the methods has achieved supremacy in functional brain imaging, and often two or more methods have to be combined in order to obtain reliable information.

Nerve cells communicate via the synapses in which the transmitter molecules carry the signal across the synaptic gap. Metabolic processes related to function mainly occur in the cortical layers rich in synapses, the neuropile, not in the cell bodies of the neurones. The synapse basically consists of the presynaptic button, the emittor of the signal substance, and the postsynaptic spine, the receptor of the signal. The biochemical activity is more organ and tissue specific than the bioelectrical activity. Therefore, research on neurotransmitters and receptors as well as research on biochemical reactions inside the cell will certainly become a dominant area of nuclear medicine.

Various ligands and drugs can be labelled with radionuclides, which allows to trace their paths in the human body. A competition between the endogeneous ligand and the radioactive ligand (exogeneous radio-ligand) exists as they bind to the same receptor site. Thus, the radioligand has to have a very high specific activity, which makes it possible to use very small doses of the tracer (in the picomolar scale). This means that even with maximal radioligand uptake there is no displacement of the endogeneous ligand, and therefore radioligands used in vivo do not cause practically any pharmacological adverse effects.

The normal receptor distribution in the brain is broadly heterogeneous, as illustrated by postmortem autoradiographic mapping (6). Throughout the examined neocortical regions receptor binding displays a characteristic laminar pattern in which the different layers show receptor densities varying from very low to high. A spatial variation in receptor densities also exists in the living human brain. How can this density variation be analysed from PET and SPET images? This is where a fractal analysis may be useful. For example, an image of the receptor distribution of an organ or tissue may be divided into subregions (2, 4, 8, 16, 32, 64, 128, etc) in order to see density variation. This will yield only one estimate of the mean receptor density but different measures of density variance. Dividing the standard deviation of densities of each subregion by the mean density will give the observation that quantifies regional density heterogeneity and that can be more precisely described by fractal analysis, as shown later. We have limited the topic of this review to receptor imaging with SPET and externalization of the fractal properties in neuropsychiatric disorders.

SPET imaging

There are several radioligands for receptor imaging with PET and SPET (7, 8). In general, SPET is considered inferior to PET because of its poorer spatial and temporal resolution and the severe limitations of appropriate SPET radionuclides used for labelling. The radioligands used in PET are certainly more physio-logicail. Most of them are labelled with ¹¹C with a half-life of 20 min, and only a few are labelled with ¹⁸F or ⁷⁶Br. PET also has finer spatial (5 mm) and temporal resolution (s) than SPET (7-10 mm and min, respectively). However, SPET has some benefits over PET. SPET allows to image up to 40 times longer than PET because of the physical half-life of ¹²³I of 13.3 h (9). This usually signifies a better signal-to-noise ratio, and there is enough time to obtain a steady state between blood and tissue concentrations of the given radioligand, which is needed for modelling and is not always available in PET studies with radioligands of a shorter half-life. In addition, the lower cost and general availability in clinical routine favour SPET as does the possibility to use two to three radiopharma-ceuticals simultaneously (one for perfusion, one for metabolism and/or one for receptor imaging). Imaging resolution of the dedicated, multihead SPET scanners in receptor studies is approaching that of PET (5 mm). However, we would like to emphasize that the total scanning time with SPET lasts 10-30 min, which means that the patient must be co-operative.

Sophisticated functional radionuclide imaging requires tailored radiopharmaceuticals for each specific question. Figure 1 shows an example of how the advantage of measuring neurotransmitter (GABA/ benzodiazepine) function instead of cerebral blood flow in interictal stage of epilepsy is particularly apparent in patients with extratemporal seizures.

Several receptor and transmitter-specific radioligands are available for SPET imaging: [¹²³I]iomazenil and [¹²³I]NNC 13-8241 for GABA/benzodiazepine receptor imaging, [¹²³I]beta-CIT and its derivatives for dopamine transporter (DAT) imaging, [¹²³I]IBZM and [¹²³I]epidepride for dopamine D₂-receptor imaging, [¹²³I]iododexetimide for muscarinic receptor imaging, [¹²³I]nor-beta-CIT for serotonin transporter imaging, and [¹²³I]R91150 for serotonin receptor imaging (8). Only initial experiences have been available with many of them, and further studies are required to establish the clinical value of these radioligands. However, the progress in the development of SPET radioligands has been very rapid, and selective radioligands ('magic bullet tracers') will soon be used for diagnostic purposes at the early stages of a disease, as well as for monitoring of the effects of new drugs and for optimizing clinical treatment.

There is also an increased interest to develop ^99mTc-based radioligands and thus to avoid the need for cyclotron-produced radionuclides for receptor imaging. Kung et al (10) recently reported the initial results on the use of [¹²³Tc]TRODAT-1 for DAT imaging of the living human brain. However, the relatively low brain uptake, low target-to-background ratio and poor imaging quality do not favour the use of the present form of [¹²³Tc]TRODAT-1 in clinical routine.

Radiation exposure of the patients in a single-tracer SPET study is reasonably small, being 4-6 mSv (effective dose). This amount corresponds to the average annual dose of background radiation in Finland.

Clinical studies

Data obtained with brain imaging, during the last 10 years have had a substantial impact on the current understanding of the pathophysiology and treatment of major mental disorders (3). In tile first phase, brain functions were studied only with cerebral blood flow and glucose metabolism procedures. These studies can give important information about the locations and the magnitudes of the changes in the metabolism of the brain in, eg patients with schi?ophrenia or major affective disorders (3, 11, 12). However, they cannot provide any information on the possible patho-physiological alterations on the neuronal level, which is essential when a pharmacological treatment is being developed or planaed.

Since the findings of Wong et al (13) and Farde et al (14) on striatal dopamine D₂-receptor densities in schizophrenic patients, a lot of evidence has accumulated on the dopaminergic alterations in schizophrenia (15,16). New radioligands have made it possible to obtain information on the presynaptic dopamine synthesis (16), on D₁-receptor occupancy and density (17, 18) and on extrastriatal D₂-receptor occupancy by different neuroleptic agents (19). The antipsychotic efficacy and the severity of extra-pyramidal side-effects may depend crucially on the selective D₂-receptor occupancy in the striatum vs extrastriatal regions (such as the temporal cortex) (19). Figure 2 shows the D₂-receptor blockade in the striatum and the temporal cortex by a typical neuroleptic (halo-peridol) and by a new atypical neuroleptic (olanzapine) imaged with [¹²³I]epidepride. Haloperidol blocks the D₂-receptors in the striatum but not in the temporal cortex, whereas olanzapine blocks the D₂-receptors in the cortex but not in the striatum. This is in line with the clinical finding that olanzapine has significantly milder extrapyramidal side-effects than haloperidol.

Specific ligands for DAT make it possible to measure dopamine activity in the presynaptic site of the synapse. Results from nonviolet alcoholics have shown decreased density of dopanine receptors (20, 21) and transporters (22) in the basal ganglia, whereas slightly higher DAT densities and reduced serotonin transporter densities have been found in habitually violent impulsive alcoholics when compared with healthy controls (23). Recent results from patients with social phobia indicate that they also have a decreased dopamine transporter density in the striatum (24).

Novel ligands for cerebral GABA/benzodiazepine receptors have enabled studies on anxiety disorders, and the results imply that cerebral benzodiazepine receptor densities and distributions are altered in panic disorder (25, 26) and generalized anxiety disorder (GAD) (27). New ligands are becoming available also for serotonin (5-HT) receptors, transporters and

presynaptic synthesis, but thus far the data on the 5-HT imaging in psychiatric disorders have been Very preliminary (23, 28-31). The new data obtained with these radioligands will certainly increase our knowledge on the pathophysiology of schizophrenia, major depression, bipolar disorders, substance abuse and anxietv disorders.

Unresolved issues of the poor imaging resolution of SPET

The sensory, motor and cognitive functions of the living human brain are performed by anatomically distinct neural processing networks, not by a single cerebral region. In addition, regional analysis of radioligand distribution and density in finer and finer derails of small brain structures is extremely difficult to perform with poor resolution PET and SPET studies. Scatter, attenuation, partial volume and reconstruction errors disturb the images. A blurred radiodistribution profile is almost alwavs seen in small regions such as the hippocampus and the raphe nucleus. Even the drawing of the true cortical mantle is almost an impossible task in PET and SPET studies, although one can use the structural characteristics of the MRI or the CT scan. Quantitative comparison between patients and healthy controls is more or less unaccurate, and each laboratory has to have its own reference values for a given studv.

Figure 2. Hatoperidol and olanzapine induce different levels of occupancy and binding at dopamine D₂-receptors. Transaxial slices in three study subjects who have been administrated 185 MBq of [¹²³I]epidepride (dopamine D,-receptor radioligand). The upper row shows images taken 45 min after injection at the level of temporal poles in a healthy male (A), in a patient pretreated with haloperidol (B), and in a patient pretreated with olanzapine (C). The lower row shows corresponding slices 3 h later at the level of the striatum. Note the different regional extrastriatal and striatal receptor uptakes in these study subjects.

Figure 3. Parkinson's disease can be imaged prior to its symptoms. Topographic three-dimensional striatal uptake of a [¹²³I]beta-CIT scan (dopamine transporter radioligand) in a 56-year-old male patient with Parkinson's disease at a very early stage. The scan has been performed 23 h after injection of 185 MBq of [¹²³I]beta-CIT. Note that the dopamine transporter has disappeared almost completely in the left putamen at a very early stage of the disease (his initial symptoms appear on the right).

Figure 1

Figure 3

Fractal analysis is a new exciting and promising method to magnify these structures of the brain and to see how new and even finer features are continuously revealed. This analysis depends on the size of the spatial or temporal ruler that we use to make our observations. Mandelbrot (32) chose the word 'fractal' to signify the breaking of an object into finer and finer fragments (pieces). In the past, our ability to understand human structural and physiological systems was hampered by our failure to appreciate their fractal properties and to understand how to analyse and interpret scale-free structures (33-35). Fractal analysis may help us to extend our knowledge on the pathophysiology of neuropsychiatric disorders. Some initial experiences of fractal analysis are available both on the spatial and temporal changes in the living human brain. However, we still lack scanners with improved spatial and temporal resolution and more selective radioligands.

Fractal analysis

Figure 3 illustrates an example of the topographical distribution of striatal DAT densities in the living human brain as imaged with [¹²³I]beta-CIT SPET. It is difficult to analyse these kinds of images. Fractal analysis might offer a solution to find alteration and abnormal variability in receptor densities and distributions associated with various brain disorders. It is well established that healthy biological systems show considerable spatial and temporal heterogeneity (34). This multiscaled fractal property (anatomical structures at different spatial scales or physiological processes at different time scales are related to each other) possesses obvious adaptive advantages and makes the subject more capable to meet the inherently unpredictable environment of daily life (33-35) (in its simplest form the daily heart rate variability). Goldberger (35) has related this property to studies on the fractal analysis of ECG: "The healthy heart dances whereas the dying organ can merely march". The lack of sufficient heterogeneity and adaptation is also found in many brain disorders (temporal variability, such as epileptic seizures and periodic behaviour of tremors observed in a wide range of neural disorders (35, 36)). Fractal analysis can describe, quantify and suggest mechanisms that may produce them.

Spatial variation in regional blood flow, metabolism and receptor density in the brain can be measured with both PET and SPET. As the regional receptor density in the smaller subregions is nonuniform (as seen from postmortem autoradiography), the overall apparent heterogeneity in receptor density must increase with the number of subregions to which the organ or tissue is 'cut'. We have characterized the

observed heterogeneity independently of the resolution scale by spatial dispersion (ie the standard deviation of the regional receptor density divided by the mean density). A fractal relation exists between the observed spatial dispersion and the number of subregions (34, 37). This relation follows the power law function:

where RD_spatial is the spatial dispersion (heterogeneity), N is the number of subregions and D is the fractal dimension. D is 1.0 for the uniform receptor density and 1.5 for the complete randomness (34). In the healthy brain D is around 1.2. The reference region (N = 1) is an arbitrarily chosen unit reference volume of the whole organ or tissue, and can be assumed to represent the 'apparent' heterogeneity of the whole organ or tissue.

The problem of calculating individual spatial dispersions can be solved by a 'box-counting' method that can be used to estimate heterogeneity along with the piece size (38). The two-dimensional space of the organ or tissue data is first divided into a grid of two boxes of same size, and the mean receptor density and its standard deviation are calculated. Next, the organ is divided into four boxes and further into smaller and smaller boxes. When the organ is divided into the smaller boxes we have, of course, the same estimates of the mean receptor density, but we also have the additional information on the variability of the receptor density which can be given by the spatial dispersion (ie standard deviation and mean). The box-counting method allows a fast and reliable determination the spatial variability of regional radioligand density (34, 36). However, we would like to emphasize that low resolution PET and SPET images are blurred with the methodological noise (depending on the imaging resolution, count density, contrast, partial volume effect and tomographic reconstruction errors). Observed dispersion RD_observed, when performed correctly, should be corrected by the methodological dispersion RD_method, ie RD²_spatial = RD²_observed - RD²_method.

For further details on fractal analysis please refer to the referenced excellent reviews and books (32-35).

Fractal analysis has been applied in a wide number of lung, heart and brain studies from pulmonary (39) and myocardial (40) blood flow distributions to auditory nerve train spikes (41). We have preliminarily applied fractal analysis to estimate regional heterogeneity of brain receptor images in healthy subjects and in patients with GAD and in type 1 and violent type 2 alcoholics (27, 37, 42). Figure 4 illustrates the characteristics of spatial heterogeneity of cortical GABA/benzodiazepine receptor densities in patients with GAD and in healthy controls. Fractal analysis revealed that the benzodiazepine receptor distribution was markedly more homogeneous in the left temporal

Figure 4. Fractal analysis of variation in cortical GABA/ benzodiazepine receptor densities. Piece size (N)-dependent variation in regional GABA/benzodiazepine receptor density of the left hemisphere in healthy females (квадратик) and in females with generalized anxiety disorder (GAD) (•) The error bars show one standard deviation. A log-log plot of the figure is also shown in the smaller image. Fractal dimension and intercept can be calculated from the linear fit of the log-log plot. The patients with GAD have a much smaller intercept (heterogeneity) than the healthy controls (27).

cortex among GAD patients than in healthy controls. The results are consistent with the general hypothesis that high regional heterogeneity of perfusion, metabolism and receptor density is necessary to maintain the ability to adapt (34, 35).

We may speculate that the fractal approach can be regarded as a primary and basic model for many systems in physiology and biology (32-37, 39-45). At least, the fractal model should be tested before going on to more complicated models. In brain studies with PET, SPET and fMRI we presume that it can be used as a metric of different heterogeneity or different lateralization within and between the study subjects and patients suffering from various neuropsychiarric disorders.

Conclusion

Nuclear medicine with modern PET and SPET provides information on the topographic distribution of neurotransmitters and receptors in the living human brain. The nuclear medicine methods are becoming more sensitive and more specific and can be used for various diagnostic purposes, as well as for optimizing various clinical treatments.

The principal finding of fractal analysis is that in the healthy brain the perfusion, metabolism and receptor density are spatially heterogeneous in a wide range, whereas in the diseased brain they are more uniform. The loss of multiscaled fractal variability in neuropsychiatric disorders usually signifies an inability to meet an inherently unpredictable environment. In the light of the important fractal features of our own anatomy and physiology, evident from macroscopic to molecular levels, this method may in the near future help us to gain a better understanding of the living human brain.

Kuikka JT, Belliveau JW, Hari R. Future of functional brain imaging. Eur J Nucl Med 1996; 23: 737-40.

eventt. Ptoc Natl Acad Sci USA 1996; 93: 14302-3.

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© The Finnish Medical Society Duodecim, Ann Med 1998; 30: 242-248