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Cerebral autoregulation (CA) is a vital protective mechanism that maintains relatively stable cerebral blood flow despite variations in systemic pressure as large as 100 Torr. It is commonly perceived to operate as a high-pass filter which transmits rapid changes in blood pressure but strongly attenuates and delays low-frequency perturbations. The ongoing search for clinically significant measures of CA integrity fuels the study of relations between the statistical properties of arterial blood pressure fluctuations (ABP) and those of blood flow velocity in major cerebral arteries, for example in middle cerebral artery (MCA). Using the method of averaged wavelet coefficients (AWC) we find that in the healthy subjects the scaling properties of both time series may be characterized by two exponents. The short time scaling exponent determines the statistical properties of fluctuations in short-time intervals while the Hurst exponent H describes the long-term fractal properties. Surprisingly, the group-averaged Hurst exponents coincide: H _ ABP = H _ MCA = 1 . To explain this effect, we employ complex continuous wavelet transforms to characterize autoregulation in terms of the wavelet gain and instantaneous phase difference between the arterial blood pressure and cerebral flow velocity. In the very low frequency (0.02–0.07 Hz) part of the spectrum, where autoregulation is most strongly pronounced, the damping of ABP slow oscillations weakly depends on frequency. In this frequency range phase difference evolves slowl y over time and has an almost uniform distribution. Thus, CA not only dampens low frequency oscillations but also randomizes their phases. However, phase randomization of fractional Brownian motion does not affect its scaling properties. Consequently, fractal dynamics of arterial pressure is essentially carried over to cerebral blood flow.

Walking is regulated through the motorcontrol system (MCS). The MCS consists of a network of neurons from the central nervous system (CNS) and the intraspinal nervous system (INS), which is capable of producing a syncopated output. The coupling of the latter two systems produces a complex stride interval time series that is characterized by fractal and multifractal properties that depend upon several biological and stress constraints. It has been shown that: (i) the gait phenomenon is essentially a rhythmic cycle that obeys particular phase symmetries in the synchronized movement of the limbs; (ii) the fractal and multifractal nature of the stride interval fluctuations become slightly more pronounced under faster or slower paced frequencies relative to the normal paced frequency of a subject; (iii) the randomness of the fluctuations increases if subjects are asked to synchronize their gait with the frequency of a metronome or if the subjects are elderly or suffering from neurodegenerative disease. Here we present a new model, called the super central pattern generator, able to reproduce these known properties of walking and discuss the physiological and psychological interpretations of the model parameters.

Although the phenomenon of 1/ f noise in heart rate has been known for more than two decades, ours has been the first systematic study showing the importance of antagonistic dynamics between the two branches of the autonomic nervous system

Squamous cell carcinoma (SCC) is the most common malignant lesion of the oral cavity. One important diagnostic problem involves differentiating histopathologically between SCC and pseudoepitheliomatous hyperplasia (PEH) of the covering epithelium present in granular cell tumour (GCT) (a benign tumour), mimicking the invasive patterns of SCC. The complexity of the epithelial connective tissue interface (ECTI) in 84 profiles from normal oral mucosa, SCC and GCT-PEH cases was analyzed using both global and local fractal dimensions. Segmentation of the epithelial compartments into theoretical cell areas was performed using a space partition procedure and the morphological properties of these “cells” were analyzed. The complexity of the GCT-PEH ECTI profiles was marginally but significantly higher than that of SCC, which was significantly higher than normal ECTI profiles. The combined fractal and cell morphology data allowed up to 100%, and 96% correct discrimination between SCC and normal oral mucosa and between SCC and GCT-PEH respectively. In conclusion, we found that the architectural features of SCC, normal oral mucosa and GCT-PEH show differences that, when quantified, could be used for aiding in the diagnostic process.

Here some basic concepts of Statistical Shape Analysis are introduced and applied to a specific problem: automatic recognition and classification of cells coming from tumor tissues, from their nuclear profiles. The technique here described, which is commonly used for the description of the mean geometrical characteristics of families of random objects and their statistical analysis, is proposed as an alternative (or in addition) to the study of an asymptotic fractal model for the contour of nuclei.

Most women undergoing treatment for early ovarian cancer have a good prognosis, but about 20% will eventually die of the disease. Identifying patients with increased risk of relapse is important, as it could be used to select patients in need for adjuvant treatment after surgery. The aim of the present study has been to analyze the prognostic value of nuclear fractal features in early ovarian cancer, and to study the complex relation between nuclear area, nuclear DNA content, nuclear gray level distribution and nuclear fractal features. We found that the monolayer nuclei from a given lesion differed widely in fractal dimension. The fractal dimension in the peripheral part of the nuclei was higher than the fractal dimension in the central part of the nuclei. The intra-patient variability of fractal dimension was larger than the inter-patient variability of the mean fractal dimension. Fractal dimension was insufficient for classification. The cell nuclei were grouped into area bins according to nuclear area. Lacunarity class distance and class difference matrices were extracted from the nuclei within each area bin. Some few area intervals contained most of the class distance information between the two prognostic classes of early ovarian cancer. The Mahalanobis values contained in the class distance matrices computed from these area bins were about four times higher than the Mahalanobis values contained in the area independent class distance matrices computed from all the nuclei. However, the lacunarity features were not sufficient to discriminate the two classes of early ovarian cancer.

The lower gengival and vestibular oral mucosa was photographed and analyzed to determine the complexity of the vascular network. Patients with hereditary non-polyposis colorectal cancer syndrome (HNPCC), newborns with true umbilical cord knots, patients with a history of infantile hypertrophic pyloric stenosis (IHPS), patients with mixed connective tissue disease (MCTD) and ageand sex-matched controls were enrolled in the study. The fractal dimensions for two regions of different box lengths ( < 740 µm and < 140 µm), the fractal dimension of the minimum path (Dmin) and the relative Lempel-Ziv complexity were calculated. The findings of this study indicate the presence of an increased vascular network complexity of the patients’ oral mucosa, giving us previously unrecognized phenotypical markers for these diseases. The increased oral vascular complexity observed may be linked to a a systemic abnormality of the extracellular matrix.

In an attempt to evaluate local architectural changes in oral epithelial premalignancy and malignancy, a quantitative method to analyse spatial cell arrangement as observed in 2D histological sections was developed based on mathematical morphology and graph theory. In total, 441 images (x20) of oral epithelium belonging to three diagnostic classes of interest (normal, dysplastic and neoplastic lesions) were assembled into collages for analysis. Epithelial cell nuclei markers were created from Haematoxylin and Eosin stained sections using colour deconvolution and morphological greyscale reconstructions. The epithelial tissue compartment was partitioned (using a digital watershed algorithm) into exclusive domains according to nuclei positions to approach the theoretical cell extents. The spatial arrangement of these “cells” was then analysed in circular neighbourhoods of two sizes where four types of constrained graph networks (minimal spanning tree, relative neighbour graph, Gabriel graph and Delaunay triangulation) were constructed over the cell centroids. From these networks a total of 29 statistical properties were recorded. The statistical analysis of the network data indicated that unbiased and reproducible quantification of tissue architectural features is feasible and may provide valuable morphological information for diagnostic purposes and tissue characterization.

Trichoblastoma, is a “benign tumour derived from or reduplicating the primitive hair germ of embrionic follicular development” . Among the different subtypes of canine trichoblastoma, Ribbon type Trichoblastoma subjectively display a very complex structure, sometimes suggestive of a self-similar design, which is a well known characteristic of fractal structures. In this study, we performed a fractal analysis of twelve (12) canine trichoblastoma in order to test the use of the fractal approach to characterise and describe the architecture of the epithelial growth of this very peculiar spontaneous canine tumour.For each case, the fractal analysis was basically performed by a FANAL ++ software, which determines the slope of the possible fractal region of a bi-asymptotic curve. The FANAL++ results were also compared with the fractal dimension (FD) calculated on the same images with the box counting method performed by a further commercially available fractal software (Benoit 1.3) which doesn’t extrapolate the fractal windows of the tumour. In the cases examined our data confirm that the subjective self-similarity sometimes observed in the growth of the epithelial component of canine trichoblastoma, reflect a true fractal pattern. Furthermore, the values of the FD calculated by FANAL ++ and Benoit 1.3 on the same images are in general comparable from a statistical point of view, although numerically different, and depending closely by the Benoit 1.3 settings. Finally, available data demonstrated a difference in the FD of the same tumour when calculated on images captured at different magnification. In particular the FD increased when the magnification decreased. The authors suggest that these findings should be considered for a standardised approach to fractal based analysis and classification of canine trichoblastoma.

The objective of this pilot study was to find out whether urodynamic curves possess fractal structure, and how this structure changes along with changes of detrusor function in patients with longlasting outflow obstruction? We analyzed 25 multichannel urodynamic curves representing normal function of urinary bladder (n=10 curves) and dysfunction of detrusor muscle (n=15 curves). The curves were analyzed by Size-Frequency algorithm, R/S algorithm or Power-Spectral algorithm. All curves analyzed possess fractal structure. This structure is defined by Size-Frequency dimension, fractal dimension, and Hurst coefficient. The latter one was found to be much lower than 0.5 for all urodynamic curves representing normal filling and voiding function of the urinary bladder. The long-lasting outflow obstruction caused increment of the Hurst coefficient close up to 0.8. Long-lasting outflow obstruction changes the regular contractions of detrusor muscle into the deterministic chaotic contractions. We hypothesize that the Hurst coefficient equal to 0.5 is a limit value which allows to distinguish between cases of benign prostatic hyperplasia which can be treated pharmacologically and those which should be treated surgically.