Fractal complexity
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Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
- MeSH
- algoritmy MeSH
- diagnóza počítačová metody MeSH
- duktální karcinom prsu MeSH
- fraktály MeSH
- hodnocení rizik metody MeSH
- lidé MeSH
- nádory prsu diagnóza patologie MeSH
- patologie metody MeSH
- počítačová simulace MeSH
- stochastické procesy MeSH
- Check Tag
- lidé MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- srovnávací studie MeSH
The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.
The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.
- MeSH
- fraktály MeSH
- histologické techniky * MeSH
- interpretace obrazu počítačem * MeSH
- lidé MeSH
- rozpoznávání automatizované MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- práce podpořená grantem MeSH
... Contents -- 1 Complexity in Health: An Introduction 1 -- Joachim R Sturmberg and Carmel M. ... ... care 19 -- Iona Heath -- Part I Complexity Theory and Methods -- 3 Understanding Complex Systems 27 ... ... -- Paul Cilliers -- 4 The Complex Nature of Knowledge 39 -- Joachim P. ... ... West -- 12 Bio-Complexity: Challenging Reductionism 193 -- Henry H.Q. ... ... Waldstein -- 25 Pain and Complex Adaptive System Theory 397 -- Cary A. ...
xxi, 954 stran : ilustrace (převážně barevné) ; 26 cm
- MeSH
- poskytování zdravotní péče MeSH
- výzkum MeSH
- zdraví MeSH
- zdravotní stav populace MeSH
- Publikační typ
- příručky MeSH
- Konspekt
- Veřejné zdraví a hygiena
- NLK Obory
- veřejné zdravotnictví
- NLK Publikační typ
- kolektivní monografie
Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).
Compression of ECG signal is essential especially in the area of signal transmission in telemedicine. There exist many compression algorithms which are described in various details, tested on various datasets and their performance is expressed by different ways. There is a lack of standardization in this area. This study points out these drawbacks and presents new compression algorithm which is properly described, tested and objectively compared with other authors. This study serves as an example how the standardization should look like. Single-cycle fractal-based (SCyF) compression algorithm is introduced and tested on 4 different databases-CSE database, MIT-BIH arrhythmia database, High-frequency signal and Brno University of Technology ECG quality database (BUT QDB). SCyF algorithm is always compared with well-known algorithm based on wavelet transform and set partitioning in hierarchical trees in terms of efficiency (2 methods) and quality/distortion of the signal after compression (12 methods). Detail analysis of the results is provided. The results of SCyF compression algorithm reach up to avL = 0.4460 bps and PRDN = 2.8236%.
Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.
- MeSH
- difuzní magnetická rezonance MeSH
- epilepsie diagnostické zobrazování MeSH
- lidé MeSH
- mozek * fyziologie MeSH
- nervová síť fyziologie MeSH
- nervové vedení fyziologie MeSH
- teoretické modely MeSH
- záchvaty diagnostické zobrazování MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- práce podpořená grantem MeSH
- srovnávací studie MeSH
Walking is an everyday activity in our daily life. Because walking affects heart rate variability, in this research, for the first time, we analyzed the coupling among the alterations of the complexity of walking paths and heart rate. We benefited from the fractal theory and sample entropy to evaluate the influence of the complexity of paths on the complexity of heart rate variability (HRV) during walking. We calculated the fractal exponent and sample entropy of the R-R time series for nine participants who walked on four paths with various complexities. The findings showed a strong coupling among the alterations of fractal dimension (an indicator of complexity) of HRV and the walking paths. Besides, the result of the analysis of sample entropy also verified the obtained results from the fractal analysis. In further studies, we can analyze the coupling among the alterations of the complexities of other physiological signals and walking paths.
- Publikační typ
- časopisecké články MeSH
... aspects of the iteration of z —• A z (1-z) for complex A and z (M1980n) 37 -- C4 Cantor and Fatou dusts ... ... ; self-squared dragons (M 1982F) 52 -- C5 The complex quadratic map and its M-set (M1983p) 73 -- C6 ... ... LIMIT SETS OF KLEINIAN GROUPS -- * C15 Introduction to papers on Kleinian groups, their fractal limit ... ... sets, and IFS: history, recollections, and acknowledgments (2003) 171 -- C16 Self-inverse fractals, ... ... Apollonian nets, and soap (M 1982F) 178 -- C17 Symmetry by dilation or reduction, fractals, roughness ...
Selected works of Benoit B. Mandelbrot ; Selecta volume C
[1st ed.] xii, 308 s. : il.
In this article, we evaluated the variations of the brain and muscle activations while subjects are exposed to different perturbations to walking and standing balance. Since EEG and EMG signals have complex structures, we utilized the complexity-based analysis. Specifically, we analyzed the fractal dimension and sample entropy of Electroencephalogram (EEG) and Electromyogram (EMG) signals while subjects walked and stood, and received different perturbations in the form of pulling and rotation (via virtual reality). The results showed that the complexity of EEG signals was higher in walking than standing as the result of different perturbations. However, the complexity of EMG signals was higher in standing than walking as the result of different perturbations. Therefore, the alterations in the complexity of EEG and EMG signals are inversely correlated. This analysis could be extended to investigate simultaneous variations of rhythmic patterns of other physiological signals while subjects perform different activities.
- Publikační typ
- časopisecké články MeSH
Measures from the theory of nonlinear dynamics were applied on complex fractionated atrial electrograms (CFAEs) in order to characterize their physiological dynamic behavior. The results were obtained considering 113 short term atrial electrograms (A-EGMs) which were annotated by three experts into four classes of fractionation according to A-EGMs signal regularity. The following measures were applied on A-EGM signals: General Correlation Dimension, Approximate Entropy, Detrended Fluctuation Analysis, Lempel-Ziv Complexity, and Katz-Sevcik, Variance and Box Counting Fractal Dimension. Assessment of disorganization was evaluated by a Kruskal Wallis statistical test. Except Detrended Fluctuation Analysis and Variance Fractal Dimension, the CFAE disorganization was found statistically significant even for low significant level alpha = 0.001. Moreover, the increasing complexity of A-EGM signals was reflected by higher values of General Correlation Dimension of order 1 and Approximate Entropy.
