scholarly journals Applications of fractal analysis to physiology

1991 ◽  
Vol 70 (6) ◽  
pp. 2351-2367 ◽  
Author(s):  
R. W. Glenny ◽  
H. T. Robertson ◽  
S. Yamashiro ◽  
J. B. Bassingthwaighte
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Temporal Correlation ◽  
Physiological Data ◽  
Fractal Properties ◽  
Fractal Analyses ◽  
Intact Organism ◽  
Physiological Systems

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.

scholarly journals Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them

2020 ◽  
Author(s):  
Alessandro Santuz ◽  
Turgay Akay
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
Activity Patterns ◽  
Surrogate Data ◽  
Time Dependent ◽  
Physiological Data ◽  
Adult Mice

AbstractTime-dependent physiological data, such as electromyogram (EMG) recordings from multiple muscles, is often difficult to interpret objectively. Here, we used EMG data gathered during mouse locomotion to investigate the effects of calculation parameters and data quality on two metrics for fractal analysis: the Higuchi’s fractal dimension (HFD) and the Hurst exponent (H). A curve is fractal if it repeats itself at every scale or, in other words, if its shape remains unchanged when zooming in the curve at every zoom level. Many linear and nonlinear analysis methods are available, each of them aiming at the explanation of different data features. In recent years, fractal analysis has become a powerful nonlinear tool to extract information from physiological data not visible to the naked eye. It can present, however, some dangerous pitfalls that can lead to misleading interpretations. To calculate the HFD and the H, we have extracted muscle synergies from normal and mechanically perturbed treadmill locomotion from the hindlimb of adult mice. Then, we used one set per condition (normal and perturbed walking) of the obtained time-dependent coefficients to create surrogate data with different fluctuations over the original mean signal. Our analysis shows that HFD and H are exceptionally sensitive to the presence or absence of perturbations to locomotion. However, both metrics suffer from variations in their value depending on the parameters used for calculations and the presence of quasi-periodic elements in the time series. We discuss those issues giving some simple suggestions to reduce the chance of misinterpreting the outcomes.New & NoteworthyDespite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchi’s fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.

FRACTAL PROPERTIES OF A NEOGENE FAULT SYSTEM IN NORTHWESTERN SICILY, ITALY

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 41-48 ◽  
Author(s):  
P. GUARNIERI ◽  
S. VINCIGUERRA ◽  
OSSERVATORIO VESUVIANO
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Integral Method ◽  
Strike Slip ◽  
Fault System ◽  
Moving Window ◽  
Correlation Integral ◽  
Distribution Property ◽  
Fractal Properties

A Neogene transcurrent fault system affecting the Apenninic-Maghrebian thrust belt, located in northwestern Sicily, has been investigated using fractal analysis. The present-day structural setting of the sector between the Palermo and Madonie Mountains is the result of the superimposition, in space and time, of two distinct deformational events, a Miocene southeast-verging thrusting followed by Messinian to Pliocene strike-slip faulting, which cuts obliquely through the compressive fronts. The spatial distribution properties of the fault array were investigated by means of a fractal analysis. Fractal dimension was computed by adopting the correlation integral method. Fractal ranges have been evidenced between 350 and 3000 m. The fractal dimension obtained for the whole array is D=1.66. The scaling spatial distribution property of the fault array has been analyzed by calculating the fractal dimension with a moving window.

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

scholarly journals Fractal Dimension and Retinal Pathology: A Meta-Analysis

2021 ◽  
Vol 11 (5) ◽  
pp. 2376
Author(s):  
Sam Yu ◽  
Vasudevan Lakshminarayanan
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Meta Analysis ◽  
Scientific Evidence ◽  
Retinal Disease ◽  
Clinical Value ◽  
Disease Category ◽  
Normal Individuals ◽  
Retinal Pathology ◽  
Meta Analyses

Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current scientific evidence regarding the relationship between fractal dimension and retinal pathology and thus assess the clinical value of retinal fractal dimension. Following the PRISMA guidelines, a literature search for research articles was conducted in several internet databases (EMBASE, MEDLINE, Web of Science, Scopus). This led to a result of 28 studies included in the final review, which were analyzed via meta-analysis to determine whether the fractal dimension changes significantly in retinal disease versus normal individuals. From the meta-analysis, summary effect sizes and 95% confidence intervals were derived for each disease category. The results for diabetic retinopathy and myopia suggest decreased retinal fractal dimension for those pathologies with the association for other diseases such as diabetes mellitus, hypertension, and glaucoma remaining uncertain. Due to heterogeneity in imaging/fractal analysis setups used between studies, it is recommended that standardized retinal fractal analysis procedures be implemented in order to facilitate future meta-analyses.

Outer Cutoff Value for the Box-Counting Method for Fractal Analysis of the Nucleus Using Kirsch Edge Detection

2020 ◽  
pp. 1-8
Author(s):  
Haruhiko Yoshioka ◽  
Kouki Minami ◽  
Hirokazu Odashima ◽  
Keita Miyakawa ◽  
Kayo Horie ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Edge Detection ◽  
Fractal Analysis ◽  
Nuclear Size ◽  
Original Position ◽  
Cytological Diagnosis ◽  
Cutoff Value ◽  
Position Bias ◽  
Box Counting ◽  
Nuclear Rotation

<b><i>Objective:</i></b> The complexity of chromatin (i.e., irregular geometry and distribution) is one of the important factors considered in the cytological diagnosis of cancer. Fractal analysis with Kirsch edge detection is a known technique to detect irregular geometry and distribution in an image. We examined the outer cutoff value for the box-counting (BC) method for fractal analysis of the complexity of chromatin using Kirsch edge detection. <b><i>Materials:</i></b> The following images were used for the analysis: (1) image of the nucleus for Kirsch edge detection measuring 97 × 122 pix (10.7 × 13.4 μm) with a Feret diameter of chromatin mesh (<i>n</i> = 50) measuring 17.3 ± 1.8 pix (1.9 ± 0.5 μm) and chromatin network distance (<i>n</i> = 50) measuring 4.4 ± 1.6 pix (0.49 ± 0.18 μm), and (2) sample images for Kirsch edge detection with varying diameters (10.4, 15.9, and 18.1 μm) and network width of 0.4 μm. <b><i>Methods:</i></b> Three types of bias that can affect the outcomes of fractal analysis in cytological diagnosis were defined. (1) Nuclear position bias: images of 9 different positions generated by shifting the original position of the nucleus in the middle of a 256 × 256 pix (28.1 μm) square frame in 8 compass directions. (2) Nuclear rotation bias: images of 8 different rotations obtained by rotating the original position of the nucleus in 45° increments (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). (3) Nuclear size bias: images of varying size (diameter: 190 pix [10.4 μm], 290 pix [15.9 μm], and 330 pix [18.1 μm]) with the same mesh pattern (network width: 8 pix [0.4 μm]) within a 512 × 512 pix square. Different outer cutoff values for the BC method (256, 128, 64, 32, 16, and 8 pix) were applied for each bias to assess the fractal dimension and to compare the coefficient of variation (CV). <b><i>Results:</i></b> The BC method with the outer cutoff value of 32 pix resulted in the least variation of fractal dimension. Specifically, with the cutoff value of 32 pix, the CV of nuclear position bias, nuclear rotation bias, and nuclear size bias were &#x3c;1% (0.1, 0.4, and 0.3%, respectively), with no significant difference between the position and rotation bias (<i>p</i> = 0.19). Our study suggests that the BC method with the outer cutoff value of 32 pix is suitable for the analysis of the complexity of chromatin with chromatin mesh.

scholarly journals Analisis Dimensi Fraktal Kejadian Gempa Dl Laut Banda Indonesia

2016 ◽  
Vol 19 (2) ◽  
pp. 108
Author(s):  
Sugeng Widada
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Approach ◽  
Study Support ◽  
Tectonic System

The Banda Sea region is an active earthquakes area which indicated by mean monthly incident of quakes more than 220. The condition is caused the area being located in the triple jucntion. Earthquakes system in this region which occur during September 2015 up to October 2016 is analyzed by fractal approach to investigate the subduction system.Earthquakes system is chaotic, so can be quantified using fractal concept. Quantify result of Banda Sea earthquakes system using Aki method is fractal dimension 2.08. It indicates that the slab was fractured by some fault in form an angle or upright possition with the subduction strike. Such a thing also be proven by the fact that the length zone of slab moved during each earthquake is not same, the variation is about 6 – 1,056 m. Based on the fractal analysis, also be identified that about 6.25 magnitute six earthquakes are expected each year. The result of study support the previous studies which propose that the tectonic system in Banda Sea region is very complex. Keywards:  Earthuakes system, fractal, Banda Sea Kawasan Laut Banda merupakan daerah aktif gempa yang ditunjukan dengan kejadian gempa rata-rata bulanan Iebih dan 220. Keadaan ini dapat dimengerti mengingat kawasan tersebut merupakan pertemuan tiga buah lempeng yang bergerak. Pola kegempaan di daerah tesebut yang tejadi pada September 2015 hingga Oktober 2016 dicoba dianalisa menggunakan pendekatan fraktal untuk mengetahui pola subduksi di daerah tersebut. Pola kegempaan merupakan suatu kejadian yang chaos, sehingga dapat dilakukan kuantisasi berdasarkan konsep fraktal. Hasil kuantisasi pola gempa Laut Banda meggunakan metode Aki diperoleh dimensi fraktal 2,08. Hal ini menunjukan bahwa slab yang menunjam dan bergerak sehingga menimbulkan gempa terbagi dalarn beberapa bagian melalui suatu sesar yang menyududut / tegak lurus jurus subduksi. Keadaan ini dikuatkan oleh hasil perhitungan panjang daerah yang bergerak untuk setiap kejadian gempa tidak sama, yaitu bervariasi dari 6 – 1.056 m. Berdasarkan analisa fraktal tersebut juga diketahui bahwa gempa dengan magnitudo 6,25 akan terjadi 6 kali dalam satu tahun. Hasil penelitian ini mendukung hasil penelitian terdahulu yang menyatakan bahwa tatanan tektonik di daerah Laut Banda sangat kompleks. Kata Kunci: Pole gempa, fraktal, Laut Banda

The fractal analysis of water trees: an estimate of the fractal dimension

2001 ◽  
Vol 8 (5) ◽  
pp. 838-844 ◽  
Author(s):  
M.C. Lanca ◽  
J.N. Marat-Mendes ◽  
L.A. Dissado
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis

Fractal analysis of rain gauges’ inhomogeneous distribution and the associated hydrological impacts: the case study of Muriaé River basin

2021 ◽  
Author(s):  
Priscila Celebrini de O. Campos ◽  
Igor Paz ◽  
Maria Esther Soares Marques ◽  
Ioulia Tchiguirinskaia ◽  
Daniel Schertzer
Keyword(s):  
Fractal Dimension ◽  
Spatial Analysis ◽  
Fractal Analysis ◽  
Probability Of Detection ◽  
Susceptibility Map ◽  
Rain Gauges ◽  
Flood Susceptibility ◽  
Susceptibility Maps ◽  
Cross Tabulation ◽  
The Cross

&lt;p&gt;The urban population growth requires an improvement in the resilient behavior of these areas to extreme weather events, especially heavy rainfall. In this context, well-developed urban planning should address the problems of infrastructure, sanitation, and installation of communities, primarily related to insufficiently gauged locations. The main objectives of this study were to analyze the impacts of in-situ rain gauges&amp;#8217; distribution associated with the elaboration of a spatial diagnosis of the occurrence of floods in the municipality of Itaperuna, Rio de Janeiro &amp;#8211; Brazil. The methodology consisted of the spatial analysis of rain gauges&amp;#8217; distribution with the help of the fractal dimension concept and investigation of flood susceptibility maps prepared by the municipality based on transitory factors (which consider precipitation in the modeling) and on permanent factors (natural flood susceptibility). Both maps were validated by the cross-tabulation method, crossing each predictive map with the recorded data of flood spots measured during a major rainfall event. The results pointed that the fractal analysis of the rain gauges&amp;#8217; distribution presented a scaling break behavior with a low fractal dimension at the small-scale range, mostly concerned in (semi-)urban catchments, highlighting the incapacity of the local instrumentation to capture the spatial rainfall variability. Thereafter, the cross-tabulation validation method indicated that the flood susceptibility map based on transitory factors presented an unsatisfactory probability of detection of floods when compared to the map based on permanent factors. These results allowed us to take into account the hydrological uncertainties concerning the insufficient gauge network and the impacts of the sparse distribution on the choice and elaboration of flood susceptibility maps that use rainfall data as input. Finally, we performed a spatial analysis to estimate the population and habitations that can be affected by floods using the flood susceptibility map based on permanent factors.&lt;/p&gt;

Fractal Properties of Financial Assets and Forcasting Financial Crisis

2018 ◽  
pp. 23-41 ◽  
Author(s):  
Inna Nekrasova ◽  
Oxana Karnaukhova ◽  
Oleg Sviridov
Keyword(s):  
Fractal Dimension ◽  
Financial Markets ◽  
Future Development ◽  
Small Time ◽  
Practical Significance ◽  
Financial Assets ◽  
Time Intervals ◽  
Price Fluctuations ◽  
Fractal Properties ◽  
Fractal Index

The chapter is aimed at identification of criteria to select financial assets for investment; observing price fluctuations at small time intervals (up to one week) as possible predictors of the future of a significant increase in the price fluctuations amplitude; determining a fractal dimension of the financial markets on the basis of R/S-analysis; constructing a fractal index indicator to identify a bifurcation point, which gives birth to a possibility of crisis phenomena in economy. Therefore, the practical significance of the chapter lies in the idea of equipping academics and practitioners with new methods and tools for analysis and forecasting future development and dynamics of the financial markets.

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