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At least 217 records · Page 12Linked to original sources
PubMed1999

[Changes in the fractal component of spectral analysis of heart rate variability and systolic blood pressure variability during the head-up tilt test].

Blood pressure and heart rate change are related to the level of physical activity, and are correlated with each other. Heart rate and blood pressure signals were investigated by coarse graining spectral analysis and changes in the harmonic and non-harmonic (fractal) power were examined during the head-up tilt test. Fourteen healthy subjects, 9 men and 5 women (mean age 30.4 +/- 1.0 years) completed the test protocol of 15 min supine rest followed by the head-up tilt (80 degrees) test. Heart rate was measured continuously with standard bipolar leads and electrocardiography. A finger cuff was placed on the left index finger for beat-by-beat recording of systolic blood pressure based on the continuous noninvasive method, and the impulse train was stored on a personal computer for spectral analysis. The harmonic component, the integrated powers in the low-frequency and high-frequency regions, and the fractal component were then calculated. The fractal component was plotted on a log power versus log frequency plane with spectral index beta estimated as the slope of the linear regression of this 1/f beta plot. RR-interval was significantly shorter during the head-up tilt position than in the supine rest position with a marked reduction in the high-frequency power. The ratio of fractal component for total power was increased and the slope beta of the 1/f beta relationship was significantly greater in the head-up tilt (1.61 +/- 0.05) than in the supine rest (0.92 +/- 0.07) position. Systolic blood pressure showed a significant increase during head-up tilt, and marked increases in high-frequency power and fractal power. However, both the ratio of fractal component for total power and the slope beta remained unchanged. Further studies are needed to clarify whether the slope beta is essentially stable or variable in some conditions.

Adult↗
PubMed1999

Fractal and spectral dimension analysis of liver fibrosis in needle biopsy specimens.

OBJECTIVE: To evaluate the usefulness of a reliable and reproducible mathematical scoring system based on fractal geometry for quantifying the irregular pattern in fibrosis commonly seen in liver biopsy specimens from chronic liver diseases. STUDY DESIGN: The study used 26 standard liver biopsy specimens obtained from patients with chronic hepatitis C virus-related liver disease. The degree of fibrosis in each specimen was estimated using a quantitative scoring system based on the computer-assisted evaluation of both the fractal and spectral dimensions of deposited collagen. The fractal dimension was then compared with the percent area of collagen measured using an image analysis system. RESULTS: The fractional dimension of its irregular shape defines fibrosis as a natural fractal structure. The complex distribution of its collagenous components (unmeasurable by means of the usual morphometric parameters) can be optimally quantified using a single numerical score that seems to be a better alternative to the semiquantitative methods adopted so far. The proposed method is reproducible, rapid and inexpensive; furthermore, supported by specific software, its mathematical approach excludes subjectivity and eliminates the external factors capable of influencing staging and classification. CONCLUSION: This study demonstrated that it is possible to quantify the irregularity of the structures of the liver in an objective manner and that the box-counting fractal dimension does not depend on the amount of collagen deposited on the slide. Furthermore, as has been found in other fields of investigation, study of the fractal properties of the liver is likely to reveal more about its structure and the pathogenesis of liver diseases.

Biopsy, Needle↗
PubMedDate not supplied

Fractal analysis of placenta mature villi in healthy, smoking and non-smoking women.

Not all the objects created by nature can be described by means of the classical Euclidean geometry rules. New, quickly developing fractal theory can provide another instrument for describing irregular surfaces of e.g. geometric structures and objects whose development results from growth, differentiation and degeneration processes. In the present study we decided to perform fractal analysis of mature, terminal villi of placenta taken from smoking and non-smoking women, during the third trimester of pregnancy. The aim of this study was to find another morphometric parameter, independent of subjective factors, which would provide new information about the studied structure. Placentas were taken from healthy women, untreated primiparas, who did not undergo any hormonal treatment, aged 18 to 27. The material was divided into: control group--placentas from non-smoking women, and two experimental groups--placentas from non-smoking up to 30 cigarettes daily and placentas from women smoking up to 30 cigarettes daily and placentas from women smoking over 30 cigarettes daily. Fractal dimension was determined by three methods: box counting, dilation and mass scaling method. Taking under consideration the results obtained in the present study it seems that fractal dimension, objectively and independently of many factors, allows to perform mathematical estimation of the parameter which is the terminal villi occurrence density within placenta. Among the applied fractal analysis methods, used for placenta terminal villi density grade estimation, the most useful seems to be the box counting method, whereas for estimating villi surface complication--the ratio--mass scaling method. Comparing obtained fractal dimension results, we have found that they increase together with the amount of cigarettes smoked during pregnancy.

Adolescent↗
PubMed1999

[Texture analysis of B-scan image using fractal dimension].

Based on the texture analysis of B-Scan image fractal model, this paper presents the liver clinical B-Scan images and their fractal characteristics. It describes the semi-fractal characteristics of B-Scan images and calculates the fractal dimension(D) of the liver B-scan images of 10 normal persons, 3 patients with cancer of the liver, and 3 patients with cirrhosis of the liver. The results indicate that Fractal Dimension (D) is an important parameter in differentiating some diseases. On the basis of the influence of Fractal Dimension (D) and scale (epsilon), this paper suggests the texture classified parameter S. The experiment results indicate that the parameter S can be used to differentiate diseases efficiently.

Algorithms↗
PubMed2004

Fractal analysis of tracheal sounds during maximal forced exhalation.

BACKGROUND: Fractal structures or processes, many of which are found in nature, are marked by the presence of a formal pattern that repeats itself even as the scale changes, a property termed 'self-similarity'. The bronchial tree is structurally a fractal system and inspiration is a fractal process. Our objective was to show that the dynamic process of emptying air from the bronchi as measured by tracheal sounds should also behave fractally over the period of time during which exhalation takes place. MATERIAL/METHODS: Twenty non-smoking patients (9 males and 11 females) aged 53.6+/-16.3 years with persistent but clinically stable moderate to severe asthma and a control group of 11 healthy non-smoking subjects (6 males and 5 females) aged 46.0+/-12.5 years were enrolled. Respiratory sounds were registered using a microphone held by an elastic band directly against the patient's skin at the level of the cricoid cartilage. Analysis was done on the average of three forced expirations made after a deep inspiration. The Hurst's coefficient was computed by Hurst's rescaled range analysis (H) and by analysis of the variance-time relationship of the aggregated process (H_v). RESULTS: Values of H and H_v were around 0.75, indicating that the sound signals were fractal over time. The responses of controls and patients to bronchodilator administration of 1 mg terbutaline were similar (p>0.05). Mean intra-subject variation coefficients were less than 15%. CONCLUSIONS: This analysis of tracheal sound during forced expiratory maneuvers confirms the dynamic fractal behavior of the respiratory system.

Adult↗
PubMedDate not supplied

Fractal analysis of the uterine contractions.

The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of time series (rescaled range analysis, power spectral analysis, roughness-length, variogram methods and wavelet method) are available. We have implemented some other algorithms for calculating D: Higuchi's fractal dimension, relative dispersion analysis, running fractal dimension, method based on mathematical morphology and method based on intensity differences. For biomedical signals results obtained by means of different algorithms are different, but consistent.

Algorithms↗
PubMed2006

[A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

Algorithms↗
PubMed1995

Local connected fractal dimensions and lacunarity analyses of 60 degrees fluorescein angiograms.

PURPOSE: The retinal vascular tree exhibits fractal characteristics. These findings relate to the mechanisms involved in the vascularization process and to the objective morphologic characterization of retinal vessels using fractal analysis. Although normal retinas show uniform patterns of blood vessels, in pathologic retinas with central vein or artery occlusions, the patterns are irregular. Because the generalized box fractal dimension fails to differentiate successfully between normal and abnormal retinal vessels in 60 degrees fluorescein angiograms, the authors have further investigated this problem using the local connected fractal dimension (alpha). METHODS: The authors studied 24 digitized 60 degrees fluorescein angiograms of patients with normal retinas and 5 angiograms of patients with central retinal vein or artery occlusion. The pointwise method estimated the local complexity of the angiogram within a finite window centered on those pixels that belong to the retinal vessels. Color-coded dimensional images of the angiograms were constructed by plotting the pixels forming the object with a color that corresponded to specific values of alpha +/- delta alpha. RESULTS: The color-coded representation allowed recognition of areas with increased or decreased local angiogram complexity. The alpha distributions showed differences between normal and pathologic retinas, which overcomes problems encountered when using the methods of calculating the generalized fractal dimensions. A multivariate linear discriminant function using parameters from the alpha distribution and a further fractal parameter--lacunarity--reclassified 23 of the 24 normal and 4 of the 5 pathologic angiograms in their original groups (total: 92.1% correct). CONCLUSIONS: This methodology may be used for automatic detection and objective characterization of local retinal vessel abnormalities.

Discriminant Analysis↗
PubMed1996

Anisotropy measurements obtained by fractal analysis of trabecular bone at the calcaneus and radius.

The resistance of bone tissue is influenced not only by bone density parameters but also by bone architecture parameters, such as the microarchitecture and anisotropy of trabecular bone. We have developed and validated a fractal analysis method for studying bone microarchitecture on roentgenograms. This technique provides reproducible measurements of the fractal dimension (D) of bone, which reflects bone texture. The fractal dimension is determined in 36 different directions; the mean of these 36 values is representative of the image. A polar diagram gives the value of D according to the angle of analysis. By decomposing this diagram using polar Fourier Transform analysis, the parameters related to the shape of the polar diagram can be determined. This diagram image analysis technique has been used for other similar diagrams and applied to the results of our fractal analysis method. Diagram shape characterization may provide information on the angular distribution of results and therefore on the anisotropy of the images under study. The purpose of this study was to compare roentgenograms of the calcaneus and radius in the same subjects to determine whether texture and anisotropy parameters discriminated between these two bones. Roentgenograms of the calcaneus and radius were obtained in ten nonosteoporotic subjects. The radius had a smaller fractal dimension than the calcaneus (mean +/- standard deviation: 1.215 +/- 0.025 and 1.285 +/- 0.066, respectively; p = 0.014). Differences in the shape of the polar diagram were found between the two bones. The mean Fourier coefficient ratio C2/C4 was considerably smaller at the calcaneus (0.63 +/- 0.50) than at the radius (4.88 +/- 3.45; p = 0.005). Our method allows quantitative characterization of texture and anisotropy differences between the calcaneus and radius. The smaller fractal dimension of the radius probably reflects the simpler architecture of this non weight-bearing bone. The differences in polar diagram shape allow to evaluate anisotropy differences between the calcaneus and radius.

Adult↗
PubMed1998

Fractal tumor stromal border in a nonequilibrium growth model.

OBJECTIVE: To examine the potential relationships of tumor growth parameters and fractal dimensionality of the resulting pattern. STUDY DESIGN: A nonequilibirum tumor growth model was developed taking into account tumor cell motility, tumor and stromal proliferation, cohesion, autocrine and paracrine growth stimulation, and tumor and stromal destruction. Ten thousand simulation runs were performed with varying settings of the control parameters. Fractal dimensionality of the tumor-stroma border was assessed in each pattern by a box counting method. RESULTS: Fractal dimensionality increased with overall tumor cell motility, heterotypic tumor-stroma adhesion and paracrine growth stimulation, and decreased with homotypic tumor-tumor adhesion, autocrine growth stimulation, and tumor and stroma destruction. CONCLUSION: Fractal dimensionality of the tumor-stroma border depends on various parameters controlling tumor growth. Some growth properties considered to be associated with an increased degree of malignancy influence fractal dimensionality in opposite directions. Therefore, determination of fractal dimensionality cannot be related directly to any particular biologic feature or to the overall biologic behavior of a tumor.

Autocrine Communication↗
PubMed2002

Fractal analysis of Daphnia motion for acute toxicity bioassay.

To quantify individual behavioral responses to toxic chemicals, the swimming motion of individual Daphnia magna was continuously monitored using a motion analysis system. The fractal dimension was introduced to compare the straightness or complexity of the swimming trajectory before and after exposure to toxic chemicals. Analysis indicated that the swimming trajectory of individual Daphnia has a fractal structure. The basal fractal dimension in the control medium was 1.35+/-0.01 (n = 50 Daphnia). Exposure to CuSO(4) (10 microg/L), organophosphorus (Dichlorvos; 10 microg/L), and carbamate (Propoxur; 500 microg/L) pesticide caused a significant increase in the fractal dimension with a latency of 60 min, reaching a maximal level of 2.26+/-0.34, 2.43+/-0.19, and 2.51+/-0.21, respectively, after a 120-min exposure. The magnitude of the change in the fractal dimension was related to the toxic chemical concentration and the exposure time. Threshold concentrations determined at 60 min of exposure were 10 microg/L for CuSO(4), 5 microg/L for Dichlorvos, and 500 microg/L for Propoxur. The toxicity index (EC(50)) values after 120 min of exposure were 6.31 microg/L, 7.64 microg/L, and 466 microg/L for CuSO(4), Dichlorvos, and Propoxur, respectively. Thus, the fractal dimension seems useful for analyzing and comparing complex trails, such as swimming trajectories, which could be used as the endpoint for an acute bioassay.

Animals↗
PubMed1998

On Correlation of Fractal Dimension of Marine Particles with Depth

Fractal dimension of marine particles/aggregates is determined from light-scattering data obtained from in situ measurements in various depths ranging from 10 to 800 m. Analysis of calculated fractal dimension data indicates a correlation of fractal dimension and depth for Drake Passage. The average fractal dimension changes from 2.9 +/- 0.1 beneath the surface to 2.0 +/- 0.1 at 800 m. This agrees with a decrease of turbulent energy dissipation rate with depth, indicating domination of shear coagulation for depths </= 400 m (D = 2.7 +/- 0.3) and coagulation due to a differential sedimentation at greater depths (D = 2.1 +/- 0.3). No correlation was found between depth and fractal dimension for the Peru upwelling area. The average fractal dimension 2.8 +/- 0.3 indicates that the shear coagulation is the dominant process throughout the water column in the upwelling area. Copyright 1998 Academic Press. Copyright 1998Academic Press

Journal Article↗
PubMed1999

Computer Simulation of the Aggregation and Sintering Restructuring of Fractal-like Clusters Containing Limited Numbers of Primary Particles.

A random particle computer simulation (in three dimensions) was conducted to investigate the structure and aggregation characteristics of small clusters (containing limited numbers of primary particles per cluster). Though an individual cluster of small size does not satisfy the power law, it was found that these aggregated clusters are fractal-like and comply with the fractal power law form in a statistical sense. This statistically averaged fractal dimension decreases as the clusters become smaller. A cluster-restructuring model is further developed to simulate the topological evolution of dendritic structured materials due to sintering at high temperatures. Results indicate that the cluster fractal dimension increases as sintering proceeds for small clusters, in contrast to results for large clusters wherein the topology is retained and the fractal dimension remains constant. A relationship of the fractal dimension change with the normalized surface area of dendrites for different-sized clusters is established. Copyright 1999 Academic Press.

Journal Article↗
PubMed2000

Structural Interpretations of Static Light Scattering Patterns of Fractal Aggregates.

A method based on static light scattering by fractal aggregates is introduced to extract structural information. In this study, we determine the scattered intensity by a fractal aggregate calculating the Structure and the Form factors noted, respectively, S(q) and F(q). We use the approximation of the mean field Mie scattering by fractal aggregates (R. Botet, P. Rannou, and M. Cabane, appl. opt. 36, 8791, 1997). This approximation is validated by a comparison of the scattering and extinction cross sections values calculated using, on the one hand, Mie theory with a mean optical index n) and, on the other hand, the mean field approximation. Scattering and extinction cross sections values differ by about 5%. We show that the mean environment of primary scatterers characterized by the optical index n(s) must be taken into account to interpret accurately the scattering pattern from fractal aggregates. Numerical simulations were done to evaluate the influence of the fractal dimension values (D(f)>2) and of the radius of gyration or the number of primary particles within the aggregates (N=50 to 250) on the scatterers' mean optical contrast (n(s)/n). This last parameter plays a major role in determining the Form factor F(q) which corresponds to the primary particles' scattering. In associating the mean optical index (n) to structural characteristics, this work provides a theoretical framework to be used to provide additional structural information from the scattering pattern of a fractal aggregate (cf. Part II). Copyright 2000 Academic Press.

Journal Article↗
PubMed2000

A Predictive Approach Using Fractal Analysis for Analyte-Receptor Binding and Dissociation Kinetics for Surface Plasmon Resonance Biosensor Applications.

A predictive approach using fractal analysis is presented for analyte-receptor binding and dissociation kinetics for biosensor applications. Data taken from the literature may be modeled, in the case of binding using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the examples presented. Predictive relationships developed for the binding and the affinity (k(diss)/k(bind)) as a function of the analyte concentration are of particular value since they provide a means by which the binding and the affinity rate coefficients may be manipulated. Relationships are also presented for the binding and the dissociation rate coefficients and for the affinity as a function of their corresponding fractal dimension, D(f), or the degree of heterogeneity that exists on the surface. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f)) leads to an increase in the binding and in the dissociation rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding and in the dissociation rate coefficient. The binding and the dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f,bind) (or D(f1)) and D(f,diss), respectively, that exists on the biosensor surface. For example, the order of dependence on D(f,bind) (or D(f1)) and D(f2) is 6.69 and 6.96 for k(bind,1) (or k(1)) and k(2), respectively, for the binding of 0.085 to 0.339 µM Fab fragment 48G7(L)48G7(H) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue immobilized on a surface plasmon resonance (SPR) biosensor. The order of dependence on D(f,diss) (or D(f,d)) is 3.26 for the dissociation rate coefficient, k(diss), for the dissociation of the 48G7(L)48G7(H)-PNP complex from the SPR surface to the solution. The predictive relationships presented for the binding and the affinity as a function of the analyte concentration in solution provide further physical insights into the reactions on the surface and should assist in enhancing SPR biosensor performance. In general, the technique is applicable to other reactions occurring on different types of biosensor surfaces and other surfaces such as cell-surface reactions. Copyright 2000 Academic Press.

Journal Article↗
PubMed2001

A Fractal Analysis Approach for the Evaluation of Hybridization Kinetics in Biosensors.

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (Sigmaplot, Scientific Graphing Software, User's Manual, Jandel Scientific, CA, 1993). It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes, in general, in the same direction for both the single-fractal and the dual-fractal analysis examples presented. The binding rate coefficient expression developed as a function of the analyte concentration in solution and the fractal dimension is of particular value since it provides a means to better control biosensor or immunosensor performance. Copyright 2001 Academic Press.

Journal Article↗
PubMed2002

A model to describe the settling behavior of fractal aggregates.

A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200x, which can capture images of particles/flocs down to 2 microm in diameter was used. The performance and technique of the settling rig were validated by comparing the measured settling rates of 30- and 50.7-microm standard particles with their theoretical settling rates calculated using Stokes' law. The measured settling rates were within 10% agreement with the calculated Stokes' velocities. The settling rates and sizes of the particles/flocs were analyzed using image analysis software called WiT 5.3. The maximum temperature gradient across the settling column was 0.1 degrees C, which effectively eliminated convective currents due to temperature differences in the settling column. A total of 1000 calcium phosphate flocs were analyzed. Calcium phosphate flocs with fractal dimensions varying from 2.3 to 2.8 were generated via orthokinetic aggregation. Measurements of fractal dimensions, using light scattering, were done simultaneously with the settling experiments and they were found to be constant. The fractal dimensions calculated using the model agreed with those obtained by light scattering to within 12%.

Journal Article↗
PubMed1990

Fractal system--a time domain approach.

A method to analyze the fractal system in the time domain is presented so that the dynamic behavior of the system can be studied. The fractal system is represented by a set of linear time-varying differential equations whose order depends on the order of the system under non-fractal condition. Four different types of fractal system are considered and their solutions in the time domain are presented. These analyses show that the fractal system is dynamically more stable with smooth changes of magnitude and less oscillatory than the non-fractal system. Examples of the physiological system of the conduction pathways in the heart and also the polarization phenomena of noble metal are presented to illustrate the phenomena.

Bundle of His↗