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At least 19 recordsLinked to original sources
PubMed1998

Analyte-Receptor Binding Kinetics for Biosensor Applications: A Single-Fractal and a Dual-Fractal Analysis of the Influence of the Fractal Dimension on the Binding Rate Coefficient.

The diffusion-limited binding kinetics of antigen (analyte) in solution to antibody (receptor) immobilized on a biosensor surface is analyzed within a fractal framework. Most of the data presented are adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot ("Scientific Graphing Procedure, User's Manual," Jandel Scientific, San Rafael, CA, 1993). A couple of examples of a dual-fractal analysis are also presented. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for the analyte-receptor systems analyzed. Binding rate coefficient expressions as a function of the fractal dimension developed for the analyte-receptor binding systems indicate the high sensitivity of the binding rate coefficient on the fractal dimension when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis and for the binding of cell surface proteins from Helicobacter pylori strain in solution to sialyl-(alpha-2,3)-lactose-conjugated (20 mol%) polyacrylamide immobilized on a resonant mirror biosensor (S. Hirmo et al., Anal. Biochem. 257, 63, 1998), the order of dependence of the binding rate coefficient, k, on the fractal dimension, Df, was 14.15. The fractional order of dependence of the binding rate coefficient(s) on the fractal dimension(s) further reinforces the fractal nature of the system. The binding rate coefficient(s) expressions developed as a function of the fractal dimension(s) are of particular value since they provide a means to better control biosensor performance by linking it to the heterogeneity on the surface and further emphasize in a quantitative sense the importance of the nature of the surface in biosensor performance. Copyright 1998 Academic Press.

Journal Article↗
PubMed2004

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates.

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.

Journal Article↗
PubMed1999

Fractal ion-channel behavior generates fractal firing patterns in neuronal models.

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a population of ion channels with either fractal or Markov gating characteristics. Fractal gating characteristics changed the form of the interspike interval histogram (ISIH) and also induced fractal behavior in the firing rate. For the HH model, the K+ conductance was represented as a collection of ion channels with either quasifractal or Markov gating properties. Fractal gating induced fractal-rate behavior without changing the ISIH. We conclude that fractal ion-channel gating activity is sufficient to account for fractal-rate firing behavior.

Action Potentials↗
PubMed1997

Characterisation of structural changes in the arterial elastic matrix by a new fractal feature: directional fractal curve.

A new fractal feature, the Directional Fractal Curve (DFC), defined over an arc of 180 and composed of 90 fractal dimensions determined at intervals of arc of 2, is developed to account for the anisotropic property of a fractal texture. The DFC algorithm is first applied to two images with different textural patterns, one without directional preference and one with a well-organised texture. The DFC of these images shows different patterns. The technique is then applied to quantify the structure of the elastic texture in the arterial wall where the elastic network was imaged by scanning electron microscopy following selective tissue digestion. The results suggest: (i) that images of the elastin matrix of the arterial wall exhibit fractal properties with directional preference, (ii) the DFC gives quantitative parameters which allow characterisation of structural changes in the elastin matrix of the arterial wall in terms of disorganisation and fragmentation of elastin fibres-conditions which are associated with medial degeneration due to normal ageing or presence of arterial disease.

Algorithms↗
PubMed2003

Fractal and periodic heart rate dynamics in fetal sheep: comparison of conventional and new measures based on fractal analysis.

The physiological significance of spectral and fractal components of spontaneous heart rate (HR) variability in the fetus remains unclear. To examine the relationship between circadian rhythms in different measures of HR variability, R-R interval time series obtained by fetal ECGs were recorded continuously over 24 h in five pregnant sheep at 116-125 days gestation. Conventional measures of short-term (STV) and long-term variability (LTV), low-frequency (LF; 0.025-0.15 cycles/beat) and high-frequency (HF; 0.2-0.5 cycles/beat) spectral powers, the LF-to-HF ratio, and fractal dimension values were calculated from 24-h ECG recordings and quantified every 60 min. STV, LTV, and LF and HF spectral powers were minimal during the day but increased significantly to their highest values at night. We found a significant positive correlation between these measures, whereas the cosinor method showed significant similarity between their circadian rhythm patterns. Fetal R-R intervals also exhibited fractal structures. Fetal HR variability had a fractal structure, which was similar between day and night. These results suggested that the circadian rhythms exhibited by STV and LTV during the day were mainly due to changes in frequency components rather than to fractal components of fetal HR fluctuation.

Animals↗
PubMed2003

Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity.

Perfusion heterogeneities in organs such as the heart obey a power law as a function of scale, a behavior termed "fractal." An explanation of why vascular systems produce such a specific perfusion pattern is still lacking. An intuitive branching tree model is presented that reveals how this behavior can be generated as a consequence of scale-independent branching asymmetry and fractal vessel resistance. Comparison of computer simulations to experimental data from the sheep heart shows that the values of the two free model parameters are realistic. Branching asymmetry within the model is defined by the relative tissue volume being fed by each branch. Vessel ordering for fractal analysis of morphology based on fed or drained tissue volumes is preferable to the commonly used Strahler system, which is shown to depend on branching asymmetry. Recently, noninvasive imaging techniques such as PET and MRI have been used to measure perfusion heterogeneity. The model allows a physiological interpretation of the measured fractal parameters, which could in turn be used to characterize vascular morphology and function.

Animals↗
PubMed2005

Fractal nature of chromatin organization in interphase chicken erythrocyte nuclei: DNA structure exhibits biphasic fractal properties.

Arrangement of chromatin in intact chicken erythrocyte nuclei was investigated by small angle neutron scattering. The scattering spectra have revealed that on the scales between 15 nm and 1.5 microm the interior of the nucleus exhibited properties of a mass fractal. The fractal dimension of the protein component of cell nucleus held constant at approximately 2.5, while the DNA organization was biphasic, with the fractal dimension slightly higher than 2 on the scales smaller than 300 nm and approaching 3 on the larger scales.

Animals↗
PubMed1998

Neurons and fractals: how reliable and useful are calculations of fractal dimensions?

In the past 15 years it has become possible to determine the fractal dimension (Df) of complex objects, including neurons, by automated image analysis methods. However, there are many unresolved issues that need to be addressed. In this paper we discuss how the Df calculated by different methods may vary and how fractal analysis may be of use for retinal ganglion cell characterization. The goal of this work was to acknowledge inherent sources of variation during measurement and evaluate current fractal analysis methods for describing structure. Our results show that different algorithms and even the same algorithm performed by different computer programs and/or experimenters may give different but consistent numerical values. All described methods demonstrated their suitability for classifying cat retinal ganglion cells into distinct groups. Our results reinforce the idea that comparison of measurements of different profiles using the same measurement method may be useful and valid even if an exact numeric value of the dimension is not realised in practice.

Animals↗
PubMed1997

Estimating fractal dimension with fractal interpolation function models.

Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS). BC is ineffective when applied to data-limited, low-resolution images; PS is based on a fractional Brownian motion (fBm) model-a model which is not universally applicable. We also present background information on the use of fractal interpolation function (FIF) models to estimate fd of data which can be represented in the form of a function. We present a new method of estimating fd in which multiple FIF models are constructed. The mean of the fd's of the FIF models is taken as the estimate of the fd of the original data. The standard deviation of the fd's of the FIF models is used as a confidence measure of the estimate. We demonstrate how the new method can be used to characterize fractal texture of medical images. In a pilot study, we generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle cell subjects. The new method showed improved separation of the image classes when compared to BC and PS methods.

Fractals↗
PubMed1994

Fractal analysis of pulmonary arteries: the fractal dimension is lower in pulmonary hypertension.

We analyzed the spatial structure of contact radiographs of barium-filled pulmonary arteries of rats raised in room air and in two environments that induce pulmonary arterial hypertension (PAH)--hypoxia and hyperoxia. We found that the spatial structure of the pulmonary arteries was fractal in both the control and the hypertensive lungs. The fractal dimension of the pulmonary arteries of the control lungs was 1.62 +/- 0.01 (mean +/- SEM), which is greater than that of both the hypoxic lungs 1.50 +/- 0.03 (p < 0.01) and the hyperoxic lungs 1.44 +/- 0.01 (p < 0.01). There was no significant difference between the hypoxic and hyperoxic lungs. The fractal dimension may be a useful clinical index to quantify pathologic changes in the pulmonary arterial tree.

Animals↗
PubMed2005

Spontaneous fractal aggregation of gold nanoparticles and controlled generation of aggregate-based fractal networks at air/water interface.

The spontaneous fractal aggregation of as-prepared cetytrimethylammonium bromide (CTAB)-capped gold nanoparticles was found to happen at the air/water interface after spreading their chloroform solution on water surfaces. Aided by Langmuir-Blodgett techniques, these fractal aggregates can be interconnected with each other to form aggregate-based fractal networks.

Journal Article↗
PubMed1997

Fractal geometry of bean root systems: correlations between spatial and fractal dimension.

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.

Computer Simulation↗
PubMed1996

Fractal analysis of spinal dorsal horn neuron discharges by means of sequential fractal dimension D.

The present study describes a new method for converting a typical point process, such as a train of neuronal action potentials (spikes), into a planar curve which is then processed by means of a fast algorithm to calculate and display the fractal dimension D values of each of a sequence of blocks having an equal and preselectable number of interspike intervals, hence the term sequential fractal dimension D (SFD). This method is fast, does not require special computing facilities, and provides a continuous, high temporal resolution display of the neuronal discharge complexity along the course of spontaneous activity or event relating changes. The method affords insight into short duration changes in neuronal behaviour in a way independent of its discharge rate. SFD analysis of spike trains from spinal dorsal horn neurons suggests that the neuronal response to a given stimulus can be expressed as changes in the discharge pattern complexity, thus revealing a novel sensory coding strategy.

Action Potentials↗
PubMed2001

Critical states and fractal attractors in fractal tongues: localization in the Harper map.

Localized states of Harper's equation correspond to strange nonchaotic attractors in the related Harper mapping. In parameter space, these fractal attractors with nonpositive Lyapunov exponents occur in fractally organized tongue-like regions which emanate from the Cantor set of eigenvalues on the critical line epsilon=1. A topological invariant characterizes wave functions corresponding to energies in the gaps in the spectrum. This permits a unique integer labeling of the gaps and also determines their scaling properties as a function of potential strength.

Journal Article↗