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PubMed1998

Application of fractal kinetics for carrier-mediated transport of drugs across intestinal epithelial membrane.

PURPOSE: Fractal kinetics was used for the analysis of the carrier-mediated transport for drugs across the intestinal epithelial cells. METHODS: The transport was examined under various agitation rates using a monolayer of Caco-2 cells and rabbit ileum sheets. RESULTS: The passive transport of antipyrine across Caco-2 cells was increased with the increasing rate of agitation and was supposed to be caused by a change in the thickness of the unstirred water layer. On the contrary, in the case of L-lactic acid transport, which follows a carrier-mediated transport mechanism, the more the agitation rate controlling the fractal dimension was increased, the more the permeability rate across the Caco-2 cells was decreased. Fractal kinetic analysis of L-lactic acid transport indicated that the permeability was caused by a single saturable process. Similar agitation effects with L-lactic acid transport were observed in the transport of phenylalanine and cephradine in Caco-2 cells. However, the permeability rates of benzoic acid and 3-O-methyl-D-glucose across Caco-2 cells and L-lactic acid transport across the rabbit ileum tissue indicated the maximum levels at a designated agitation rate. This phenomenon was likely to be caused by the agitation effects controlling not only the fractal environment but also the unstirred water layer. CONCLUSIONS: Carrier-mediated transports are well defined by fractal kinetics rather than classical kinetic analysis. Fractal kinetics are one of the important areas for understanding and confirming the properties of a carrier-mediated transport process.

3-O-Methylglucose↗
PubMed2005

Fractal and noisy CBV dynamics in humans: influence of age and gender.

The complexity of spontaneous cerebral blood volume (CBV) fluctuations can emerge from random, fractal, or chaotic processes. Our aims were to define the contribution of these patterns to the observed complexity and to evaluate the effect of age and gender on it. The total hemoglobin content as the measure of CBV was monitored by near-infrared spectroscopy on volunteers (men n = 19, age = 20 to 78 years; women n = 23, age = 21 to 79 years). Random and fractal patterns were distinguished by the spectral index (beta). Chaos was identified by surrogate analysis of the correlation dimension (a static chaotic parameter, the dimension of the correlation integral) and the largest Lyapunov exponent (a dynamic chaotic parameter, the rate of exponential divergence of the system states from a perturbed initial condition over the chaotic attractor). In spontaneous CBV fluctuations, both fast random and slow fractal dynamics are present separately in their spectra by a cutoff frequency, f'. Below f' the pattern is fractal, in that power rises inversely with frequency as 1/f(beta). f' decreases with age in men and women alike (F1: up to 0.12+/-0.06 Hz versus F2: up to 0.05+/-0.04 Hz at P = 0.015, and M1: up to 0.16+/-0.05 Hz versus M2: up to 0.11+/-0.04 Hz at P = 0.044). Neither pre- nor postmenopausal age groups (1 and 2, respectively) showed a (low)beta gender difference. Surrogate analysis showed that CBV dynamics cannot be characterized on the grounds of deterministic chaos. Cerebral blood volume fluctuates in a complex, bimodal manner in humans, in that the fast dynamics has no structure, while the slow dynamics exhibits a self-similar, that is, fractal temporal structure. The range of fluctuation amplitudes produced by fractal dynamics is always larger than that of random fluctuations, and it shrinks with an altered structuring in aging women only.

Adult↗
PubMed1996

Fractal analysis of capacitating human spermatozoa.

While head centroid-derived kinematic values have been determined for the trajectories of hyperactivated human spermatozoa, the definitions are not robust with respect to image sampling frequency and track analysis methods. The determination of the fractal dimension of a trajectory has been suggested as an alternative descriptive parameter for hyperactivated motility. Here, we have investigated two methods for the determination of the fractal dimension of a trajectory. A simple but useful equation was found to be: D = log(n)/[log (n + log (d/L)], where the n is the number of intervals in the trajectory, d is the planar extent of the curve and L is the length of the trajectory. This equation was not influenced by scaling of the trajectory. A fractal dimension (D) >=1.30 was found to define hyperactivated trajectories, and D <= 1.20 defined non-hyperactivated trajetories, reconstructed at both 30 and 60 Hz. However, when circling tracks were studied, all had D > 1.30, even though they were classified as non-hyperactivated by curvilinear velocity and/or amplitude of lateral head displacement values. An analysis of a series of non-ideal track segments suggested a relationship between a track's linearity and its fractal dimension. It was determined by a linear regression analysis that the fractal dimension of a trajectory was inversely proportional to its linearity (r = -0.77, P < 0.001). Although the fractal dimension of a trajectory is a good indicator of its regularity (describing its space-filling properties), it should not be used as the sole criterion for the classification of a trajectory as hyperactivated.

Fractals↗
PubMed2006

Skeleton and fractal scaling in complex networks.

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.

Escherichia coli↗
PubMed1999

Use of super-water-repellent fractal surfaces in the crystallization of macromolecules.

The effect of fractal surfaces on protein crystallization has been investigated. A super-water-repellent fractal surface consisting of alkylketene dimers was formed on microscope cover slips. Crystallization experiments with hen egg-white lysozyme using the sitting-drop vapour-diffusion method have been undertaken on the fractal and conventionally siliconized surfaces. The size of the crystals obtained on the fractal surface is significantly larger than on the conventionally siliconized surface. The number of crystals on the fractal surface is markedly smaller than on the conventionally siliconized surface. The results clearly indicate that the fractal surface is very effective and promising in the crystallization of macromolecules using the sitting-drop vapour-diffusion method.

Animals↗
PubMed2006

A fast and efficient hybrid fractal-wavelet image coder.

The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. Fast fractal encoding using Fisher's domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees (SPIHT) coding, on the remaining coefficients. Furthermore, image details and wavelet progressive transmission characteristics are maintained, no blocking effects from fractal techniques are introduced, and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme promotes an average of 94% reduction in encoding-decoding time comparing to the pure accelerated Fractal coding results. The simulations also compare the results to the SPIHT wavelet coding. In both cases, the new scheme improves the subjective quality of pictures for high-medium-low bitrates.

Algorithms↗
PubMed1996

Measurement of pulmonary blood flow by fractal analysis of flow heterogeneity in isolated canine lungs.

Regional heterogeneity of lung blood flow can be measured by analyzing the relative dispersion (RD) of mass (weight)-flow data. Numerous studies have shown that pulmonary blood flow is fractal in nature, a phenomenon that can be characterized by the fractal dimension and the RD for the smallest realizable volume element (piece size). Although information exists for the applicability of fractal analysis to pulmonary blood flow in whole animal models, little is known in isolated organs. Therefore, the present study was done to determine the effect of blood flow rate on the distribution of pulmonary blood flow in the isolated blood-perfused canine lung lobe by using fractal analysis. Four different radiolabeled microspheres (141Ce, 95Nb, 85Sr, and 51Cr), each 15 microns in diameter, were injected into the pulmonary lobar artery of isolated canine lung lobes (n = 5) perfused at four different flow rates (flow 1 = 0.42 +/- 0.02 l/min; flow 2 = 1.12 +/- 0.07 l/min; flow 3 = 2.25 +/- 0.17 l/min; flow 4 = 2.59 +/- 0.17 l/min), and the pulmonary blood flow distribution was measured. The results of the present study indicate that under isogravimetric blood flow conditions, all regions of horizontally perfused isolated lung lobes received blood flow that was preferentially distributed to the most distal caudal regions of the lobe. Regional pulmonary blood flow in the isolated perfused canine lobe was heterogeneous and fractal in nature, as measured by the RD. As flow rates increased, fractal dimension values (averaging 1.22 +/- 0.08) remained constant, whereas RD decreased, reflecting more homogeneous blood flow distribution. At any given blood flow rate, high-flow areas of the lobe received a proportionally larger amount of regional flow, suggesting that the degree of pulmonary vascular recruitment may also be spatially related.

Animals↗
PubMed2000

Exercise alters fractal dimension and spatial correlation of pulmonary blood flow in the horse.

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) and spatial correlations. On average, the fractal dimension decreased with exercise (trot 1.216 to gallop 1.173; P < 0. 05) despite a variable fractal dimension at rest. Spatial correlation of flow to neighboring pieces increased with exercise (trot 0.57 +/- 0.074 to gallop 0.73 +/- 0.051) and was inversely correlated with fractal dimension, indicating better spatial correlation as blood flow distribution becomes more uniform. This is the first study to document a change in fractal dimension as a result of increasing pulmonary blood flow. Spatial differences in response to vasoregulatory mediators may play a role in this phenomenon.

Algorithms↗
PubMed2004

Fractal fluctuations in human respiration.

The present study was designed to characterize respiratory fluctuations in awake, healthy adult humans under resting conditions. For this purpose, we recorded respiratory movements with a strain-gauge pneumograph in 20 subjects. We then used Allan factor, Fano factor, and dispersional analysis to test whether the fluctuations in the number of breaths, respiratory period, and breath amplitude were fractal (i.e., time-scale-invariant) or random in occurrence. Specifically, we measured the slopes of the power laws in the Allan factor, Fano factor, and dispersional analysis curves for original time series and compared these with the slopes of the curves for surrogates (randomized data sets). In addition, the Hurst exponent was calculated from the slope of the power law in the Allan factor curve to determine whether the long-range correlations among the fluctuations in breath number were positively or negatively correlated. The results can be summarized as follows. Fluctuations in all three parameters were fractal in nine subjects. There were four subjects in whom only the fluctuations in number of breaths and breath amplitude were fractal, three subjects in whom only the fluctuations in number of breaths were fractal, and two subjects in whom only fluctuations in breath number and respiratory period were fractal. Time-scale-invariant behavior was absent in the two remaining subjects. The results indicate that, in most cases, apparently random fluctuations in respiratory pattern are, in fact, correlated over more than one time scale. Moreover, the data suggest that fractal fluctuations in breath number, respiratory period, and breath amplitude are controlled by separate processes.

Adult↗
PubMed2005

Fractal noises and motions in time series of presympathetic and sympathetic neural activities.

We used Allan factor analysis to classify time series of the discharges of single presympathetic neurons in the cat medullary lateral tegmental field (LTF) and rostral ventrolateral medulla (RVLM) and of the postganglionic vertebral sympathetic nerve. These time series fell into two classes of fractal-based point processes characterized by statistically self-similar behavior reflecting long-range correlations among data points. Classification of a time series as either a fractional Gaussian noise (fGn)-or fractional Brownian motion (fBm)-based point process depended on the scaling exponent, alpha, of the power law in the Allan factor curve. fGn is defined as 0 < alpha < 1 and fBm as 1 < alpha < 3. The process responsible for the fractal spike trains of 11 of 12 classifiable LTF neurons with sympathetic nerve-related activity was fGn. In contrast, the process responsible for the fractal spike trains of eight of nine classifiable RVLM presympathetic neurons was fBm. The time series of simultaneously recorded vertebral sympathetic nerve discharge and the arterial pulse also were fBm-based signals. Because a fBm signal is the cumulative sum of the elements comprising the corresponding fGn signal, these results show smoothing of fractal time series in a feedforward direction from medullary presympathetic neurons to postganglionic sympathetic neurons. This may involve integration by RVLM neurons of their LTF inputs or independent fractal processes acting at different levels of the network controlling sympathetic nerve discharge. Whether feedforward smoothing of fractal signals is a feature in other neural systems is open to investigation.

Action Potentials↗
PubMed1995

Human discrimination of surface slant in fractal and related textured images.

Slant-discrimination thresholds were measured for textures with the property that their power spectra, when log transformed, are inversely proportional to log spatial frequency: P(f) alpha f-beta. As the exponent beta changes from high values to low values, the slope of the power spectrum of the image decreases. As the parameter passes through values in the fractal range the resulting texture changes from having the appearance of a cloud-like surface through to a granite-like surface. Exponents below the fractal range produce textures that converge towards the appearance of a random grey-level noise pattern. Since fractal patterns are self-similar at a range of scales, one might think it would be difficult to recover changes in depth in fractal images; however, slant-discrimination thresholds did not differ substantially as a function of the slope of the power spectrum. Reducing the size of the viewing aperture increased thresholds significantly, suggesting that slant discrimination benefits from a global analysis. The effect of texture regularity on perceived slant was investigated using bandpassed fractal textures. As the bandwidth of a bandpass filter is reduced, the bandpassed texture was perceived to be increasingly more slanted than its fractal counterpart.

Form Perception↗
PubMed2005

Fractal geometry of airway remodeling in human asthma.

RATIONALE: Airway wall remodeling is an important aspect of asthma. It has proven difficult to assess quantitatively as it involves changes in several components of the airway wall. OBJECTIVE: To develop a simple method for quantifying the overall severity of airway wall remodeling in asthmatic airways using fractal geometry. METHODS: Negative-pressure silicone rubber casts of lungs were made using autopsy material from three groups: fatal asthma, nonfatal asthma, and nonasthma control. All subjects were lifelong nonsmokers. A fractal dimension was calculated on two-dimensional digital images of each cast. RESULTS: Nonasthma control casts had smooth walls and dichotomous branching patterns with nontapering segments. Asthmatic casts showed many abnormalities, including airway truncation from mucous plugs, longitudinal ridges, and horizontal corrugations corresponding to elastic bundles and smooth muscle hypertrophy, respectively, and surface projections associated with ectatic mucous gland ducts. Fractal dimensions were calculated from digitized images using an information method. The average fractal dimensions of the airways of both the fatal asthma (1.72) and nonfatal asthma (1.76) groups were significantly (p<0.01 and p=0.032, respectively) lower than that of the nonasthma control group (1.83). The lower fractal dimension of asthmatic airways correlated with a decreased overall structural complexity and pathologic severity of disease. CONCLUSION: Fractal analysis is a simple and useful technique for quantifying the chronic structural changes of airway remodeling in asthma.

Adolescent↗
PubMed1999

Analyte-receptor binding kinetics for different types of biosensors. A fractal analysis.

A fractal analysis is presented for analyte-receptor binding kinetics for different types of biosensor applications. Data taken from the literature may be modeled using a single-fractal analysis, a single- and a dual-fractal analysis, or a dual-fractal analysis. The latter two methods represent a change in the binding mechanism as the reaction progresses on the surface. Predictive relationships developed for the binding rate coefficient as a function of the analyte concentration are of particular value since they provide a means by which the binding rate coefficients may be manipulated. Relationships are presented for the binding rate coefficients as a function of the fractal dimension Df or the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity on the surface (increase in Df) leads to an increase in the binding 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 rate coefficient. The binding rate coefficient is rather sensitive to the degree of heterogeneity, Df, that exists on the biosensor surface. For example, the order of dependence on Df1 is 7.25 for the binding rate coefficient k1 for the binding of a Fab fragment of an antiparaquat monoclonal antibody in solution to an antigen in the form of a paraquat analog immobilized on a sensor surface. The predictive relationships presented for the binding rate coefficient and the fractal dimension as a function of the analyte concentration in solution provide further physical insights into the binding reactions on the surface, and should assist in enhancing biosensor performance. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.

Biosensing Techniques↗
PubMed1995

[Measurement and analysis of monophasic action potentials using fractally coated electrodes--II].

The monophasic action potential (MAP) represents a summed signal formed by overlapping action potentials of myocardial cells close to the tip of the lead. Analysis of the MAP therefore provides detailed information about the electrophysiological effects of autonomous nervous and pharmacological influences on the myocardium, for example adrenergic or cholinergic stimulation of the heart. All known MAP recordings were obtained with Ag/AgCl electrodes, which, thanks to their low polarization properties, ensure reliable MAP measurement. Owing to their toxicity and inadequate long-term stability, however, Ag/AgCl electrodes cannot be implanted. With the aim of making MAP measurement available for implantable devices, fractally coated leads were therefore developed. The aim of the present study was to evaluate the in vivo measurement of fractally coated leads which are characterized by negligible polarization, low impedance over a wide frequency range, high biocompatibility and good long-term stability. In addition, as a result of their extremely high Helmholtz capacities (up to 50 mF/cm2), fractally coated leads permit stimulation and virtually undisturbed recording of MAP with the same pair of electrodes. For the evaluation of MAP measurements with fractally coated leads, a quadrupolar catheter enabling simultaneous MAP recordings with 2 Ag/AgCl electrodes and 2 fractally coated leads was devised. The stimulation pulses were always applied via the fractally coated leads. With both types of electrode, with spontaneous excitation and stimulation, the well-known MAP morphology, with amplitudes of between 10 and 25 mV in the ventricle, and between 5 and 10 mV in the atrium, was seen.(ABSTRACT TRUNCATED AT 250 WORDS)

Atropine↗
PubMed2006

A model for enhanced nucleation of protein crystals on a fractal porous substrate.

The phenomenon of enhanced nucleation and crystallization of proteins on porous silicon (PS) is theoretically studied and explained. The PS layer is treated as a fractal structure, and a new mechanism of local supersaturation associated with the fractality is proposed. It is shown that the number of adsorbed molecules on a fragment with a fractal surface significantly exceeds that on one with flat surfaces. For a fractal PS surface, a local concentration of molecules that is sufficient for nucleation is possible inside and in the close vicinity of the pores, even when the average conditions in the bulk of the solution correspond to metastability. The wide distribution of fractal pore size is favorable for the crystallization of a wide range of macromolecules using the same sample. In addition, the PS technology is very flexible, allowing tailoring the pore size and concentration as well as the fractal properties to specific proteins by changing the fabrication conditions.

Computer Simulation↗
PubMed2005

Flocculation control study based on fractal theory.

A study on flocculation control based on fractal theory was carried out. Optimization test of chemical coagulant dosage confirmed that the fractal dimension could reflect the flocculation degree and settling characteristics of aggregates and the good correlation with the turbidity of settled effluent. So that the fractal dimension can be used as the major parameter for flocculation system control and achieve self-acting adjustment of chemical coagulant dosage. The fractal dimension flocculation control system was used for further study carried out on the effects of various flocculation parameters, among which are the dependency relationship among aggregates fractal dimension, chemical coagulant dosage, and turbidity of settled effluent under the conditions of variable water quality and quantity. And basic experimental data were obtained for establishing the chemical coagulant dosage control model mainly based on aggregates fractal dimension.

Aluminum Hydroxide↗
PubMed2005

Fractal analysis of bone architecture at distal radius.

Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass.

Absorptiometry, Photon↗
PubMed1999

[Fractal analysis and arterial hypertension].

Fractal analysis is a new tool allowing to study the complexity of cardiovascular variability. This approach may be useful for investigating regulatory mechanisms. In fractal terms, homeostasis required an optimal organisation of complexity (beta coefficient close to 1): conversely, some pathological situations have proven to be associated with an altered organisation of fractals (beta coefficient different from 1). Our study aimed at determining if hypertension was associated with an alteration of the fractal component of blood pressure (BP) or heart rate (HR) variability. Eighty-eight subjects referred for high BP entered the study. BP was measured in ambulatory conditions by an automatic device during 24 hours (ABP). BP and HR were then recorded beat-to-beat by a Finapres and an ECG during 30 minutes at rest. The beta coefficient was obtained by coarse-graining spectral analysis from the BP and RR interval time series. This method has proven its interest for breaking down cardiovascular variability into an harmonic component and a non harmonic one, this latter containing fractal elements. Spontaneous baroreflex sensitivity was assessed by the method of sequences. The percentage of fractals contained in BP and RR signals remained relatively stable despite the increasing severity of hypertension. A significant but loose correlation was found between the beta coefficient of RR and ABP (r = 0.23, p = 0.053 with systolic ABP; r = 0.25, p = 0.03 with diastolic ABP). No correlation could be disclosed between ABP and the beta coefficient of BP. The beta coefficient of RR was significantly correlated with the spontaneous baroreflex sensitivity (-0.59, p < 0.0001). It is concluded that it is rather the complexity of HR signal than that of BP which is altered during hypertension. This may suggest that some regulatory processes are lost or less efficient. The correlation reported between the baroreflex gain and the beta coefficient of RR interval may reflect, in fact, an alteration of the parasympathetic drive. Globally, these results emphasise the importance of HR and probably cardiac output in the pathophysiology of high BP.

Baroreflex↗