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PubMed1995

On the fractal nature of heart rate variability in humans: effects of respiratory sinus arrhythmia.

The purpose of the present study was to investigate the basic fractal nature of the variability in resting heart rate (HRV), relative to that in breathing frequency (BFV) and tidal volume (TVV), and to test the hypothesis that fractal HRV is due to the fractal BFV and/or TVV in humans. In addition, the possible fractal nature of respiratory volume curves (RVC) and HRV was observed. In the first study, eight subjects were tested while they sat quietly in a comfortable chair for 60 min. Beat-to-beat R-R intervals, i.e., HRV, and breath-by-breath BFV and TVV were measured. In the second study, six subjects were tested while they were in the supine position for 20-30 min. The RVC was monitored continuously together with HRV. Coarse-graining spectral analysis (Yamamoto, Y., and R. L. Hughson, Physica D 68: 250-264, 1993) was applied to these signals to evaluate the percentage of random fractal components in the time series (%Fractal) and the spectral exponent (beta), which characterizes irregularity of the signals. The estimates of beta were determined for each variable only over the range normally used to evaluate HRV. Values for %Fractal and beta of both BFV and TVV were significantly (P < 0.05) greater than those for HRV. In addition, there was no significant (P > 0.05) correlation between the beta values of HRV relative to either BFV (r = 0.14) or TVV (r = 0.34). RVC showed a smooth oscillation as compared with HRV; %Fractal for RVC (42.3 +/- 21.7%, mean +/- SD) was significantly (P < 0.05) lower than that for HRV (78.5 +/- 4.2%).(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed2004

A fractal analysis of the radial distribution of bronchial capillaries around large airways.

We analyzed published measurements of the bronchial circulation and airway wall (Anderson JC, Bernard SL, Luchtel DL, Babb AL, and Hlastala MP. Respir Physiol Neurobiol 132: 329-339, 2002) and determined that the radial distribution of bronchial capillary cross-sectional area was fractal. We limited our analysis to bronchial capillaries, diameter < or =10 mum, that resided between the epithelial basement membrane and adventitia-alveolar boundary, the airway wall tissue. Thirteen different radial distributions of capillary-to-tissue area were constructed simply by changing the number of annuli (i.e., the annular size) used to form each distribution. For the 13 distributions created, these annuli ranged in size from to of the size of the airway wall area. Radial distributions were excluded from the fractal analysis if the sectioning procedure resulted in an annulus with a radial thickness less than the diameter of a capillary. To determine the fractal dimension for a given airway, the coefficient of variation (CV) for each distribution was calculated, and ln(CV) was plotted against the logarithm of the relative piece area. For airways with diameter >2.4 mm, this relationship was linear, which indicated the radial distribution of bronchial capillary cross-sectional area was fractal with an average fractal dimension of 1.27. The radial distribution of bronchial capillary cross-sectional area was not fractal around airways with diameter <1.5 mm. We speculated on how the fractal nature of this circulation impacts the distribution of bronchial blood flow and the efficiency of mass transport during health and disease. A fractal analysis can be used as a tool to quantify and summarize investigations of the bronchial circulation.

Anatomy, Cross-Sectional↗

PubMed1999

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory.

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

Adolescent↗

PubMed2000

Fractal analysis of nuclear medicine images for the diagnosis of pulmonary emphysema: interpretations, implications, and limitations.

OBJECTIVE: The purpose of this study was to investigate, on images obtained in nuclear medicine examinations, the physical meanings and consequent implications of fractal analysis developed in a recent study that was reported to be effective in quantifying the heterogeneous distribution of carbon particle radioaerosol in the lungs. MATERIALS AND METHODS: Fractal dimensions were computed for 108 sets of radionuclide imaging data from 28 patients according to the methods in a previous report, and were then correlated with the ratio of tissue areas segmented at two thresholds (15% and 35% of maximal radioactivity). RESULTS: Fractal dimension was found to linearly correlate with the ratio natural logarithm of tissue areas segmented at two different threshold levels (n = 108, r = 0.999), with regression slope accurately predicted (error = 0.06%). Bland-Altman analysis showed that fractal dimensions ranging from 0.2 to 1.9 can be explained by this area ratio with disagreement of only 5.13% at two standard deviations; thus, fractal dimension seems to be an over-simplified parameter unrelated to spatial heterogeneity of radioaerosol distribution. CONCLUSION: The analysis of this study suggested that the fractal dimension defined in a previous report was limited to the indication of the percentage area of low-radioactivity regions with respect to total tissue area in the image. Because the fractal dimension partially reflects, but is not specific to, a certain degree of focal spots of low radioactivity, we suggest using fractal analysis in clinical practice only with careful control and thorough understanding of the physical meanings.

Fractals↗

PubMed2005

[Fractal analysis of trabecular architecture: with special reference to slice thickness and pixel size of the image].

Many analyses of bone microarchitecture using three-dimensional images of micro CT (microCT) have been reported recently. However, as extirpated bone is the subject of measurement on microCT, various kinds of information are not available clinically. Our aim is to evaluate usefulness of fractal dimension as an index of bone strength different from bone mineral density in in-vivo, to which microCT could not be applied. In this fundamental study, the relation between pixel size and the slice thickness of images was examined when fractal analysis was applied to clinical images. We examined 40 lumbar spine specimens extirpated from 16 male cadavers (30-88 years; mean age, 60.8 years). Three-dimensional images of the trabeculae of 150 slices were obtained by a microCT system under the following conditions: matrix size, 512 x 512; slice thickness, 23.2 em; and pixel size, 18.6 em. Based on images of 150 slices, images of four different matrix sizes and nine different slice thicknesses were made using public domain software (NIH Image). The threshold value for image binarization, and the relation between pixel size and the slice thickness of an image used for two-dimensional and three-dimensional fractal analyses were studied. In addition, the box counting method was used for fractal analysis. One hundred forty-five in box counting was most suitable as the threshold value for image binarization on the 256 gray levels. The correlation coefficients between two-dimensional fractal dimensions of processed images and three-dimensional fractal dimensions of original images were more than 0.9 for pixel sizes < or =148.8 microm at a slice thickness of 1 mm, and < or =74.4 microm at one of 2 mm. In terms of the relation between the three-dimensional fractal dimension of processed images and three-dimensional fractal dimension of original images, when pixel size was less than 74.4 microm, a correlation coefficient of more than 0.9 was obtained even for the maximal slice thickness (1.74 mm) examined in this study.

Adult↗

PubMed2000

Heterogeneity of cerebral blood flow: a fractal approach.

AIM: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon 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.

Aged↗

PubMed2001

Fractal analysis of cerebral blood flow distribution in Alzheimer's disease.

UNLABELLED: This study describes a method for quantifying cerebral blood flow (CBF) distribution in Alzheimer's disease (AD) from SPECT images obtained with (99m)Tc-hexamethylpropyleneamine oxime (HMPAO) by 3-dimensional fractal analysis (3D-FA). METHODS: HMPAO SPECT was performed on 68 patients with probable AD and 14 healthy control subjects. We delineated the CBF images using 4 cutoff levels (35%, 40%, 45%, and 50% of the maximal voxel radioactivity) and measured the total number of voxels in the areas surrounded by the contours obtained with each cutoff level. We calculated fractal dimensions from the relationship between the total number of voxels and the cutoff levels transformed into natural logarithms. RESULTS: The fractal dimensions (mean +/- SD) for patients with probable AD and healthy subjects were 0.74 +/- 0.33 and 0.52 +/- 0.09, respectively. A significant difference in the fractal dimension was found between groups (P = 0.001). Statistically significant correlations were obtained between the fractal dimension and the Mini-Mental State Examination score (r = -0.598; P < 0.0001) and between the fractal dimension and the AD Assessment Scale (r = 0.670; P < 0.0001). The fractal dimensions for subjects with clinical dementia rates (CDRs) of 0, 1, 2, and 3 were 0.52 +/- 0.09, 0.63 +/- 0.21, 0.77 +/- 0.23 (P < 0.05 vs. the group with a CDR of 1), and 1.43 +/- 0.49 (P < 0.0001 vs. the group with a CDR of 2), respectively. CONCLUSION: Quantification of CBF distribution on SPECT images in AD was possible using 3D-FA. The fractal dimension was well correlated with the cognitive impairment, as assessed in neuropsychologic tests. 3D-FA may be a useful method for objectively evaluating the progression of AD.

Aged↗

PubMed2002

Fractal dimensions of human brain cortex vessels during the fetal period.

BACKGROUND: Fractal dimensions always involve some averaging with respect to the given geometrical object. The classical geometrical description includes overly detailed geometrical information, rendering the precise formulation of equations ineffective. The problems associated with the functionality and growth of biological systems according to their observed geometrical shape require a specific approach. MATERIAL/METHODS: The material consists of 50 brains, 4th to 8th month of fetal life, length C.-R. 83-220 mm. The material was examined using the Pickworth method, computer image analysis (Imtronic, Scion for Windows 1998, and Elf v. 4.2), and fractal analysis. Various transformations were applied: numeric filters, statistical filters, binary geometrical transformations, arithmetical operations. Fractal analysis employs the 'box-counting' fractal dimension. RESULTS: The cortex vein net maintains the fetal character, with a large number of anastomoses, also present in adults. The size of cortex branches amounts to 100-200 microm. The reduction of some of the anastomoses during the early stages of evolution comes from an increase in the vessels' caliber. During the 4th month, the fractal dimension is 1.26, increasing to 1.53 at month 5. Rapid growth of the fractal dimension has been observed until the 6th and 7th months. This means an increased complexity level and feed volume in the brain. CONCLUSIONS: Fractals constitute a promising and effective tool to estimate the structures of brain vessels. The fractal dimension varies during the fetal period. This shows the close correspondence between the structure and functionality.

Algorithms↗

PubMed2002

Fractal characteristics of brain vessel microangioarchitecture during the fetal period.

BACKGROUND: Studies of human telencephalon during the fetal period are rare. Recent technologies, such as the Pickworth method, ultraviolet, infrared, and computer image systems, now enable the observation of such barely accessible structures. The present study constitutes an evaluation of the microangioarchitecture of brain vessels during the fetal period and the creation of a fractal model to describe it. Studies formulated in the language of fractals have never previously been applied in modeling brain vessels. MATERIAL/METHODS: We studied 100 brains in the 4th to 8th month of fetal life, using the Pickworth method, computer image analysis under three different systems, the POV-RAY program, and fractal analysis. RESULTS: The POV-RAY program was used to generate 3-dimensional, tree-like structures. This requires three scaling parameters: length, vessel diameter, and the angle between the branches and the central axis. The vessel structure was modeled by fractals with condensation point. Moreover, these tree-like fractals have different one-sided dimensions. In making fractal models we treated these one-sided dimensions as numerically evaluated parameters of the theory. Of course, the accuracy of the proposed models depends upon the accurate prediction by a fractal of the examined structure. CONCLUSIONS: Brain vessels can be modeled with the help of fractals with condensation points, which have differentiated one-sided dimensions.

Blood Vessels↗

PubMed2004

Fractal dimension in aspiration cytology smears of breast and cervical lesions.

OBJECTIVE: To standardize the automated measurement of fractal dimension on cytologic smears and compare the fractal dimension of benign and malignant breast cells and cervical lesions on cytologic material to evaluate its role in the discrimination of benign from malignant cells. STUDY DESIGN: We randomly selected fine needle aspiration cytology smears of 42 cases of infiltrating duct carcinoma and 38 cases of fibroadenoma of the breast. Similarly, 16 cervical carcinoma and 20 normal cervical smears were selected for study. Ten cells were selected randomly from each case. Box counting of fractal dimension of malignant and benign cells was achieved with an image cytometer (Leica, Cambridge, England) using Quantimet 600 software (Leica). Then a well-spaced grid with multiple small boxes of a particular pixel length was superimposed on the cell. The dimension of the box was selected as 4, 8 and 16 pixels. With the help of a logical "AND" operation, we counted the number of boxes touching the peripheral margin of the cell nuclei. For each cell, the log-log graph of 1 per box size was plotted against the number of boxes touching the peripheral rim of the cell. The slope of each graph was identified using the least-squares method of regression analysis. RESULTS: The mean fractal dimension of malignant cells was 0.8536 +/- 0.1120 as compared to 0.8403 +/- 0.1115 in benign cell groups. The Mann-Whitney U test showed a significant difference in fractal dimension in these 2 groups (P = .05). The mean fractal dimension of malignant cells from the cervix was 0.8656 +/- 0.1499 as compared to 0.8315 +/- 0.1312 in benign cells. The Mann-Whitney U test showed a significant difference in fractal dimension in these 2 groups (P < .02). CONCLUSION: Fractal dimension may be a helpful adjunctive technique to discriminate between benign and malignant cells.

Algorithms↗

PubMed2002

Fractal tumor growth of ovarian cancer: sonographic evaluation.

OBJECTIVE: The objective of this study was to determine whether sonographically depicted ovarian tumor growth is fractal, and the mean fractal dimension differs according to stages of the disease and histologic types. METHODS: The fractal dimensions of outlines of sonographically depicted solid components in 160 ovarian tumors were measured using a box-counting method. RESULTS: The mean fractal dimensions of the surface of intracystic solid components in serous, mucinous, endometrioid, and clear cell adenocarcinoma were 1.259, 1.243, 1.238, and 1.182, respectively. These values were significantly greater than the topological dimension of a line (=1). The value was significantly higher in stage I or II (1.381) than stage III or IV (1.205) in serous carcinoma (P = 0.02), but not significantly different in clear cell carcinoma (1.187 and 1.172, respectively). In stage I or II, the value of serous carcinoma (1.381) was significantly higher than that of clear cell carcinoma (1.187) (P = 0.03). The value of mucinous cystadenoma of low malignant potential was 1.337, which was also significantly greater than 1. The mean fractal dimensions of outlines of solid tumors in cases with dysgerminoma and thecoma-fibroma were 1.036 and 1.023, respectively. These values were not significantly different from 1. CONCLUSION: This study shows that the surface of solid components in cystic epithelial ovarian cancers has a fractal structure, and the mean fractal dimension may differ according to stages of the disease and histologic types. Fractal geometry, a vocabulary of irregular shapes, can be useful for describing the pathological architecture of ovarian tumors and for yielding insights into the mechanisms of tumor growth.

Adenocarcinoma↗

PubMed1998

Intrasolid Interfacial Fractality of a Less-Crystalline Solid.

Small angle X-ray scattering (SAXS) measurements have been carried out on pitch (PIT) and cellulose (CEL)-based activated carbon fibers (ACFs). In the higher angle region, the scattering intensity did not obey the classical Porod's law. This suggests that ACFs have a rough surface and their roughness is expressed by the concept of surface fractal. The surface fractal dimension was determined from SAXS for each ACF. ACFs were treated at high temperature in argon in order to control the nanographitic crystallinity. PIT and CEL lost their microporosity upon heat treatment above 1773 and 2073 K, respectively. These nonporous ACFs showed also a strong SAXS caused by the electron density difference at the interface between microcrystalline and amorphous phase. This interface also had a fractal dimension, which was defined as the interfacial fractal dimension. The surface or interfacial fractal dimension of ACF depended on the heating temperature. As the treating temperature increased, the surface or interfacial fractal dimension decreased from 2.8 to 2.0. Both PIT and CEL showed a similar temperature dependence on each other. The surface or interfacial fractal dimension was reduced with the growth of nanographites, and upon heating at 3173 K, the intrasolid interfacial fractal dimension became 2. Copyright 1998 Academic Press.

Journal Article↗

PubMed2005

Determination of the fractal dimension of microbial flocs from the change in their size distribution after breakage.

The fractal dimension is of ultimate importance in the description of the properties and behavior of microbial flocs in biological wastewater treatment systems. However, the methods for the measurement of the fractal dimension have not been well-established. In this study, a new method is developed to determine the fractal dimension of biological flocs in activated sludge (AS) suspensions. The new method utilizes the particle size distribution (PSD) of the sludge flocs measured by image processing under a microscope. Mechanical breakage is conducted for the sludge sample to create a change in the PSD. On the basis of the self-similarity of fractal aggregates, the fractal dimension of the AS flocs can be calculated from a comparison between the original PSD and the altered PSD by breakage. It is determined that the sludge flocs grown in laboratory bioreactors with sludge ages of 5, 10, and 20 days have fractal dimensions of 2.07, 2.21, and 2.36. The sludge collected from a full-scale AS treatment plant has a fractal dimension of 1.99. This new method overcomes the deficiencies of other existing methods. It is easier to use and provides more reliable results in the determination of the fractal dimension of biological flocs and other similar aggregate samples.

Bioreactors↗

PubMed2005

An experimental study of gas adsorption on fractal surfaces.

The validity of the fractal versions of the FHH and BET theories for describing the adsorption of butane and nitrogen on a variety of partially dehydroxylated silica surfaces has been tested. The fractal dimensions obtained from adsorption data have been compared with those obtained completely independently using SAXS. It was found that the fractal dimensions obtained from butane adsorption isotherms, using both the fractal FHH and fractal BET theories, agreed well with the corresponding values obtained from SAXS over overlapping length scales. However, in general, a systematic deviation between the fractal dimension obtained from nitrogen adsorption and that obtained from SAXS was observed. The fractal dimensions obtained from nitrogen adsorption were consistently larger than those obtained from SAXS, which is the opposite of what has often been found in the literature. It has been suggested that the differences in the suitability of the adsorption theories tested to describe butane and nitrogen adsorption is due to the significant difference between the interaction strengths of these two different molecules with silica surfaces. A modified theory that can account for the discrepancy between the fractal dimensions obtained from nitrogen adsorption and SAXS has been proposed. The implications of the new theory for the accuracy of nitrogen adsorption BET surface areas for silicas are discussed.

Journal Article↗

PubMed1998

Minimum sperm trajectory length for reliable determination of the fractal dimension.

The aim of this study was to determine the minimum track length required for the reliable calculation of the fractal dimension of trajectories of capacitating human spermatozoa. Manually reconstructed trajectories classified previously as hyperactivated or non-hyperactivated were re-analyzed. The trajectories were reconstructed at 60 Hz, and each comprised 61 points (corresponding to 1 s movement). The trajectories were 'split' to give the equivalent of 2 x 31 point, 3 x 21 point, 4 x 16 point and 6 x 11 point track segments and the fractal dimension determined for each. The fractal dimensions of each track segment within each trajectory were compared using paired t-tests. No significant difference was observed between the fractal dimensions of track segments of equal length, irrespective of the motility pattern. However, significant differences in fractal dimension values were observed when segments of different lengths were compared (P<0.01). For the non-hyperactivated tracks, the fractal dimension was consistently below the hyperactivation threshold level for only the 31 point segments. The hyperactivated tracks consistently had fractal dimension values above the threshold level when segments of 16 points or longer were analysed. Therefore, the minimum track length for the determination of reliable fractal dimension values was 31 points, corresponding to an image sampling time of 0.5 s at 60 Hz, although it could be used as a screening method for the identification of hyperactivated motility for track segments of greater than 11 points (corresponding to 0.17 s movement).

False Positive Reactions↗

PubMed1990

Microbial growth patterns described by fractal geometry.

Fractal geometry has made important contributions to understanding the growth of inorganic systems in such processes as aggregation, cluster formation, and dendritic growth. In biology, fractal geometry was previously applied to describe, for instance, the branching system in the lung airways and the backbone structure of proteins as well as their surface irregularity. This investigation applies the fractal concept to the growth patterns of two microbial species, Streptomyces griseus and Ashbya gossypii. It is a first example showing fractal aggregates in biological systems, with a cell as the smallest aggregating unit and the colony as an aggregate. We find that the global structure of sufficiently branched mycelia can be described by a fractal dimension, D, which increases during growth up to 1.5. D is therefore a new growth parameter. Two different box-counting methods (one applied to the whole mass of the mycelium and the other applied to the surface of the system) enable us to evaluate fractal dimensions for the aggregates in this analysis in the region of D = 1.3 to 2. Comparison of both box-counting methods shows that the mycelial structure changes during growth from a mass fractal to a surface fractal.

Fungi↗

PubMed1989

[The application of fractal technics for the enhancement of radiographic images].

This paper deals with digital radiological image processing, with a special emphasis on quantitative measurement extraction aimed at discriminating different lung pathologies. Texture analysis of these images, not easily performed by the human eye, can be carried out by means of fractal techniques, which allow different textures to be characterized by a single parameter--i.e. the fractal dimension. To extract the fractal dimension of an image, the so-called "blanket" method is employed, which allows the average fractal dimension of an image area to be evaluated. The result of this processing is a new image whose points are assigned the average fractal dimension value of the area they belong to. The behaviors of fractal dimension histograms related to various simulations of lung pathologies are notably different, which allows such pathologies to be effectively characterized and differentiated on a quantitative basis. The radiographic images the "blanket" method was applied to are related to simulations of both pathological and healthy tissues. The behaviors of fractal dimension histograms and the average fractal dimension values allow the characterization of the different pathologies both for single tissues and in case of superimposition of a healthy tissue on a pathological one. The promising simulation results have encouraged us to carry out the present experimental investigation in the field of lung neoplasms.

Humans↗

PubMed2000

Evaluation of skin damage caused by percutaneous absorption enhancers using fractal analysis.

Fractal analysis of the cross-sectional morphology of rat skin was conducted to evaluate pathologic changes evoked by percutaneous absorption enhancers. Male hairless rats (WBN/Ht-ILA), 8 weeks old, weighing 160 to 180 g were used. Under anesthetization, glass cells (10-mm inner diameter) were attached to the rats' abdomens, and test solutions containing various mixtures of the percutaneous absorption enhancers, sodium lauryl sulfate, isopropanol, 2-methyl-1-butanol, and sodium myristate were applied. Six hours after application, the solutions were removed and the abdominal skin was excised. Skin cross sections were analyzed with a charge-coupled device (CCD) camera. Image data taken by the CCD camera were fed into a desktop digital computer; then the fractal dimension of each skin cross section was determined on the basis of the box-counting algorithm. A pathologic study was also performed on the skin treated with the test solution. All sections of skin were examined with an optical photo microscope. Pathologic findings were classified into five levels. The total irritation score (TIS) was defined as the summation of damage levels in all regions. Only with the administration of hydrogel containing 2-methyl-1-butanol or sodium lauryl sulfate were positive values of TIS observed. However, the TIS values were independent of the concentration of these components. The most severe skin damage was evoked by application of sodium lauryl sulfate. Noticeable skin damage was also seen with 2-methyl-1-butanol. No irritation to the skin resulted from treatment with isopropanol or sodium myristate. When test solution containing sodium lauryl sulfate was applied to the skin, a remarkable increment in fractal dimensions was noted. This may suggest that the structure of the skin was greatly compromised as a result of sodium lauryl sulfate application. Although no change in fractal dimension was observed as a result of application of the test solution containing only 25% isopropanol, the fractal dimension of skin cross section gradually increased with increasing concentrations of isopropanol, 2-methyl-1-butanol or sodium myristate in the test solutions. The increment of fractal dimension was around 0.4. Thus, the skin structure was also altered by the application of high concentrations of these compounds. Although the relevance to humans is not known, fractal analysis of skin structure is thought to be useful as a novel method for detecting skin damage that is brought about by the application of percutaneous absorption enhancers.

Animals↗