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PubMed2002

A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces.

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.

Alitretinoin↗

PubMed2001

Analysis of fractal dimension of O2A glial cells differentiating in vitro.

Fractal dimension is a quantitative measure of morphological complexity. Glial cells of the oligodendrocyte-type 2 astrocyte (O2A) lineage exhibit increasing morphological complexity as they differentiate in vitro. Enriched populations of O2A progenitor cells isolated from neonatal rat cerebral hemispheres or optic nerves were allowed to differentiate in vitro, and their fractal dimensions were measured over time. The fractal dimensions of the maturing cells correlated with perceived complexity; cells with elaborate process branching had larger fractal dimensions than cells with a simpler morphology. An analysis of changes in fractal dimension revealed distinct rates of growth for both oligodendrocytes and type 2 astrocytes. The fractal dimension remained constant over a 10-fold range in optical magnification, demonstrating that cultured O2A glial cells exhibit self-similarity, a defining characteristic of fractal objects. These results illustrate that fractal dimension analysis of maturing cell populations is a useful method for quantitatively describing the process of cell differentiation.

Animals↗

PubMedDate not supplied

Antigen-antibody binding kinetics for biosensor applications. A dual-fractal analysis.

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The fit obtained by a dual-fractal analysis is compared with that obtained from a single-fractal analysis. In some cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (San Rafael, CA). These examples are presented. It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase (or decrease, a single example is presented for this case) as the reaction progresses on the biosensor surface. For example, for the binding of monoclonal antibody MAb 49 in solution to surface-immobilized antigen, a 90.4% increase in the fractal dimension (Df1 to Df2) from 1.327 to 2.527 leads to an increase in the binding rate coefficient (k1 to k2) by a factor of 9.4 from 11.74 to 110.3. The different examples analyzed and presented together provide a means by which the antigen-antibody reactions may be better controlled by noting the magnitude of the changes in the fractal dimension and in the binding rate coefficient as the reaction progresses on the biosensor surface.

Antigen-Antibody Reactions↗

PubMed2001

Perfusion heterogeneity in human skeletal muscle: fractal analysis of PET data.

Muscle blood flow has been shown to be heterogeneous at the voxel by voxel level in positron emission tomography (PET) studies using oxygen-15 labelled water. However, the limited spatial resolution of the imaging device does not allow direct measurement of true vascular flow heterogeneity. Fractal dimension (D) obtained by fractal analysis describes the relationship between the relative dispersion and the size of the region studied, and has been used for the assessment of perfusion heterogeneity in microvascular units. This study was undertaken to evaluate fractal characteristics of PET perfusion data and to estimate perfusion heterogeneity in microvascular units. Skeletal muscle blood flow was measured in healthy subjects using [15O]water PET and the fractal characteristics of blood flow in resting and exercising skeletal muscle were analysed. The perfusion heterogeneity in microvascular units was estimated using the measured heterogeneity (relative dispersion, RD = SD/mean) and D values. Heterogeneity due to methodological factors was estimated with phantoms and subtracted from the flow data. The number of aggregated voxels was inversely correlated with RD both in phantoms (Pearson r = -0.96-0.97) and in muscle (Pearson r = -0.94) when both parameters were expressed using a logarithmic scale. Fractal dimension was similar between exercising (1.13) and resting (1.14) muscles and significantly lower than the values in the phantoms with different activity levels (1.27-1.29). Measured flow heterogeneity values were 20% +/- 6% (exercise) and 27% +/- 5% (rest, P < 0.001), whereas estimated flow heterogeneity values in microvascular units (1 mm3) were 35% +/- 14% (exercise) and 49% +/- 14% (rest, P < 0.01). In conclusion, these results show that it is feasible to apply fractal analysis to PET perfusion data. When microvascular flow heterogeneity is estimated using fractals, perfusion appears to be more heterogeneous in microvascular units than when obtained by routine spatial analysis of PET data. Analysis of flow heterogeneity using PET and fractals could provide new insight into physiological conditions and diseases associated with changes in peripheral vascular function.

Adult↗

PubMed1994

Comparative fractal analysis of cultured glia derived from optic nerve and brain demonstrate different rates of morphological differentiation.

O-2A progenitor cells derived from neonatal rat cerebral hemispheres or optic nerves, were induced to differentiate in culture into either oligodendrocytes or type 2 astrocytes. The fractal dimensions, a measure of morphological complexity, of the differentiating glial cells were measured over time. Analysis of the changes in fractal dimension (D) with respect to time revealed specific rates of growth for each glial phenotype and a specific final D. The time course of these changes is well fit by a simple mathematical model. While brain-derived oligodendrocytes matured faster than the astrocytes, they ultimately attained comparable levels of complexity, with similar maximum fractal dimensions. Oligodendrocytes from nerve also matured faster than nerve derived astrocytes, in contrast, however, they attained a greater morphological complexity than nerve astrocytes. While the brain-derived oligodendrocytes showed a faster rate of maturation than their optic nerve counterparts, astrocytes from both regions had similar rates of morphological differentiation. Self-similarity, a defining property of fractal objects was investigated, by determining the fractal dimension of cells over a range of magnifications. The calculated fractal dimension remained constant over a 10-fold range in optical magnification, illustrating that cultured glial cells exhibit this important characteristic of fractal objects. In addition, we analyzed the branching patterns of glial processes by the Sholl method and found that the results were not as interpretable or meaningful as those of fractal analysis.

Animals↗

PubMed2005

Changes in fractal features of fetal heart rate during pregnancy.

OBJECTIVE: Our objective was to examine whether heart rate time series of healthy normal fetuses possess fractal properties and, if so, to determine whether consistent changes in fractal features according to gestational age exist. DESIGN OF THE STUDY: One hundred nineteen fetal heart rate (FHR) recordings in 55 singleton pregnancies between the 22nd and 41st weeks were analyzed. Fractal analysis developed by Higuchi was performed. Changes of fractal dimension were examined according to gestational age. RESULTS: Two characteristic scaling regions were present in each FHR trace. The fractal dimension defined within 500 ms to 5 s (D(S); median 1.396, range 1.273-1.642) was lower than that defined longer than 30 s (D(L); median 1.933, range 1.492-2.049) in every case. These two values were significantly different (p<0.001). There was a statistically significant difference in the values of D(S) between (22-29 weeks, mean 1.323), (30-33 weeks, mean 1.443) (p=0.004), (34-35 weeks, mean 1.418) (p=0.002), (36 weeks, mean 1.409) (p=0.030), (37-38 weeks, mean 1.394) (p=0.006), and (40-41 weeks, mean 1.452) (p=0.001), respectively. D(S) values between (40-41 weeks), (37-38 weeks) (p=0.012), and (39 weeks, mean 1.369) (p=0.030), respectively, were also significantly different. The values of D(L) decreased from 22-39 weeks (median 1.941) to 40-41 weeks (median 1.891) (p=0.008). CONCLUSIONS: Two distinct fractal structures within the FHR variation were identified. Fractal features of heart rate of healthy normal fetuses change significantly during pregnancy period. Fractal analysis may be useful for evaluating FHR variation.

Adult↗

PubMed2003

A fractal analysis of analyte-estrogen receptor binding and dissociation kinetics using biosensors: environmental effects.

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ER) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. Both cases are analyzed: unliganded as well as liganded. The influence of different ligands is also analyzed. A better understanding of the kinetics provides physical insights into the interactions and suggests means by which appropriate interactions (to promote correct signaling) and inappropriate interactions such as with xenoestrogens (to minimize inappropriate signaling and signaling deleterious to health) may be better controlled. The fractal approach is applied to analyte-ER interaction data available in the literature. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor chip surface. In general, the binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity on the surface. For example, the binding rate coefficient, k, exhibits a 4.60 order of dependence on the fractal dimension, D(f), for the binding of unliganded and liganded VDR mixed with GST-RXR in solution to Spp-1 VDRE (1,25-dihydroxyvitamin D(3) receptor element) DNA immobilized on a sensor chip surface (Cheskis and Freedman, Biochemistry 35 (1996) 3300-3318). A single-fractal analysis is adequate in some cases. In others (that exhibit complexities in the binding or the dissociation curves) a dual-fractal analysis is required to obtain a better fit. A predictive relationship is also presented for the ratio K(A)(=k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). This has biomedical and environmental implications in that the dissociation and binding rate coefficients may be used to alleviate deleterious effects or enhance beneficial effects by selective modulation of the surface. The K(A) exhibits a 112-order dependence on the ratio of the fractal dimensions for the ligand effects on VDR-RXR interaction with specific DNA.

Biophysical Phenomena↗

PubMed2001

Tissue as a self-organizing system with fractal dynamics.

Cell is a supramolecular dynamic network. Screening of tissue-specific cDNA library and results of Relative RT-PCR indicate that the relationship between genotype, (i.e., dynamic network of genes and their protein regulatory elements) and phenotype is non-bijective, and mendelian inheritance is a special case only. This implies non-linearity, complexity, and quasi-determinism, (i.e., co-existence of deterministic and non-deterministic events) of dynamic cellular network; prerequisite conditions for the existence of fractal structure. Indeed, the box counting method reveals that morphological patterns of the higher order, such as gland-like structures or populations of differentiating cancer cells possess fractal dimension and self-similarity. Since fractal space is not filled out randomly, a variety of morphological patterns of functional states arises. The expansion coefficient characterizes evolution of fractal dynamics. The coefficient indicates what kind of interactions occurs between cells, and how far from the limiting integer dimension of the Euclidean space the expanding population of cells is. We conclude that cellular phenomena occur in the fractal space; aggregation of cells is a supracollective phenomenon (expansion coefficient > 0), and differentiation is a collective one (expansion coefficient < 0). Fractal dimension or self-similarity are lost during tumor progression. The existence of fractal structure in a complex tissue system denotes that dynamic cellular phenomena generate an attractor with the appropriate organization of space-time. And vice versa, this attractor sets up physical limits for cellular phenomena during their interactions with various fields. This relationship can help to understand the emergence of extraterrestial forms of life. Although those forms can be composed of non-carbon molecules, fractal structure appears to be the common feature of all interactive biosystems.

Animals↗

PubMedDate not supplied

A kinetic study of analyte-receptor binding and dissociation for biosensor applications: a fractal analysis for two different DNA systems.

A fractal analysis of DNA binding and dissociation kinetics on biosensor surfaces is presented. The fractal approach provides an attractive, convenient method to model the kinetic data taking into account the effects of surface heterogeneity brought about by ligand immobilization. The fractal technique can be used in conjunction or as an alternate approach to conventional modeling techniques, such as the Langmuir model, saturation model, etc. Examples analyzed include a DNA molecular beacon biosensor and a plasmid DNA-(cationic polymer) interaction biosensor. The molecular beacon example provides some insights into the nature of the surface and how it influences the binding rate coefficients. The DNA-cationic polymer interaction example provides some quantitative results on the binding and dissociation rate coefficients. 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 results indicate 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 example presented. Relationships are presented for the binding rate coefficients as a function of their corresponding fractal dimension, D(f), which is an indication of the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity of the surface (increase in D(f)) leads to an increase in the binding rate coefficient.

Biosensing Techniques↗

PubMed1996

Fractal dimension in radiographic analysis of alveolar process bone.

OBJECTIVES: This in vitro study examined radiographic fractal dimension changes in alveolar process bone during simulated osteoporosis. STUDY DESIGN: Ten specimens of human maxillary alveolar process bone were progressively decalcified, and the percentage of calcium lost at each decalcification stage was quantified. Four radiographs of each specimen, together with an aluminum step-wedge, were exposed at 70 kVp at each stage. The test set of 560 radiographs was digitized, identical bony regions of interest were selected from the density-corrected images of each specimen, the regions were digitally filtered to reduce film-grain noise, and fractal dimension was computed on a line-to-line basis. Correlation analysis quantified the relationship between calcium loss and fractal dimension change. Analysis of variance and Duncan's multiple range test determined whether a difference existed in fractal dimension computed from images at x-ray beam angulations of -5, 0, and +5 degrees. RESULTS: A strong correlation (average r = -0.94, p < or = 0.0037) was found between generalized demineralization and decreasing fractal dimension. In every bone sample fractal dimension changed significantly (p < or = 0.0189) with angular change. CONCLUSIONS: Radiographic fractal dimension holds promise for detecting simulated osteoporosis in the maxilla under ideal conditions, but the sensitivity of fractal dimension to small x-ray beam angular change renders its clinical application questionable.

Alveolar Process↗

PubMed1997

The characterization of broadband ultrasound attenuation and fractal analysis by biomechanical properties.

The purpose of this study was to show how the difference in structure affects the mechanical properties of bone and if BUA or fractal analysis is able to detect these changes in mechanical properties. A total of 38 cancellous bone cubes were obtained from seven bovine tibiae (32 specimens) and one human tibia (6 specimens). BUA was measured in the superior/inferior (SI), medial/lateral (ML), and anterior/posterior (AP) directions for each specimen. The fractal dimension was estimated by using the continuous alternating sequential filter (CASF) pyramid approach to handle fractal dimension estimation of small images. Nondestructive compressive tests were also performed in the three orthogonal directions for each sample. The correlations between BUA and density were statistically significant for all three directions. The correlation between BUA and elastic modulus varied depending on the direction in which the two parameters were measured. The best correlation was in the AP directions (r = 0.75, p < 0.0001), followed by the ML direction (r = 0.52, p = 0.0006), and finally the SI direction (r = 0.18, p = 0.28). The only significant correlation between fractal dimension and density was in the SI direction (r = 0.39, p = 0.015). There was significant correlation between fractal dimension and elastic modulus in all three directions, but the direction that exhibited the best correlation was the SI direction (r = 0.61, p < 0.0001). The correlation coefficients for the AP and ML directions were 0.45 (p = 0.0046) and 0.34 (p = 0.0377), respectively. A multivariate model, carried out to predict the elastic modulus from the BUA or fractal dimension including density, demonstrated that the correlation coefficient significantly increased in all three directions for BUA and fractal dimension. After adjustment for density, significant relationships between elastic modulus and BUA or fractal dimension were still found (p < 0.05).

Animals↗

PubMedDate not supplied

Dual-fractal analysis for antigen--antibody binding kinetics for biosensor applications.

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor and other surfaces is analyzed within a fractal framework. Often, the binding kinetics may be described by a single-fractal analysis. In some cases, the binding curve exhibits complexities. Then, for these cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This indicates a change in the reaction mechanism on the surface. It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase as the reaction progresses on the biosensor surface. For example, for the binding of 10 nM insulin growth factor-1 in solution to insulin growth factor binding protein-1 immobilized on a biosensor surface, a 64% increase in the fractal dimension from 1.73 (Df1) to 2.85 (Df2) leads to an increase in the binding rate coefficient by a factor of 31.8 from 3.92 (k1) to 125 (k2). Furthermore, as the IGF-1 concentration in solution increases from 10 to 80 nM in solution, k2 and Df2 exhibit a linear increase. k1 and Df1 exhibit a linear increase with the reciprocal of the IGF-1 concentration in solution. The different examples analyzed and presented together provide a means by which the antigen-antibody reactions may be better controlled by noting the magnitude of the changes in the fractal dimension and in the binding rate coefficient as the reaction progresses on the biosensor surface. Also, the magnitude of the changes in the binding rate coefficients (k1 and k2) and in the fractal dimensions (Df1 and Df2) as different parameters are changed for the different biosensor applications are of particular value, since they provide us with a measure or extent of changes in the binding rate coefficient on changing different experimental parameter values. It is of interest to note the effect of different parameters on the extent or heterogeneity that exists on the surface and how this influences the binding rate coefficients. This may be one method to help manipulate or control the binding rate coefficients on the reaction surface.

Antigen-Antibody Complex↗

PubMed1998

The effects of projection geometry and trabecular texture on estimated fractal dimensions in two alveolar bone models.

OBJECTIVES: To study the effects of trabecular texture and projection geometry on estimates of fractal dimensions from simulated alveolar bone. METHODS: Two models, one scale-variant and the other relatively scale-invariant, were used. Projections of 2-D slices through both the models were calculated, a uniform series of projections computed for the angular orientations between (0 degree and 180 degrees). Results of the 128 stacked projections are the projection of the 3-D object from different angles. Power spectra were produced by calculating the squared magnitude from the data and plotted as the logarithm of the power against the logarithm of the frequency, to give the fractal dimension. RESULTS: In the scale-variant model, the alveolar trabecular texture produced with a relatively thicker cylindrical diameter yielded a smaller fractal dimension (t = 8.44, P = 0.00). Linear regression analysis showed that the correlation between projection angle and the resulting fractal dimension was low for both the thicker cylinder (r = 0.02, P = 0.82), and for thinner cylinder (r = 0.02, P = 0.84). The scale-invariant model, also yielded a relatively smaller estimated fractal dimension (t = 7.23, P = 0.00). However, the correlation between projection angle and the resulting estimate of the fractal dimension was found to be low for both trabecular configurations (r = 0.10, P = 0.29 and r = 0.07, P = 0.45 respectively). CONCLUSIONS: Fractal dimensions increased when the diameter of the simulated cylindrical trabeculae decreased irrespective of the differences in self-similarity. The degree to which they varied with projection angle was relatively less for the scale-invariant (self-similar) model. However, fractal dimensions changed significantly with projection geometry.

Alveolar Process↗

PubMed2001

Analysis of fractal dimensions of rat bones from film and digital images.

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

Analysis of Variance↗

PubMed1995

Quantitative characterization of electron micrograph image using fractal feature.

In this investigation, texture analysis was carried out on electron micrograph images. Fractal dimensions and spatial grey level co-occurrence matrices statistics were estimated on each homogeneous region of interest. The fractal model has the advantages that the fractal dimension correlates to the roughness of the surface and is stable over transformations of scale and linear transforms of intensity. It can be calculated using three different methods. The first method estimates fractal dimension based on the average intensity difference of pixel pairs. In the second method, fractal dimension is determined from the Fourier transformed domain. Finally, fractal dimension can be estimated using reticular cell counting approach. Moreover, automatic image segmentation was performed using fractal dimensions, spatial grey level co-occurrence matrices statistics, and grey level thresholding. Each image was segmented into a number of regions corresponding to distinctly different morphologies: heterochromatin, euchromatin, and background. Fractal dimensions and spatial grey level co-occurrence matrices statistics were found to be able to characterize and segment electron micrograph images.

Cell Count↗

PubMed2006

Fractal-wavelet image denoising revisited.

The essence of fractal image denoising is to predict the fractal code of a noiseless image from its noisy observation. From the predicted fractal code, one can generate an estimate of the original image. We show how well fractal-wavelet denoising predicts parent wavelet subtress of the noiseless image. The performance of various fractal-wavelet denoising schemes (e.g., fixed partitioning, quadtree partitioning) is compared to that of some standard wavelet thresholding methods. We also examine the use of cycle spinning in fractal-based image denoising for the purpose enhancing the denoised estimates. Our experimental results show that these fractal-based image denoising methods are quite competitive with standard wavelet thresholding methods for image denoising. Finally, we compare the performance of the pixel- and wavelet-based fractal denoising schemes.

Algorithms↗

PubMed2002

Discrimination of walking patterns using wavelet-based fractal analysis.

In this paper, we attempted to classify the acceleration signals for walking along a corridor and on stairs by using the wavelet-based fractal analysis method. In addition, the wavelet-based fractal analysis method was used to evaluate the gait of elderly subjects and patients with Parkinson's disease. The triaxial acceleration signals were measured close to the center of gravity of the body while the subject walked along a corridor and up and down stairs continuously. Signal measurements were recorded from 10 healthy young subjects and 11 elderly subjects. For comparison, two patients with Parkinson's disease participated in the level walking. The acceleration signal in each direction was decomposed to seven detailed signals at different wavelet scales by using the discrete wavelet transform. The variances of detailed signals at scales 7 to 1 were calculated. The fractal dimension of the acceleration signal was then estimated from the slope of the variance progression. The fractal dimensions were significantly different among the three types of walking for individual subjects (p < 0.01) and showed a high reproducibility. Our results suggest that the fractal dimensions are effective for classifying the walking types. Moreover, the fractal dimensions were significantly higher for the elderly subjects than for the young subjects (p < 0.01). For the patients with Parkinson's disease, the fractal dimensions tended to be higher than those of healthy subjects. These results suggest that the acceleration signals change into a more complex pattern with aging and with Parkinson's disease, and the fractal dimension can be used to evaluate the gait of elderly subjects and patients with Parkinson's disease.

Acceleration↗

PubMed1995

High correlation of fractals for regional blood flows among resting and exercising skeletal muscles.

The regional blood flow distributions within single skeletal muscles are markedly uneven both at rest and during exercise hyperemia. Fractals adequately describe this perfusion heterogeneity in the resting lateral head of the gastrocnemius muscle as well as in the myocardium. Recently, we provided evidence that the fractal dimension for the blood flow distributions in this resting muscle was strongly correlated with that of the myocardium in the same rabbit. Prompted by this hitherto unknown observation, we have now examined 1) whether fractals also describe perfusion distributions within muscles with a varying metabolic activity, and 2) whether the fractal dimensions for blood flow distributions to these muscles were correlated. We used pentobarbital-anesthetized rabbits and cats. The regional distributions of blood flow within various skeletal muscles were estimated by microsphere trapping. The data unequivocally showed that the perfusion distributions could be described with fractals both in resting and in exercising muscle in both species, the corresponding fractal dimensions ranging from 1.36 to 1.41. The fractal dimensions were markedly correlated (r2 ranged from 0.82 to 0.88) when both various resting and resting plus exercising muscles were compared in the same animal. This surprising finding of high correlations for the fractal dimensions among various muscles within one animal provides a novel characteristic of blood flow heterogeneity.

Animals↗