Cross-sectional infarct edge jaggedness does not influence ventricular electrical stability in a rabbit model of late myocardial infarct healing

Previous studies have suggested that the jaggedness of the healed or healing infarct edge influences cardiac electrical stability. However, these findings have been based on histological observations rather than quantitative measurements. The aim of this study was to assess infarct jaggedness by calculating its fractal dimension and to examine how this influences cardiac electrical stability during late infarct healing in the rabbit. Using programmed electrical stimulation, it was found that the fractal dimension did not differ significantly in 19 rabbits that had inducible ventricular tachycardia and 16 that did not. We conclude from these studies in the mature rabbit that infarct edge jaggedness does not influence the ease with which ventricular tachycardia is induced during late myocardial infarct healing.     

Cross-sectional infarct edge jaggedness does not influence ventricular electrical stability in a rabbit model of late myocardial infarct healing

Abstract

Previous studies have suggested that the jaggedness of the healed or healing infarct edge influences cardiac electrical stability. However, these findings have been based on histological observations rather than quantitative measurements. The aim of this study was to assess infarct jaggedness by calculating its fractal dimension and to examine how this influences cardiac electrical stability during late infarct healing in the rabbit. Using programmed electrical stimulation, it was found that the fractal dimension did not differ significantly in 19 rabbits that had inducible ventricular tachycardia and 16 that did not. We conclude from these studies in the mature rabbit that infarct edge jaggedness does not influence the ease with which ventricular tachycardia is induced during late myocardial infarct healing.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

Mapping the spatial variation of mitral valve elastic properties using air-pulse optical coherence elastography

The mitral valve is a highly heterogeneous tissue composed of two leaflets, anterior and posterior, whose unique composition and regional differences in material properties are essential to overall valve function. While mitral valve mechanics have been studied for many decades, traditional testing methods limit the spatial resolution of measurements and can be destructive. Optical coherence elastography (OCE) is an emerging method for measuring viscoelastic properties of tissues in a noninvasive, nondestructive manner. In this study, we employed air-pulse OCE to measure the spatial variation in mitral valve elastic properties with micro-scale resolution at 1 mm increments along the radial length of the leaflets. We analyzed differences between the leaflets, as well as between regions of the valve. We found that the anterior leaflet has a higher elastic wave velocity, which is reported as a surrogate for stiffness, than the posterior leaflet, most notably at the annular edge of the sample. In addition, we found a spatial elastic gradient in the anterior leaflet, where the annular edge was found to have a greater elastic wave velocity than the free edge. This gradient was less pronounced in the posterior leaflet. These patterns were confirmed using established uniaxial tensile testing methods. Overall, the anterior leaflet was stiffer and had greater heterogeneity in its mechanical properties than the posterior leaflet. This study measures differences between the two mitral leaflets with greater resolution than previously feasible and demonstrates a method that may be suitable for assessing valve mechanics following repair or during the engineering of synthetic valve replacements.     

Applications of fractal analysis to physiology

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.     

用于识别心电图的BP网络系统

基于ＢＰ神经网络算法和心电图（ＥＣＧ）识别的原理,作者系统地探讨了ＢＰ网络用于心电图识别的方法并设计了一个用ＢＰ网络识别三种类型（ＥＣＧ）一正常、下壁心肌心梗塞和前间壁心肌梗搴系统。实验结果较好。     

Differences in distensibility between the anterior and posterior walls of the left ventricle in dogs

Nonuniformity of myocardial systolic and diastolic performance in the normal left ventricle has been recognized by a number of investigators. Lack of homogeneity in diastolic properties might be caused by or related to differences in the distensibility of different regions of the left ventricular (LV) wall. Thus, we compared the end-diastolic transmural pressure-strain relations in both the anterior and posterior LV walls in seven anesthetized dogs during two interventions (pulmonary artery constriction and aortic constriction). Transmural pressure was defined as the difference between LV intracavitary pressure and local pericardial pressure. LV pressure was measured using a micromanometer; pericardial pressures over the LV anterior and posterior walls were measured with balloon transducers. Circumferentially oriented pairs of sonomicrometer crystals were implanted in the midwall of the anterior and posterior walls of the LV to measure segment lengths. Strains were calculated as (L-L0)/L0, where L was the instantaneous segment length and L0 was the segment length when transmural pressure was zero. The pattern of end-diastolic transmural pressure--strain relations was similar in all dogs. The change in strain in the posterior wall was always greater than that in the anterior wall. Opening the pericardium did not affect the difference in distensibility of the anterior and posterior walls. The results suggest that the posterior wall is more compliant than the anterior wall (that is, for a given difference in transmural pressure, the local segment length change of the posterior wall was greater). This seems consistent with other observations, which suggest that the posterior wall might make a greater contribution to diastolic filling.     

科尔沁沙地农田沙漠化演变中土壤颗粒分形特征

研究了科尔沁沙地农田沙漠化过程中土壤的粗粒化和养分的贫瘠化特征 ,土壤颗粒分形维数的变化特征 ,以及分形维数与土壤性状的关系。结果表明 :土壤沙粒含量越高 ,土壤分形维数越低 ,表征农田沙漠化程度越高 ;土壤颗粒分形维数与土壤有机 C、全 N、粘粉粒含量之间存在显著的线性关系。说明分形维数能很好地表征农田沙漠化演变中土壤结构和养分状况以及沙漠化的程度 ,可作为评价土壤沙漠化演变的一项综合性定量指标。     

川南天然常绿阔叶林人工更新后土壤团粒结构的分形特征

运用分形模型研究了川南天然常绿阔叶林及其人工更新成檫木(Sassafras tzumu)林、柳杉(Cryptomeria fortunei)林和水杉(Metasequoia glyptostroboides)林后土壤团粒结构,探讨了分形维数与林地土壤水源涵养功能、肥力特征和微生物数量之间的关系。结果表明:天然常绿阔叶林人工更新后土壤团粒结构的分形维数和结构体破坏率增大、土壤物理性质变差、养分含量和微生物数量降低,3种人工林中,檫木林较好、水杉林次之、柳杉林最差;土壤团聚体、水稳性团聚体和水稳性大团聚体含量越高分形维数越小;在湿筛条件下,土壤结构体破坏率随分形维数的降低而减小;土壤团粒结构的分形维数与土壤物理性质、养分含量和微生物数量之间存在显著的回归关系。这表明天然常绿阔叶林人工更新后由于不同林分对林地土壤组成结构的维护效果不同,导致更新后林地土壤物理、化学和生物性质变化,林地土壤团粒结构的变化,进而影响其分形维数的大小。因此,分形维数可作为天然常绿阔叶林及其人工更新后林地土壤水源涵养功能、肥力特征和微生物活动情况的一项综合性定量化评价指标。同时,为保护天然常绿阔叶林、选择适宜的更新树种和天然常绿阔叶林人工更新后林地土壤的科学管理提供依据,也为退耕还林中树种的选择提供参考。     

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

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

Temporal pattern of posterior positional identity in mouse limb buds

This study describes the temporal pattern of posterior positional identity in mouse limb bud cells. To do this wedges of tissue from the posterior edge of mouse limb buds at various stages (limb stages: Wanek et al., 1989b. J. Exp. Zool. 249, 41-49) were grafted to the anterior edge of a host chick embryo wing bud. Grafts of mouse posterior cells are able to induce the formation of supernumerary digits every time when they are taken from buds from stage 3 through stage 6. At stage 7, the frequency declines and by stage 8 the chick cells no longer respond. The results indicate a change in tissue properties at stage 7, which progresses by stage 8 to the point at which posterior positional identity is no longer detectable by this assay. These temporal changes in this aspect of limb pattern formation can be used as an additional criterion to guide the identification of genes involved in the specification of posterior positional identity.     

Visual discrimination of fractal borders.

The ideas of fractals and fractal dimension are here translated into the realm of visual psychophysics. Borders between two fields of different luminance were used. Because of the finite grain of the visual system, fractal dimension need be defined only within a certain size range. For a fractal dimension of 1.15, the just-detectable difference in fractal dimension was found to be about 0.0085, rising to about 0.015 for a fractal dimension of 1.25. Reducing exposure duration from 1 s to 0.33 s decreases sensitivity to differences in fractal dimension, but there was no gain in increasing the exposure duration. Good visual observers who are naive to the task require some training before reaching optimal performance. The ability to discriminate fractal dimension differs between fractal edges of the same fractal dimension that were generated with differing statistical programs. Even after considerable training, an observer makes 29% errors when asked to distinguish a fractal edge generated with a Gaussian random walk from one with a rectangular random walk. Gaussian random walk fractals can be more easily distinguished from Poissonian and Cauchy ones.     

Using fractal dimensions for characterizing tortuosity of animal trails

ABSTRACT. The tortuosity of mite trails was characterized by their fractal dimension, which is the non-Euclidean dimension varying between 1 (completely straight) and 2 (so tortuous that the complete two-dimensional space is used). This index was shown to be a good, discriminative index for mite trails, which is a completely new use of the fractal dimension. The value of this index is compared with other tortuosity indices.     

The Fractal Dimension as a Measure of the Quality of Habitats

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments ( Pinus sylvestris L. ) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, 'dimension-like' exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches.     

Use of the fractal dimension for the analysis of electroencephalographic time series

 Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. Received: 21 November 1996 / Accepted in revised form: 1 July 1997     

Chinese medicinal formula Guan-Xin-Er-Hao protects the heart against oxidative stress induced by acute ischemic myocardial injury in rats

Guan-Xin-Er-Hao (GXEH) is a Chinese medicine formula for treating ischemic heart diseases (IHD) and has a favorable effect. Our aim was to examine whether or not acute oral GXEH could protect the heart against myocardial infarction and apoptosis in acute myocardial ischemic rats. If so, we would explain the antioxidative mechanism involved. The left anterior descending coronary artery was occluded to induce myocardial ischemia in hearts of Sprague-Dawley rats. At the end of the 3 h ischemic period (or 24 h for infarct size), we measured the myocardial infarct size, myocardial apoptosis and the activities of antioxidative enzymes. GXEH reduced infarct size, myocardial apoptosis and the serum level of malondialdehyde (MDA), increased the activities of total antioxidant capacity (T-AOC), superoxide dismutase (SOD) and GSH-peroxidase (GPX) activities and the serum level of glutathione (GSH). GXEH exerts significant cardioprotective effects against acute ischemic myocardial injury in rats, likely through its antioxidation and antilipid peroxidative properties, and thus may be used as a promising agent for both prophylaxis and treatment of IHD.     

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean D_b = 1.45) with respect to their 2‐D coiled counterparts (mean D_b = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.     

Fractal dimension of the middle meningeal vessels: variation and evolution in Homo erectus, Neanderthals, and modern humans

The middle meningeal vascular network leaves its traces on the endocranial surface because of the tight relationship between neurocranial development and brain growth. Analysing the endocast of fossil specimens, it is therefore possible to describe the morphology of these structures, leading inferences on the cerebral physiology and metabolism in extinct human groups. In this paper, general features of the meningeal vascular traces are described for specimens included in the Homo erectus, Homo neanderthalensis, and Homo sapiens hypodigms. The complexity of the arterial network is quantified by its fractal dimension, calculated through the box-counting method. Modern humans show significant differences from the other two taxa because of the anterior vascular dominance and the larger fractal dimension. Neither the fractal dimension nor the anterior development are merely associated with cranial size increase. Considering the differences between Neanderthals and modern humans, these results may be interpreted in terms of phylogeny, cerebral functions, or cranial structural network.