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.     

Neuronal Morphology: Shape Characteristics and Models

This paper is focused on quantification (morphometry) and modeling of neuronal morphological complexity. First, computer-aided methods for reconstruction, processing, and analysis of raw morphological data are reviewed. Then, topological and metrical measures are touched upon. Fractal measures (together with the extension of multiscale fractal dimension) are presented more explicitly. Models of neuronal arborizations are differentiated between reconstruction models and growth models (stochastic or mechanistic). The growth model approach is discussed in more detail. The methods presented are applied to several types of neurons and shown to have considerable discriminative power. Recent developments stress the importance of these methods for optimizing virtual neuronal trees in view of functional characteristics of the neurons. Neirofiziologiya/Neurophysiology, Vol. 40, No. 4, pp. 366–372, July–August, 2008.     

The ultrastructure of the central nervous system neurons and synapses in the edible snail under a high concentration of potassium ions]

The morphometric and electron microscopic results on neuronal and synaptic ultrastructure of central nervous system of Helix pomatia snail, incubated in vitro in media with high potassium ion concentration are represented in the present paper. The activation of glial cells is revealed with its close attachment to neurons. The energization of neuronal mitochondria and signs of cytoplasmatic oedema are clearly visible. The penetration of glial endings in the large neuronal branches and the synaptic vesicles confluence in neuronal endings are found.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

北京东灵山地区辽东栎林种群空间分布分形分析

通过植物个体的坐标点与模拟冠幅的分形维数的分析,对辽东栎林内不同种群沿海拔梯度变化的空间分布格局和种群动态进行了比较和讨论。结果表明:模拟冠幅分形分析方法更适于分析具有大小不等、复杂多样的冠幅的植物个体空间分布格局。随着海拔的升高,不同种群的空间占据能力也随之变化。辽东栎种群的空间分布占绝对优势地位,分形维数可达1.9811;五角枫种群则逐步下降,分形维数最低为0.1170。低海拔山坡六道木种群空间占据能力较强,高海拔山坡照山白种群有较大的空间占据能力。在一定的环境条件下,不同的种群可能具有相近的空间占据能力,但对乔木层与灌木层来说,相同的分形维数的内涵是不同的。冠幅的分形维数作为表征植物种群空间占据能力的工具,是种群动态分析和种群分布格局研究的的重要指标之一。     

红树植物木榄幼树斑块形状的分形分析

应用分形理论分析了山口国家级红树林自然保护区木榄幼树斑块形状的分形特征。木榄幼树斑块在整体水平上的分形维数为 1 .1 2 ,而单个斑块的分形维数介于 1 .1 7～ 1 .3 7之间。分形维数的大小与斑块形状的复杂程度密切相关。频谱法和周长 -面积法都适用于分析幼树斑块形状的分形特征。     

异质景观条件下江汉平原土壤的空间分异

景观异质与土壤分异息息相关。以DEM数据为基础,以海拔50m、100m为界,将江汉平原划分为平原湖区景观、平缓岗地景观及起伏丘陵景观3种类型。在ArcG IS 10支持下,将江汉平原土壤图与景观类型图进行叠置分析,提取不同景观类型片区各土壤亚类斑块周长、面积等信息,计算了各景观类型片区各土壤亚类的分维数、平均斑块面积、稳定度等信息,定量分析了江汉平原各景观类型片区土壤空间分异特征,结论如下:(1)不同景观类型区各土壤亚类分布差异明显,起伏丘陵景观区主要以红壤和黄棕壤地带性土壤为主;平原湖区潮土和水稻土等耕作土非常发育;平缓岗地区地带性土壤和耕作土壤平分秋色。(2)连片性较好的土壤亚类呈现不同的景观选择性:耕作土集中分布于平原湖区景观片区;地带性土壤多集中分布于丘陵和岗地景观片区。(3)平原湖区面积很大,各类土壤都有发育的空间,土壤亚类之间分维数和稳定度差别比较大;平缓岗地景观区由于面积非常局限,土壤亚类发生发育受到空间的限制,边界破碎化,分维数平均都比较大,斑块镶嵌结构均比较复杂,稳定度差别较小。(4)主要土壤亚类的分维数和稳定性指数值一定程度地反映了各主要土壤亚类的最匹配的景观类型,即能够提供其发生发育的最佳条件。研究有利于深入认识土壤形成和演化规律,为土壤资源的合理利用及定向培育服务。     

高寒草地甘肃臭草根系分形结构的坡向差异性

根系分形结构是植物根系构型应对环境异质性的表型可塑性结果, 可反映植物对生长环境的适应策略。利用ArcGIS建立研究区域的数字高程模型, 并提取坡向数据, 采用全根挖掘和Win-RHIZO根系分析仪相结合的方法, 研究了祁连山北坡高寒退化草地不同坡向甘肃臭草(Melica przewalskyi)的根系分形结构。结果表明: 随着坡向由北坡向东坡、西坡、南坡转变, 草地群落的密度、高度和土壤含水量逐渐减小, 甘肃臭草种群的密度、高度以及根系分形丰度呈逐渐增大的趋势、分形维数逐渐减小; 不同坡向甘肃臭草根系分形维数和分形丰度间的相关性存在差异(p < 0.05), 南坡和北坡甘肃臭草根系分形维数分形丰度之间存在极显著负相关关系(p < 0.01), 东坡和西坡之间存在显著负相关关系(p < 0.05), 甘肃臭草根系分形维数和分形丰度存在着“此消彼长”的权衡关系; 随着坡向由北坡向东坡、西坡、南坡转变, 甘肃臭草根系分形维数和分形丰度回归方程的标准化主轴(SMA)斜率逐渐增大(p < 0.05), 说明在干旱的南坡, 根系所开发利用的相同体积的土壤内, 根系分支更少、更稀疏。不同坡向甘肃臭草合理权衡根系分形维数和分形丰度的资源配置模式, 体现了植物根系构型构建的资源投资权衡机制。     

泾河流域分县景观格局特征及相关性

景观生态主要是研究生态系统的空间格局。因而很有必要对空间格局进行数量化的分析,在此基础上进行科学管理。应用斑块数、斑块面积、斑块密度、优势度、聚集度和分维数计算了泾河流域31个县景观格局的特征,首次以景观特征值为基础,将研究区域各县景观进行分类,并对不同类型的景观特征及相关性进行分析。结果表明,近年来流域破碎化程度有所增加,各景观指数值在研究区域之间变异很大。优势度和聚集度比较高的区域土地利用较单一,常常是以农用地为主导如咸阳、泾阳和乾县,或以农地和草地共同主导如环县。而优势度和聚集度较低的区域,土地利用较多样化,农地、林地和草地面积比例相近,如泾源、平凉、陇县、宁县和旬邑,这些县位于黄土丘陵沟壑区和黄土高塬沟壑区。高优势度、高聚集度和低分维数的区域为陕西省咸阳市,为泾河流域冲积平原区,土地利用以大面积的农用地为主导。景观指数的相关分析表明,3种主要的土地利用面积比例之间存在极显著负相关,林地面积和优势度、聚集度有极显著负相关,而草地面积和分维数存在极显著正相关,分维数高的县位于泾河流域中游的黄土高原沟壑区,分维数低的县位于下游河谷阶地和关中平原和黄土高原交界处。这种相关性表明了自然地貌及人类活动对景观的影响和干扰作用。     

基于RS和GIS的开封市土地覆盖分形

以RS和GIS为技术手段,利用开封市0.61m空间分辨率的QuickBird卫星遥感数据,采用分形几何方法研究了斑块的面积效应和覆盖类型分形的关系,并对覆盖类型的分形特征差异等进行了分析。结果表明,开封市防护林地和农田的平均斑块面积较大,分维数也较大,而水体的分维数较小,说明防护林和农田斑块的边界结构特征比水体更为复杂。斑块的分维值具有尺度依赖性,同一类型中大的斑块往往具有较大的分维值,其原因是大斑块经常出现不同类型的斑块相互嵌套,小斑块则很少出现甚至不出现这种现象。     

Fractal root system of Melica przewalskyi along different aspect in degraded grassland

Aims Fractal root system is phenotypic plasticity result of plant root architecture to respond to environmental heterogeneity, may reflect the growth strategy of plants to adapt to environmental conditions. Our objective was to explore the relationship between root fractal dimension and fractal abundance of fractal root system of Melica przewalskyi population in response to aspect variation in the northwest of China. Methods The study site was located in a degraded alpine grassland on the northern slope in Qilian Mountains, Gansu Province, China. Survey and sampling were carried out at 40 plots which were set up along four slope aspects transects with 20 m distance between adjacent plots. Handheld GPS was used to determine the elevation, longitude and latitude of each plot. ArcGIS was used to set up digital elevation model (DEM). Community traits were investigated and six individuals roots of M. przewalskyi were collected randomly at each plot. The samples were cleaned and divided into different organs, then scanning the root with the Win-RHIZO for measurements of fractal dimension and fractal abundance in laboratory, and their biomass were then measured after being dried at 80 °C in an oven. Important findings With the slope aspect turned from north to east, west, and south, the density, height and soil moisture content of the plant community displayed a pattern of initial decline, the height, density, root fractal abundance of M. przewalskyi increased and the root fractal dimension decreased. The root fractal dimension was negatively associated with the fractal abundance in all aspects, but the relationship varied along the slope aspects gradient; there was a highly significant negative correlation (p < 0.01) between the root fractal dimension and fractal abundance at north slope and south slope aspect, whereas the correlation only reached a significant level (p < 0.05) at the east slope aspect and west slope aspect; indicating that there is a trade-off between the root fractal dimension and fractal abundance. In addition, when the slope aspect changed from north to east, west and south, the standardized major axis (SMA) slope of the regression equation in the scaling relationships between root fractal dimension and fractal abundance increased (p < 0.05), indicating that the roots of M. przewalskyi at the droughty southern slope have less branch and more sparse in the same soil volume of root exploitation and utilization. Consequently, the resource allocation pattern on reasonable trade-off between root fractal dimension and fractal abundance in different slope aspect of M. przewalskyi, reflects the relationship between the income and the cost of construction of plant root architecture.     

Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method

The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.     

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。     

Fractal dimension of antibody‐PEG precipitate: Light microscopy for the reconstruction of 3D precipitate structures

Protein and in particular antibody precipitation by PEG is a cost‐effective alternative for the first capture step. The 3D structure of precipitates has a large impact on the process parameters for the recovery and dissolution, but current technologies for determination of precipitate structures are either very time consuming (cryo‐TEM) or only generate an average fractal dimension (light scattering). We developed a light microscopy based reconstruction of 3D structures of individual particles with a resolution of 0.1–0.2 µm and used this method to characterize particle populations generated by batch as well as continuous precipitation in different shear stress environments. The resulting precipitate structures show a broad distribution in terms of fractal dimension. While the average fractal dimension is significantly different for batch and continuous precipitation, the distribution is broad and samples overlap significantly. The precipitate flocs were monofractal from micro‐ to nanoscale showing a random but consistent nature of precipitate formation. We showed that the fractal dimension and 3D reconstruction is a valuable tool for characterization of protein precipitate processes. The current switch from batch to continuous manufacturing has to take the 3D structure and population of different protein precipitates into account in their design, engineering, and scale up.     

The nonlinear parameters of interference EMG of two day old human newborns

Temporal structure of interference electromyogram (iEMG) was studied in healthy two days old human newborns (n = 76) using the non-linear parameters (correlation dimension, fractal dimension, correlation entropy). It has been found that the non-linear parameters of iEMG were time-dependent because they were decreasing within the first two days of life. Also, these parameters were sensitive to muscle function, because correlation dimension, fractal dimension, and correlation entropy of iEMG in gastrocnemius muscle differed from the other muscles. The non-linear parameters were proven to be independent of the iEMG amplitude. That model of early ontogenesis may be of potential use for investigation of anti-gravitation activity.     

Intraspecific,size-dependent variation in the movement behaviour of a brackish-water isopod: a resource-free laboratory experiment

Intraspecific variability represents an important, yet inadequately investigated factor affecting the movement behaviour and ecology of mobile organisms. Here, the influence of sex, seasonality and body size on the movement behaviour of the brackish isopod Lekanesphaera hookeri were examined under resource-free laboratory conditions. The mean step length, total path length and average speed were determined twice during the year for adult and juvenile isopods encompassing a 10-fold range in body length. The scale-independent fractal dimension D was used to quantify the tortuosity of the movement paths. No relationships were observed between sex or season and all the movement metrics. In contrast, isopods' body size scaled negatively with the fractal dimension D of movement paths with a breakpoint at 2.6 mm, roughly corresponding to the size of morphometric maturation. No other relationships were observed between the body length of isopods and mean step length, total path length and average speed. The results indicate a sex- and season-independent ontogenetic shift in movement behaviour in L. hookeri. This suggests that in sphaeromatid isopods post-embryonic development determines not only continuous variations in size and proportions, but also a discontinuous change in the movement strategy adopted to interact with the surrounding space. Overall, these findings underscore the need to account explicitly for such changes in models predicting the spatial distribution of organisms characterised by wide intra-population size variation.     

Fractal analysis of the Orce skull sutures

Methods of fractal geometry (Mandelbrot, 1983) are used here to analyse the relative complexity of the sagittal and lambdoid sutures visible in the skull fragment formed by parts of an occipital squame and parietals found in a sealed deposit at the early Lower Pleistocene site of Venta Micena (Orce, Granada, Spain), generally regarded as human bone but occasionally suggested as belonging to an equid. For comparison with the fossil, corresponding sutures of various primates (hominids, pongids and cercopithecids) and two other groups of mammals (equids and ruminants) were analysed using the computer program FRACTAL-D (Slice, 1989) in order to determine their fractal dimensions as a measure of differential sutural design complexity. The results show that the fractal dimension of the Venta Micena skull sutures lies within the range of variation for infant specimens of both modern and Plio-Pleistocene hominids. Sutural complexity in young pongids and cercopithecids overlaps the range of fractal dimensions found in hominids, whereas values obtained from equids and ruminants are significantly greater than those for all the primates analysed here. Therefore, in terms of fractal dimension measures of relative complexity, the sutures preserved in the Venta Micena fossil could not have belonged to an equid (pace Agusti & Moyà-Sola, 1987); rather, its fractal dimension is consistent with the attribution of the fossil to an infant of Homo sp.     

褐飞虱(Nilaparvata lugens)发生的分形性质研究

运用分形理论以安徽省庐江县植保站和江苏省吴县值保站1979～1990年及太湖地区农科所1986～1998年间褐飞虱发生的田间系统调查资料为例,对褐飞虱发生的性质进行了探讨。结果表明：(1)庐江站、吴县站和太湖地区农科所褐飞虱发生在一定标度域内具有分形性质。其分维值分别为0．7158、0．52l2和0．2816;(2)褐飞虱发生的分维值是表征一定标度区间的发生程度差异的一个新的参数,分维值大,则发生程度轻,反之则重(3)分维数D值与褐飞虱发生的聚集程度是密切相关的,D值小聚集程度大,反之聚集程度小,D值可以作为褐E虱聚集分布程度的一个指标;(4)褐飞虱发生具有多重分形结构,其广义维数谱Dq曲线可以用于褐飞虱发生的预测预报。     

不同光照条件下假俭草生长格局的分形研究

应用分形几何的原理和方法,研究不同光照条件下假俭草的生长格局。结果表明,假俭草具有自相似性的生长过程。不同光照条件下,假俭草具有不同的分形维数和相应的生物量积累规律。生物量积累速率随着分形维数的增大而增大。分形维数同时反映了假俭草的分枝能力和对空间的占据能力。假俭草种群具有依据外界条件而调节生长格局的生态适应能力。     

山东泰山地区景观结构变化及其分形分析

将泰山风景区划分为 8个区域 11个基本景观类型 ,包括松林、栎林、刺槐林、侧柏林、针阔叶混交林、经济林、灌丛、裸岩、荒地、水体、建筑。在此基础上 ,利用 3S技术和分形理论对各个景观要素进行了分析 ,并讨论了景观特性及其变化的分形性质。结果表明 :(1)分维值的大小反映了景观斑块面积、斑块数量和平均斑块面积等因素的相互作用 ,在一定尺度下分维的大小反映了区域内景观斑块的不规则程度和复杂程度 ,斑块越不规则、越复杂 ,其分维越大 ,反之亦然。在泰山地区 ,自 1986年至 2 0 0 1年 ,刺槐林一直保持着较高的分维值 ,其它景观类型的分维值则差别不大 ,而针阔叶混交林的分维值变化较大 ;(2 )森林景观受多种因子的影响 ,在高海拔区域主要受垂直地带性规律影响为主 ,在旅游区主要受人类活动的影响为主 ,15 a来各个区域分形维数的总体变化趋势相似 ;(3)大部分区域在 2 0 0 1年的景观多样性、破碎度高于 1986年的 ,而景观优势度则略为下降