AN “ASYMPTOTIC FRACTAL” APPROACH TO THE MORPHOLOGY OF MALIGNANT CELL NUCLEI

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 326-335 ◽  
Author(s):  
GABRIEL LANDINI ◽  
JOHN W. RIPPIN
Keyword(s):  
Fractal Dimension ◽  
Oral Cancer ◽  
Malignant Cell ◽  
Computer Memory ◽  
Cell Nuclei ◽  
Topological Dimension ◽  
Fractal Approach ◽  
Linear Discrimination ◽  
Boundary Length ◽  
Transmission Electron

To investigate quantitatively nuclear membrane irregularity, 672 nuclei from 10 cases of oral cancer (squamous cell carcinoma) and normal cells from oral mucosa were studied in transmission electron micrographs. The nuclei were photographed at ×1400 magnification and transferred to computer memory (1 pixel=35 nm). The perimeter of the profiles was analysed using the “yardstick method” of fractal dimension estimation, and the log-log plot of ruler size vs. boundary length demonstrated that there exists a significant effect of resolution on length measurement. However, this effect seems to disappear at higher resolutions. As this observation is compatible with the concept of asymptotic fractal, we estimated the parameters c, L and Bm from the asymptotic fractal formula Br=Bm {1+(r/L)c}−1, where Br is the boundary length measured with a ruler of size r, Bm is the maximum boundary for r→0, L is a constant, and c=asymptotic fractal dimension minus topological dimension (D−Dt) for r→∞. Analyses of variance showed c to be significantly higher in the normal than malignant cases (P<0.001), but log(L) and Bm to be significantly higher in the malignant cases (P<0.001). A multivariate linear discrimination analysis on c, log(L) and Bm re-classified 76.6% of the cells correctly (84.8% of the normal and 67.5% of the tumor). Furthermore, this shows that asymptotic fractal analysis applied to nuclear profiles has great potential for shape quantification in diagnosis of oral cancer.

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton 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.

scholarly journals Visualization of Chromatin in the Yeast Nucleus and Nucleolus Using Hyperosmotic Shock

2021 ◽  
Vol 22 (3) ◽  
pp. 1132
Author(s):  
Nicolas Thelen ◽  
Jean Defourny ◽  
Denis L. J. Lafontaine ◽  
Marc Thiry
Keyword(s):  
Osmotic Shock ◽  
Size Composition ◽  
Yeast Cells ◽  
Exponential Growth Phase ◽  
Cell Nuclei ◽  
Hyperosmotic Shock ◽  
Christmas Trees ◽  
Transmission Electron ◽  
Active Transcription ◽  
Decondensed Chromatin

Unlike in most eukaryotic cells, the genetic information of budding yeast in the exponential growth phase is only present in the form of decondensed chromatin, a configuration that does not allow its visualization in cell nuclei conventionally prepared for transmission electron microscopy. In this work, we studied the distribution of chromatin and its relationships to the nucleolus using different cytochemical and immunocytological approaches applied to yeast cells subjected to hyperosmotic shock. Our results show that osmotic shock induces the formation of heterochromatin patches in the nucleoplasm and intranucleolar regions of the yeast nucleus. In the nucleolus, we further revealed the presence of osmotic shock-resistant DNA in the fibrillar cords which, in places, take on a pinnate appearance reminiscent of ribosomal genes in active transcription as observed after molecular spreading (“Christmas trees”). We also identified chromatin-associated granules whose size, composition and behaviour after osmotic shock are reminiscent of that of mammalian perichromatin granules. Altogether, these data reveal that it is possible to visualize heterochromatin in yeast and suggest that the yeast nucleus displays a less-effective compartmentalized organization than that of mammals.

scholarly journals Scope of Conventional and Fractal Morphometry in Oral Potentially Malignant Disorders and Oral Cancer

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Paresh Kumar Behera ◽  
Diksha Mohapatra
Keyword(s):  
Image Analysis ◽  
Fractal Dimension ◽  
Oral Cancer ◽  
World Health ◽  
Oral Potentially Malignant Disorders ◽  
Potentially Malignant Disorders ◽  
Risk Of Malignancy ◽  
Potentially Malignant ◽  
Health Organization

World Health Organization (WHO) defined the terminology ‘Oral Potentially malignant disorders’ (OPMD) as the presence of risk of malignancy in a lesion or condition either during the time of initial diagnosis or at a future date with the commonly accepted prevalence of 1–5%. All OPMDs may not transform into malignancy, many factors have been explored which effectively assess the risk of malignant transformation in OPMDs including many clinical, pathological and molecular factors. Qualitative & experimental factors of different cells in cytological preparations and/or biopsy specimens are reliable parameters for pathologists. The analysis and assessment of histological units can be enhanced by image analysis assisted by a computer that can be used for statistical comparisons. Fractal geometry is considered to be an ideal method of image analysis in quantitative microscopy & histopathology. Fractal dimension analysis is not only limited to determining cell and tumour types but can also be used for determining cellular behaviours in vitro such as cell migration, apoptosis and cellular differentiation, which can be a useful characterization of oral cancer lines and further help in the treatment planning. Keywords: Oral Cancer, Oral Potentially Malignant Disorders (OPMDs), Conventional morphometry, Fractal Dimension, Photomicrograph

scholarly journals Analisis Dimensi Fraktal Kejadian Gempa Dl Laut Banda Indonesia

2016 ◽  
Vol 19 (2) ◽  
pp. 108
Author(s):  
Sugeng Widada
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Approach ◽  
Study Support ◽  
Tectonic System

The Banda Sea region is an active earthquakes area which indicated by mean monthly incident of quakes more than 220. The condition is caused the area being located in the triple jucntion. Earthquakes system in this region which occur during September 2015 up to October 2016 is analyzed by fractal approach to investigate the subduction system.Earthquakes system is chaotic, so can be quantified using fractal concept. Quantify result of Banda Sea earthquakes system using Aki method is fractal dimension 2.08. It indicates that the slab was fractured by some fault in form an angle or upright possition with the subduction strike. Such a thing also be proven by the fact that the length zone of slab moved during each earthquake is not same, the variation is about 6 – 1,056 m. Based on the fractal analysis, also be identified that about 6.25 magnitute six earthquakes are expected each year. The result of study support the previous studies which propose that the tectonic system in Banda Sea region is very complex. Keywards:  Earthuakes system, fractal, Banda Sea Kawasan Laut Banda merupakan daerah aktif gempa yang ditunjukan dengan kejadian gempa rata-rata bulanan Iebih dan 220. Keadaan ini dapat dimengerti mengingat kawasan tersebut merupakan pertemuan tiga buah lempeng yang bergerak. Pola kegempaan di daerah tesebut yang tejadi pada September 2015 hingga Oktober 2016 dicoba dianalisa menggunakan pendekatan fraktal untuk mengetahui pola subduksi di daerah tersebut. Pola kegempaan merupakan suatu kejadian yang chaos, sehingga dapat dilakukan kuantisasi berdasarkan konsep fraktal. Hasil kuantisasi pola gempa Laut Banda meggunakan metode Aki diperoleh dimensi fraktal 2,08. Hal ini menunjukan bahwa slab yang menunjam dan bergerak sehingga menimbulkan gempa terbagi dalarn beberapa bagian melalui suatu sesar yang menyududut / tegak lurus jurus subduksi. Keadaan ini dikuatkan oleh hasil perhitungan panjang daerah yang bergerak untuk setiap kejadian gempa tidak sama, yaitu bervariasi dari 6 – 1.056 m. Berdasarkan analisa fraktal tersebut juga diketahui bahwa gempa dengan magnitudo 6,25 akan terjadi 6 kali dalam satu tahun. Hasil penelitian ini mendukung hasil penelitian terdahulu yang menyatakan bahwa tatanan tektonik di daerah Laut Banda sangat kompleks. Kata Kunci: Pole gempa, fraktal, Laut Banda

Fractal Approach on Quantitative Analysis of Micro Pore Structure of Isotropic Consolidated Clay

2011 ◽  
Vol 250-253 ◽  
pp. 1846-1851
Author(s):  
Xiao Xuan Liu ◽  
Ji Ru Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Soil Consolidation ◽  
Koch Curve ◽  
Sem Images ◽  
Fractal Approach ◽  
Consolidation Pressure ◽  
Size Number ◽  
Isotropic Consolidation

The micro pore structure of isotropic consolidated clay was studied by using a scanning electron microscope (SEM). A digital imaging technique was applied to analyze the evolution of size, number of pores and their distributions in the process of isotropic consolidation according to the SEM images. Based on the fractal concepts of Koch curve and Sierpinski carpet, the Koch fractal dimension Dk and the Sierpinski fractal dimensionDsof soil pores are obtained from the measured data. The variations of bothDkandDsfollowing the change of micro pore parameters and mechanical properties of clay are investigated. The results show that the porosity and pore size decreases as the consolidation pressure increases, and the range of pore size becomes narrower.Dkreflects the degree of irregularity of the pore-solid interface in soil, and the larger theDkthe more irregular the soil pore profile. The distribution of Dkwas found in agreement with a total normal distribution in soil pore. The magnitude ofDsreflects the variation of porosity of clay under isotropic consolidation. Large fractal corresponds to large consolidation pressure and small porosity.Dsdisplays a significant linear regression relationship with porosity, consolidation pressure, consolidation deformation of clay and an exponential growth relationship with permeability coefficient of clay. Both Dk andDsis sensitive to isotropic consolidation of soil and they may be cited as useful indicators for soil consolidation.

scholarly journals From the slit-island method to the Ising model: Analysis of irregular grayscale objects

2014 ◽  
Vol 24 (1) ◽  
pp. 49-63 ◽  
Author(s):  
Przemysław Mazurek ◽  
Dorota Oszutowsk A-M Ażurek
Keyword(s):  
Image Analysis ◽  
Fractal Dimension ◽  
Ising Model ◽  
Image Data ◽  
Input Image ◽  
Cell Nuclei ◽  
Cervical Cell ◽  
Atypical Cells ◽  
Model Context ◽  
Slit Island Method

Abstract The Slit Island Method (SIM) is a technique for the estimation of the fractal dimension of an object by determining the area- perimeter relations for successive slits. The SIM could be applied for image analysis of irregular grayscale objects and their classification using the fractal dimension. It is known that this technique is not functional in some cases. It is emphasized in this paper that for specific objects a negative or an infinite fractal dimension could be obtained. The transformation of the input image data from unipolar to bipolar gives a possibility of reformulated image analysis using the Ising model context. The polynomial approximation of the obtained area-perimeter curve allows object classification. The proposed technique is applied to the images of cervical cell nuclei (Papanicolaou smears) for the preclassification of the correct and atypical cells.

scholarly journals The Use of Fractal Features from the Periphery of Cell Nuclei as a Classification Tool

1999 ◽  
Vol 19 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Birgitte Nielsen ◽  
Fritz Albregtsen ◽  
Håvard E. Danielsen
Keyword(s):  
Normal Liver ◽  
Analysis Tool ◽  
Cell Nuclei ◽  
Bhattacharyya Distance ◽  
Prior Probabilities ◽  
Hepatocellular Carcinomas ◽  
Transmission Electron ◽  
Mouse Liver Cell ◽  
A Cell ◽  
Classification Tool

A polygonization‐based method is used to estimate the fractal dimension and several new scalar lacunarity features from digitized transmission electron micrographs (TEM) of mouse liver cell nuclei. The fractal features have been estimated in different segments of 1D curves obtained by scanning the 2D cell nuclei in a spiral‐like fashion called “peel‐off scanning”. This is a venue to separate estimates of fractal features in the center and periphery of a cell nucleus. Our aim was to see if a small set of fractal features could discriminate between samples from normal liver, hyperplastic nodules and hepatocellular carcinomas. The Bhattacharyya distance was used to evaluate the features. Bayesian classification with pooled covariance matrix and equal prior probabilities was used as the rule for classification. Several single fractal features estimated from the periphery of the cell nuclei discriminated samples from the hyperplastic nodules and hepatocellular carcinomas from normal ones. The outer 25–30% of the cell nuclei contained important texture information about the differences between the classes. The polygonization‐based method was also used as an analysis tool to relate the differences between the classes to differences in the chromatin structure.

scholarly journals Organization of Highly Acetylated Chromatin around Sites of Heterogeneous Nuclear RNA Accumulation

1998 ◽  
Vol 9 (9) ◽  
pp. 2491-2507 ◽  
Author(s):  
Michael J. Hendzel ◽  
Michael J. Kruhlak ◽  
David P. Bazett-Jones
Keyword(s):  
Histone Deacetylases ◽  
Active Regions ◽  
Fibroblast Cell ◽  
Cell Nuclei ◽  
Transmission Electron ◽  
Interchromatin Granule ◽  
Nuclear Rna ◽  
Interchromatin Granules ◽  
The Individual ◽  
Rna Accumulation

Histones found within transcriptionally competent and active regions of the genome are highly acetylated. Moreover, these highly acetylated histones have very short half-lives. Thus, both histone acetyltransferases and histone deacetylases must enrich within or near these euchromatic regions of the interphase chromatids. Using an antibody specific for highly acetylated histone H3, we have investigated the organization of transcriptionally active and competent chromatin as well as nuclear histone acetyltransferase and deacetylase activities. We observe an exclusion of highly acetylated chromatin around the periphery of the nucleus and an enrichment near interchromatin granule clusters (IGCs). The highly acetylated chromatin is found in foci that may reflect the organization of highly acetylated chromatin into “chromonema” fibers. Transmission electron microscopy of Indian muntjac fibroblast cell nuclei indicates that the chromatin associated with the periphery of IGCs remains relatively condensed, most commonly found in domains containing chromatin folded beyond 30 nm. Using electron spectroscopic imaging, we demonstrate that IGCs are clusters of ribonucleoprotein particles. The individual granules comprise RNA-rich fibrils or globular regions that fold into individual granules. Quantitative analysis of individual granules indicates that they contain variable amounts of RNA estimated between 1.5 and >10 kb. We propose that interchromatin granules are heterogeneous nuclear RNA-containing particles, some of which may be pre-mRNA generated by nearby transcribed chromatin. An intermediary zone between the IGC and surrounding chromatin is described that contains factors with the potential to provide specificity to the localization of sequences near IGCs.

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