@2024 Afarand., IRAN
ISSN: 2251-8215 Sarem Journal of Reproductive Medicine 2017;1(1):3-8
ISSN: 2251-8215 Sarem Journal of Reproductive Medicine 2017;1(1):3-8
Physical Structure Study of Bone Marrow Regarding Fractal Model and Diffusion Limited Growth Phenomenon
ARTICLE INFO
Article Type
Original ResearchAuthors
Salehian P. (*)Mohaghegh A. (1)
Khosravi M. (1)
(*) Sarem Cell Research Center (SCRC), Sarem Women’s Hospital, Tehran, Iran
(1) Medicine Department, Medicine Faculty, Tehran University of Medical Sciences, Tehran, Iran
Correspondence
Article History
Received: August 28, 2015Accepted: January 9, 2016
ePublished: February 15, 2017
BRIEF TEXT
Scientists have long been thinking of defining a mathematical model for natural objects; in 1979, a German scientist, Benoit Mandelbrot, solved this problem by defining a non- Euclidean geometry called fractal geometry. Indeed, using this kind of non-Euclidean geometry, it is possible to mathematically define structures such as trees, snow crystals, and galactic clusters that are morphologically non-compliant with Euclidean geometry [1].
… [2]. Fractals are objects or phenomena that dispersion of each of its component is equal to total dispersion. The dispersion of components in a building or fractal phenomenon follows the formula N=KrDf, in which N is the number of the components, R is the radius of the sphere or circle that limits those components. K is the constant number and Df is the fractional coefficient of that object. Df represents any fractal object, which means that with the help of Df, the dispersion of the components of the object can be calculated and predict its geometric shape. In recent years, in medical sciences like other sciences such as physics and chemistry, fractal geometry has been used to define the physical structure of body components. Examples of these studies can be found in the study of blood vessel structures [3] or the diffusion of brain neurons [4]. Also, these studies have been used to determine the pathological pattern of various lesions. For example, to interpret the dispersion of pigmented skin lesions [5], abnormal chest image in interstitial lung tissue diseases (ILD) [6] and the interpretation of Pap smear [7], fractal geometry has been used and numerous other examples have been recorded in various journals. The structure of bone marrow protects the three-dimensional structure and contrasts the various components of bone marrow. These conflicts are controlled by complex mechanisms, which result in the creation of multiplicative patterns and averages that we call them the Normal Range [8]. …various growth factors such as lymphokines, cytokines, growth factors and their receptors along with complex molecules, such as integrins, play an essential role in the evolution and development of bone marrow cells [9] and produce a number of specific structures that in morphology they appear to be formed of “repetitive units” [10]. These units have placed between fatty spaces, and when geometric dimensions and geometric structure relationship are protected, it controls the release of adult cells. The important thing about the fractal factor is that the fractal factor of the numerical biological structure is between 1.6-1.7 (because the fractal factor in growth phenomena is limited to propagation of 1.6-1.7).
The purpose of this study was to investigate the physical structure of bone marrow based on mathematical model of fractals and growth-limited phenomena of propagation.
31 slides of bone marrow patients were selected from the archives of pathological samples of Pathology Department of Rasoul-e-Akram Hospital from October 1991 to October 1996. The samples were all from the lilac Crest area of the patients, and they were related to patients who had been referred to the center for the study of anemia of thrombocytopenia, leukemia, multiple myeloma, or metastatic tumors (before or after treatment).
Out of 31 selected samples, 21 were from males and 10 were from females. The average age was 50 years (from 18 to 75 years old) and the length of each sample was about 1 to 2 cm. and they had been dehydrated and paraffin embedded with routine fixation and decalcified processes. The samples were cut to 3-5 micrometer in diameter and stained with haematoxylin and eosin.
The samples were examined under a light microscope as well as bone marrow diseases. All of the slides entered the study were morphologically normal and no abnormal building or disease process was observed. To capture the morphology of the samples with a magnification of 20, a computer shot was captured by a Cas 200 device. A random image was taken from each slide in four different regions, and in all images, a cell group (not fat) was placed in the center of the image. A total of 31 bone marrow samples and 124 microscopic images were analyzed by Image Cytometry using the Image Pro Plus software. In each image, eight circular concentric circles were analyzed. Each circle had twice the surface of tis inner circle. At each circular surface, the overall cell structure was measured (its size was obtained by subtracting the entire surface of the circle from the fat level) and the total surface of cell nuclei was also analyzed. In addition, 9 samples of 36 microscopic images, which were selected randomly from 31 samples, were printed and they were investigated with four concentric circular circuits in the number of cores. Therefore, three different, but at the same time, related parameters were analyzed in terms of the shape and dimension of the fractal: 1) total surface cell (total surface area of the bone marrow from the fat level); 2) the surface of nucleus, and 3) the number of bone marrow cells (number of nucleus). If x represents the Sn pattern of the bone marrow from the fractal dimensions with the fractal factor Df, then for each radius of the circle r, the formula X ~ rDf will be applied. Therefore, Df is obtained from the slope of the log regression line Log r-Log X. The inner radius of the circle was 7.57 micrometers (equivalent to 377 pixels). To calculate the regression line angle coefficient, Excel 5 software was used. All statistical calculations and comparisons (T test) were performed using SPSS 7 software.
Based on the three analyzed parameters, the special structure of fractal bone marrow cells are shown (Fig. 1; a to c). The mean cellularity in 124 microscopic image was 55.51±22.00 %. In order to reject any errors in the calculation of the mean fractal coefficient, the fractal coefficient for the five concentric circle surface was also recalculated. The results of this study did not show significant difference with the results of the main study (p<0.05). The finding showed that if the larger circular surface was used in the study, the results did not show a significant difference with the current result. The results of this study were compared with the results of the study by Naeem et al. [11] by the t-test, which did not show a significant difference (p<0.05; Table 3).
… [12-14].In this study, the bone marrow biopsy under light microscope forms a two dimensional system. In this system, the total fractional coefficient (for cellularity 40-60%) is calculated to be DfMean=1.68±0.13 which is coordinated with the fractal coefficient derived from the growth phenomena. … [15]. In this study, the bone marrow adheres to a fractal pattern and the fact that its fractal coefficient is unmatched by similar amounts in limited growth phenomena indicates that the spatial structure of the hematopoietic cells within the bone marrow is dependent on the release of regulatory cytokines in the environment. If the mechanism for creating a three-dimensional bone marrow structure in healthy people follows a pattern of growth factors limited to spread, the 3D-strucutre of the bone marrow will have a fractional coefficient of 2.45. This 3D structure is very complex and branchy [16]. The existence of similar structures of growth factors limited to the spread in the bone marrow may reveal some of its pathological processes. In 1998, Sahimi et al., during publication of article titled “Bone marrow fractal dimension in metastatic complications”, proved that when bone marrow cancer metastasizes, the fractal factor increases from normal value 1.72±0.10% to 1.98±0.20. This finding clearly shows that the lack of fractal structure in metastatic lesions can lead to a loss of control of structural adjustment mechanisms of the bone marrow and the Milieu-interior internal environment of the bone marrow in such a way that it creates peripheral blood changes such as roblastosis Leuko-eryth. This finding also may provide a way for interpretation of the physiopathology of bone marrow diseases. S. Organ et al. from the Izmir University of Medical Sciences in Turkey published an article in 2009 in which the calculation of the bone fractal coefficient in calcium absorption images using the X-Ray method was applied to detect the effect of parathyroid adenoma hyperparathyroidism in order to distinguish it from other osteoporosis factors.
To determine the non-fractal nature of bone marrow pathological processes, there is a need for further research in each of the areas of disease, and our advice to respected researchers is to study and research in the field of fractal numbers in other blood diseases.
Under normal conditions, the fractal factor is about 1.7 in the two dimensional and three-dimensional levels. This study, which was conducted for the first time in Iran, proved that the structure of the bone marrow is fractal.
TABLES and CHARTS
Show attach fileCITIATION LINKS
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[2]Peitgen HO, Saupe D, Barnsley MF. The science of fractal images. Berlin: Springerverlag; 1988.
[3]Peitgen HO, Richter PH. The beauty of fractals. Berlin: Springerverlag; 1986.
[4]DewdneyAK.Computer recreations: Leaping into Lyapunov space. Sci Am. 1995; 265(3):178-81.
[5]Matsuo T, Okeda R, Takahashi M, Funtata M. Characterization of bifurcating structure of blood vessels using fractal dimension. Forma. 1990;5(1):19-27.
[6]Caserta F, Stanley HE, Eldred WD, Daccord G, Hausman RE, Nittman J. Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape. Phys Rev Lett. 1990;64(1):95-98.
[7]Cross SS. Fractal and integer-dimensional geometric analysis of pigmented skin lesions. Am J Dermatopathol. 1995;17(4):374-8.
[8]Kido S, Ikezoe J, Naito H, Tamura S, Machi S. Fractal analysis of interstitial lung abnormalities in chest radiography. Radiographics. 1995;15(6):1457-64.
[9]Guilluad M, Doudkine A, Garner D, MacAulay C, Palcic B. Malignancy associated changes in Cervical Smears: Systematic changes in cytometric features with the grade of dysplasia. Anal Cell Pathol. 1995;9(3):191-204.
[10]Naeim F, Moatamed F, Sahimi M. Morphogenesis of the bone marrow: Fractal structures and diffusion limited growth. Blood. 1996;87(12):5027-31.
[11]Kaushansky K, Karplus PA. Hematopoietic growth factors: Understanding functional diversity and structural terms. Blood. 1993;82(11):3229-40.
[12]Anderson WAD, Kissane JM. Anderson’s pathology. St Louis: mosby. 1990. p.1379, 1990.
[13]Kumar V, Abbas AK, Aster JC. Robbins & Cotran pathologic basis of disease. Amsterdam: Elsevier Health Sciences. 2014. p.728- 729.
[14]Naeim F, Moatamed F, Sahimi M. Morphogenesis of the bone marrow: Fractal structures and diffusion limited growth. Blood. 1996;87(12):5027-31.
[15]Moatamed F, Sahimi M, Naemi F. Fractal dimension of the bone marrow in metastatic lesions. Hum Pathol. 1998;29(11):1299-303.
[16]Ergun S, Saracoglu A, Gunen P, Ozpinar B. Application of Fractal analysis in hyperparathyroidism. Dentomaxillofac Radiol. 2009;38(5):281-8.
[2]Peitgen HO, Saupe D, Barnsley MF. The science of fractal images. Berlin: Springerverlag; 1988.
[3]Peitgen HO, Richter PH. The beauty of fractals. Berlin: Springerverlag; 1986.
[4]DewdneyAK.Computer recreations: Leaping into Lyapunov space. Sci Am. 1995; 265(3):178-81.
[5]Matsuo T, Okeda R, Takahashi M, Funtata M. Characterization of bifurcating structure of blood vessels using fractal dimension. Forma. 1990;5(1):19-27.
[6]Caserta F, Stanley HE, Eldred WD, Daccord G, Hausman RE, Nittman J. Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape. Phys Rev Lett. 1990;64(1):95-98.
[7]Cross SS. Fractal and integer-dimensional geometric analysis of pigmented skin lesions. Am J Dermatopathol. 1995;17(4):374-8.
[8]Kido S, Ikezoe J, Naito H, Tamura S, Machi S. Fractal analysis of interstitial lung abnormalities in chest radiography. Radiographics. 1995;15(6):1457-64.
[9]Guilluad M, Doudkine A, Garner D, MacAulay C, Palcic B. Malignancy associated changes in Cervical Smears: Systematic changes in cytometric features with the grade of dysplasia. Anal Cell Pathol. 1995;9(3):191-204.
[10]Naeim F, Moatamed F, Sahimi M. Morphogenesis of the bone marrow: Fractal structures and diffusion limited growth. Blood. 1996;87(12):5027-31.
[11]Kaushansky K, Karplus PA. Hematopoietic growth factors: Understanding functional diversity and structural terms. Blood. 1993;82(11):3229-40.
[12]Anderson WAD, Kissane JM. Anderson’s pathology. St Louis: mosby. 1990. p.1379, 1990.
[13]Kumar V, Abbas AK, Aster JC. Robbins & Cotran pathologic basis of disease. Amsterdam: Elsevier Health Sciences. 2014. p.728- 729.
[14]Naeim F, Moatamed F, Sahimi M. Morphogenesis of the bone marrow: Fractal structures and diffusion limited growth. Blood. 1996;87(12):5027-31.
[15]Moatamed F, Sahimi M, Naemi F. Fractal dimension of the bone marrow in metastatic lesions. Hum Pathol. 1998;29(11):1299-303.
[16]Ergun S, Saracoglu A, Gunen P, Ozpinar B. Application of Fractal analysis in hyperparathyroidism. Dentomaxillofac Radiol. 2009;38(5):281-8.