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Michalak KP. How to estimate the correlation dimension of high-dimensional signals? CHAOS (WOODBURY, N.Y.) 2014; 24:033118. [PMID: 25273198 DOI: 10.1063/1.4891185] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The paper presents improvements to the Takens-Ellner (TE) algorithm estimating the correlation dimension (d) of high-dimensional signals. The signal being the sum of 4 Lorenz signals and possessing the correlation dimension d approximately equal to 8 was analyzed. The conversion of TE to the classic Grassberger-Proccacia (GP) algorithm is presented that shows the advantage of TE over the GP algorithm. The maximal d estimated for the given number of points in phase space is significantly higher for the TE algorithm than for the GP algorithm. The formula for the precision of individual d estimation is presented. The paper shows, how to estimate the distance corresponding to the end of the Linear Scaling Region in the correlation integral function, even before starting the procedure of d estimation. It makes it possible to reject the majority of longer distances from the analysis reducing the computation time considerably.
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Affiliation(s)
- Krzysztof Piotr Michalak
- Laboratory of Vision Science and Optometry, Faculty of Physics, Adam Mickiewicz University of Poznań, Umultowska Street 85, 61-614 Poznań, Poland and Nanobiomedical Center of Poznań Umultowska Street 85, 61-614 Poznań, Poland
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KHRANOVSKAYA NATALYA, OREL VALERII, GRINEVICH YURIY, ALEKSEENKO OXANA, ROMANOV ANDRIY, SKACHKOVA OXANA, DZYATKOVSKAYA NATALYA, BURLAKA ANATOLIY, LUKIN SERGEY. MECHANICAL HETEROGENIZATION OF LEWIS LUNG CARCINOMA CELLS CAN IMPROVE ANTIMETASTATIC EFFECT OF DENDRITIC CELLS. J MECH MED BIOL 2012. [DOI: 10.1142/s0219519411004757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The effect of mechanically heterogenized (MCH) microparticles of tumor cells (TCs) on antimetastatic action of dendritic cells (DCs) is studied in C57BL/6 mice with Lewis' carcinoma. DCs isolated from mice spleens and loaded with MCH-TCs are analyzed with flow cytometry methods. MCH-TCs are analyzed with optical and/or electron microscopy. The paper describes an original high-precision medical microvibromill with high-acceleration linear induction motor that generates magnetic levitation to produce mechanical heterogenization of TCs. MCH-TCs have a more asymmetric morphology, larger surface and higher internal structure heterogeneity, and higher concentration of free radicals with respect to conventionally treated TCs. The rate of DCs maturity, being affected by pre-incubation with MCH-TCs is found to be higher than its counterpart treated with conventional TCs. DCs loaded with MCH-TCs show a significantly higher ability to induce proliferation of allogeneic lymphocytes in mixed leukocyte reaction. The inhibition index of metastases formation increases from 42% (conventional TCs) to 66% when DCs are treated with MCH-TCs. The present results demonstrate the feasibility of increasing antimetastatic activity of DCs-based vaccines when MCH-TCs is used for their loading. Mathematical model is developed in order to simulate the processes of capture, processing and presentation of tumor antigens by DCs when using conventional TCs or MCH-TCs.
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Affiliation(s)
- NATALYA KHRANOVSKAYA
- Experimental Oncology Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - VALERII OREL
- Medical Physics & Bioengineering Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - YURIY GRINEVICH
- Clinical Immunology Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - OXANA ALEKSEENKO
- Cytology Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - ANDRIY ROMANOV
- Medical Physics & Bioengineering Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - OXANA SKACHKOVA
- Experimental Oncology Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - NATALYA DZYATKOVSKAYA
- Medical Physics & Bioengineering Laboratory, National Cancer Institute, 33/43 Lomonosov Street, Kyiv, 03022, Ukraine
| | - ANATOLIY BURLAKA
- R. E. Kavetsky Institute of Experimental Pathology, Oncology and Radiobiology of National Academy of Sciences of Ukraine, 45, Vasil'kovsky Street, Kyiv, 03022, Ukraine
| | - SERGEY LUKIN
- R. E. Kavetsky Institute of Experimental Pathology, Oncology and Radiobiology of National Academy of Sciences of Ukraine, 45, Vasil'kovsky Street, Kyiv, 03022, Ukraine
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OREL VALERIYE, DZYATKOVSKAYA NATALIYAN, DANKO MICHAILI, ROMANOV ANDRIYV, MEL'NIK YURII, GRINEVICH YURIA, MARTYNENKO SVETLANAV. SPATIAL AND MECHANOEMISSION CHAOS OF MECHANICALLY DEFORMED TUMOR CELLS. J MECH MED BIOL 2011. [DOI: 10.1142/s0219519404000886] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The development and spreading of tumor process is accompanied by changes in nonlinear (chaotic) dynamics of mechanochemical interaction process in the group of cells. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we suggested that treatment by mechanically deformed (MD) syngeneic tumor cells (STC) would be accompanied by changed influence on malignant growth. The objective of this work was to compare spatial, mechanoemission (ME) chaos of MD STC of carcinoma Lewis and melanoma B16 and their malignant growth. MD STC preparation included the aseptic removal of the animal tumor, lyophilization and next mechanical deformation in the microvibratory mill. The suspension of non-deformed or MD STC was injected intraperitoneally. Morphological, morphometric and mechanoemission studies used for estimate of spatial chaos and heterogeneity structure in tumor cells and blood. For Lewis carcinoma the reduction of spatial and ME chaos of cells is accompanied by regression in tumor growth and metastasis. For melanoma B16 the decrease of spatial chaos and the increase of ME chaos in cells is accompanied by initiation of tumor growth and metastasis. These results illustrated equivalent tendencies in chaos changing in spatial and ME chaos for carcinoma Lewis, while opposite tendencies were observed for melanoma B16. Blood ME of mice with melanoma B16 have greater ME chaos in comparison with animals with Lewis carcinoma. This confirmed that the concept of deterministic chaos is hierarchical for the host during cancer process. Results of comparative analysis between spatial, mechanoemission chaos of MD STC and malignant growth could be useful for gain a better understanding relationship of nonlinear biomechanical processes to tumor cells.
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Affiliation(s)
- VALERIY E. OREL
- Physics-Technical Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | | | - MICHAIL I. DANKO
- Physics-Technical Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - ANDRIY V. ROMANOV
- Physics-Technical Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - YURI I. MEL'NIK
- Physics-Technical Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - YURI A. GRINEVICH
- Clinical Immunology Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - SVETLANA V. MARTYNENKO
- Clinical Immunology Laboratory, Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
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OREL VALERIYE, GRINEVICH YURIA, DZYATKOVSKAYA NATALIYAN, DANKO MICHAILI, ROMANOV ANDRIYV, MEL'NIK YURII, MARTYNENKO SVETLANAV. SPATIAL AND MECHANOEMISSION CHAOS OF MECHANICALLY DEFORMED TUMOR CELLS. J MECH MED BIOL 2011. [DOI: 10.1142/s0219519403000806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The development and spend of the tumor process is accompanied by changes in non-linear (chaotic) dynamics of mechanochemical interaction process in the group of cells. Taking into consideration spatial irregularity and heterogeneity of internal structures of tumor cells, we suggested that treatment by mechanically deformed (MD) syngeneic tumor cells (STC) would be accompanied by changed influence on malignant growth. The objective of this work was to compare spatial, mechanoemission (ME) chaos of MD STC of carcinoma Lewis and melanoma B16 and their malignant growth. MD STC preparation included the aseptic removal of the animal tumor, lyophilization and next mechanical deformation in the microvibratory mill. The suspension of non-deformed or MD STC was injected intraperitoneally. Morphological, morphometric and mechanoemission studies were used for the estimate of spatial chaos and heterogeneity structure in tumor cells and blood. For Lewis carcinoma, the reduction of spatial and ME chaos of cells is accompanied by regression in tumor growth and metastasis. For melanoma B16, the decrease of spatial chaos and the increase of ME chaos in cells are accompanied by the initiation of tumor growth and metastasis. These results illustrated equivalent tendencies in chaos changing in spatial and ME chaos for carcinoma Lewis, while opposite tendencies were observed for melanoma B16. Blood ME of mice with melanoma B16 have greater ME chaos in comparison with animals with Lewis carcinoma. This confirmed that the concept of deterministic chaos is hierarchical for the host during cancer process. Results of comparative analysis between spatial, mechanoemission chaos of MD STC and malignant growth could be useful to gain a better understanding relationship of non-linear biomechanical processes to tumor cells.
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Affiliation(s)
- VALERIY E. OREL
- Physics-Technical laboratory, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - YURI A. GRINEVICH
- Clinical Immunology Laboratory Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | | | - MICHAIL I. DANKO
- Physics-Technical laboratory, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - ANDRIY V. ROMANOV
- Physics-Technical laboratory, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - YURI I. MEL'NIK
- Physics-Technical laboratory, 33/43 Lomonosov str., Kiev, 03022, Ukraine
| | - SVETLANA V. MARTYNENKO
- Clinical Immunology Laboratory Institute of Oncology, 33/43 Lomonosov str., Kiev, 03022, Ukraine
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Boquete L, Ortega S, Miguel-Jiménez JM, Rodríguez-Ascariz JM, Blanco R. Automated detection of breast cancer in thermal infrared images, based on independent component analysis. J Med Syst 2010; 36:103-11. [PMID: 20703744 DOI: 10.1007/s10916-010-9450-y] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2009] [Accepted: 02/16/2010] [Indexed: 10/19/2022]
Abstract
Breast cancer, among women, is the second-most common cancer and the leading cause of cancer death. It has become a major health issue in the world over the past decades and its incidence has increased in recent years mostly due to increased awareness of the importance of screening and population ageing. Early detection is crucial in the effective treatment of breast cancer. Current mammogram screening may turn up many tiny abnormalities that are either not cancerous or are slow-growing cancers that would never progress to the point of killing a woman and might never even become known to her. Ideally a better screening method should find a way of distinguishing the dangerous, aggressive tumors that need to be excised from the more languorous ones that do not. This paper therefore proposes a new method of thermographic image analysis for automated detection of high tumor risk areas, based on independent component analysis (ICA) and on post-processing of the images resulting from this algorithm. Tests carried out on a database enable tumor areas of 4 × 4 pixels on an original thermographic image to be detected. The proposed method has shown that the appearance of a heat anomaly indicating a potentially cancerous zone is reflected as an independent source by ICA analysis of the YCrCb components; the set of available images in our small series is giving us a sensitivity of 100% and a specificity of 94.7%.
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Affiliation(s)
- Luciano Boquete
- Electronics Department, University of Alcalá, Alcalá de Henares, Madrid, Spain.
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