The dynamics of tumorgrowth and cells pattern morphology
The mathematical modeling of tumor growth is an approach to explain thecomplex nature of these systems. A model that describes tumor growth wasobtained by using a mesoscopic formalism and fractal dimension. This modeltheoretically predicts the relation between the morphology of the cellpattern and t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.547 |
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| author | Elena Izquierdo-Kulich Margarita Amigó de Quesada Carlos Manuel Pérez-Amor Magda Lopes Texeira José Manuel Nieto-Villar |
| author_facet | Elena Izquierdo-Kulich Margarita Amigó de Quesada Carlos Manuel Pérez-Amor Magda Lopes Texeira José Manuel Nieto-Villar |
| author_sort | Elena Izquierdo-Kulich |
| collection | DOAJ |
| description | The mathematical modeling of tumor growth is an approach to explain thecomplex nature of these systems. A model that describes tumor growth wasobtained by using a mesoscopic formalism and fractal dimension. This modeltheoretically predicts the relation between the morphology of the cellpattern and the mitosis/apoptosis quotient that helps to predict tumorgrowth from tumoral cells fractal dimension. The relation between the tumormacroscopic morphology and the cell pattern morphology is also determined.This could explain why the interface fractal dimension decreases with theincrease of the cell pattern fractal dimension and consequently with theincrease of the mitosis/apoptosis relation. Indexes to characterize tumoralcell proliferation and invasion capacities are proposed and used to predictthe growth of different types of tumors. These indexes also show that theproliferation capacity is directly proportional to the invasion capacity.The proposed model assumes: i) only interface cells proliferate and invadethe host, and ii) the fractal dimension of tumoral cell patterns, canreproduce the Gompertzian growth law. |
| format | Article |
| id | doaj-art-e5dcf8bceb4844a189df65e654663767 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e5dcf8bceb4844a189df65e6546637672025-01-24T01:59:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016354755910.3934/mbe.2009.6.547The dynamics of tumorgrowth and cells pattern morphologyElena Izquierdo-Kulich0Margarita Amigó de Quesada1Carlos Manuel Pérez-Amor2Magda Lopes Texeira3José Manuel Nieto-Villar4Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, HavanaDepartment of Physical-Chemistry, Faculty of Chemistry, University of Havana, HavanaDepartment of Physical-Chemistry, Faculty of Chemistry, University of Havana, HavanaDepartment of Physical-Chemistry, Faculty of Chemistry, University of Havana, HavanaDepartment of Physical-Chemistry, Faculty of Chemistry, University of Havana, HavanaThe mathematical modeling of tumor growth is an approach to explain thecomplex nature of these systems. A model that describes tumor growth wasobtained by using a mesoscopic formalism and fractal dimension. This modeltheoretically predicts the relation between the morphology of the cellpattern and the mitosis/apoptosis quotient that helps to predict tumorgrowth from tumoral cells fractal dimension. The relation between the tumormacroscopic morphology and the cell pattern morphology is also determined.This could explain why the interface fractal dimension decreases with theincrease of the cell pattern fractal dimension and consequently with theincrease of the mitosis/apoptosis relation. Indexes to characterize tumoralcell proliferation and invasion capacities are proposed and used to predictthe growth of different types of tumors. These indexes also show that theproliferation capacity is directly proportional to the invasion capacity.The proposed model assumes: i) only interface cells proliferate and invadethe host, and ii) the fractal dimension of tumoral cell patterns, canreproduce the Gompertzian growth law.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.547pattern cell morphology.mesoscopic modelfractalstochastic modeltumor growth |
| spellingShingle | Elena Izquierdo-Kulich Margarita Amigó de Quesada Carlos Manuel Pérez-Amor Magda Lopes Texeira José Manuel Nieto-Villar The dynamics of tumorgrowth and cells pattern morphology Mathematical Biosciences and Engineering pattern cell morphology. mesoscopic model fractal stochastic model tumor growth |
| title | The dynamics of tumorgrowth and cells pattern morphology |
| title_full | The dynamics of tumorgrowth and cells pattern morphology |
| title_fullStr | The dynamics of tumorgrowth and cells pattern morphology |
| title_full_unstemmed | The dynamics of tumorgrowth and cells pattern morphology |
| title_short | The dynamics of tumorgrowth and cells pattern morphology |
| title_sort | dynamics of tumorgrowth and cells pattern morphology |
| topic | pattern cell morphology. mesoscopic model fractal stochastic model tumor growth |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.547 |
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