2011, 8(4): 987-997. doi: 10.3934/mbe.2011.8.987

Morphogenesis and aggressiveness of cervix carcinoma

1. 

Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

2. 

Institute of Oncology and Radiobiology, Havana, Cuba

3. 

Faculty of Physics, University of Havana, Havana, Cuba

Received  March 2010 Revised  February 2011 Published  August 2011

A mathematical model was obtained to describe the relation between the tissue morphology of cervix carcinoma and both dynamic processes of mitosis and apoptosis, and an expression to quantify the tumor aggressiveness, which in this context is associated with the tumor growth rate. The proposed model was applied to Stage III cervix carcinoma in vivo studies. In this study we found that the apoptosis rate was signicantly smaller in the tumor tissues and both the mitosis rate and aggressiveness index decrease with Stage III patients’ age. These quantitative results correspond to observed behavior in clinical and genetics studies.
Citation: Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, José Manuel Nieto-Villar. Morphogenesis and aggressiveness of cervix carcinoma. Mathematical Biosciences & Engineering, 2011, 8 (4) : 987-997. doi: 10.3934/mbe.2011.8.987
References:
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S. A. Frank, "Dynamics of Cancer,", H. Allen Orr, (2007).   Google Scholar

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J. W. Baish and R. K. Jain, Fractals and cancer,, Cancer Res., 60 (2000), 3683.   Google Scholar

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R. Sedivy, Ch. Windischberger, K. Svozil, E. Moser and G. Breitenecker, Fractal analysis: An objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri,, Gynecologic Oncology, 75 (1999), 78.  doi: 10.1006/gyno.1999.5516.  Google Scholar

[8]

E. M. Toledo Cuevas and A. García Carrancá, P53 and human papillomavirus in the carcinogenesis of the uterine cervix,, Rev. Invest. Clín, 48 (1996), 59.   Google Scholar

[9]

T. Prempree, V. Patanaphan, W. Sewchand and R. M. Scott, The influence of patients' age and tumor grade on the prognosis of carcinoma of the cervix,, Cancer, 51 (1983), 764.   Google Scholar

[10]

E. Izquierdo-Kulich, M. Amigó de Quesada, C. M. Pérez-Amor, M. Lopes Texeira and J. M. Nieto-Villar, The dynamics of tumor growth and cells pattern morphology,, Mathematical Biosciences and Engineering, 6 (2009), 547.   Google Scholar

[11]

N. G. van Kampen, "Stochastic Processes in Physics and Chemistry,", N. H. Publications, (1992).   Google Scholar

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C. W. Gardiner, "Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences," Third edition, Springer Series in Synergetics, 13,, Springer-Verlag, (2004).   Google Scholar

[13]

R. W. Tsang, A. W. Fyles, Y. Li, M. M. Rajaraman, W. Chapman, M. Pintilie and C. S. Wong, Tumor proliferation and apoptosis in human uterine cervix carcinoma I: Correlations between tumor proliferation and apoptosis,, Radiother Oncol, 50 (1999), 85.  doi: 10.1016/S0167-8140(98)00120-0.  Google Scholar

show all references

References:
[1]

S. A. Frank, "Dynamics of Cancer,", H. Allen Orr, (2007).   Google Scholar

[2]

J. W. Baish and R. K. Jain, Fractals and cancer,, Cancer Res., 60 (2000), 3683.   Google Scholar

[3]

G. Landini, "Complexity in Tumour Growth Patterns,", Fractals in Biology and Medicine, (1998).   Google Scholar

[4]

Robbins and Cotran, eds., "Pathologic Basis of Disease,", Elsevier, (2005).   Google Scholar

[5]

L. Norton, Conceptual and practical implications of breast tissue geometry: Toward a more effective, less toxic therapy,, Oncologist, 10 (2005), 370.   Google Scholar

[6]

E. Sabo, A. Boltenko, Y. Sova, A. Stein, S. Kleinhaus and M. B. Resnick, Microscopic analysis and significance of vascular architectural complexity in renal cell carcinoma,, Clinical Cancer Research, 7 (2001), 533.   Google Scholar

[7]

R. Sedivy, Ch. Windischberger, K. Svozil, E. Moser and G. Breitenecker, Fractal analysis: An objective method for identifying atypical nuclei in dysplastic lesions of the cervix uteri,, Gynecologic Oncology, 75 (1999), 78.  doi: 10.1006/gyno.1999.5516.  Google Scholar

[8]

E. M. Toledo Cuevas and A. García Carrancá, P53 and human papillomavirus in the carcinogenesis of the uterine cervix,, Rev. Invest. Clín, 48 (1996), 59.   Google Scholar

[9]

T. Prempree, V. Patanaphan, W. Sewchand and R. M. Scott, The influence of patients' age and tumor grade on the prognosis of carcinoma of the cervix,, Cancer, 51 (1983), 764.   Google Scholar

[10]

E. Izquierdo-Kulich, M. Amigó de Quesada, C. M. Pérez-Amor, M. Lopes Texeira and J. M. Nieto-Villar, The dynamics of tumor growth and cells pattern morphology,, Mathematical Biosciences and Engineering, 6 (2009), 547.   Google Scholar

[11]

N. G. van Kampen, "Stochastic Processes in Physics and Chemistry,", N. H. Publications, (1992).   Google Scholar

[12]

C. W. Gardiner, "Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences," Third edition, Springer Series in Synergetics, 13,, Springer-Verlag, (2004).   Google Scholar

[13]

R. W. Tsang, A. W. Fyles, Y. Li, M. M. Rajaraman, W. Chapman, M. Pintilie and C. S. Wong, Tumor proliferation and apoptosis in human uterine cervix carcinoma I: Correlations between tumor proliferation and apoptosis,, Radiother Oncol, 50 (1999), 85.  doi: 10.1016/S0167-8140(98)00120-0.  Google Scholar

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