Growth Study of Cancer within Organ through the Models on Stochastic Non-linear Programming
Abstract:
The growth and loss of cancer cell population within an organ are influenced by their birth, death and migration processes. These issues may be observed during the presence and absence of chemotherapy also. In this paper, stochastic non-linear programming problems were formulated for getting the decision parameters on growth and loss of cancer cells in an organ subject to the constraints of its related health indicators. While formulating the objective function and subjective constraints based on the derived statistical measures in the works of Tirupathi rao et. al. [9,10]. The decision parameters of the developed programming problem are predicted and analyzed the dynamics of cancer cell size in different situations.
Author(s):
DOI:
Keywords:
References:
Christopher J. Portier, Annette Kopp-Shneider, Claire D. Sherman, Calculating tumor incidence rates in Stochastic model of carcinogenesis, Mathematical Biosciences, 135, 129-146 (1996).
Quinn, D.W., The method of Characteristics applied to a stochastic two-stage model of carcinogenesis, Mathl. Comput. Modeling, 25(7), 1-13 (1997).
David G. Kendall, Birth – and – death processes, and the theory of carcinogenesis, Biometrika, 47(1), 13-21 (1960).
Iyer, K.S.S., Saksena, V. N., A Stochastic Model for the growth of cells in cancer, Biometrics, 6(3), 401-410 (1970).
Lance A. Liotta, Gerald M. Saidel, Jerome Kleinerman, Stochastic model for metastases formation, Biometrics, 32(3), 535-550 (1976).
Madhavi, K., Tirupathi Rao, P, Reddy, P.R.S., Optimal Drug administration for cancer chemotherapy through Stochastic Programming, American Journal of Applied Mathematics and Mathematical Sciences, 2(1), 37-45 (2013).
Srinivasan, S.K., Ranganathan, C.R., An Age-dependent stochastic model for carcinogenesis, Mathematical Biosciences, 57,155-174 (1981).
Pinho, S.T.R., A chemotherapy model for the treatment of cancer with metastasis, Mathematical and computer modelling, 36, 773-803 (2002).
Tirupathi Rao Padi, Jayabharathiraj. J., Naveen Kumar, B.N., Lakshmi Usha, C., Rajasekhara Reddy, P., Stochastic Modelling of Tumor Growth within Organ during chemotherapy using Bivariate Birth, Death and Migration Processes, IOSR Journal of Mathematics, 10(3), 01-08 (2014).
Tirupathi Rao Padi, Jayabharathiraj. J., Naveen Kumar, B.N., Lakshmi Usha, C., Rajasekhara Reddy, P., Stochastic Modeling for Tumor Growth within organ through Bivariate Birth, Death and Migration Processes, Journal of International Academic Research for Multidisciplinary, 2(5), 205-217 (2014).
Tirupathi Rao, P., Flora Evangil, D., Madhavi, K., Stochastic Programming on Optimal Drug Administration for Two-stage Cancer treatment problems, International Journal of Green Computing, 3(1), 1-10 (2012).
Tirupathi Rao. P., Srinivasa Rao. K., Padmalatha. K., Stochastic Models for Optimal Drug Administration in Cancer chemotherapy, International Journal of Engineering Science and Technology, 2(5), 859-865 (2010).
