Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body

Bayru Haftu Hindeya; Samba Narasimha Murthy

doi:doi:10.11648/j.acm.20160502.18

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Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body

Bayru Haftu Hindeya, Samba Narasimha Murthy

Published in Applied and Computational Mathematics (Volume 5, Issue 2)

Received: 20 April 2016 Accepted: 29 April 2016 Published: 12 May 2016

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Abstract

This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.

Published in	Applied and Computational Mathematics (Volume 5, Issue 2)
DOI	10.11648/j.acm.20160502.18
Page(s)	83-90
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Avascular, Tumor, Monomolecular, Time Delay Logistic, Gompertz, Proliferating Cells, Quiescent Cells, Necrotic Cells

References

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[2]	Anne Talkington and Rick Durrett, “Estimating tumor growth rates in vivo” Dept. of Math, Duke University, Durham, NC (November 19, 2014) 1-27.
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[4]	E. O. Alzahrani, AsimAsiri, M. M. El-Dessoky, Y. Kuang, “Quiescence as an explanation of Gompertzian tumor growth revisited”, Mathematical Biosciences 254 (2014) 76–82.
[5]	Frank Kozusko, Zeljko Bajzer, “Combining Gompertzian growth and cell population dynamics”, www.elsevier.com/locate/mbs, Mathematical Biosciences 185 (2003) 153–167.
[6]	Heiko Enderling and Mark A. J Chaplain, “Mathematical Modeling of Tumor Growth and Treatment”, USA, (2014).
[7]	Keng-Cheng Ang, “Analysis of tumor growth with MATLAB”, National Institute of education, Nanyang Technological University, Singapore.
[8]	Nicholas F. Britton, “Essential Mathematical Biology”, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK, (2003).
[9]	Purnachandra Rao Koya, Ayele Taye Goshu, “Generalized Mathematical Model for Biological Growth”, Open Journal of Modeling and Simulation, 2013, 1, 42-53.http://dx.doi.org/10.4236/ojmsi.2013.14008.
[10]	P. Waliszewski, J. Konarski, “A Mystery of the Gompertz Function” Dept. of Theoretical Chemistry, University of Poznan, Grunwaldzka 6, 60-780 Poznan, Poland, 277-286.
[11]	Sebastein Benzekry, Clare Lamont, Afshin Beheshti, Amanda Tracz, John M. L. Ebos, Lynn Hlatky, Philip Hahnfeldt,” Classical Mathematical Models for Descriptionand Prediction of Experimental Tumor Growth”, sebastien.benzekry@inria.fr, 1-56.
[12]	Tan Liang Soon and AngKeng Cheng, “A numerical simulation of avascular tumor growth”, Nanyang Tech. University, Singapore, ANZIAM J.46 (E) pp. C909-C917, (2005).
[13]	Travis Portz, Yang Kuang, and John D. Nagy, “A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy” AIP ADVANCES 2, 011002 (2012).
[14]	Urszula Forys, Anna Marcinisk-Czochra, “Logistic EquationsIn Tumor Growth Modeling” Int. J. Appl. Math. Comp. Sci., 2003, Vol. 13, No. 3, 317–325.
[15]	Purnachandra Rao Koya, Ayele Taye Goshu and Mohammed Yiha Dawed. Modelling Predator Population assuming that the prey follows Richards Growth model. European Journal of Academic Essays (EJAE). Vol. 1, No. 9, 2014, pp. 42-51. http://euroessays.org/wp-content/uploads/2014/10/EJAE-279.pdfhttp://euroessays.org/archieve/vol-1-issue-9.
[16]	Ayele Taye Goshu, Purnachandra Rao Koya. Predator Population Dynamics Involving Exponential Integral Function when Prey follows Gompertz Model. Open Journal of Modelling and Simulation (OJMSi). Vol. 3, 2015, pp 70–80. http://dx.doi.org/10.4236/ojmsi.2015.33008.
[17]	Mohammed Yiha Dawed, Purnachandra Rao Koya, Temesgen Tibebu. Analysis of prey – predator system with prey population experiencing critical depensation growth function. American Journal of applied Mathematics. Vol. 3, No. 6, 2015, Pp. 327–334. Doi: 10.11648/j.ajam.20150306.23.

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APA Style

Bayru Haftu Hindeya, Samba Narasimha Murthy. (2016). Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Applied and Computational Mathematics, 5(2), 83-90. https://doi.org/10.11648/j.acm.20160502.18

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ACS Style

Bayru Haftu Hindeya; Samba Narasimha Murthy. Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Appl. Comput. Math. 2016, 5(2), 83-90. doi: 10.11648/j.acm.20160502.18

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AMA Style

Bayru Haftu Hindeya, Samba Narasimha Murthy. Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Appl Comput Math. 2016;5(2):83-90. doi: 10.11648/j.acm.20160502.18

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@article{10.11648/j.acm.20160502.18,
  author = {Bayru Haftu Hindeya and Samba Narasimha Murthy},
  title = {Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {83-90},
  doi = {10.11648/j.acm.20160502.18},
  url = {https://doi.org/10.11648/j.acm.20160502.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.18},
  abstract = {This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.},
 year = {2016}
}

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TY  - JOUR
T1  - Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body
AU  - Bayru Haftu Hindeya
AU  - Samba Narasimha Murthy
Y1  - 2016/05/12
PY  - 2016
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DO  - 10.11648/j.acm.20160502.18
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PB  - Science Publishing Group
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AB  - This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.
VL  - 5
IS  - 2
ER  -

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Author Information

Bayru Haftu Hindeya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Samba Narasimha Murthy

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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APA Style

Bayru Haftu Hindeya, Samba Narasimha Murthy. (2016). Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Applied and Computational Mathematics, 5(2), 83-90. https://doi.org/10.11648/j.acm.20160502.18

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ACS Style

Bayru Haftu Hindeya; Samba Narasimha Murthy. Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Appl. Comput. Math. 2016, 5(2), 83-90. doi: 10.11648/j.acm.20160502.18

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AMA Style

Bayru Haftu Hindeya, Samba Narasimha Murthy. Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body. Appl Comput Math. 2016;5(2):83-90. doi: 10.11648/j.acm.20160502.18

Copy | Download

@article{10.11648/j.acm.20160502.18,
  author = {Bayru Haftu Hindeya and Samba Narasimha Murthy},
  title = {Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {83-90},
  doi = {10.11648/j.acm.20160502.18},
  url = {https://doi.org/10.11648/j.acm.20160502.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.18},
  abstract = {This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Application of Growth Functions to Describe the Dynamics of Avascular Tumor in Human Body
AU  - Bayru Haftu Hindeya
AU  - Samba Narasimha Murthy
Y1  - 2016/05/12
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160502.18
DO  - 10.11648/j.acm.20160502.18
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 83
EP  - 90
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160502.18
AB  - This paper deals with the applications of mathematical growth functions such as monomolecular, time delay logistic and Gompertz functions to describe the dynamics of avascular tumor growth. In this case we analyze the steady state of the modified systems of the model using Jacobean matrix to show that it is stable on the nontrivial stationary points of each applications. Numerical simulation of the growth functions is implemented by using “ode45” in MATLAB and graphical outputs are presented to show differences in evaluation of tumor sub-populations. We also find that the tumor cells increases with time so that the nutrient is disproportional to the number of cells and they transform in to quiescent and necrotic cells that cause cancer.
VL  - 5
IS  - 2
ER  -

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