Two Numerical Solutions for Solving a Mathematical Model of the Avascular Tumor Growth

Sıla Övgü KORKUT UYSAL; Neslişah İMAMOĞLU KARABAŞ; Yasemin BAŞBINAR

doi:https://doi.org/10.30621/jbachs.957601

Makale detayları

Two Numerical Solutions for Solving a Mathematical Model of the Avascular Tumor Growth

Yazarlar:

Sıla Övgü KORKUT UYSAL | Neslişah İMAMOĞLU KARABAŞ | Yasemin BAŞBINAR

Yayıncı:

Dokuz Eylul University

Ana Başlıklar:

Sağlık teşvikleri

Dergi:

Journal of Basic and Clinical Health Sciences 2021 Vol.5 Issue 3, pp.156-164

Belge Tipi:

Makale

Yayın Tarihi:

9/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000493137

Sıklık:

Üç Yıllık

eISSN:

2564-7288

DOI:

https://doi.org/10.30621/jbachs.957601

Özet:

 

Objectives: Cancer which is one of the most challenging health problems overall the world is composed of various processes: tumorigenesis, angiogenesis, and metastasis. Attempting to understand the truth behind this complicated disease is one of the common objectives of many experts and researchers from different fields. To provide deeper insights any prognostic and/or diagnostic scientific contribution to this topic is so crucial. In this study, the avascular tumor growth model which is the earliest stage of tumor growth is taken into account from a mathematical point of view. The main aim is to solve the mathematical model of avascular tumor growth numerically.  
Methods:  This study has focused on the numerical solution of the continuum mathematical model of the avascular tumor growth described by Sharrett and Chaplin. Unlike the existing recent literature, the study has focused on the methods for the temporal domain. To obtain the numerical schemes the central difference method has been used in the spatial coordinates. This discretization technique has reduced the main partial differential equation into an ordinary differential equation which will be solved successively by two alternative techniques: the 4th order Runge-Kutta method (RK4) and the three-stage strongly-stability preserving Runge-Kutta method (SSP-RK3). 
Results:  The model has been solved by the proposed methods. The numerical results are discussed in both mathematical and biological angles. The biological compatibility of the methods is depicted in various figures. Besides biological outputs, the accuracies of the methods have been listed from a mathematical point of view. Furthermore, the rate of convergence of the proposed methods has also been discussed computationally.
Conclusion: All recorded results are evidence that the proposed schemes are applicable for solving such models. Moreover, all exhibited figures have proved the biological compatibility of the methods. It is observed that the quiescent cells which are one of the most mysterious cells in clinics tend to become proliferative for the selected parameters.

Makale detayları

Two Numerical Solutions for Solving a Mathematical Model of the Avascular Tumor Growth

Yazarlar: Sıla Övgü KORKUT UYSAL | Neslişah İMAMOĞLU KARABAŞ | Yasemin BAŞBINAR

Yayıncı: Dokuz Eylul University

Ana Başlıklar: Sağlık teşvikleri

Dergi: Journal of Basic and Clinical Health Sciences 2021 Vol.5 Issue 3, pp.156-164

Belge Tipi: Makale

Yayın Tarihi: 9/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000493137

Sıklık: Üç Yıllık

eISSN: 2564-7288

DOI: https://doi.org/10.30621/jbachs.957601

Sayı

Yazarlar:

Sıla Övgü KORKUT UYSAL | Neslişah İMAMOĞLU KARABAŞ | Yasemin BAŞBINAR

Yayıncı:

Dokuz Eylul University

Ana Başlıklar:

Sağlık teşvikleri

Dergi:

Journal of Basic and Clinical Health Sciences 2021 Vol.5 Issue 3, pp.156-164

Belge Tipi:

Makale

Yayın Tarihi:

9/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000493137

Sıklık:

Üç Yıllık

eISSN:

2564-7288

DOI:

https://doi.org/10.30621/jbachs.957601