Mathematical Approach for Effect of Growth on the Mechanical Stresses during Soft Tissues and Avascular Tumor

Authors

S. R. Mahmoud, Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia\\ Mathematics Department, Science Faculty, Sohag University, Sohag , Egypt.Follow
Shafeek. A. Ghaleb, Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia\\ Mathematics Department, Applied Science Faculty, Thamar University, Thamar, Yemen.Follow
A. K. Alzahrani, Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.Follow
E. Ghandourah, Department of Nuclear Engineering , Faculty of Engineering, King Abdulaziz University, Saudi Arabia.Follow

Author Country (or Countries)

Egypt.

Abstract

In this Paper, the mathematical model for the study of the distribution of mechanical stresses by the cells within the soft tissues and tumor tissue is discussed. To describe the impact of isotropic growth on the mechanical stresses based on the linear elasticity theory and to study the process of continuous growth. Constitutive law to describe a linearly elastic tumor with continuous volume growth is combined in the model. Two examples is discussed, First case, in one dimensional model of tumor growth in rectangular tube, The model is solved in terms of radial displacement and stresses. In the second case, the effect of isotropic growth during a compressible material is solved in terms of radial displacement and stresses. The implications of two examples and possible model developments are investigated. Comparisons are made with the results in the two cases and numerical results are given and illustrated graphically for each case considered.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110512

Recommended Citation

R. Mahmoud, S.; A. Ghaleb, Shafeek.; K. Alzahrani, A.; and Ghandourah, E. (2017) "Mathematical Approach for Effect of Growth on the Mechanical Stresses during Soft Tissues and Avascular Tumor," Applied Mathematics & Information Sciences: Vol. 11: Iss. 5, Article 12.
DOI: http://dx.doi.org/10.18576/amis/110512
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss5/12