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Constitutive Modeling of Nonlinear Tumor Growth; A Finite Element Approach

Hosseinalizadeh, Mohammad | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56618 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza
  7. Abstract:
  8. Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate and induces apoptosis. Additionally, compression of intratumor blood vessels has negative impacts on drug delivery system. Despite the great importance of the mechanical forces on the pathology of cancer, there are limited studies on the constitutive modeling of tumors. In this study, first, the tumor growth inside a rigid cylinder with an exponential growth function is represented, a model mimicking the growth of ductal carcinoma. Then, a mathematical model of a spherical tumor growth with a Gompertz growth function is represented. Using the notion of multiple natural configurations, the volumetric growth and mechanical response of tumor are splited into two separate contributions. Three hyperelastic models, the Neo-Hookean, the Mooney-Rivlin and the Ogden model are used to represent the mechanical response of the tumor. The main goal of this study is to investigate the effect of tumor constitutive model on the stress exerted on tumor during growth process. Also a parametric analysis is represented on the stiffness of the normal tissue surrounding the tumor and on the bulk modulus of the tumor tissue. The results of this study has been verified with the experimental and computational results of the previous research. Interestingly, we found that the evolution of stress in the tumor is dependent on the selection of the constitutive equation. The Ogden model is capable of describing the nonlinear stress-strain response of the tumor in experimental tests. The compressive stresses exerted on tumor in rigid cylinder model, as a result of Mooney-Rivlin and Neo-Hookean models’ predictions differ by 9.6% and 14.3% compared to the Ogden model prediction. Also, in spherical tumor model, The compressive stresses exerted on tumor, as a result of Mooney-Rivlin and Neo-Hookean models’ predictions differ by 7% and 11% compared to the Ogden model prediction
  9. Keywords:
  10. Constitutive Modeling ; Solid Tumors ; Finite Element Method ; Bulk Modulus ; Tumor Growth ; Mechanical Force ; Numerical Solution ; Surrounding Tissue Interaction

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