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Research Papers

Finite Element Modeling of Avascular Tumor Growth Using a Stress-Driven Model

[+] Author and Article Information
Faezeh Iranmanesh

Department of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439955961, Iran
e-mail: f.iranmanesh@ut.ac.ir

Mohammad Ali Nazari

Department of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439955961, Iran
e-mail: manazari@ut.ac.ir

1Corresponding author.

Manuscript received February 5, 2017; final manuscript received June 9, 2017; published online June 22, 2017. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 139(8), 081009 (Jun 22, 2017) (10 pages) Paper No: BIO-17-1045; doi: 10.1115/1.4037038 History: Received February 05, 2017; Revised June 09, 2017

Tumor growth being a multistage process has been investigated from different aspects. In the present study, an attempt is made to represent a constitutive-structure-based model of avascular tumor growth in which the effects of tensile stresses caused by collagen fibers are considered. Collagen fibers as a source of anisotropy in the structure of tissue are taken into account using a continuous fiber distribution formulation. To this end, a finite element modeling is implemented in which a neo-Hookean hyperelastic material is assigned to the tumor and its surrounding host. The tumor is supplied with a growth term. The growth term includes the effect of parameters such as nutrient concentration on the tumor growth and the tumor's solid phase content in the formulation. Results of the study revealed that decrease of solid phase is indicative of decrease in growth rate and the final steady-state value of tumor's radius. Moreover, fiber distribution affects the final shape of the tumor, and it could be used to control the shape and geometry of the tumor in complex morphologies. Finally, the findings demonstrated that the exerted stresses on the tumor increase as time passes. Compression of tumor cells leads to the reduction of tumor growth rate until it gradually reaches an equilibrium radius. This finding is in accordance with experimental data. Hence, this formulation can be deployed to evaluate both the residual stresses induced by growth and the mechanical interactions with the host tissue.

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Figures

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Fig. 1

Finite element representation of tumor tissue and its surrounding host

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Fig. 2

Experimental and model predicted radius of MU89 line tumor spheroid versus time

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Fig. 3

Radial stresses generated in tumor and its surrounding host

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Fig. 4

Circumferential stresses generated in tumor and its surrounding host

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Fig. 5

(a) First and (b) third principal stress variation as a function of radius in tumor and host tissue at day 20

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Fig. 6

Radius of tumor versus time for five different values of ϕs

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Fig. 7

Radial stress inside tumor and through the surrounding host for five different values of ϕs

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Fig. 8

Circumferential stress inside tumor and through the surrounding host for five different values of ϕs

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Fig. 9

Variation of radius of tumor spheroid versus time for the three sets of βi′s

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Fig. 10

Ellipsoidal tumor at the last time point

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