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Toward understanding the boundary propagation speeds in tumor growth models

Publication ,  Journal Article
Liu, JG; Tang, M; Wang, L; Zhou, Z
Published in: SIAM Journal on Applied Mathematics
January 1, 2021

At the continuous level, we consider two types of tumor growth models: the cell density model, based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations, and the free boundary model, as the incompressible limit of the former, is more tractable when investigating the boundary propagation. In this work, we aim to investigate the boundary propagation speeds in those models based on asymptotic analysis of the free boundary model and efficient numerical simulations of the cell density model. We derive, for the first time, some analytical solutions for the free boundary model with pressure jumps across the tumor boundary in multidimensions with finite tumor sizes. We further show that in the large radius limit, the analytical solutions to the free boundary model in one and multiple spatial dimensions converge to traveling wave solutions. The convergence rate in the propagation speeds are algebraic in multidimensions as opposed to the exponential convergence in one dimension. We also propose an accurate front capturing numerical scheme for the cell density model, and extensive numerical tests are provided to illustrate the analytical findings.

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Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 2021

Volume

81

Issue

3

Start / End Page

1052 / 1076

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Liu, J. G., Tang, M., Wang, L., & Zhou, Z. (2021). Toward understanding the boundary propagation speeds in tumor growth models. SIAM Journal on Applied Mathematics, 81(3), 1052–1076. https://doi.org/10.1137/19M1296665
Liu, J. G., M. Tang, L. Wang, and Z. Zhou. “Toward understanding the boundary propagation speeds in tumor growth models.” SIAM Journal on Applied Mathematics 81, no. 3 (January 1, 2021): 1052–76. https://doi.org/10.1137/19M1296665.
Liu JG, Tang M, Wang L, Zhou Z. Toward understanding the boundary propagation speeds in tumor growth models. SIAM Journal on Applied Mathematics. 2021 Jan 1;81(3):1052–76.
Liu, J. G., et al. “Toward understanding the boundary propagation speeds in tumor growth models.” SIAM Journal on Applied Mathematics, vol. 81, no. 3, Jan. 2021, pp. 1052–76. Scopus, doi:10.1137/19M1296665.
Liu JG, Tang M, Wang L, Zhou Z. Toward understanding the boundary propagation speeds in tumor growth models. SIAM Journal on Applied Mathematics. 2021 Jan 1;81(3):1052–1076.

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 2021

Volume

81

Issue

3

Start / End Page

1052 / 1076

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics