Journal of Biological Physics

, Volume 44, Issue 3, pp 361–400 | Cite as

In vivo mimicking model for solid tumor towards hydromechanics of tissue deformation and creation of necrosis

  • Bibaswan DeyEmail author
  • G. P. Raja Sekhar
  • Sourav Kanti Mukhopadhyay
Original Paper


The present work addresses transvascular and interstitial fluid transport inside a solid tumor surrounded by normal tissue (close to an in vivo mimicking setup). In general, biological tissues behave like a soft porous material and show mechanical behavior towards the fluid motion through the interstitial space. In general, forces like viscous drag that are associated with the fluid flow may compress the tissue material. On the macroscopic level, we try to model the motion of fluids and macromolecules through the interstitial space of solid tumor and the normal tissue layer. The transvascular fluid transport is assumed to be governed by modified Starling’s law. The poroelastohydrodynamics (interstitial hydrodynamics and the deformation of tissue material) inside the tumor and normal tissue regions is modeled using linearized biphasic mixture theory. Correspondingly, the velocity distribution of fluid is coupled to the displacement field of the solid phase (mainly cellular phase and extracellular matrix) in both the normal and tumor tissue regions. The corresponding velocity field is used within the transport reaction equation for fluids and macromolecules through interstitial space to get the overall solute (e.g., nutrients, drug, and other macromolecules) distribution. This study justifies that the presence of the normal tissue layer plays a significant role in delaying/assisting necrosis inside the tumor tissue. It is observed that the exchange process of fluids and macromolecules across the interface of the tumor and normal tissue affects the effectiveness factor corresponding to the tumor tissue.


Biphasic mixture theory Effectiveness factor Necrotic core Peclet number Interstitial space 



The authors are thankful to Mr. Abhirup Mookherjee, Department of Biotechnology, Indian Institute of Technology Kharagpur, India for suggestions. The first author has received financial support from Indian Institute of Technology, Kharagpur (Ministry of Human Resource and Development, Government of India) with grant no: IIT/Acad(PGS&R)/F.II/2/11MA/91R03 during his stay at IIT Kharagpur as a regular institute research scholar.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Bibaswan Dey
    • 1
    • 2
    Email author
  • G. P. Raja Sekhar
    • 2
  • Sourav Kanti Mukhopadhyay
    • 3
  1. 1.SRM Research Institute, Department of MathematicsSRM Institute of Science and TechnologyKancheepuramIndia
  2. 2.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  3. 3.Department of BiotechnologyIndian Institute of Technology KharagpurKharagpurIndia

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