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

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.

Hydrodynamics and convection enhanced macromolecular fluid transport in soft biological tissues: Application to solid tumor.

This work addresses a theoretical framework for transvascular exchange and extravascular transport of solute macromolecules through soft interstitial space inside a solid tumor. Most of the soft biological tissues show materialistic properties similar to deformable porous material. They exhibit mechanical behavior towards the fluid motion since the solid phase of the tumor tissue gets compressed by the drag force that is associated with the extracellular fluid flow. This paper presents a general view about the transvascular and interstitial transport of solute nutrients inside a tumor in the macroscopic level. Modified Starling׳s equation is used to describe transvascular nutrient transport. On the macroscopic level, motion of extracellular fluid within the tumor interstitium is modeled with the help of biphasic mixture theory and a spherical symmetry solution is given as a simpler case. This present model describes the average interstitial fluid pressure (IFP), extracellular fluid velocity (EFV) and flow rate of extracellular fluid, as well as the deformation of the solid phase of the tumor tissue as an immediate cause of extracellular fluid flow. When the interstitial transport is diffusion dominated, an analytical treatment of advection-diffusion-reaction equation finds the overall nutrient distribution. We propose suitable criteria for the formation of necrosis within the tumor interstitium. This study introduces some parameters that represent the nutrient supply from tumor blood vessels into the tumor extracellular space. These transport parameters compete with the reversible nutrient metabolism of the tumor cells present in the interstitium. The present study also shows that the effectiveness factor corresponding to a first order nutrient metabolism may reach beyond unity if the strength of the distributive solute source assumes positive non-zero values.