Interstitial Stress and Fluid Pressure Within a Growing Tumor

Abstract

A solid tumor is composed of a population of cells that is expanding as a result of cell division. With dense cell packing, the solid matrix of the interstitial tissue is subject to residual stress. In addition, elevated interstitial fluid pressure (IFP) has been reported by researchers for a number of solid tumors. These features were incorporated into a mathematical model that predicts the mechanical response of a solid tumor within its host environment. A theoretical framework accounting for volumetric expansion, transvascular exchange and extravascular transport of fluids was developed using poroelastic theory, and applied to a spherical, vascularized, alymphatic tumor undergoing small growth increments. Simulations of tumor IFP were similar to those predicted by Jain and Baxter, showing elevated IFP that is driven by microvascular fluid pressure. Tumor growth, tissue stiffness, and IFP contribute to the compressive stresses predicted in the solid tumor interior. Tensile and compressive stresses were predicted in adjacent host tissues corresponding to radial and circumferential directions, respectively. An application of this model includes a solid stress-based framework for predicting regions of vascular collapse within the tumor interior.

A Model for Interstitial Drainage Through a Sliding Lymphatic Valve

“…The Poisson's ratio (ν) and the Young's Modulus (E) are given in [26] for soft tissue as ν = 0.35 and E = 10 4 Pa. This gives λ = 8642 Pa and µ = 3704 Pa. We note that the Poisson ratio thus calculated is consistent with measurements made in [4,47]. With these parameter ranges E is in the range 5 × 10 4 Pa to 1.3 × 10 5 Pa, which is consistent with the studies by [18,26].…”

“…The vascular permeability of a blood capillary, L p , was measured in various normal tissues by Jain et al [25], Levick [34], Pusenjak [41], Baxter and Jain [4] and Sarntinoranont et al [47] and estimated to be in the range 2.78 × 10 −11 m 2 skg −1 to 1.37 × 10 −9 m 2 skg −1 . We take the average value L p = 7.0 × 10 −10 m 2 skg −1 .…”

Perfusion CT Assessment of Tissue Hemodynamics Following Hepatic Arterial Infusion of Increasing Doses of Angiotensin II in a Rabbit Liver Tumor Model

“…Elevated fl uid pressure, as well as mechanical stress generated by tumor cells and their interaction with the extracellular matrix (interstitial stress), causes narrowing and collapse of intratumoral blood vessels ( 19 ), which limit the delivery of intraarterially administered therapeutic agents. Since the blood vessels in hepatic tumors, including VX2 cancers, commonly lack smooth muscle ( 20,21 ), the arterial infusion of vasoconstricting agents should constrict vessels in the normal liver while leaving the tumor vessels unaffected.…”

USNCTAM perspectives on mechanics in medicine

“…Most models are fluid-fluid mixture models such as [129,130], whereas fewer are solid-fluid models. The latter of which either consider the tumour as a solid, permeated by IF [131] or are composed of an ECM permeated by one or several fluids [132]. This last one seems to be the most versatile and will be considered in more detail.…”