Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

Abstract

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model.

Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors

“…Results of high IFP in tumors are discussed in our previous studies [2,16,17] and in the experimental results of Arifin et al [29] and Huber et al [30]. Maximum value of IFP in spherical tumors (1 cm radius) for baseline values in Table 1 is 1529.5 Pa which is close to the studies of Jain et al [31], Chauhan et al [32], and Arfin et al [33].…”

Effect of remodeled tumor-induced capillary network on interstitial flow in cancerous tissue

“…The modeling has multi-scales nature. The model is summarized in following section; The more detail of simulation is introduced in last our group work [12].…”

“…The right hand side of Equation (9) is the mass source obtained by Starilng's equation. In this study, a source term for mass flow is considered to the righthand side of Equation (9) wherever there is a capillary; otherwise, the right-hand side of Equation (9) is simply zero, or mathematically (For more detail see [12])…”

“…The detail of algorithm of solution and value of parameter and boundary condition is mentioned in [12].…”

Numerical simulation of the tumor interstitial fluid transport: Consideration of drug delivery mechanism

“…In the angiogenesis, tangled networks of microvasculature are formed throughout the tumor for nourishment of cancer cells. Among most important work in this scope one can refer to Anderson andChaplain (1998), Stéphanou et al (2006), Harrington et al (2007), G. Zhao et al (2007), Cai et al (2011), Soltani andChen (2013), Yifat and Gannot (2014) and Sefidgar et al (2015). Despite the number of numerical investigations that have been accomplished on the tumor angiogenesis, however fewer studies are focused on the tumor interstitial pressure distribution, which may be influenced by either tissues configurations or their physiological properties.…”