2.1. Interstitial Fluid Transport 2.1.1. Mass Conservation Equation This is described by ∂ρ∂t+∇·(ρv)=(Fv−Fly)ρ, (1) where ρ and v are the density and velocity of the interstitial

fluid, respectively. Fv is the interstitial fluid loss from the blood vessels per unit volume of tumour tissue, and Fly is the fluid absorption rate by the lymphatics per unit volume of tumour tissue. Fv and Fly are given by Starling’s law Fv=KvSV[pv−pi−σT(πv−πi)], (2) where Kv is the hydraulic conductivity of the microvascular wall, S/V is the surface area of blood vessels per unit volume of tumour tissue, pv and pi are the vascular and interstitial fluid pressures, respectively, σT Inhibitors,research,lifescience,medical represents the average osmotic reflection coefficient for plasma protein, πv is the osmotic pressure of the plasma, and πi is that of interstitial Inhibitors,research,lifescience,medical fluid. The lymphatic drainage, Fly, is related to the pressure difference between the interstitial fluid and lymphatics: Fly=KlySlyV(pi−ply), (3) where Kly is the hydraulic conductivity of the lymphatic wall, Sly/V is the surface area of lymphatic vessels per unit volume of tumour tissue, and ply is the intralymphatic

pressure. 2.1.2. Momentum Conservation Equation Since the intercapillary distance (33–98μm [19, 20]) is usually 2-3 orders of magnitude smaller than the length scale for Inhibitors,research,lifescience,medical Inhibitors,research,lifescience,medical drug transport (approximately 70mm in this study), it is reasonable to treat the tumour and its surrounding tissues as porous media, for which the Navier-Stokes equations are applicable. By ignoring the gravitational effect, the momentum equation is expressed as ∂(ρv)∂t+∇·(ρvv)=−∇pi+∇·τ+F, (4)

where τ is the stress tensor which is given by τ=μ[∇v+(∇v)T]−23μ(∇·v)I, (5) where I is the unit tensor. The last term in (4), F, represents the Darcian GPCR Compound Library clinical trial resistance to fluid flow through Inhibitors,research,lifescience,medical porous media and is given by F=Wμv+12Cρ|v|v, (6) and W is a diagonal matrix with all diagonal elements calculated as W=κ−1, (7) where μ is the dynamic viscosity of interstitial fluid, C is the prescribed matrix of the inertial loss term, and κ is the permeability of the interstitial Adenosine triphosphate space. Since the velocity of interstitial fluid is very slow (|v | 1) [15], the inertial loss term can be neglected when compared to the Darcian resistance. In addition, the interstitial fluid is treated as incompressible with a constant viscosity. Hence, (6) can be reduced to F=Wμv. (8) 2.2. Drug Transport Drug transport is described by equations for the free and bound drug concentrations in the interstitial fluid and the intracellular concentration. 2.2.1. Free Doxorubicin Concentration in the Interstitial Fluid (Cfe) This is described by ∂Cfe∂t+∇·(Cfev)=Dfe∇2Cfe+Si, (9) where Dfe is the diffusion coefficient of free doxorubicin.