Figure 5.

Illustration of a perfusion and transport model. Intravascular and interstitial flow is characterized by the laws of Poiseuille, Starling, and Darcy. Inset a illustrates Poiseuille’s and Starling’s law. Poiseuille’s law relates intravascular flow (Q_v, blue arrows in inset a) to the radius of the vessel (R), the dynamic viscosity of blood μ, and the gradient of the intravascular pressure p_v. Starling’s law relates the rate of extravasation (J_v, red arrows in inset b) to the hydraulic conductivity of the vessel wall (L_p), the vascular surface area (S), the reflection coefficient (σ), the vascular oncotic pressure (π_v), and the interstitial oncotic pressure (π_t). Inset b shows an illustration of Darcy’s law which relates the interstitial flow velocity (m_t, blue arrows in inset b) to the interstitial tissue hydraulic conductivity (κ), and the gradient of interstitial pressure (p_t). These three relations are found throughout the literature on the physical modeling of tumor associated vascular flow and angiogenesis.