Figure 1 depicts the computational geometry and the flow signalling and tumour cell density dynamics. The main as sumptions are as follows blood is an incompressible, Newtonian fluid and the blood vessel is straight and rigid. the tumour interstitium is homogeneous, with a uniform distribution of nutrients and pH. tumour cells are stationary, leading to the assumption that the selleck bio tumour interstitium has a fixed outer boundary. all tumour cells are distributed uniformly, identical and alive initially. These as sumptions are made with the understanding that the key ingredients are reasonably represented in the initial model and that individual assumptions may be relaxed in subse quent studies. Detailed descriptions of each of the elements are given in the following sections.

A brief overview of the mathematical equations for different regions in the compu tational domain is presented in Figure 2, with symbols and values of parameters defined in Tables 1 and 2. Tumour blood flow The model accounts for the coupling between vascular, transmural and interstitial fluid flow since tumour blood vessels are highly permeable. Blood flow is assumed to be steady, which is acceptable here as it is capable of serving as a fundamental platform to investigate the dynamic be haviour of drug transport and intracellular events without imposing further complexities related to pulsatile blood flow. Flow within the blood vessel is governed by the Navier of information in the model.

Mathematical models Stokes equations The current modelling framework includes basic descrip tions of blood flow, drug transport, intracellular apoptosis Where �� is blood density, u is blood viscosity, u is blood velocity vector with subscript v denoting vascular space, and Pv is vascular blood pressure. Eqn. 1a and Eqn. 1b are solved subject to the following boundary conditions Fluid motion in the interstitial space is described by Darcys law where K represents interstitial hydraulic conductivity, and ui and Pi are blood velocity vector and fluid pressure in the interstitium. The boundary conditions for Eqn. 3a and Eqn. 3b are The boundary conditions described by Eqn. 2a and Eqn. 2b specify a constant arterial and venous pressure at the inlet and outlet of the vessel, respectively. BC assumes a transmural velocity in the normal direction of the blood vessel. BC assigns the ambient pressure at all boundaries of the interstitium . BC prescribes a transmural velocity Dacomitinib normal to the vessel wall. The transmural velocity, JF can be calculated using Starlings law Where Lp selleck chemicals DZNeP is vascular hydraulic conductivity, ��d is osmotic reflection coefficient, and ��v and ��i are osmotic pressure in the vascular and insterstitial space, respectively.