Abstract:Modeling of the spatial-temporal distribution of therapeutics in the
tumor (continuum approach)
Within this project a mathematical model that describes the intra-tumoral distribution of a targeted
protein therapeutic under consideration of the input signal and the
topographical constraints as well as cellular architecture of the tumor (tumor vessels, cellular and
acellular components of the stroma, malignant tumor cells) will be developed.
In modelling the time and spatial evolution of the targeting agents within the tumor a continuum approach will be applied.
For the implementation of this model the tumor is assumed to be a porous medium
composed of cell surface subcompartments, interstitial pore fluids and the vascular compartment.
The mass balance equations for the injected agent involve the diffusive and convective fluxes
through the vascular compartment, transport across the microvascular wall, and transport through
the interstitial compartment. During the transport the therapeutic agent may bind specifically to the
targets. The quantitative information about the morphological parameter of the tumor is extracted
from the experimental observations described below. For numerical integration of the system of
partial differential equations (PDE) the box method is used which is a local mass conservation
finite volume approach that allows the use of finite element meshes.