Numerical solution of a model for brain cancer progression after therapy

Abstract

We present a numerical scheme used to investigate a mathematical model of tumor growth which incorporates multiple disparate timescales. We simulate the model with different initial data. The initial conditions explored herein correspond to a small remnant of tumor tissue left after surgical resection. Our results indicate that tumor regrowth begins at the pre‐surgery tumor‐healthy tissue interface and penetrates back into the original tumor area. This growth is rate‐limited by the reformation of the tumor vascular network.

Key words:

• theoretical oncology
• mathematical models
• numerical methods

Notes

The work of the first author was partially supported by NSF grant DMS‐0509597. The second author was partially supported by NSF grant DMS‐0436341 and the grant DMS/NIGMS‐0342388 jointly funded by NIH and NSF