A model of angiogenesis by hybrid systems with delay on the piecewise constant part

Date

2009-09-01

Author

Karasözen, Bülent
Kahraman, Mustafa

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An important approach towards understanding the cancer dynamics is the modeling of angiogenesis process. There have been several attempts to model this process. Among them angiogenesis models with time delays, caused by the physical distance between the tumor and the vessel, are the most realistic ones. Recent studies have suggested that those delays can cause oscillatory behavior in the angiogenesis process. In this work we employed piecewise linear hybrid systems with delay on the piecewise constant part. Our approach is based on piecewise linearization of the system behavior where the delays occur at threshold crossings and state transitions. Piecewise linear systems with a single threshold for each variable are useful in approximating and modeling the dynamical systems especially when the model might need to be calibrated by the observations. Therefore, we used piecewise linear systems where the delays are introduced in piecewise constant part of the equations. Our approach allows tractable approximation of the angiogenesis process with possible advances of incorporating more variables, involving the effect of some possible external inputs, and possible adjustment or correction of parameters by observations.

Subject Keywords

Hybrid systems, Time delay, Bifurcations, Angiogenesis

URI

https://hdl.handle.net/11511/30606

Journal

JOURNAL OF PROCESS CONTROL

DOI

https://doi.org/10.1016/j.jprocont.2009.05.003

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen and M. Kahraman, “A model of angiogenesis by hybrid systems with delay on the piecewise constant part,” JOURNAL OF PROCESS CONTROL, pp. 1257–1264, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30606.