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

Date

2009-09-01

Author

Karasözen, Bülent
Kahraman, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

153
views

0
downloads

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

Suggestions

OpenMETU
Core

A comparative study of autoregressive neural network hybrids Taşkaya Temizel, Tuğba (2005-06-01) Many researchers have argued that combining many models for forecasting gives better estimates than single time series models. For example, a hybrid architecture comprising an autoregressive integrated moving average model (ARIMA) and a neural network is a well-known technique that has recently been shown to give better forecasts by taking advantage of each model's capabilities. However, this assumption carries the danger of underestimating the relationship between the model's linear and non-linear componen...
A mathematical modeling and approximation of gene expression patterns by linear and quadratic regulatory relations and analysis of gene networks Yılmaz, Fatma Bilge; Weber, Gerhard Wilhelm; Department of Scientific Computing (2004) This thesis mainly concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary di erential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of o...
A Microwave Imaging Model for Biomedical Applications ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2017-07-14) A microwave imaging model is presented for detection of breast cancer tissues by combining the finite element method and the transformation electromagnetics approach. An inverse scattering problem is formulated based on genetic optimization algorithm, and its expensive cost function evaluations are accelerated by using the transformation electromagnetics approach, which allows using a uniform or rectangular mesh even when irregular geometries are present inside the domain. Simulation results are demonstrate...
Modeling stochastic hybrid systems with memory with an application to immune response of cancer dynamics Gökgöz, Nurgül; Öktem, Hakan; Piazza, Carla; Department of Scientific Computing (2014) Dynamics of cancer involve some complex interactions like immune system responses. Many different models of immune response to tumor growth exist in the literature. Most of the available models are first principles models which have problems in determining the model parameters. For potential use in treatment planning, a model should be able to adopt to subject by subject variability and unknown factors. However, such an approach for a complicated problem like cancer dynamics has some drawbacks. First of all...
An integrated, dynamic model for cardiovascular and pulmonary systems Yılmaz, Neval A; Eyüboğlu, Behçet Murat; Department of Electrical and Electronics Engineering (2006) In this thesis an integrated, dynamic model for cardiovascular and respiratory systems has been developed. Models of cardiopulmonary system, airway mechanics and gas exchange that preexisted in literature have been reviewed, modified and combined. Combined model composes the systemic and pulmonary circulations, left/right ventricles, tissue/lung compartments, airway/lung mechanics and gas transportation. Airway resistance is partitioned into three parts (upper, middle, small airways). A collapsible airways ...

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.