Document Type : Full Research Paper


1 M.Sc. student, Electrical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran



A tumor cannot grow more than a few millimeters without a blood supply (avascular tumor), and for further growth it must initiate angiogenesis process. A vascularized tumor, which is permeated with blood vessels, rapidly increases in mass because of the new source of oxygen. In this study, a discrete mathematical model of angiogenesis process with considering the penetration of blood flow through the vessels in the two-dimensional network is presented. This structure is coupled with an adaptive model of sprouts spacing along the parent blood vessel at the beginning of the angiogenesis process. Then, progression of these sprouts in the extracellular matrix and their penetration into the tumor as well as penetration of blood flow through the capillary structure is presented. This model incorporates three steps of adaptive sprout spacing along the parent blood vessel, sprout progression, and blood flow and network remodeling. Then, based on the simulated vasculature network, oxygentransmission and other vital chemicals needed for continuous tumor growth are simulated. In this model we assumed that the growth of the tumor is driven by cell division. The tumor growth and angiogenesis are coupled by the changes of micro environment including oxygen, tumor growth factor, and the extracellular matrix concentration. Also, we have tried to create space and time adaptations in parameters of the model.


Main Subjects

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