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Iranian Journal of Medical Physics، جلد ۱۲، شماره ۳، صفحات ۱۴۵-۱۶۶
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عنوان انگلیسی Two Dimensional Mathematical Model of Tumor Angiogenesis: Coupling of Avascular Growth and Vascularization
چکیده انگلیسی مقاله Introduction As a tumor grows, the demand for oxygen and nutrients increases and it grows further if acquires the ability to induce angiogenesis. In this study, we aimed to present a two-dimensional continuous mathematical model for avascular tumor growth, coupled with a discrete model of angiogenesis. Materials and Methods In the avascular growth model, tumor is considered as a single mass, which uptakes oxygen through diffusion and invades the extracellular matrix (ECM). After the tumor reaches its maximum size in the avascular growth phase, tumor cells may be in three different states (proliferative, quiescent and apoptotic), depending on oxygen availability. Quiescent cells are assumed to secrete tumor angiogenic factors, which diffuse into the surrounding tissue until reaching endothelial cells. The mathematical model for tumor angiogenesis is consisted of a five-point finite difference scheme to simulate the progression of endothelial cells in ECM and their penetration into the tumor. Results The morphology of produced networks was investigated, based on various ECM degradation patterns. The generated capillary networks involved the rules of microvascular branching and anastomosis. Model predictions were in qualitative agreement with experimental observations and might have implications as a supplementary model to facilitate mathematical analyses for anti-cancer therapies. Conclusion Our numerical simulations could facilitate the qualitative comparison between three layers of tumor cells, their TAF-producing abilities and subsequent penetration of micro-vessels in order to determine the dynamics of microvascular branching and anastomosis in ECM and three different parts of the tumor. 
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نویسندگان مقاله فریده حسینی | farideh hosseini
1-department of electrical engineering, faculty of engineering, ferdowsi university of mashhad, mashhad, iran

سازمان اصلی تایید شده: دانشگاه فردوسی (Ferdowsi university)

نادیا نقوی | nadia naghavi
1-department of electrical engineering, faculty of engineering, ferdowsi university of mashhad, mashhad, iran

سازمان اصلی تایید شده: دانشگاه فردوسی (Ferdowsi university)

نشانی اینترنتی http://ijmp.mums.ac.ir/article_6217.html
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زبان مقاله منتشر شده en
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نوع مقاله منتشر شده Original Paper
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