16376

16376

مدل رياضي براي شكل گيري مويرگي و توسعه ي رگ زايي تومور

كارشناسي ارشد

رياضي كاربردي

شهريور 1395

دكتر جليل رشيدي نيا

دكتر مرتضي گرشاسبي

رياضي

در اين پايان نامه نظريه فرايند عروقي شدن رشد تومور را مطالعه مي كنيم،مهاجرت و تكثير سلول هاي ”اندوتليال ” (EC) در شكل گيري جديد رگ هاي خوني در طول رگ زايي تومور ايفاي نقش مي كند. در ساده ترين نسخه از مدل، عروق تومور فاكتور رشد رگ زايي تومور (TGF) را ترشح مي كند،به طوري كه از ميان ماده خارج سلولي (ECM) به همسايگي عروق جايي كه سلول هاي ”اندوتليال” را براي توليد پروتئاز تحريك مي كند و به عنوان كاتاليزور براي تجزيه فيبرونكتين از ديواره مويرگ و ECM عمل مي كند. سلول هاي ”اندوتليال” سپس TGF را براي برگشت به تومور،تكثير و شكل گيري شبكه مويرگي جديد حركت مي دهند. مدل ارائه شده در اين پايان نامه شامل دو مكانيزم براي عملكرد رگ زايي مي باشد. در اولين مكانيزم، به طور تجربي نشان داده شده كه فعاليت هاي آنژيواستاتين به عنوان مهاركننده ”پروتئاز” است.در دومين مكانيزم براي توليد مهاركننده پروتئاز به وسيله سلول هاي”اندوتليال” نوع ”ميچل منتن” پيشنهاد مي گردد، از نظر رياضي مكانيزم قبلي به عنوان پايه اي براي اين مكانيزم است.تفاوت مدل ما از ديگر پروسه هاي مدل سازي رگ زايي تومور در اين موارد متمركز شده است: 1- فرايند سازي در سطح سلول براساس زيست شيمي 2- حركت سلول ها بر پايه نظريه تقويت شده قدم زني تصادفي است 3- معادله هاي انتقال استاندارد براي انتشار گونه هاي ملكولي متخلخل

1395/11/03

1/1/1900 12:00:00 AM

Abstract In this thesis, we study a mathematical model for the tumor vascularization theory of tumor growth.Migration an​d proliferation of endothelial cells in performed an​d newly formed blood vessels during tumor angiogenesis.In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease that acts as a catalyst to degrade the fibronectin of the capillary wall an​d the ECM. The endothelial cells then move up the TGF gradient back to the tumor, proliferating an​d forming a new capillary network. In the model presented here, we include two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as a protease inhibitor.A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis–Menten type. Mathematically, this mechanism includes the former as a subcase. Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks; (3) standard transport equations for the diffusion of molecular species in porous media. One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the oneset of vascularization an​d the rate of capillary tip growth observed in rabbit cornea experiments. ٨4 Finally an analysisis performed to find the numerical solution of a mathematical model for capillary formationin tumor angiogenesis.Firstly, a time stepping approach is employed for the time derivative,then a mesh free process based on a global collocation method using the radial basis functions(RBFs)is applied for solving the problem. Stability analysis of the method is investigated. Because of non-availability of the exact solutions , efficiency an​d accuracy of the method is demonstrated, by comparison with existing methods. Also the method is successfully applied for solving the problem with high values of the cell diffusion constant ,which many of the available methods are not applicable for solving these cases. Keywords: Tumor angiogenesis, Endothelial cells, Inhibitor, Radial basis functions