شبیه‌سازی رشد و تقسیم تومور تحت نیروهای محرکه شیمیایی با استفاده از روش میدان فاز

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان

چکیده

در این مقاله، رشد و تقسیم تومورها با استفاده از روش میدان فاز بررسی می‌گردد. با در نظر گرفتن محیط تومور به عنوان سیال، رشد و تقسیم تحت نیروهای محرکه شیمیایی مطالعه می‌شود. برای شبیه‌سازی مرز مشترک جداکننده تومور و ماده زمینه خارج سلولی، روابط فشار رشد، میدان سرعت و غلظت‌های مختلف به صورت جفت شده با معادلات میدان فاز استفاده می‌شوند. همچنین، فرایندهایی مانند کموتاکسی و هپتوتاکسی و شرایط مختلفی از شبکه‌بندی حل، شکل اولیه تومور، ضخامت مرز مشترک و ضریب کشش سطحی در مدل‌سازی تکامل تومور استفاده می‌شوند. نتایج نشان می‌دهد که در تومورهایی با شکل اولیه بیضی‌گون کشیده‌تر، رشد تسریع می‌شود؛ اما، شکل نهایی تغییری نمی‌کند. با استفاده از این مدل، محدوده‌ای برای ضخامت مرز مشترک به دست آمد که در آن رشد به صورت غیرفیزیکی متوقف می‌شود. هم چنین، محدوده فیزیکی برای ضریب کشش سطحی به نحوی به دست آمد که کمتر از آن، توقف رشد و بیشتر از آن، باز شدن بیش از حد مرز مشترک رخ می‌دهد. با اضافه شدن هپتوتاکسی و به خصوص کموتاکسی، نرخ رشد تومور افزایش می‌یابد. اولی موجب تقسیم شدن، در حالی که دومی باعث شاخه‌ای شدن تومور می‌گردد. هرچه ضریب بیشتر باشد، شاخه‌ای شدن بیشتر به وقوع می‌پیوندد. کموتاکسی نسبت به هپتوتاکسی اثر بیشتری بر روی شکل و سرعت تغییرات تومور می‌گذارد. با ترکیب اثر هر دو عامل، تقسیم و شاخه‌ای شدن، به صورت هم‌زمان، دیده می‌شود. نتایج به دست آمده در درک بهتر عوامل کلیدی در رشد و تقسیم تومور کمک می‌کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Simulation of Tumor Growth and Division Under Chemical Driving Forces Using the Phase Field Method

نویسندگان [English]

  • Peyman Naderi
  • Mehdi Javanbakht
  • Ahmadreza Pishevar
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
چکیده [English]

In this paper, growth and division of tumors are investigated using the phase field modeling. By considering the environment as fluid, conditions such as chemotaxis and haptotaxis processes are used to study the growth and division of tumors. In this model, growth pressure, velocity field and different concentrations coupled with the phase field equation are used to simulate the membrane of the tumor, separating it from the extracellular matrix (ECM). Also, processes such as chemotaxis and haptotaxis, different meshes, initial tumor ovalities, interface thicknesses and surface tensions are used to model the tumor evolution. The obtained results show that in tumors with higher initial ovality, the evolution accelerates but the morphology remains unchanged. Using this model, a membrane thickness range is found, out of which the growth is unphysically suppressed. Large and small surface tension coefficient suppresses the growth and leads to the interface widening, respectively. The physical range of the surface tension coefficient is also found, below which the growth is suppressed and above which interface widening occurs. The rate of tumor growth increases by adding the haptotaxis and in particular, chemotaxis. The former results in tumor dividing while the latter causes the tumor branching. Higher taxis coefficient results in higher branching rate. Chemotaxis shows a larger effect on the tumor morphology and kinetics than the haptotaxis. Combining both mechanisms leads to simultaneous tumor division and branching. The obtained results help for a better understanding of the key parameters in tumor growth and division.

کلیدواژه‌ها [English]

  • Growth and Division
  • Phase Field Theory
  • Chemical Forces
  • Numerical Solution Parameters
  • Tumor Evolution

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