نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 کارشناسی ارشد، گروه فیزیک پزشکی و مهندسی پزشکی، دانشکده‌ی پزشکی، دانشگاه علوم پزشکی تهران، تهران، ایران / مرکز تحقیقات فناوری‌های بیومدیکال و رباتیک، تهران، ایران

2 کارشناسی ارشد، دانشکده‌ی برق، گروه مهندسی پزشکی، دانشگاه زنجان، زنجان، ایران

3 استادیار، دانشکده‌ی مهندسی برق و کامپیوتر، دانشگاه فنی بوئین‌زهرا، بوئین‌زهرا، ایران

4 استاد، مرکز تحقیقات سلولی مولکولی، دانشگاه علوم پزشکی قزوین، قزوین، ایران

5 دانشیار، گروه فیزیک پزشکی و مهندسی پزشکی، دانشکده‌ی پزشکی، دانشگاه علوم پزشکی تهران، تهران، ایران / مرکز تحقیقات فناوری‌های بیومدیکال و رباتیک، تهران، ایران

10.22041/ijbme.2020.117568.1540

چکیده

طبق آمارهای جهانی، تا سال 2040 میلادی هر ساله 5/27 میلیون نفر به بیماری سرطان مبتلا خواهند شد، از این رو شناخت و درک عمیق‌تر مکانیسم عمل‌کرد سرطان و پاسخ سیستم ایمنی به آن بسیار ضروری می‌باشد. امروزه از مدل­های محاسباتی به طور گسترده برای دست‌یابی به دینامیک­­‌های سیستم ایمنی-سرطان استفاده می‌شود. مدل مورد استفاده در این مطالعه بر مبنای معادلات دیفرانسیل معمولی بوده و به طور مکانیکی تعاملات بین سلول‌های تومور، CTL، NK و MDSC را مدل می­کند. سلول‌های CTL و NK مهم‌ترین سلول‌های سیستم ایمنی تطبیقی و ذاتی در تقابل با سلول‌های تومور هستند در حالی که سلول‌های MDSC به عنوان سلول‌های نابالغ سیستم ایمنی در محیط التهابی به سرکوب پاسخ ایمنی می­پردازند. در پارامترهای کینتیک مدل‌های محاسباتی، به دلیل خطا در اندازه‌گیری داده‌های آزمایشگاهی in vivo و in vitro، ابهام، اطلاعات غیردقیق، داده‌های ناکامل و تغییرات سیستم ایمنی-سرطان افراد و ویژگی‌های دینامیک سیستم ایمنی-سرطان، عدم قطعیت وجود دارد که با استفاده از تئوری فازی می­توان آن را مدل‌سازی کرد. از این رو در مدل سیستم ایمنی-سرطان مورد استفاده در این مطالعه، به برخی از پارامترهای کینتیک مدل، به جای اختصاص یک عدد قطعی، یک عدد فازی با تابع تعلق مثلثی اختصاص داده شده و اثر عدم قطعیت موجود در پارامترهای کینتیک مدل معادلات دیفرانسیل معمولی بر عدم قطعیت دینامیک اجزای سیستم مورد بررسی قرار گرفته است. در این مطالعه برای اولین بار از عدد فازی برای مدل‌سازی عدم قطعیت موجود در پارامترهای مدل ODE استفاده شده است. نتایج شبیه‌سازی نشان می‌دهد که افزایش/کاهش باند عدم قطعیت پارامترهای کینتیک مدل سبب افزایش/کاهش در باند عدم قطعیت دینامیک سلول‌ها می­شود. هم‌چنین نتایج شبیه‌سازی با فرض پارامترهای قطعی و فازی برای مدل نشان می­دهد که تکرار درمان 5-FU باعث می­شود تا تومور به طور چشم‌گیری سرکوب و نابود شود. 

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A Mathematical Model of Tumor-Immune System with Fuzzy Parameters

نویسندگان [English]

  • Sajad Shafiekhani 1
  • Amin Mashayekhi Shams 2
  • Seyed Yashar Banihashem 3
  • Nematollah Gheibi 4
  • Amir Homayoun Jafari 5

1 M.Sc., Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran / Research Center for Biomedical Technologies and Robotics, Tehran, Iran

2 M.Sc., Electrical Department, Biomedical Engineering Faculty, University of Zanjan, Zanjan, Iran

3 Assistant Professor, Department of Electrical and Computer Engineering, Buein Zahra Technical University, Buein Zahra, Iran

4 Professor, Cellular and Molecular Research Center, Qazvin University of Medical Science, Qazvin, Iran

5 Associate Professor, Department of Medical Physics and Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran / Research Center for Biomedical Technologies and Robotics, Tehran, Iran

چکیده [English]

According to cancer’s global statistics, there will be 27.5 million new cases of cancer each year by 2040, therefore, it is crucial to achieve a deeper understanding of the cancer progression mechanisems and immune system functions in response to it. Nowadays, computational models are widely used to capture dynamics of the tumor- immune system (TIS). The proposed model on this manuscript is on the basis of the ordinary differential equations which mechanistically models the interactions of tumor cells, CTLs, NKs and MDSCs. CTLs and NK cells are the most important cells of adaptive and innate immune system, respectively that encounter with tumor cells, while MDSCs as immature immune cells suppress the immune responses in the inflammatory environments. Due to the error of the in-vivo/in-vitro experiments, vagueness, imprecise information, incomplete data and natural variability of the tumor-immune system emerges between different individuals, the kinetic parameters of computational models are uncertain that this uncertainty can be captured by fuzzy sets. Hence, we assign fuzzy numbers with triangular membership functions instead of crisp numbers to some kinetic parameters of the tumor–immune system model. In fact, the uncertainty in the kinetic parameters of the ordinary differential equations affects the dynamic of the system species. In this essay, for the first time, a fuzzy number has been used to model the uncertainty of the parameters of the ODE model. Our data reveals that increasing/decreasing the uncertainty region of the model's fuzzy parameters increases/decreases the uncertainty region of dynamics of species. Furtheremore, the simulations of the model in the crisp setting of parameters show that the repition of 5-FU treatment for inhibition of MDSCs dramatically inhibits tumor cells and eradicate tumor.

کلیدواژه‌ها [English]

  • ode
  • Tumor-Immune
  • Fuzzy number
  • Dynamic
  • 5-FU
  • Cancer

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