یک مدل ریاضی برای بررسی جریان خون به‌عنوان جریان سیال کراس در طول رگ گرفته شده
محورهای موضوعی : آماراحمدرضا حقیقی 1 , نیکو پیرهادی 2 , محمد شهبازی اصل 3
1 - دانشیار، گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه فنی و حرفه‌ای، تهران، ایران
2 - کارشناسی ارشد، گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه صنعتی ارومیه، ارومیه، ایران
3 - دکتری، گروه ریاضی کاربردی، دانشکده علوم پایه، دانشگاه تبریز، تبریز، ایران
کلید واژه: "Tapered Artery", "Cross Fluid", "Finite Difference Method", "Non-symmetric Stenosis", "Pulsatile Blood Flow",
چکیده مقاله :
در این تحقیق یک مدل دوبعدی برای جریان خون پالسی در طول رگ مخروطی با گرفتگی غیرمتقارن شبیه‌سازی شده است. جریان خون به‌عنوان سیال کراس در یک لوله استوانه الاستیک با گرفتگی غیرمتقارن نسبت به جهت محوری و هندسه‌ی وابسته به زمان مدلسازی می‌شود. دیواره عروق گرفته شده در طول رگ انعطاف‌پذیر و غیرانعطاف‌پذیر باهم مقایسه شده است. از فرض گرفتگی خفیف برای ساده کردن معادلات حاکم بر جریان استفاده می‌شود. با اعمال نگاشت مناسب شبکه‌ی کسینوسی گرفته شده به یک شبکه‌ی مستطیلی و صلب تبدیل می‌گردد. معادلات ناویر-استوکس حاکم بر جریان خون برای میدان سرعت با استفاده از روش تفاضلات متناهی حل می‌شود. به منظور اثبات درستی نتایج به دست آمده در تحقیق حاضر، نتایج حاصل با نتایج تحقیقات پیشین مورد مقایسه قرار گرفته و درستی مدل ارایه شده به اثبات رسیده است. مشخصه‌های اصلی جریان خون از قبیل دبی حجمی، مقاومت در برابر جریان، تنش برشی دیواره از روی پروفیل سرعت بدست آمده است. نمودارهای دوبعدی برای پارامترهای مختلفی از توزیع سرعت در شکل‌های مختلف ارایه شده است.
In this research, a two-dimensional model of pulsatile blood flow through a tapered artery with a non-symmetric stenosis is simulated. The blood flow as a cross fluid is modeled in an elastic cylindrical tube with an axially non-symmetric stenosis and a time-dependent geometry. The velocity of blood flow is compared within an elastic artery and an inelastic artery. Mild stenosis approximation is applied to simplify the governing equations. By applying an appropriate coordinate transformation, a cosine elastic artery turns into a rectangular and rigid artery. Using the finite difference method the Navier-Stokes equations governing the dynamics of the blood flow are numerically solved for velocity field. The correctness of the proposed model is proved through a comparison between the obtained results the present study and the previously obtained ones by others. The blood flow characteristics including resistive impedances, volumetric flow rate, and wall shear stress are obtained via the axial velocity profile. Various Two-dimensional diagrams for different parameters of the velocity distribution are also provided.
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