حل عددي جريان ريزقطبي ضرباني خون در رگ ويسكوالاستيك و مقايسه‌ي آن با رگ صلب و الاستيك

Numerical Simulation of Pulsatile Micropolar Blood Flow in a Viscoelastic Artery and Comparison with Rigid and Elastic Arteries

در سال هاي اخير، شبيه سازي عددي مدل هاي اندركنش سيال و جامد بسيار مورد توجه قرار گرفته است. ديناميك سيالات با حركت نوساني اهميت زيادي در زمينه‌ي سيستم هاي قلبي و عروقي انسان دارد. هدف اين مطالعه استنتاج روشي عددي به‌منظور توصيف دقيق تر جريان خون به‌عنوان سيالي ريزقطبي در رگ ويسكوالاستيك با جاه‌بجايي بزرگ ديواره و گراديان فشار ضرباني است. شبيه سازي با اعمال شرايط مرزي مناسب به روش لاگرانژي ـ اويلري دلخواه براي ديواره‌ي صلب، الاستيك و ويسكوالاستيك در محيط پيوسته كسرات و كلاسيك انجام گرفته و با نتايج آزمايشگاهي مقايسه شده است. برخي ضرايب مجهول در معادلات طي اين مراحل به دست مي آيد. به‌كمك حل عددي، فشار و سرعت هاي جريان محاسبه شده است. نتايج اين مطالعه نشان مي‌دهد كه انتخاب مدل سيال ريزقطبي خون و مدل ويسكوالاستيك رگ، با توجه به مزدوج‌بودن معادلات سيال و جامد موجب افزايش تطابق نتايج عددي بر داده هاي معتبر آزمايشگاهي مي شود.

Under normal physiological conditions, the transport of blood in the human circulatory system depends entirely on the pumping action of the heart producing a pulsatile pressure gradient throughout the arterial system. The theory of microfluids exhibits the microscopic effects arising from the local structure, and the micro-motion of the fluid elements was developed. Such fluids support stress and body moments, including rotary inertia. There is a subclass of microfluids, namely, micropolar fluids, which support couple stress, body couples, microrotational effects and microrotational inertia. The micropolar fluid, e.g. liquid crystals, suspensions and animal blood etc., consists of randomly oriented bar-like elements or dumbbell molecules, and each volume element has a microrotation about its centroid, described in an average sense by the skew-symmetric gyration tensor. From a continuum point of view, the classical Navier-Stokes equations are incapable of explaining the theory of micropolar fluid as they contain no proper mechanism to account for the cellular microrotations. In this paper, an unsteady pulsatile laminar blood flow through a viscoelastic artery with large displacement and Cosserat continuum assumption has been developed and numerically investigated, where the blood was assumed to be a micropolar fluid. A finite difference Cosserat formulation is developed within the principles of continuum mechanics. Fluid flow simulation has been undertaken in different states, like a rigid flexible wall, together with classical theory. By comparing experimental data with Cosserat theory results, some unknown coefficients have been determined. The pressure and velocities of unsteady pulsatile blood flow have been obtained according to these coefficients by using a pressure correction numerical solution approach for fluid and coupling with solid equations. An arbitrary Lagrangian-Eulerian approach has been selected for fluid-structure interaction in this paper. The achieved results are in good agreement with experiment data and other analytical solution results. Results in this paper show that the micropolar fluid model of blood and the viscoelastic model of the artery, despite the existence of fluid solid interaction, increase, in accordance with the numerical results of valid experimental data.