A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Impiombato, Andrea Natale; Civita, Giorgio La; Orlandi, Francesco; Zinani, Flávia Schwarz Franceschini; Rocha, Luíz Alberto Oliveira; Biserni, Cesare

doi:10.3390/dynamics1010002

Cited by 8 publications

(3 citation statements)

References 18 publications

(32 reference statements)

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“…To meet an agreement with no slip boundary conditions at rigid boundaries, we require that the inlet velocities v inlet f (t, y) and v inlet s (t, y) have the Poiseuille-like profile versus the vertical variable y [40].…”

Section: Resultsmentioning

confidence: 99%

Flows of Dense Suspensions of Polymer Particles through Oblique Bifurcating Channels: Two Continua Approach

Shelukhin

Антонов

2022

Polymers

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A two-velocity mathematical model is proposed for dense suspension flows through channel bifurcations. Equations agree with thermodynamic laws and they are suitable for both heavy and light particles. The pulsatile mode of injection of particles is considered. In the 2D-case, we address the issue of partitioning particles and study how a loss of particles into the side branch depends on the bifurcation angle. A qualitative agreement with experiment data are established. We capture the Zweifach–Fung effect. We treat polymer particles as a phase enjoying the rheology of the Bingham viscoplastic material. We prove that the polymer particle distribution between two branches correlates with the averaged-in-time Bingham number in these branches.

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Section: Resultsmentioning

confidence: 99%

Flows of Dense Suspensions of Polymer Particles through Oblique Bifurcating Channels: Two Continua Approach

Shelukhin

Антонов

2022

Polymers

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“…It has been demonstrated that when 𝛼 < 1, the flow is expected to follow the pulsating pressure gradient faithfully, and the velocity profiles exhibit a parabolic shape. When 𝛼 > 1, the velocity profiles are no longer parabolic, and the flow is out of phase in time with respect to the pressure gradient [85]. 𝛼 > 1 are commonly observed in blood vessels with a diameter larger than 3 mm such as the femoral arteries [86,87].…”

Section: Fluid Modelmentioning

confidence: 99%

Fluid-Structure Interactions of Peripheral Arteries Using a Coupledin silicoandin vitroApproach

Schoenborn

Lorenz²,

Kuo³

et al. 2023

Preprint

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Vascular compliance is considered both a cause and a consequence of cardiovascular disease and a significant factor in the mid- and long-term patency of vascular grafts. However, the biomechanical effects of localised changes in compliance, such as during plaque development or after bypass grafting and stenting, cannot be satisfactorily studied with the available medical imaging technologies or surgical simulation materials. To address this unmet need, we developed a coupled silico-vitro platform which allows for the validation of numerical fluid-structure interaction (FSI) results as a numerical model and physical prototype. This numerical one-way and two-way FSI study is based on a three-dimensional computer model of an idealised femoral artery which is validated against patient measurements derived from the literature. The numerical results are then compared with experimental values collected from compliant arterial phantoms. Phantoms within a compliance range of 1.4 - 68.0%/100mmHg were fabricated via additive manufacturing and silicone casting, then mechanically characterised via ring tensile testing and optical analysis under direct pressurisation with differences in measured compliance ranging between 10 - 20% for the two methods. One-way FSI coupling underestimated arterial wall compliance by up to 14.71% compared to two-way FSI modelling. Overall, Smooth-On Solaris matched the compliance range of the numerical and in vivo patient models most closely out of the tested silicone materials. Our approach is promising for vascular applications where mechanical compliance is especially important, such as the study of diseases which commonly affect arterial wall stiffness, such as atherosclerosis, and the model-based design, surgical training, and optimisation of vascular prostheses.

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“…The Plug profile is the uniform velocity at the inlet, while the Parabolic profile obtained from Poiseuille's equation, and therefore, they cannot present all the characteristics generated due to transitional effects. Although the Womersley profile (Womersley, 1955) is necessary to present transient effects especially for large 𝛼 values, applicability and implementation of the Womersley equation as an inlet boundary condition can be difficult because of the Bessel functions and imaginary numbers that it contains (Campbell et al, 2012;Impiombato et al, 2021). Therefore, in literature, most of the studies utilize Plug or Parabolic profile with long entrance lengths to obtain fully developed condition (Stamatopoulos et al, 2010), rather than the Womersley profile, which increases the computation time.…”

Section: Introductionmentioning

confidence: 99%

Gi̇ri̇ş Hiz Profi̇li̇ Ve Gi̇ri̇ş Uzunluğunun Abdomi̇nal Aort Anevri̇zmasi Hemodi̇nami̇ği̇ Si̇mülasyonlarina Etki̇si̇

RAMAZANLI,

SERT,

YAVUZ

2023

Isı Bilimi Ve Tekniği Dergisi

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In computational Abdominal Aortic Aneurysm (AAA) hemodynamics studies, along with adjusting the problem geometry, mesh, transport, turbulence and rheology models; setting up boundary conditions (BC) is also a very important step which affect the reliability and accuracy of the hemodynamic assessment. The transient effects of physiological flow are well described by the Womersley profile, though its application might be difficult due to the complex nature of functions involved. Conversely, in literature, studies utilizing Plug or Parabolic profiles as inlet boundary conditions generally requires large entrance lengths to obtain the exact characteristics of the Womersley profile. In the current study, the differences arising between those boundary conditions, Womersley, Parabolic and Plug, with different entrance lengths, L_(ent )=D,3D and 11D, are examined by comparing the results with a Base condition, which is a solution obtained with ensured fully-developed flow before entering the aneurysm sac at two physiological flow conditions with mean Reynolds numbers, 〖Re〗_m=340 and 1160. The results reveal that with increasing mean flow rate, applying the complex Womersley equation might not be necessary. For the inlet flow waveform with 〖Re〗_m=1160, the Parabolic profile can be used instead of the Womersley profile by supplying an entrance length L_(ent )= 3D. On the other hand, the Plug profile requires an entrance length at least L_(ent )= 11D to replicate the Base condition for waveform with 〖Re〗_m=340.

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A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Cited by 8 publications

References 18 publications

Flows of Dense Suspensions of Polymer Particles through Oblique Bifurcating Channels: Two Continua Approach

Flows of Dense Suspensions of Polymer Particles through Oblique Bifurcating Channels: Two Continua Approach

Fluid-Structure Interactions of Peripheral Arteries Using a Coupledin silicoandin vitroApproach

Gi̇ri̇ş Hiz Profi̇li̇ Ve Gi̇ri̇ş Uzunluğunun Abdomi̇nal Aort Anevri̇zmasi Hemodi̇nami̇ği̇ Si̇mülasyonlarina Etki̇si̇

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