Numerical Approximation of Nonlinear, Non-Newtonian Arterial Blood Flow in human Circulatory System

E.C. Akah¹ , J. Chukwuchekwa² , A.V. Onuche³

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.2 , pp.36-42, Apr-2022

Online published on Apr 30, 2022

Copyright © E.C. Akah, J. Chukwuchekwa, A.V. Onuche . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we investigate the e?ects of uncertainties of parameters involved in the elastic and viscoelastic constitutive equation for blood ?ow model recently proposed by Bertaglia et al (2020). An IMEX ?nite volume stochastic collocation scheme which guarantees spectral convergence in the stochastic space is imminent. When the variability of flow rate and velocity waveforms is compared to the variability of pressure and area, the concluding ones are significantly more susceptible to the parametric errors underpinning the mechanical characterization of vessel walls. The scheme is consistent with the equilibrium limit, which corresponds to the asymptotic elastic behavior for small relaxation times. Simulations done considering both the simple elastic and the more realistic viscoelastic constitutive law show that the great uncertainty of the viscosity parameter plays a key role in the forecast of pressure waveforms, adding to the confidence interval of this variable. In-vivo recorded patient-specific pressure data lies within the confidence interval of the output gotten with the proposed methodology and anticipations of the computed pressures are comparable to the recorded waveforms.

Key-Words / Index Term :
Stochastic partial differential equations, Viscoelastic fluids, collocation method, spectral convergence in stochastic space

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