skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • NSF Public Access
  • Search Results
  • Inlet and Outlet Boundary Conditions and Uncertainty Quantification in Volumetric Lattice Boltzmann Method for Image-Based Computational Hemodynamics
Title: Inlet and Outlet Boundary Conditions and Uncertainty Quantification in Volumetric Lattice Boltzmann Method for Image-Based Computational Hemodynamics
Inlet and outlet boundary conditions (BCs) play an important role in newly emerged image-based computational hemodynamics for blood flows in human arteries anatomically extracted from medical images. We developed physiological inlet and outlet BCs based on patients’ medical data and integrated them into the volumetric lattice Boltzmann method. The inlet BC is a pulsatile paraboloidal velocity profile, which fits the real arterial shape, constructed from the Doppler velocity waveform. The BC of each outlet is a pulsatile pressure calculated from the three-element Windkessel model, in which three physiological parameters are tuned by the corresponding Doppler velocity waveform. Both velocity and pressure BCs are introduced into the lattice Boltzmann equations through Guo’s non-equilibrium extrapolation scheme. Meanwhile, we performed uncertainty quantification for the impact of uncertainties on the computation results. An application study was conducted for six human aortorenal arterial systems. The computed pressure waveforms have good agreement with the medical measurement data. A systematic uncertainty quantification analysis demonstrates the reliability of the computed pressure with associated uncertainties in the Windkessel model. With the developed physiological BCs, the image-based computation hemodynamics is expected to provide a computation potential for the noninvasive evaluation of hemodynamic abnormalities in diseased human vessels.  more » « less
Award ID(s):
1803845
PAR ID:
10381937
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
Date Published:
Journal Name:
Fluids
Volume:
7
Issue:
1
ISSN:
2311-5521
Page Range / eLocation ID:
30
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; ; ; (, Scientific Reports)
    Abstract Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems. 
    more » « less
  2. (, Journal of Engineering and Science in Medical Diagnostics and Therapy)
    Abstract Pulsatile pressure at an artery is a collection of harmonics of the heartbeat. This study examines harmonics of pulsatile pressure at different ages and its effect on other pulsatile parameters and waveform-based clinical indices. Based on a vibrating-string model of the arterial tree, wave velocity and characteristic impedance are related to arterial stiffness and radius. Blood velocity, wall shear stress (WSS), and driving force on the left ventricle (LV) are related to pulsatile pressure. Reflection magnitude and return time are related to input impedance. These relations are applied to pulsatile pressure and blood velocity at the ascending aorta (AA) and the carotid artery (CA) at different ages in a database to calculate harmonics of all the pulsatile parameters and reflection magnitude and return time at each harmonic. Harmonics of pulsatile pressure varies with aging and between the two arteries. Reflection magnitude and return time vary between harmonics. While wave reflection manifests the arterial tree (i.e., arterial stiffness and radius) and termination, harmonics of pulsatile pressure is a combination of the LV, the arterial tree, and termination. Harmonics of pulsatile pressure dictates harmonics of WSS and affects endothelial function. Harmonics of pulsatile pressure needs to serve as an independent clinical index indicative of the LV function and endothelial function. Reflection magnitude and return time of the 1st harmonic of pulsatile pressure serve as clinical indices indicative of arterial stiffness and radius. 
    more » « less
  3. (, Journal of Engineering and Science in Medical Diagnostics and Therapy)
    Abstract A tube-load model is used to reconstruct aortic pressure waveform from peripheral pressure waveform. Yet, the reconstructed aortic pressure waveform is greatly affected by load impedance used. In this work, a vibrating-string model for closed-loop wave transmission and reflection between the aorta and periphery is developed to examine the roles of all the parameters involved in aortic pressure waveform. The arterial pulsatile wave theory gives rise to the standard one-dimensional wave equation for a vibrating string. A vibrating-string model based on radial displacement of the arterial wall is developed to relate aortic pressure waveform to peripheral pressure waveform, relate load impedance to input impedance, and derive theoretical expressions for associated clinical indices. The vibrating-string model is extended to incorporate blood velocity and is further connected to the left ventricle (LV) to study the role of the LV in aortic pressure waveform. The difference between the vibrating-string model and the tube-load model is also examined. Load impedance is identified as an indispensable independent parameter for reconstruction of aortic pressure waveform with accuracy, and its physiologically realistic harmonic dependence can only be obtained from the measured input impedance. The derived expressions for clinical indices interpret some clinical findings and underscore the role of harmonics in clinical indices. Some misconceptions in the tube-load model are revealed, including load impedance and characteristic impedance. This work clarifies the role of harmonics-dependence of load impedance and harmonics of aortic pressure waveform in determining clinical indices. 
    more » « less
  4. (, Journal of Engineering and Science in Medical Diagnostics and Therapy)
    Abstract This study examines radial and axial displacement of the arterial wall under the influence of harmonics and wave reflection for the role of axial wall displacement in pulsatile wave propagation. The arterial wall is modeled as an initially-tensioned thin-walled orthotropic tube. In conjunction with three pulsatile parameters in blood flow, a free wave propagation analysis is conducted on the governing equations of the arterial wall and no-slip conditions at the blood-wall interface to obtain the frequency equation and pulsatile parameter expressions under different harmonics. The influence of wave reflection is then added to pulsatile parameter expressions. With the harmonic values of measured pulsatile pressure and blood flow rate at the ascending aorta in the literature, the waveforms of radial wall displacement, axial wall displacement, and wall shear stress are calculated under different orthotropicity and axial initial tension. The developed theory and calculated results indicate that (1) difference in waveform between blood flow rate, wall shear stress, and axial wall displacement is caused by harmonics, rather than wave reflection; (2) Axial wall displacement does not affect blood flow rate, radial wall displacement, and wall shear stress; (3) Besides wall shear stress, radial wall displacement gradient also contributes to axial wall displacement and its contribution is adjusted by axial initial tension; (4) different wave reflections only noticeably affect the maximum and minimum values of wall shear stress; and (5) The amplitude and waveform of axial wall displacement are predominantly dictated by axial elasticity and axial initial tension, respectively. 
    more » « less
  5. (, Journal of Engineering and Science in Medical Diagnostics and Therapy)
    Abstract Given the wide utility of radial vibration of the arterial wall for clinical values, this paper presents a theoretical study on the relations of radial vibration of the arterial wall to pulsatile parameters in blood flow. Pulse wave propagation in an artery is formulated as a combination of the governing equations of blood flow and the arterial wall and no-slip conditions at the blood-wall interface and is analyzed to obtain the wave velocity and the theoretical expressions for blood flow rate and radial wall displacement in terms of pulsatile pressure. With the harmonics of a pulse signal, theoretical relations of radial vibration of the arterial wall to pulsatile parameters in blood flow are derived under two conditions: without and with wave reflection. These theoretical relations identify the assumptions for the simplified relations employed in the utility of radial vibration of the arterial wall for clinical values. With the arterial wall treated as a unit-mass vibration system, these simplified relations are utilized for extraction of arterial indices from radial vibration of the arterial wall. Other applications of such relations for clinical values are discussed, and the interaction between the arterial wall and blood flow is further revealed from the perspective of energy and one-dimensional wave equations. With harmonics and wave reflection considered, the derived theoretical expressions for radial wall vibration, pulsatile parameters in blood flow, and the relations between them provide theoretical guidance for improving their interpretation of clinical values with clearly defined physiological implications and assumptions. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email