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Mathematical Biosciences and Engineering

2012, Volume 9, Issue 1: 61-74. doi: 10.3934/mbe.2012.9.61
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An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model

  • 1.
    Department of Biomedical Engineering, North Carolina State University, Raleigh, NC 27695-7115
  • 2.
    Department of Biomedical Engineering, Engineering Building 3, RM 4204B, North Carolina State University, Raleigh, NC 27695-7115
  • Received: 01 February 2011 Accepted: 29 June 2018 Published: 01 December 2011

  • MSC : Primary: 82C21, 92C35, 74S05; Secondary: 68W40.

  • When modeling the cardiovascular system, the use of boundary conditions that closely represent the interaction between the region of interest and the surrounding vessels and organs will result in more accurate predictions. An often overlooked feature of outlet boundary conditions is the dynamics associated with regulation of the distribution of pressure and flow. This study implements a dynamic impedance outlet boundary condition in a one-dimensional fluid dynamics model using the pulmonary vasculature and respiration (feedback mechanism) as an example of a dynamic system. The dynamic boundary condition was successfully implemented and the pressure and flow were predicted for an entire respiration cycle. The cardiac cycles at maximal expiration and inspiration were predicted with a root mean square error of $0.61$ and $0.59$ mm Hg, respectively.

    Citation: Rachel Clipp, Brooke Steele. An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 61-74. doi: 10.3934/mbe.2012.9.61

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  • When modeling the cardiovascular system, the use of boundary conditions that closely represent the interaction between the region of interest and the surrounding vessels and organs will result in more accurate predictions. An often overlooked feature of outlet boundary conditions is the dynamics associated with regulation of the distribution of pressure and flow. This study implements a dynamic impedance outlet boundary condition in a one-dimensional fluid dynamics model using the pulmonary vasculature and respiration (feedback mechanism) as an example of a dynamic system. The dynamic boundary condition was successfully implemented and the pressure and flow were predicted for an entire respiration cycle. The cardiac cycles at maximal expiration and inspiration were predicted with a root mean square error of $0.61$ and $0.59$ mm Hg, respectively.


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    2. L. Mihaela Paun, Mitchel J. Colebank, Mette S. Olufsen, Nicholas A. Hill, Dirk Husmeier, Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation, 2020, 17, 1742-5689, 20200886, 10.1098/rsif.2020.0886
    3. Tao Du, Dan Hu, David Cai, Timothy W. Secomb, Outflow Boundary Conditions for Blood Flow in Arterial Trees, 2015, 10, 1932-6203, e0128597, 10.1371/journal.pone.0128597
    4. Mitchel J. Colebank, M. Umar Qureshi, Sudarshan Rajagopal, Richard A. Krasuski, Mette S. Olufsen, A multiscale model of vascular function in chronic thromboembolic pulmonary hypertension, 2021, 321, 0363-6135, H318, 10.1152/ajpheart.00086.2021
    5. Callyn J. Kozitza, Mitchel J. Colebank, Juan Pablo Gonzalez-Pereira, Naomi C. Chesler, Luke Lamers, Alejandro Roldán-Alzate, Colleen M. Witzenburg, Estimating pulmonary arterial remodeling via an animal-specific computational model of pulmonary artery stenosis, 2024, 1617-7959, 10.1007/s10237-024-01850-6
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  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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