An evaluation of dynamic outlet boundary conditions in a 1D fluid dynamics model

Rachel Clipp; Brooke Steele

doi:10.3934/mbe.2012.9.61

Article Contents

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

Rachel Clipp^1, and
Brooke Steele^2,

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: February 2011

Revised: August 2011

Published: December 2011

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Abstract

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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Mathematics Subject Classification: Primary: 82C21, 92C35, 74S05; Secondary: 68W40.

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