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Research Papers

Structured Tree Impedance Outflow Boundary Conditions for 3D Lung Simulations

[+] Author and Article Information
Andrew Comerford

Institute for Computational Mechanics, Technische Universität München, D-85747 Garching, Germanycomerford@lnm.mw.tum.de

Christiane Förster

Institute for Computational Mechanics, Technische Universität München, D-85747 Garching, Germany

Wolfgang A. Wall1

Institute for Computational Mechanics, Technische Universität München, D-85747 Garching, Germanywall@lnm.mw.tum.de

1

Corresponding author.

J Biomech Eng 132(8), 081002 (Jun 15, 2010) (10 pages) doi:10.1115/1.4001679 History: Received April 08, 2009; Revised March 11, 2010; Posted April 28, 2010; Published June 15, 2010; Online June 15, 2010

In this paper, we develop structured tree outflow boundary conditions for modeling the airflow in patient specific human lungs. The utilized structured tree is used to represent the nonimageable vessels beyond the 3D domain. The coupling of the two different scales (1D and 3D) employs a Dirichlet–Neumann approach. The simulations are performed under a variety of conditions such as light breathing and constant flow ventilation (which is characterized by very rapid acceleration and deceleration). All results show that the peripheral vessels significantly impact the pressure, however, the flow is relatively unaffected, reinforcing the fact that the majority of the lung impedance is due to the lower generations rather than the peripheral vessels. Furthermore, simulations of a hypothetical diseased lung (restricted flow in the superior left lobe) under mechanical ventilation show that the mean pressure at the outlets of the 3D domain is about 28% higher. This hypothetical model illustrates potential causes of volutrauma in the human lung and furthermore demonstrates how different clinical scenarios can be studied without the need to assume the unknown flow distribution into the downstream region.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Segmented lung model (up to seven generations) used in the numerical simulations

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Figure 2

Geometry with computational mesh (a) enlarged portion of the trachea and bronchi and (b) higher generations also showing outlet extensions required for better modeling of the outflow boundary conditions

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Figure 3

Inflow curves utilized in the simulations (a) light breathing (Qmean=0.2 l/s) and light activity (Qmean=0.5 l/s) and (b) constant flow mechanical ventilation. Note the ventilation curve was chosen based on the high slew rates and oscillations, which occur in the profile to understand how these affect lung mechanics.

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Figure 4

Pressure flow relationship at the inlet to the trachea during the acceleratory part of the inspiratory phase (normal breathing). The pressure drops are similar to the values reported in literature.

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Figure 5

Zoomed in area of the bronchial airway demonstrating flow vectors at max inspiration for light activity. The flow is characterized by complex recirculation and skewing of high velocity regions to inner walls of bifurcations due to the vessel branching.

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Figure 6

Comparison of pressure contours, for light activity, at maximum inspiration: (a) traction free boundary condition (up to seven generations) and (b) impedance boundary condition(up to 17 generations). With the impedance conditions the maximum pressure is approximately 44% higher. Note the lower limit of the scale is set to 5 Pa for visual comparison purposes and for the traction free condition the pressure at the outlets is virtually zero, meaning the pressure in the rest of the tree would be negative.

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Figure 7

Normalized pressure-flow relationship in the bronchial airway. Evidently the pressure and flow are consistently in phase throughout the cycle. This is more noticeable for impedance conditions, where a narrowing of the loop is observed. For the impedance condition, the temporal development of pressure is more rapid. The difference in flowrate between the two conditions is marginal with the flowrate being overall reduced under impedance conditions (data not directly shown, however, at each point along the two above curves the flow is nearly identical).

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Figure 8

Mean pressure for light activity along two different centerlines leading into the left (gray) and right (black) lobes of the lung

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Figure 9

Pressure distribution for light breathing plotted along a centerline of the right lobe for two different diameter diminishing ratios (α=β=0.5 and α=β=0.9) in a Weibel tree. The pressure is higher in the faster diminishing tree due to higher impedance levels calculated in the downstream domain.

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Figure 10

Pressure flow distribution for light activity in different generations of the lung under healthy and diseased conditions (partial occlusion of the superior left lobe): (a) second generation left lobe, (b) third generation superior left lobe, (c) third generation inferior left lobe, and (d) third generation inferior right lobe.

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Figure 11

Comparison of normalized pressure versus flow relationship for normal breathing and mechanical ventilation. Evidently the higher frequency ventilation results in a widening of the pressure-flow loop implying a greater phase difference between pressure and flow.

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Figure 12

Pressure flow distribution in different generations of the lung under healthy and diseased conditions (partial occlusion of the left superior lobe): (a) second generation left lobe, (b) third generation superior left lobe, (c) third generation inferior left lobe, and (d) third generation inferior right lobe

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Figure 13

Comparison of pressure distribution (t=0.5 s) under healthy and diseased conditions (superior left lobe occluded). The pressure distribution is elevated throughout the model, hence, overdistension of the alveoli is potentially possible.

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