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Research Papers

Confocal Image-Based Computational Modeling of Nitric Oxide Transport in a Rat Mesenteric Lymphatic Vessel

[+] Author and Article Information
John T. Wilson

Department of Bioengineering,
Imperial College London,
South Kensington Campus,
London SW7 2AZ,UK;
Department of Biomedical Engineering,
Texas A&M University,
5045 Emerging Technologies Building,
3120 TAMU,
College Station, TX 77843

Wei Wang, David C. Zawieja

Department of Systems Biology and Translational Medicine,
Texas A&M Health Science Center,
702 Southwest H.K. Dodgen Loop,
Temple, TX 76504

Augustus H. Hellerstedt

Department of Biomedical Engineering,
Texas A&M University,
5045 Emerging Technologies Building,
3120 TAMU,
College Station, TX 77843

James E. Moore,

Department of Bioengineering,
Imperial College London,
South Kensington Campus,
London SW7 2AZ, UK;
Department of Biomedical Engineering,
Texas A&M University,
5045 Emerging Technologies Building,
3120 TAMU,
College Station, TX 77843

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received November 19, 2012; final manuscript received March 4, 2013; accepted manuscript posted April 24, 2013; published online April 24, 2013. Assoc. Editor: Tim David.

J Biomech Eng 135(5), 051005 (Apr 24, 2013) (8 pages) Paper No: BIO-12-1570; doi: 10.1115/1.4023986 History: Received November 19, 2012; Revised March 04, 2013; Accepted March 08, 2013

The lymphatic system plays important roles in protein and solute transport as well as in the immune system. Its functionality is vital to proper homeostasis and fluid balance. Lymph may be propelled by intrinsic (active) vessel pumping or passive compression from external tissue movement. With regard to the former, nitric oxide (NO) is known to play an important role modulating lymphatic vessel contraction and vasodilation. Lymphatic endothelial cells (LECs) are sensitive to shear, and increases in flow have been shown to cause enhanced production of NO by LECs. Additionally, high concentrations of NO have been experimentally observed in the sinus region of mesenteric lymphatic vessels. A computational flow and mass transfer model using physiologic geometries obtained from confocal images of a rat mesenteric lymphatic vessel was developed to determine the characteristics of NO transport in the lymphatic flow regime. Both steady and unsteady analyses were performed. Production of NO was shear-dependent; basal cases using constant production were also generated. Simulations revealed areas of flow stagnation adjacent to the valve leaflets, suggesting the high concentrations observed here experimentally are due to minimal convection in this region. LEC sensitivity to shear was found to alter the concentration of NO in the vessel, and the convective forces were found to profoundly affect the concentration of NO at a Péclet value greater than approximately 61. The quasisteady analysis was able to resolve wall shear stress within 0.15% of the unsteady case. However, the percent difference between unsteady and quasisteady conditions was higher for NO concentration (6.7%). We have shown high NO concentrations adjacent to the valve leaflets are most likely due to flow-mediated processes rather than differential production by shear-sensitive LECs. Additionally, this model supports experimental findings of shear-dependent production, since removing shear dependence resulted in concentrations that are physiologically counterintuitive. Understanding the transport mechanisms and flow regimes in the lymphatic vasculature could help in the development of therapeutics to treat lymphatic disorders.

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Figures

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Fig. 1

Geometry of the fluid region of the rat mesenteric lymphatic vessel. Panel 1: Side view of the lymphatic fluid region with arrows indicating (A) valve leaflet insertion point and (B) trailing edge of the valve leaflets. The valve leaflets are represented by gaps on either side of the vessel, because the fluid (not solid) region was reconstructed for simulations. Panel 2: Down-the-barrel view of lymphatic geometry. Panel 3: Skewed view of the lymphatic geometry. Note that 200-μm extensions (extensions not shown in illustration) were added at both the inlet and outlet of the vessel to accommodate flow simulations.

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Fig. 5

WSS and corresponding NO production distributions. Top: Distribution of axial WSS for Pe = 91; middle: dimensionless NO production for Pe = 91 and Wo = 0.2; bottom: dimensionless NO production for Pe = 91 and Wo = 1.14.

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Fig. 6

Contours of NO at the wall of the vessel for various Pe values. Top: Surface concentration for Pe = 15 and Wo = 1.14; middle: surface concentration for Pe = 61 and Wo = 1.14; bottom: surface concentration for Pe = 212 and Wo = 1.14. Increasing the average Pe value resulted in less wall concentration; however, enhanced Pe values beyond Pe = 61 up until Pe = 212 only resulted in an rms difference in NO concentration of 3.7%.

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Fig. 4

Representative streamlines for a simulation run at Re = 0.22. Areas of flow stagnation were observed adjacent to the valve leaflets. Although these appear vortex-like in nature, these are regions of essentially zero velocity.

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Fig. 3

Transient velocity from a rat mesenteric lymphatic vessel used for time-dependent simulations. The raw waveform taken from the literature [15] was interpolated using a 0.05-s time step, resulting in a velocity profile consisting of values obtained through a sampling frequency of 180 points for 9.0 s. A, B, and C are locations along the velocity where instantaneous WSS and NO values were extracted. These points correspond to the maximal, transitional, and minimum values of velocity, respectively. Note the duration of a typical contractile cycle is approximately 3.0 s.

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Fig. 2

Range of NO production values with constant γ = 10. For shear-dependent cases, Wo was varied from 0.1 to 1.14, corresponding to increasing levels of LEC shear-sensitivity. Basal level productions B1 and B5 correspond to dimensionless production values of 0.09 and 0.5, respectively.

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Fig. 7

Concentration plotted in the radial direction at an axial location downstream of the valve leaflets

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Fig. 8

Concentration sampled at the wall across a range of Pe and Wo values. Top: point upstream of the valve leaflets; middle: point of highest axial WSS; bottom: point downstream of the valve leaflets.

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Fig. 9

Concentration at the wall at a location upstream of the terminal edges of the lymphatic valve leaflets

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Fig. 10

Comparison of steady WSS and NO values versus axial position to that of the unsteady case at time points A, B, and C, corresponding to 3.3 s, 3.9 s, and 4.25 s, respectively. WSS values were normalized to corresponding inlet Poiseuille value of WSS.

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