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The lymphatic system is an important defense function system in the human body. It is also critical to humoral homeostasis. Local dysfunction will cause edema, immune deficiency, and a high incidence. There are intraluminal valves in the lymphatic system, which allows the lymph fluid to flow to the large veins and heart. It has three major immune functions. First, it can resist bacterial viruses and protect the human body from disease attacks. Secondly, it is supplemented by lymphocytes to remove the products produced by metabolism. In the end, The damaged organs and tissues are repaired by lymphocytes to restore normal physiological functions. The lymphatic system does not have the same pump as the heart of the blood circulatory system. The driving of lymph is mainly done by the spontaneous contraction of the lymphatics (the lung lymphatic system is compressed by the alveoli). The autonomic contraction cycle of lymphatic vessels is caused by the increase of Ca2+ in lymphocytes, and the contraction drives the fluid to produce shearing force. The shearing force produces nitric oxide synthase (eNOS) in lymphatic endothelial cells, and eNOS increases NO and increases NO. Decreasing Ca2+ relaxes lymphatic vessels, fluid shear rate decreases after lymphatic vessel relaxation, eNOS decreases, NO decreases, Ca2+ increases, lymphocytes contract, and a new cycle begins. It can be seen that the concentration of NO and its distribution play a key role in the contraction of lymphatic vessels. Obviously, export pressure affects the shear rate of fluid in the lymphatics, which in turn affects the concentration of NO and the contraction of lymphatic vessels. To investigate the effect of lymphatic outlet pressure on lymphatic vessel contraction, we established a lattice Boltzmann model to simulate the initial lymphatic vessels embedded in porous tissue and the collecting lymphatic vessels with two pairs of valves. The valve is the main source of NO. Once contraction begins, the contraction is spontaneous, self-sustaining, and the system exhibits non-linear dynamics. This model can reproduce NO and The interaction of Ca2+ and the spontaneous contraction of lymphatic vessels, and the distribution of NO under different outlet pressures and their average values were studied.
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Keywords:
- Lymphatic vessel /
- lattice Boltzmann method /
- valve /
- NO
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Zhang L M 2012 Role of ATP-Sensitive Potassium Channels in Nitric Oxide in Regulating the Function of Isolated Lymphatic Pump in Hemorrhagic Shock(Zhangjiakou: Hebei North University) (in Chinese)
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[8] 赵彤彤 2018 多孔介质含天然气水合物多相流动LBM模拟 (太原: 太原理工大学)
Zhao T T 2018 LBM Simulation of Multiphase Flow of Natural Gas Hydrate in Porous Media (Taiyuan: Taiyuan University of Technology) (in Chinese)
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Google Scholar
[10] Li H B, Mei Y M, Maimon N, Padera T P, Baish J W, Munn L L 2019 SCIENTIFICREPORTS 9 2045
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 D2 Q9晶格玻尔兹曼模型的微观速度
Figure 1. Microscopic velocity of D2 Q9 lattice Boltzmann model.
图 2 反向弹回示意图
Figure 2. Bounceback.
图 3 淋巴管段示意图
Figure 3. Lymphatic section.
图 4 静止状态下淋巴管瓣膜
Figure 4. The lymphatic valves at rest.
图 5 t = 2.296 s时, NO浓度分布图
Figure 5. t = 3.003 s, NO concentration distribution map.
图 6 NO平均浓度与压强差关系图
Figure 6. Relationship between NO average concentration and pressure difference.
表 1 Ca2+与NO的化学参数
Table 1. Chemical parameters of Ca2+ and NO.
参数 单位 数值 NO ${D_{{\rm{NO}}}}$ cm2/s 1.2 × 10–4 $K_{{\rm{NO}}}^ - $ s–1 3.7594 $K_{{\rm{NO}}}^ + $ 无量纲 400 Ca2+ ${D_{{\rm{Ca}}}}$ cm2/s 6.5 × 10–6 $K_{{\rm{Ca}}}^{-}$ s–1 37.6 $K_{{\rm{Ca}}}^{+}$ s–1 1.2 $K_\delta ^ + $ s–1 15038 ${C_{{\rm{th}}}}$ 无量纲 0.015 ${R_{{\rm{Ca}}}}$ cm 0.005 ${K_{{\rm{Ca}}, {\rm{NO}}}}$ 无量纲 5.3 h 无量纲 0.03 
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表 2 淋巴管与瓣膜参数
Table 2. Parameters of Lymphatic and valve.
参数 单位 数值 淋巴管 ${k_{\rm{M}}}$ ${\rm{dynes}}$ 7.6 × 10–5 ${k_{\rm{E}}}$ ${\rm{dynes}}/{{\rm{cm}}^{\rm{2}}}$ 4.52 ${k_{\rm{B}}}$ ${\rm{dynes}} /{{\rm{cm}}^2}$ 9045 ${k_{\rm{r}}}$ dynes·s/cm 4.8 × 10–9 ${k_{{\rm{NO}}}}$ 无量纲 1 ${R_{\rm{l}}}$ cm 0.003 ${R_{\rm{0}}}$ cm 0.005 瓣膜 $k_{\rm{B}}^\nu $ dynes /cm2 0—0.2 $k_{\rm{E}}^\nu $ dynes /cm2 9.0 × 10–4 $k_{\rm{r}}^\nu $ dynes /cm2 0.0091 A cm–1 1500 $\varDelta $ cm 2 × 10–4
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表 3 出口压强高于入口压强时正压力差
Table 3. Positive pressure when outlet pressure is higher than inlet pressure.
正压力差 ${{\rho _{{\rm{out}}}}} /$g·cm–3 1.0020 1.0015 1.0010 1.0008 1.0006 1.0004 1.0002 ${\Delta \rho }/$g·cm–3 0.0020 0.0015 0.0010 0.0008 0.0006 0.0004 0.0002 ${\Delta P} /$g·cm–1·s–2 60.3 45.225 30.15 24.12 18.09 12.06 6.03
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表 4 出口压强低于入口压强时负压力差
Table 4. Negative pressure when outlet pressure is lower than inlet pressure.
负压力差 ${\rho _{{\rm{out}}}}/$g·cm–3 1.0000 0.99998 0.99996 0.9998 0.9996 $\Delta \rho /$g·cm–3 0 –0.00002 –0.00004 –0.0002 –0.0004 $\Delta P/$g·cm–1·s–2 0 –0.603 –1.206 –6.03 –12.06
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[1] Louveau A, Smirnov I, Keyes T J, Eccles J D, Rouhani S J, Peske J D, Derecki N C, Castle D, Mandell J W, Lee K S, Harris T H, Kipnis J 2015 Nature 523 377
[2] Margaris K N, Black R A 2012 J. R. Soc. Interface 9 601
Google Scholar
[3] Macdonald A J, Arkill K P, Tabor G R, McHale N G, Winlove C P 2008 Am. J. Physiol. Heart C. 295 305
Google Scholar
[4] 张立民 2012 ATP敏感性钾通道在一氧化氮调节失血性休克大鼠离体淋巴管泵功能中的作用 (张家口: 河北北方学院)
Zhang L M 2012 Role of ATP-Sensitive Potassium Channels in Nitric Oxide in Regulating the Function of Isolated Lymphatic Pump in Hemorrhagic Shock(Zhangjiakou: Hebei North University) (in Chinese)
[5] 秦立鹏, 牛春雨, 赵自刚 2011 生理科学进展 42 237
Qin L P, Niu C Y, Zhao Z G 2011 Advances in Physiological Sciences 42 237
[6] Kunert C, Baish J W, Liao S, Padera T P, Munn L L 2015 PNAS 112 10938
Google Scholar
[7] Baish J W, Kunert C, Padera T P, Munn LL 2016 PLoS Comput. Biol. 12 1005
[8] 赵彤彤 2018 多孔介质含天然气水合物多相流动LBM模拟 (太原: 太原理工大学)
Zhao T T 2018 LBM Simulation of Multiphase Flow of Natural Gas Hydrate in Porous Media (Taiyuan: Taiyuan University of Technology) (in Chinese)
[9] Shan X, Chen H 1993 Phys. Rev. E 47 1815
Google Scholar
[10] Li H B, Mei Y M, Maimon N, Padera T P, Baish J W, Munn L L 2019 SCIENTIFICREPORTS 9 2045
[11] Chen, Chen, Martnez, Matthaeus 1991 Phys. Rev. Lett. 67 27
[12] Qian Y H, D’HumièresD, Lallemand P 1992 Europhys. Lett. 17 479
Google Scholar
[13] Sukop M C, ThorneJr D T2010 Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers (Berlin: Springer Publishing Company) p36
[14] Pujol F, Hodgson T, Martinezcorral I, Prats A C, Devenport D, Takeichi M, Genot E, Mäkinen T, Francis-West P, Garmy-Susini B, Tatin F 2017 Arterioscl. Thromb. Vas. Biol. 37 1732
Google Scholar
[15] Scallan J P, Davis M J 2013 J. Physiol. 591 250
[16] Kawai Y, Yokoyama Y, Kaidoh M 2010 Am. J. Physiol. 298 647
Google Scholar
[17] Ladd A J C, Verberg R 2001 J. Stat. Phys. 104 1191
Google Scholar
[18] He X, Doolen G 1997 J. Comput. Phys. 134 306
Google Scholar
[19] H Glenn B, Olga Yu G, Zawieja D C 2011 Ame. J. Physiol. Heart C. 301 1897
Google Scholar
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