Abstract
The model of lymph flow in the lymphatic system in the quasi-one-dimensional approach is considered. The graph of the lymphatic system is introduced. It contains 543 arcs and 478 nodes. One hundred and sixty one arcs represent lymph nodes. The graph is anatomically adequate and is spatially consistent with appropriate graph of the cardiovascular system. For description of lymph flow, the system of quasi-one-dimensional hemodynamic equations is used. Lymph flow is numerically investigated in realistic topology under different pressure gradients for different body orientation—horizontal and vertical positions. It is shown that hydrodynamic patterns of lymph flow in vertical and horizontal cases differ radically from each other. The model of valves in trunks and ducts is proposed, and influence of such valves on global lymph flow under pressure gradient is investigated. The values of pressure gradient needed for existence of adequate flow in different cases are obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
E.I. Borzyak, V.Y. Bocharov, M.R. Sapin, Medicine (1993, in Russian)
N.P. Reddy, T.A. Krouskop, P.H. Newell Jr., Blood Vessels 12, 261 (1975)
A.J. Macdonald, K.P. Arkill, G.R. Tabor, N.G. McHale, C.P. Winlove, Am. J. Physiol. Heart Circ. Physiol. 295, H305 (2008)
C.D. Bertram, C. Macaskill, J.E. Moore Jr., J. Biomech. Eng. 133, 011008 (2011)
E. Rahbar, J.E. Moore Jr., J. Biomech. 44, 1001 (2011)
C.M. Quick, A.M. Venugopal, A.A. Gashev, D.C. Zawieja, R.H. Stewart, Am. J. Physiol. Regul. Integr. Comp. Physiol. 292, R1510 (2007)
R.F. Schmidt, G. Thews (eds.), Human Physiology, 2nd completely revised edn. (Springer, 1987)
K.N. Margaris, R.A. Black, J. R. Soc. Interface 9, 601 (2012)
M.V. Abakumov, K.V. Gavrilyuk, N.B. Esikova, A.V. Lukshin, S.I. Mukhin, N.V. Sosnin, V.F. Tishkin, A.P. Favorskii, Differ. Equ. 33, 895 (1997)
G.A. Bocharov, VIII-th Conference on Mathematical Models and Numerical Methods in Biomathematics (2016)
S. Simakov, T. Gamilov, Y.N. Soe, Rus. J. Numer. Anal. Math. Model. 28, 485 (2013)
Acknowledgements
Authors would like to thank all interested in the current work, especially Prof. M. V. Abakumov and Prof. V. B. Koshelev for their valuable notes and fruitful discussion on this work.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Mozokhina, A.S., Mukhin, S.I. (2018). Pressure Gradient Influence on Global Lymph Flow. In: Mondaini, R. (eds) Trends in Biomathematics: Modeling, Optimization and Computational Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-91092-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-91092-5_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91091-8
Online ISBN: 978-3-319-91092-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)