Pressure Gradient Influence on Global Lymph Flow
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.
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.
- 1.E.I. Borzyak, V.Y. Bocharov, M.R. Sapin, Medicine (1993, in Russian)Google Scholar
- 2.N.P. Reddy, T.A. Krouskop, P.H. Newell Jr., Blood Vessels 12, 261 (1975)Google Scholar
- 7.R.F. Schmidt, G. Thews (eds.), Human Physiology, 2nd completely revised edn. (Springer, 1987)Google Scholar
- 9.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)Google Scholar
- 10.G.A. Bocharov, VIII-th Conference on Mathematical Models and Numerical Methods in Biomathematics (2016)Google Scholar
- 11.S. Simakov, T. Gamilov, Y.N. Soe, Rus. J. Numer. Anal. Math. Model. 28, 485 (2013)Google Scholar