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2013 | OriginalPaper | Chapter

Multiscale Modelling of Lymphatic Drainage

Authors : Tiina Roose, Gavin Tabor

Published in: Multiscale Computer Modeling in Biomechanics and Biomedical Engineering

Publisher: Springer Berlin Heidelberg

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Abstract

In this chapter we will describe the latest developments in the area of lymphatic modelling. The lymphatic system is one of the key elements of the human circulation, serving the dual functions of draining interstitial fluid and returning this to the general blood circulation, together with processing this lymph fluid which is a key component of the body’s immune response system. Compared to the main cardiovascular system however, remarkably little modelling has been attempted. At the same time, the distribution of pumping activity (contractile lymphangions coupled with simple valves) throughout the system, passive primary lymphatics and complex lymph nodes combining to form an active network, makes the system a prime candidate for multiscale modelling.

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Arkill, K.P., Moger, J., Winlove, C.P.: The structure and mechanical properties of collecting lymphatic vessels: an investigation using multimodal nonlinear microscopy. J. Anat. 216, 547–555 (2010)CrossRef

Baldazzi, V., Paci, P., Bernaschi, M., Castiglione, F.: Modelling lymphocyte homing and encounters in lymph nodes. BMC Bioinform. 10, 387–398 (2009)CrossRef

Bergel, D.H.: The static elastic properties of the arterial wall. J. Physiol. 156, 445–457 (1961)

Berk, D.A., Swartz, M.A., Leu, A.J., Jain, R.K.: Transport in lymphatic capillaries. II. Microscopic velocity measurement with fluorescence photobleaching. Am. J. Physiol. Heart Circ. Physiol. 270, H330–H337 (1996)

Bertram, C.D., Macaskill, C., Moore, J.E.: Simulation of a chain of collapsible contracting lymphangions with progressive valve closure. J. Biomech. Eng. 133, 011008-1–011008-10 (2011)

Boardman, K.C., Swartz, M.A.: Interstitial flow as a guide for lymphangiogenesis. Circ. Res. 92, 801–808 (2003)CrossRef

Cassella, M., Skobe, M.: Lymphatic vessel activation in cancer. Ann. N. Y. Acad. Sci. 979, 120–130 (2002)CrossRef

Collins, T.P., Tabor, G.R., Young, P.G.: A computational fluid dynamics study of inspiratory flow in orotracheal geometries. Med. Biol. Eng. Comput. 45(9), 829–836 (2007)CrossRef

Drake, R.E., Allen, S.J., Katz, J., Gabel, J.C., Laine, G.A.: Equivalent circuit technique for lymph flow studies. Am. J. Physiol. Heart Circ. Physiol. 251, H1090–H1094 (1986)

10.

Friedman, A., Lolas, G.: Analysis of a mathematical model of tumor lymphangiogeneis. Math. Models Meth. Appl. Sci. 15, 95–107 (2005)MathSciNetMATHCrossRef

11.

Fung, Y.C.: Biomechanics: Circulation. 2nd edn. Springer, New York (1997)CrossRef

12.

Galie, P., Spilker, R.L.: A two-dimensional computational model of lymph transport across primary lymphatic valves. J. Biomech. Eng. 131, 1297–1307 (2009)CrossRef

13.

Gnepp, D.R.: Lymphatics. In: Staub, N.C., Taylor, A.E. (eds) Edema, pp. 263–298. Raven Press, New York (1984)

14.

Gnepp, D.R., Green, F.H.: Scanning electron microscopy of collecting lymphatic vessels and their comparison to arteries and veins. Scan. Electron Microsc. 3, 756–762 (1979)

15.

Gnepp, D.R., Green, F.H.Y.: Scanning electron-microscopic study of canine lymphatic vessels. Lymphology 13(2), 91–99 (1980)

16.

Grotberg, J.B., Jensen, O.E.: Biofluid mechanics in flexible tubes. Ann. Rev. Fluid Mech. 36, 121–147 (2004)MathSciNetCrossRef

17.

Guo, Z., Sloot, P.M.A., Tay, J.C.: A hybrid agent-based approach for modeling microbiological systems. J. Theor. Biol. 255, 163–175 (2008)MathSciNetCrossRef

18.

Hajjami, H.M.-E., Petrova, T.V.: Developmental and pathological lymphangiogenesis: from models to human disease. Histochem. Cell Biol. 130, 1063–1078 (2008)CrossRef

19.

Jain, R.K.: Delivery of molecular and cellular medicine to solid tumors. Adv. Drug Deliv. Rev. 46, 149–168 (2001)CrossRef

20.

Jussila, L., Alitalo, K.: Vascular growth factors and lymphangiogenesis. Physiol. Rev. 82, 673–700 (2002)

21.

Lambert, M.W., Benoit, J.N.: Mathematical model of intestinal lymph flow and lymphatic pumping. FASEB J. 6(5), A2078 (1992)

22.

Lauweryns, J.M.: Stereomicroscopic funnel-like architecture of pulmonary lymphatic valves. Lymphology 4(4), 125–132 (1971)

23.

Leak, L.V.: Electron microscopic observations on lymphatic capillaries and the structural components of the connective tissue-lymph interface. Microvasc. Res. 2, 361–391 (1970)CrossRef

24.

Li, B., Silver, I., Szalai, J. P., Johnson, M. G.: Pressure–volume relationships in sheep mesenteric lymphatic vessels in situ: response to hypovolemia. Microvasc. Res. 56, 127–138 (1998)CrossRef

25.

Macdonald, A., Tabor, G., Winlove, C.P., Arkill, K., McHale, N.: Computational and experimental analysis of lymphatic valves. J. Biomech. 39(Suppliment 1), S295 (2006)

26.

Macdonald, A., Tabor, G., Winlove, P., Arkill, K., McHale, N.: The fluid dynamics of lymphatic vessels. Poster presentation at Cardiovascular Haemodynamics and Modelling, 25th–27th September 2005, Edinburgh (2005)

27.

Macdonald, A.J.: The fluid dynamics of lymphatic vessels. PhD thesis, University of Exeter (2007)

28.

Macdonald, A.J., Arkill, K.P., Tabor, G.R., McHale, N.G., Winlove, C.P.: Modeling flow in collecting lymphatic vessels: one-dimensional flow through a series of contractile elements. Am. J. Physiol. Heart Circ. Physiol. 295, H305–H313 (2008)CrossRef

29.

Marzo, A., Luo, X.Y., Bertram, C.D.: Three-dimensional collapse and steady flow in thick-walled flexible tubes. J. Fluids Struct. 20, 817–835 (2005)CrossRef

30.

McHale, N.G., Roddie, I.C.: The effect of transmural pressure on pumping activity in isolated bovine lymphatic vessels. J. Physiol. 261, 255–269 (1976)

31.

Mendoza, E., Schmid-Schönbein, G.W.: A model for mechanics of primary lymphatic valves. J. Biomech. Eng. 125:407–414 (2003)

32.

Mirski, H.P., Miller, M.J., Linderman, J.J., Kirschner, D.E.: Systems biology approaches for understanding cellular mechanisms of immunity in lymph nodes during infection. J. Theor. Biol. 287, 160–170 (2011)CrossRef

33.

Murray, C.D.: The physiological principle of minimum work: 1. The vascular system and the cost of blood volume. Proc. Natl Acad. Sci. USA 12(3), 207–214 (1926)CrossRef

34.

Quick, C.M., Ngo, B.L., Venugopal, A.M., Stewart, R.H.: Lymphatic pump-conduit duality: contraction of postnodal lymphatic vessels inhibits passive flow. Am. J. Physiol. Heart Circ. Physiol. 296, H662–H668 (2009)CrossRef

35.

Quick, C.M., Venugopal, A.M., Gashev, A.A., Zawieja, D.C., Stewart, R.H.: Intrinsic pump-conduit behavior of lymphangions. Am. J. Physiol. Regul. Integr. Comp. Physiol. 292, R1510–R1518 (2007)CrossRef

36.

Rahbar, E., Moore, J.E.: A model of a radially expanding and contracting lymphangeon. J. Biomech. 44, 1001–1007 (2011)CrossRef

37.

Reddy, N.P., Krouskop, T.A., Newell, P.H.: Biomechanics of a lymphatic vessel. Blood Vessels 12, 261–278 (1975)

38.

Reddy, N.P., Krouskop, T.A., Newell, P.H.: A computer model of the lymphatic system. Comp. Biol. Med. 7, 181–197 (1977)CrossRef

39.

Roose, T., Fowler, A.C.: Network development in biological gels: role in lymphatic vessel development. Bull. Math. Biol. 70(6), 1772–1789 (2008)

40.

Roose, T., Swartz, M.A.: Multiscale modeling of lymphatic drainage from tissues using homogenization theory. J. Biomech. 45, 107–115 (2012)CrossRef

41.

Schmid-Schönbein, G.: The second valve system in lymphatics. Lymphat. Res. Biol. 1, 25–29 (2003)CrossRef

42.

Schmid-Schönbein, G.W.: Microlymphatics and lymph flow. Physiol. Rev. 70(4), 987–1028 (1990)

43.

Schmid-Schonbein, G.W.: Microlymphatics and lymph flow. Physiol. Rev. 70, 987–1026 (1990)

44.

Sherwin, S.J., Franke, V., Peiró, J., Parker, K.: One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math. 47, 217–250 (2003)MATHCrossRef

45.

Shi, Y., Lawford, P., Hose, R.: Review of zero-D and 1-D models of blood flow in the cardiovascular system. Biomed. Eng. OnLine 10, 33 (2011)CrossRef

46.

Shim, E.B., Kamm, R.D.: Numerical simulation of steady flow in a compliant tube or channel with tapered wall thickness. J. Fluids Struct. 16(8), 1009–1027 (2002)CrossRef

47.

Skobe, M., Hawighorst, T., Jackson, D.G., Prevo, R., Janes, L., Velasco, P., Riccardi, L., Alitalo, K., Claffey, K., Detmar, M.: Induction of tumor lymphangiogenesis by VEGF-C promotes breast cancer metastasis. Nat. Med. 7(2), 192–198 (2001)CrossRef

48.

Stacker, S.A., Achen, M.G., Jussila, L., Baldwin, M.E., Alitalo, K.: Lymphangiogenesis and cancer metastasis. Nat. Rev. Cancer 2, 573–583 (2002)

49.

Suga, H., Sagawa, K.: Mathematical interrelationship between instantaneous ventricular pressure–volume ratio and myocardial force–velocity relation. Ann. Biomed. Eng. 1, 160–181 (1972)CrossRef

50.

Suga, H., Sagawa, K.: Instantaneous pressure–volume relations and their ratio in the excised, supported canine left ventricle. Circ. Res. 35, 117–126 (1974)CrossRef

51.

Suga, H., Sagawa, K., Shoukas, A.A.: Load independence of the instantaneous pressure–volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ. Res. 32, 314–322 (1973)CrossRef

52.

Swartz, M.A., Fleury, M.E.: The physiology of the lymph system. Ann. Rev. Biomed. Eng. 9, 229–256 (2007)CrossRef

53.

Swartz, M.A., Kaipainen, A., Netti, P.A., Boucher, Y., Grodzinsky, A.J., Jain, R.K.: Mechanics of interstitial-lymphatic fluid transport: theoretical foundation and experimental validation. J. Biomech. 32, 1297–1307 (1999)CrossRef

54.

Trzewik, J., Mallipattu, S.K., Artmann, G.M., Delano, F.A., Schmid-Schönbein, G.W.: Evidence for a second valve system in lymphatics: endothelial microvalves. FASEB J. 15, 1711–1717 (2001)

55.

Venugopal, A.M., Quick, C.M., Laine, G.A., Stewart, R.H.: Optimal postnodal lymphatic network structure that maximizes active propulsion of lymph. Am. J. Physiol. Heart Circ. Physiol. 296, H303–H309 (2009)

56.

Venugopal, A.M., Stewart, R.H., Laine, G.A., Dongaonkar, R.M., Quick, C.M.: Lymphangion coordination minimally affects mean flow in lymphatic vessels. Am. J. Physiol. Heart Circ. Physiol. 293, H1183–H1189 (2007)CrossRef

57.

Venugopal, A.M., Stewart, R.H., Laine, G.A., Quick, C.M.: Nonlinear lymphangion pressure–volume relationship minimizes edema. Am. J. Physiol. Heart Circ. Physiol. 299, H876–H882 (2010)CrossRef

58.

Weller, H.G., Tabor, G., Jasak, H., Fureby, C.: A tensorial approach to computational continuum mechanics using object orientated techniques. Comput. Phys. 12(6), 620–631 (1998)CrossRef

59.

Young, P.G., Beresford-West, T.B.H., Coward, S.R.L., Notarberardino, B., Walker, B., Abdul-Aziz, A.: An efficient approach to converting 3D image data into highly accurate computational models. Phil. Trans. R. Soc. A 366, 3155–3173 (2008)MathSciNetCrossRef

60.

Zawieja, D.C.: Contractile physiology of lymphatics. Lymphat. Res. Biol. 7(2), 87–96 (2009)CrossRef

61.

Zweifach, B.W., Prather, J.W.: Micromanipulation of pressure in terminal lymphatics in the mesentery. Am. J. Physiol. 288(5), 1326–1331 (1975)

Title: Multiscale Modelling of Lymphatic Drainage
Authors: Tiina Roose
Gavin Tabor
Publisher: Springer Berlin Heidelberg
Book: Multiscale Computer Modeling in Biomechanics and Biomedical Engineering
Print ISBN: 978-3-642-36481-5

Electronic ISBN: 978-3-642-36482-2

Copyright Year: 2013
DOI: https://doi.org/10.1007/8415_2012_148