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Fluid pumping of peristaltic vessel fitted with elastic valves

Published online by Cambridge University Press:  11 May 2021

Ki Tae Wolf Open the ORCID record for Ki Tae Wolf [Opens in a new window] ,
J. Brandon Dixon Open the ORCID record for J. Brandon Dixon [Opens in a new window]  and
Alexander Alexeev Open the ORCID record for Alexander Alexeev [Opens in a new window]
Ki Tae Wolf
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
J. Brandon Dixon
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, GA30332, USA Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
Alexander Alexeev*
Affiliation:
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
*
† Email address for correspondence: alexander.alexeev@me.gatech.edu
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Abstract

Using numerical simulations, we probe the fluid flow in an axisymmetric peristaltic vessel fitted with elastic bi-leaflet valves. In this biomimetic system that mimics the flow generated in lymphatic vessels, we investigate the effects of the valve and vessel properties on pumping performance of the valved peristaltic vessel. The results indicate that valves significantly increase pumping by reducing backflow. The presence of valves, however, increases the viscous resistance, therefore requiring greater work compared to valveless vessels. The benefit of the valves is the most significant when the fluid is pumped against an adverse pressure gradient and for low vessel contraction wave speeds. We identify the optimum vessel and valve parameters leading to the maximum pumping efficiency. We show that the optimum valve elasticity maximizes the pumping flow rate by allowing the valve to block the backflow more effectively while maintaining low resistance during the forward flow. We also examine the pumping in vessels where the vessel contraction amplitude is a function of the adverse pressure gradient, as found in lymphatic vessels. We find that, in this case, the flow is limited by the work generated by the contracting vessel, suggesting that the pumping in lymphatic vessels is constrained by the performance of the lymphatic muscle. Given the regional heterogeneity of valve morphology observed throughout the lymphatic vasculature, these results provide insight into how these variations might facilitate efficient lymphatic transport in the vessel's local physiologic context.

JFM classification

Biological Fluid Dynamics: Flow-vessel interactions Biological Fluid Dynamics: Peristaltic pumping
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Akl, T.J., Coté, G.L., Nepiyushchikh, Z.V., Gashev, A.A. & Zawieja, D.C. 2011 Measuring contraction propagation and localizing pacemaker cells using high speed video microscopy. J. Biomed. Opt. 16, 026016.CrossRefGoogle ScholarPubMed
Alexeev, A. & Balazs, A.C. 2007 Designing smart systems to selectively entrap and burst microcapsules. Soft Matt. 3, 1500–1505.CrossRefGoogle ScholarPubMed
Alexeev, A., Verberg, R. & Balazs, A.C. 2005 Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules 38, 10244–10260.CrossRefGoogle Scholar
Alexeev, A., Verberg, R. & Balazs, A.C. 2006 Designing compliant substrates to regulate the motion of vesicles. Phys. Rev. Lett. 96, 148103.CrossRefGoogle ScholarPubMed
Baish, J.W., Kunert, C., Padera, T.P. & Munn, L.L. 2016 Synchronization and random triggering of lymphatic vessel contractions. PLOS Comput. Biol. 12, e1005231.CrossRefGoogle ScholarPubMed
Ballard, M., Wolf, K.T., Nepiyushchikh, Z., Dixon, J.B. & Alexeev, A. 2018 Probing the effect of morphology on lymphatic valve dynamic function. Biomech. Model. Mechanobiol. 17, 1343–1356.CrossRefGoogle ScholarPubMed
Bertram, C. 2020 Modelling secondary lymphatic valves with a flexible vessel wall: how geometry and material properties combine to provide function. Biomech. Model. Mechanobiol. 19, 2081–2098.CrossRefGoogle ScholarPubMed
Bertram, C., Macaskill, C., Davis, M. & Moore, J. 2014 a Development of a model of a multi-lymphangion lymphatic vessel incorporating realistic and measured parameter values. Biomech. Model. Mechanobiol. 13, 401–416.CrossRefGoogle Scholar
Bertram, C.D., Macaskill, C., Davis, M.J. & Moore, J.E. 2016 Consequences of intravascular lymphatic valve properties: a study of contraction timing in a multi-lymphangion model. Am. J. Physiol. Heart Circ. Physiol. 310, H847–H860.CrossRefGoogle Scholar
Bertram, C., Macaskill, C. & Moore, J. 2011 Simulation of a chain of collapsible contracting lymphangions with progressive valve closure. J. Biomech. Engng 133, 011008.CrossRefGoogle ScholarPubMed
Bertram, C., Macaskill, C. & Moore, J. 2014 b Incorporating measured valve properties into a numerical model of a lymphatic vessel. Comput. Meth. Biomech. Biomed. Engng 17, 1519–1534.CrossRefGoogle ScholarPubMed
Böhme, G. & Müller, A. 2013 Analysis of non-Newtonian effects in peristaltic pumping. J. Non-Newtonian Fluid Mech. 201, 107–119.CrossRefGoogle Scholar
Brouillard, P., Boon, L. & Vikkula, M. 2014 Genetics of lymphatic anomalies. J. Clin. Invest. 124, 898–904.CrossRefGoogle ScholarPubMed
Burton-Opitz, R. & Nemser, R. 1917 The viscosity of lymph. Am. J. Physiol.-Legacy Cont. 45, 25–29.CrossRefGoogle Scholar
Buxton, G.A., Verberg, R., Jasnow, D. & Balazs, A.C. 2005 Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys. Rev. E 71, 056707.CrossRefGoogle ScholarPubMed
Castorena-Gonzalez, J.A., Srinivasan, R.S., King, P.D., Simon, A.M. & Davis, M.J. 2020 Simplified method to quantify valve back-leak uncovers severe mesenteric lymphatic valve dysfunction in mice deficient in connexins 43 and 37. J. Physiol. 598, 2297–2310.CrossRefGoogle ScholarPubMed
Castorena-Gonzalez, J.A., Zawieja, S.D., Li, M., Srinivasan, R.S., Simon, A.M., de Wit, C., de la Torre, R., Martinez-Lemus, L.A., Hennig, G.W. & Davis, M.J. 2018 Mechanisms of connexin-related lymphedema: a critical role for Cx45, but not Cx43 or Cx47, in the entrainment of spontaneous lymphatic contractions. Circulat. Res 123, 964–985.CrossRefGoogle Scholar
Cha, B., Geng, X., Mahamud, M.R., Fu, J., Mukherjee, A., Kim, Y., Jho, E.-H., Kim, T.H., Kahn, M.L. & Xia, L. 2016 Mechanotransduction activates canonical Wnt/β-catenin signaling to promote lymphatic vascular patterning and the development of lymphatic and lymphovenous valves. Genes Develop. 30, 1454–1469.CrossRefGoogle ScholarPubMed
Cha, B., Geng, X., Mahamud, M.R., Zhang, J.Y., Chen, L., Kim, W., Jho, E.-H., Kim, Y., Choi, D. & Dixon, J.B. 2018 Complementary Wnt sources regulate lymphatic vascular development via PROX1-dependent Wnt/β-catenin signaling. Cell Rep. 25, 571–584.CrossRefGoogle ScholarPubMed
Choi, D., Park, E., Jung, E., Cha, B., Lee, S., Yu, J., Kim, P.M., Lee, S., Hong, Y.J. & Koh, C.J. 2019 Piezo1 incorporates mechanical force signals into the genetic program that governs lymphatic valve development and maintenance. JCI Insight 4, e125068.CrossRefGoogle ScholarPubMed
Connington, K., Kang, Q., Viswanathan, H., Abdel-Fattah, A. & Chen, S. 2009 Peristaltic particle transport using the lattice Boltzmann method. Phys. Fluids 21, 053301.CrossRefGoogle Scholar
Davis, M.J., Rahbar, E., Gashev, A.A., Zawieja, D.C. & Moore, J.E. 2011 Determinants of valve gating in collecting lymphatic vessels from rat mesentery. Am. J. Physiol. Heart Circ. Physiol. 301, H48–H60.CrossRefGoogle ScholarPubMed
Davis, M.J., Scallan, J.P., Wolpers, J.H., Muthuchamy, M., Gashev, A.A. & Zawieja, D.C. 2012 Intrinsic increase in lymphangion muscle contractility in response to elevated afterload. Am. J. Physiol. Heart Circ. Physiol. 303, H795–H808.CrossRefGoogle ScholarPubMed
Dixon, J.B. 2010 Lymphatic lipid transport: sewer or subway? Trends Endocrinol. Metabol. 21, 480–487.CrossRefGoogle ScholarPubMed
Eisenhoffer, J., Kagal, A., Klein, T. & Johnston, M. 1995 Importance of valves and lymphangion contractions in determining pressure gradients in isolated lymphatics exposed to elevations in outflow pressure. Microvasc. Res. 49, 97–110.CrossRefGoogle ScholarPubMed
Gashev, A.A., Davis, M.J., Delp, M.D. & Zawieja, D.C. 2004 Regional variations of contractile activity in isolated rat lymphatics. Microcirculation 11, 477–492.CrossRefGoogle ScholarPubMed
Gashev, A.A., Davis, M.J. & Zawieja, D.C. 2002 Inhibition of the active lymph pump by flow in rat mesenteric lymphatics and thoracic duct. J. Physiol. 540, 1023–1037.CrossRefGoogle ScholarPubMed
Gashev, A.A., Zhang, R.-Z., Muthuchamy, M., Zawieja, D.C. & Davis, M.J. 2012 Regional heterogeneity of length–tension relationships in rat lymph vessels. Lymphatic Res. Biol. 10, 14–19.CrossRefGoogle ScholarPubMed
Hanasoge, S., Ballard, M., Hesketh, P.J. & Alexeev, A. 2017 Asymmetric motion of magnetically actuated artificial cilia. Lab on a Chip 17, 3138–3145.CrossRefGoogle ScholarPubMed
Hariharan, P., Seshadri, V. & Banerjee, R.K. 2008 Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms. Math. Comput. Model. 48, 998–1017.CrossRefGoogle Scholar
Ikomi, F. & Schmid-Schonbein, G. 1996 Lymph pump mechanics in the rabbit hind leg. Am. J. Physiol. Heart Circ. Physiol. 271, H173–H183.CrossRefGoogle ScholarPubMed
Jamalian, S., Bertram, C.D., Richardson, W.J. & Moore, J.E. 2013 Parameter sensitivity analysis of a lumped-parameter model of a chain of lymphangions in series. Am. J. Physiol. Heart Circ. Physiol. 305, H1709–H1717.CrossRefGoogle ScholarPubMed
Jamalian, S., Davis, M.J., Zawieja, D.C. & Moore, J.E. 2016 Network scale modeling of lymph transport and its effective pumping parameters. PloS one 11, e0148384.CrossRefGoogle ScholarPubMed
Kassis, T., Yarlagadda, S.C., Kohan, A.B., Tso, P., Breedveld, V. & Dixon, J.B. 2016 Postprandial lymphatic pump function after a high-fat meal: a characterization of contractility, flow, and viscosity. Am. J. Physiol. Gastrointest. Liver Physiol. 310, G776–G789.CrossRefGoogle ScholarPubMed
Kazenwadel, J., Betterman, K.L., Chong, C.-E., Stokes, P.H., Lee, Y.K., Secker, G.A., Agalarov, Y., Demir, C.S., Lawrence, D.M. & Sutton, D.L. 2015 GATA2 is required for lymphatic vessel valve development and maintenance. J. Clin. Invest. 125, 2979–2994.CrossRefGoogle ScholarPubMed
Kornuta, J.A., Nepiyushchikh, Z., Gasheva, O.Y., Mukherjee, A., Zawieja, D.C. & Dixon, J.B. 2015 Effects of dynamic shear and transmural pressure on wall shear stress sensitivity in collecting lymphatic vessels. Am. J. Physiol. Regul. Integr. Compar. Physiol. 309, R1122–R1134.CrossRefGoogle ScholarPubMed
Kunert, C., Baish, J.W., Liao, S., Padera, T.P. & Munn, L.L. 2015 Mechanobiological oscillators control lymph flow. Proc. Natl Acad. Sci. 112, 10938–10943.CrossRefGoogle ScholarPubMed
Ladd, A. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104, 1191–1251.CrossRefGoogle Scholar
Lapinski, P.E., Kwon, S., Lubeck, B.A., Wilkinson, J.E., Srinivasan, R.S., Sevick-Muraca, E. & King, P.D. 2012 RASA1 maintains the lymphatic vasculature in a quiescent functional state in mice. J. Clin. Invest. 122, 733–747.CrossRefGoogle Scholar
Lapinski, P.E., Lubeck, B.A., Chen, D., Doosti, A., Zawieja, S.D., Davis, M.J. & King, P.D. 2017 RASA1 regulates the function of lymphatic vessel valves in mice. J. Clin. Invest. 127, 2569–2585.CrossRefGoogle ScholarPubMed
Lauweryns, J.M. & Boussauw, L. 1973 The ultrastructure of lymphatic valves in the adult rabbit lung. Z. Zellforsch. Mikrosk. Anat. 143, 149–168.CrossRefGoogle ScholarPubMed
MacDonald, A.J., Arkill, K.P., Tabor, G.R., McHale, N.G. & Winlove, C.P. 2008 Modeling flow in collecting lymphatic vessels: one-dimensional flow through a series of contractile elements. Am. J. Physiol. Heart Circ. Physiol. 295, H305–H313.CrossRefGoogle ScholarPubMed
Mao, W. & Alexeev, A. 2014 Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166.CrossRefGoogle Scholar
Margaris, K. & Black, R.A. 2012 Modelling the lymphatic system: challenges and opportunities. J. R. Soc. Interface 9, 601–612.CrossRefGoogle ScholarPubMed
Masoud, H., Bingham, B.I. & Alexeev, A. 2012 Designing maneuverable micro-swimmers actuated by responsive gel. Soft Matt. 8, 8944–8951.CrossRefGoogle Scholar
McGeown, J., McHale, N. & Thornbury, K. 1988 Arterial pulsation and lymph formation in an isolated sheep hindlimb preparation. J. Physiol. 405, 595–604.CrossRefGoogle Scholar
Moore, J.E. & Bertram, C.D. 2018 Lymphatic system flows. Annu. Rev. Fluid Mech. 50, 459–482.CrossRefGoogle ScholarPubMed
Mortimer, P.S. & Rockson, S.G. 2014 New developments in clinical aspects of lymphatic disease. J. Clin. Invest. 124, 915–921.CrossRefGoogle ScholarPubMed
Ohhashi, T., Azuma, T. & Sakaguchi, M. 1980 Active and passive mechanical characteristics of bovine mesenteric lymphatics. Am. J. Physiol. Heart Circ. Physiol. 239, H88–H95.CrossRefGoogle ScholarPubMed
Ostoja-Starzewski, M. 2002 Lattice models in micromechanics. Appl. Mech. Rev. 55, 35–60.CrossRefGoogle Scholar
Pan, W.R., le Roux, C.M. & Levy, S.M. 2011 Alternative lymphatic drainage routes from the lateral heel to the inguinal lymph nodes: anatomic study and clinical implications. ANZ J. Surgery 81, 431–435.CrossRefGoogle ScholarPubMed
Pan, W.R., le Roux, C.M., Levy, S.M. & Briggs, C.A. 2010 The morphology of the human lymphatic vessels in the head and neck. Clin. Anatomy 23, 654–661.CrossRefGoogle ScholarPubMed
Petrova, T.V., Karpanen, T., Norrmén, C., Mellor, R., Tamakoshi, T., Finegold, D., Ferrell, R., Kerjaschki, D., Mortimer, P. & Ylä-Herttuala, S. 2004 Defective valves and abnormal mural cell recruitment underlie lymphatic vascular failure in lymphedema distichiasis. Nat. Med. 10, 974–981.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 1987 A study of peristaltic flow. J. Fluid Mech. 180, 515–527.CrossRefGoogle Scholar
Quick, C.M., Venugopal, A.M., Gashev, A.A., Zawieja, D.C. & Stewart, R.H. 2007 Intrinsic pump-conduit behavior of lymphangions. Am. J. Physiol. Regul. Integr. Compar. Physiol. 292, R1510–R1518.CrossRefGoogle ScholarPubMed
Rachid, H. & Ouazzani, M. 2015 Mechanical efficiency of peristaltic pumping of a Newtonian fluid between two deformable coaxial tubes with different phases and amplitudes. Eur. Phys. J. Plus 130, 122.CrossRefGoogle Scholar
Rahbar, E. & Moore, J.E. 2011 A model of a radially expanding and contracting lymphangion. J. Biomech. 44, 1001–1007.CrossRefGoogle Scholar
Rao, A.R. & Usha, S. 1995 Peristaltic transport of two immiscible viscous fluids in a circular tube. J. Fluid Mech. 298, 271–285.CrossRefGoogle Scholar
Razavi, M.S., Nelson, T.S., Nepiyushchikh, Z., Gleason, R.L. & Dixon, J.B. 2017 The relationship between lymphangion chain length and maximum pressure generation established through in vivo imaging and computational modeling. Am. J. Physiol. Heart Circ. Physiol. 313, H1249–H1260.CrossRefGoogle ScholarPubMed
Reddy, N.P., Krouskop, T.A. & Newell, P.H. Jr. 1977 A computer model of the lymphatic system. Comput. Biol. Med. 7, 181–197.CrossRefGoogle ScholarPubMed
Reddy, N.P., Palmieri, V. & Cochran, G. 1981 Subcutaneous interstitial fluid pressure during external loading. Am. J. Physiol. Regul. Integra. Compar. Physiol. 240, R327–R329.CrossRefGoogle ScholarPubMed
Sabine, A., Agalarov, Y., Maby-El Hajjami, H., Jaquet, M., Hägerling, R., Pollmann, C., Bebber, D., Pfenniger, A., Miura, N. & Dormond, O. 2012 Mechanotransduction, PROX1, and FOXC2 cooperate to control connexin37 and calcineurin during lymphatic-valve formation. Develop. Cell 22, 430–445.CrossRefGoogle ScholarPubMed
Sabine, A., Bovay, E., Demir, C.S., Kimura, W., Jaquet, M., Agalarov, Y., Zangger, N., Scallan, J.P., Graber, W. & Gulpinar, E. 2015 FOXC2 and fluid shear stress stabilize postnatal lymphatic vasculature. J. Clin. Invest. 125, 3861–3877.CrossRefGoogle ScholarPubMed
Scallan, J.P., Wolpers, J.H., Muthuchamy, M., Zawieja, D.C., Gashev, A.A. & Davis, M.J. 2012 Independent and interactive effects of preload and afterload on the pump function of the isolated lymphangion. Am. J. Physiol. Heart Circul. Physiol. 303, H809–H824.CrossRefGoogle ScholarPubMed
Shapiro, A.H., Jaffrin, M.Y. & Weinberg, S.L. 1969 Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech. 37, 799–825.CrossRefGoogle Scholar
Skalak, T., Schmid-Schönbein, G. & Zweifach, B. 1984 New morphological evidence for a mechanism of lymph formation in skeletal muscle. Microvasc. Res. 28, 95–112.CrossRefGoogle ScholarPubMed
Succi, S. 2001 The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press.Google Scholar
Sutera, S.P. & Skalak, R. 1993 The history of Poiseuille's law. Annu. Rev. Fluid Mech. 25, 1–20.CrossRefGoogle Scholar
Swartz, M.A. 2001 The physiology of the lymphatic system. Adv. Drug Deliver. Rev. 50, 3–20.CrossRefGoogle ScholarPubMed
Takabatake, S., Ayukawa, K. & Mori, A. 1988 Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech. 193, 267–283.CrossRefGoogle Scholar
Tripathi, D. 2013 Study of transient peristaltic heat flow through a finite porous channel. Math. Comput. Model. 57, 1270–1283.CrossRefGoogle Scholar
Uchida, S. & Aoki, H. 1977 Unsteady flows in a semi-infinite contracting or expanding pipe. J. Fluid Mech. 82, 371–387.CrossRefGoogle Scholar
Watson, D.J., Sazonov, I., Zawieja, D.C., Moore, J.E. & van Loon, R. 2017 Integrated geometric and mechanical analysis of an image-based lymphatic valve. J. Biomech. 64, 172–179.CrossRefGoogle ScholarPubMed
Webb, R.C. Jr. & Starzl, T. 1953 The effect of blood vessel pulsations on lymph pressure in large lymphatics. Bull. Johns Hopkins Hospital 93, 401–407.Google ScholarPubMed
Wilson, J.T., van Loon, R., Wang, W., Zawieja, D.C. & Moore, J.E. 2015 Determining the combined effect of the lymphatic valve leaflets and sinus on resistance to forward flow. J. Biomech. 48, 3584–3590.CrossRefGoogle ScholarPubMed
Yeh, P.D. & Alexeev, A. 2016 Effect of aspect ratio in free-swimming plunging flexible plates. Comput. Fluids 124, 220–225.CrossRefGoogle Scholar
Zawieja, D.C. 2009 Contractile physiology of lymphatics. Lymphat. Res. Biol. 7, 87–96.CrossRefGoogle ScholarPubMed
Zawieja, S.D., Castorena-Gonzalez, J.A., Scallan, J.P. & Davis, M.J. 2018 Differences in L-type Ca2+ channel activity partially underlie the regional dichotomy in pumping behavior by murine peripheral and visceral lymphatic vessels. Am. J. Physiol. Heart Circ. Physiol. 314, H991–H1010.CrossRefGoogle ScholarPubMed
Zawieja, D.C., Davis, K.L., Schuster, R., Hinds, W.M. & Granger, H.J. 1993 Distribution, propagation, and coordination of contractile activity in lymphatics. Am. J. Physiol. Heart Circ. Physiol. 264, H1283–H1291.CrossRefGoogle ScholarPubMed
Zien, T.-F. & Ostrach, S. 1970 A long wave approximation to peristaltic motion. J. Biomech. 3, 63–75.CrossRefGoogle ScholarPubMed

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