Probing the effect of morphology on lymphatic valve dynamic function

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The lymphatic system is vital to the circulatory and immune systems, performing a range of important functions such as transport of interstitial fluid, fatty acid, and immune cells. Lymphatic vessels are composed of contractile walls and lymphatic valves, allowing them to pump lymph against adverse pressure gradients and to prevent backflow. Despite the importance of the lymphatic system, the contribution of mechanical and geometric changes of lymphatic valves and vessels in pathologies of lymphatic dysfunction, such as lymphedema, is not well understood. We develop a fully coupled fluid–solid, three-dimensional computational model to interrogate the various parameters thought to influence valve behavior and the consequences of these changes to overall lymphatic function. A lattice Boltzmann model is used to simulate the lymph, while a lattice spring model is used to model the mechanics of lymphatic valves. Lymphatic valve functions such as enabling lymph flow and preventing backflow under varied lymphatic valve geometries and mechanical properties are investigated to provide an understanding of the function of lymphatic vessels and valves. The simulations indicate that lymphatic valve function is optimized when valves are of low aspect ratio and bending stiffness, so long as these parameters are maintained at high enough values to allow for proper valve closing. This suggests that valve stiffening could have a profound effect on overall lymphatic pumping performance. Furthermore, dynamic valve simulations showed that this model captures the delayed response of lymphatic valves to dynamic flow conditions, which is an essential feature of valve operation. Thus, our model enhances our understanding of how lymphatic pathologies, specifically those exhibiting abnormal valve morphologies such as has been suggested to occur in cases of primary lymphedema, can lead to lymphatic dysfunctions.

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  1. Alexeev A, Balazs AC (2007) Designing smart systems to selectively entrap and burst microcapsules. Soft Matter 3:1500–1505

  2. Alexeev A, Verberg R, Balazs AC (2005) Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules 38:10244–10260

  3. Alexeev A, Verberg R, Balazs AC (2006) Designing compliant substrates to regulate the motion of vesicles. Phys Rev Lett 96:148103

  4. Baish JW, Kunert C, Padera TP, Munn LL (2016) Synchronization and random triggering of lymphatic vessel contractions. PLoS Comput Biol 12:e1005231

  5. Bertram C, Macaskill C, Davis M, Moore J (2014a) Development of a model of a multi-lymphangion lymphatic vessel incorporating realistic and measured parameter values. Biomech Model Mechanobiol 13:401–416

  6. Bertram C, Macaskill C, Davis MJ, Moore JE (2016) Consequences of intravascular lymphatic valve properties: a study of contraction timing in a multi-lymphangion model. Am J Physiol Heart Circ Physiol 310(7):H847–H860.

  7. Bertram C, Macaskill C, Moore J (2011) Simulation of a chain of collapsible contracting lymphangions with progressive valve closure. J Biomech Eng 133:011008

  8. Bertram C, Macaskill C, Moore J (2014b) Incorporating measured valve properties into a numerical model of a lymphatic vessel. Comput Methods Biomech Biomed Eng 17:1519–1534

  9. Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511

  10. Buxton GA, Clarke N (2006) Computational phlebology: the simulation of a vein valve. J Biol Phys 32:507–521

  11. Buxton GA, Verberg R, Jasnow D, Balazs AC (2005) Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys Rev E 71:056707

  12. Caulk AW, Dixon JB, Gleason RL (2016) A lumped parameter model of mechanically mediated acute and long-term adaptations of contractility and geometry in lymphatics for characterization of lymphedema. Biomech Model Mechanobiol 15:1601–1618

  13. Caulk AW, Nepiyushchikh ZV, Shaw R, Dixon JB, Gleason RL (2015) Quantification of the passive and active biaxial mechanical behaviour and microstructural organization of rat thoracic ducts. J R Soc Interface 12:20150280

  14. Davis MJ, Moore JE, Zawieja DC, Gahsev AA, Scallan JP (2012) Lymphatic valve lock in response to modest gravitational loads: a contributing mechanism to peripheral lymphedema? FASEB J 26(677):672

  15. Davis MJ, Rahbar E, Gashev AA, Zawieja DC, Moore JE (2011) Determinants of valve gating in collecting lymphatic vessels from rat mesentery. Am J Physiol Heart Circ Physiol 301:H48–H60

  16. Dixon JB, Greiner ST, Gashev AA, Cote GL, Moore JE, Zawieja DC (2006) Lymph flow, shear stress, and lymphocyte velocity in rat mesenteric prenodal lymphatics. Microcirculation 13:597–610

  17. Einstein DR, Del Pin F, Jiao X, Kuprat AP, Carson JP, Kunzelman KS, Cochran RP, Guccione JM, Ratcliffe MB (2010) Fluid-structure interactions of the mitral valve and left heart: comprehensive strategies, past, present and future. Int J Numer Methods Biomed Eng 26:348–380

  18. 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

  19. Freudiger S, Hegewald J, Krafczyk M (2008) A parallelisation concept for a multi-physics lattice Boltzmann prototype based on hierarchical grids. Prog Comput Fluid Dyn 8:168–178

  20. Gashev AA, Davis MJ, Delp MD, Zawieja DC (2004) Regional variations of contractile activity in isolated rat lymphatics. Microcirculation 11:477–492

  21. Gashev AA, Zhang R-Z, Muthuchamy M, Zawieja DC, Davis MJ (2012) Regional heterogeneity of length-tension relationships in rat lymph vessels. Lymphat Res Biol 10:14–19

  22. Hanasoge S, Ballard M, Hesketh PJ, Alexeev A (2017) Asymmetric motion of magnetically actuated artificial cilia. Lab Chip 17:3138–3145

  23. Jamalian S, Bertram CD, Richardson WJ, Moore JE (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

  24. Jamalian S, Davis MJ, Zawieja DC, Moore JE (2016) Network scale modeling of lymph transport and its effective pumping parameters. PLoS ONE 11:e0148384

  25. Kandhai D, Koponen A, Hoekstra AG, Kataja M, Timonen J, Sloot PMA (1998) Lattice-Boltzmann hydrodynamics on parallel systems. Comput Phys Commun 111:14–26

  26. Kassis T, Yarlagadda SC, Kohan AB, Tso P, Breedveld V, Dixon JB (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

  27. Kim H, Lu J, Sacks MS, Chandran KB (2006) Dynamic simulation pericardial bioprosthetic heart valve function. J Biomech Eng 128:717–724

  28. Kunert C, Baish JW, Liao S, Padera TP, Munn LL (2015) Mechanobiological oscillators control lymph flow. Proc Natl Acad Sci 112:10938–10943

  29. Ladd AJC, Verberg R (2001) Lattice-Boltzmann simulations of particle-fluid suspensions. J Stat Phys 104:1191–1251

  30. Lapinski PE, Lubeck BA, Chen D, Doosti A, Zawieja SD, Davis MJ, King PD (2017) RASA1 regulates the function of lymphatic vessel valves in mice. J Clin Investig 127:2569–2585

  31. Lauweryns JM, Boussauw L (1973) The ultrastructure of lymphatic valves in the adult rabbit lung. Z Zellforsch Mikrosk Anat 143:149–168

  32. Le TB, Sotiropoulos F (2013) Fluid–structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle. J Comput Phys 244:41–62

  33. MacDonald AJ, Arkill KP, Tabor GR, McHale NG, Winlove CP (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

  34. Mao W (2013) Modeling particle suspensions using lattice Boltzmann method. Ph.D. thesis, Georgia Institute of Technology

  35. Mao WB, Alexeev A (2014) Motion of spheriod particles in shear flow with inertia. J Fluid Mech 749:145–166

  36. Masoud H, Bingham BI, Alexeev A (2012) Designing maneuverable micro-swimmers actuated by responsive gel. Soft Matter 8:8944–8951

  37. Moore JE, Bertram CD (2018) Lymphatic system flows. Annu Rev Fluid Mech 50:459–482

  38. Nepiyushchikh ZV, Chakraborty S, Wang W, Davis MJ, Zawieja DC, Muthuchamy M (2011) Differential effects of myosin light chain kinase inhibition on contractility, force development and myosin light chain 20 phosphorylation of rat cervical and thoracic duct lymphatics. J Physiol 589:5415–5429

  39. Nipper ME, Dixon JB (2011) Engineering the lymphatic system. Cardiovasc Eng Technol 2:296–308

  40. Ostoja-Starzewski M (2002) Lattice models in micromechanics. Appl Mech Rev 55:35–60

  41. Pan WR, le Roux CM, Levy SM (2011) Alternative lymphatic drainage routes from the lateral heel to the inguinal lymph nodes: anatomic study and clinical implications. ANZ J Surg 81:431–435

  42. Petrova TV, 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

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

  44. Rahbar E, Weimer J, Gibbs H, Yeh AT, Bertram CD, Davis MJ, Hill MA, Zawieja DC, Moore JE (2012) Passive pressure–diameter relationship and structural composition of rat mesenteric lymphangions. Lymphat Res Biol 10:152–163

  45. Razavi MS, Nelson TS, Nepiyushchikh Z, Gleason RL, Dixon JB (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

  46. Reddy NP, Krouskop TA, Newell PH (1977) A computer model of the lymphatic system. Comput Biol Med 7:181–197

  47. Sabine A, Bovay E, Demir CS, Kimura W, Jaquet M, Agalarov Y, Zangger N, Scallan JP, Graber W, Gulpinar E (2015) FOXC2 and fluid shear stress stabilize postnatal lymphatic vasculature. J Clin Investig 125:3861

  48. Sacks MS, He Z, Baijens L, Wanant S, Shah P, Sugimoto H, Yoganathan A (2002) Surface strains in the anterior leaflet of the functioning mitral valve. Ann Biomed Eng 30:1281–1290

  49. Sacks MS, Yoganathan AP (2007) Heart valve function: a biomechanical perspective. Philos Trans R Soc Lond B Biol Sci 362:1369–1391

  50. Satofuka N, Nishioka T (1999) Parallelization of lattice Boltzmann method for incompressible flow computations. Comput Mech 23:164–171

  51. Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford

  52. Swartz MA (2001) The physiology of the lymphatic system. Adv Drug Deliv Rev 50:3–20

  53. Tian W, Rockson SG, Jiang X, Kim J, Begaye A, Shuffle EM, Tu AB, Cribb M, Nepiyushchikh Z, Feroze AH (2017) Leukotriene B4 antagonism ameliorates experimental lymphedema. Sci Transl Med 9:eaal3920

  54. Velivelli AC, Bryden KM (2006) Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger’s equation. Phys A Stat Mech Appl 362:139–145

  55. Wang W, Nepiyushchikh Z, Zawieja DC, Chakraborty S, Zawieja SD, Gashev AA, Davis MJ, Muthuchamy M (2009) Inhibition of myosin light chain phosphorylation decreases rat mesenteric lymphatic contractile activity. Am J Physiol Heart Circ Physiol 297:H726–H734

  56. Wilson JT, van Loon R, Wang W, Zawieja DC, Moore JE (2015) Determining the combined effect of the lymphatic valve leaflets and sinus on resistance to forward flow. J Biomech 48:3584–3590

  57. Yeh PD, Alexeev A (2016a) Biomimetic flexible plate actuators are faster and more efficient with a passive attachment. Acta Mech Sin 32:1001–1011

  58. Yeh PD, Alexeev A (2016b) Effect of aspect ratio in free-swimming plunging flexible plates. Comput Fluids 124:220–225

  59. Zawieja DC (2009) Contractile physiology of lymphatics. Lymphat Res Biol 7:87–96

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Financial support from the National Science Foundation (CMMI-1635133) is gratefully acknowledged. The authors would also like to acknowledge David Zawieja at Texas A&M University for providing access to and assistance with rat isolated lymphatic vessels and John Peroni at the University of Georgia for assistance with obtaining sheep lymphatic vessels.

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Correspondence to Alexander Alexeev.

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Ballard, M., Wolf, K.T., Nepiyushchikh, Z. et al. Probing the effect of morphology on lymphatic valve dynamic function. Biomech Model Mechanobiol 17, 1343–1356 (2018).

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  • Computational simulations
  • Biomechanics
  • Lymphatic valve
  • Lymph transport
  • Lymphedema