On the Physics Underlying Longitudinal Capillary Recruitment

  • Jacques M. HuygheEmail author
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 1097)


Numerous researchers have found that capillary vessel haematocrit depends on the vasodilatory state of the arterioles. At rest, vessel haematocrit is down to 15 %, suggesting a red blood cell velocity three times higher than the plasma velocity. This finding is analysed in the context of present understanding of propulsion of red blood cells (RBCs) and plasma by means of the arteriovenous pressure gradient. Interfacial forces between the red blood cells and the plasma are proposed as a rational explanation of the observed red blood cell velocities. While the arteriovenous pressure gradient across the capillaries propels the red blood cell and the plasma jointly, interfacial forces along the red blood cell membrane can propel RBCs at the cost of the plasma. Different options are explored for the physical origin of these interfacial forces and oxygen gradients are found to be the most probable source.



The author acknowledges support from the STW-foundation, the Technological Branch of the Netherlands Organisation of Scientific Research NWO, and the Ministery of Economic Affairs of the Netherlands, for project 12538, Interfacial aspects of Ionised Media. The author thanks Dr. Sami Musa (University of Limerick and Eindhoven University of Technology) and dr. Orest Shardt (University of Limerick) for enlightening discussions and for commenting the manuscript.


  1. Anderson JL (1989) Colloid transport by interfacial forces. Annu Rev Fluid Mech 21:61CrossRefGoogle Scholar
  2. Anderson JL, Prieve DC (1991) Diffusiophoresis caused by gradients of strongly adsorbing solutes. Langmuir 7:403–406CrossRefGoogle Scholar
  3. Carvalho H, Pittman RN (2008) Longitudinal and radial gradients of PO2 in the hamster cheek pouch microcirculation. Microcirculation 15:215–224CrossRefGoogle Scholar
  4. Casagrande L (1949) Electroosmosis in soils. Géotechnique 1:159–177CrossRefGoogle Scholar
  5. Copp SW, Ferreira LF, Herspring KF, Musch TI, Poole DC (2009) The effects of aging on capillary hemodynamics in contracting rat spinotrapezius muscle. Microvasc Res 77:113–119CrossRefGoogle Scholar
  6. Derjaguin BV, Dukhin SS (1971) Application of thermodynamics of irreversible processes to the electrodiffusion theory of electrokinetic effects. Res Surface Forces 3:169Google Scholar
  7. Derjaguin BV, Sidorenkov GP, Zubashchenkov EA, Kiseleva EV (1947) Kinetic phenomena in boundary films of liquids. Kolloidn Zh 9:335–347Google Scholar
  8. Derjaguin BV, Dukhin SS, Korotkova AA (1961) Diffusiophoresis in electrolyte solutions and its role in the mechanism of film-formation from rubber latexes by the method of ionic deposition. Kolloidn Zh 23:53Google Scholar
  9. Derjaguin BV, Dukhin SS, Koptelova MM (1972) Capillary osmosis through porous partitions and properties of boundary layers of solutions. J Colloid Interface Sci 38:584–595CrossRefGoogle Scholar
  10. Ebel JP, Anderson JL, Prieve DC (1988) Diffusiophoresis of latex particles in electrolyte gradients. Langmuir 4:396CrossRefGoogle Scholar
  11. Florea D, Musa S, Huyghe JM, Wyss HM (2014) Long-range repulsion of colloids driven by ion-exchange and diffusiophoresis. Proc Natl Acad Sci USA 111: 6554–6559CrossRefGoogle Scholar
  12. Fåhræus R, Lindqvist T (1931) The viscosity of the blood in narrow capillary tubes. Am J Physiol 96:562–568Google Scholar
  13. Frisbee JC, Barclay JK (1998) Microvascular hematocrit and permeability-surface area product in contracting canine skeletal muscle in situ. Microvasc Res 55: 153–164CrossRefGoogle Scholar
  14. Freund JB (2013) The flow of red blood cells through a narrow spleen-like slit. Phys Fluids 25:110007Google Scholar
  15. Han Y, Weinbaum S, Spaan JAE, Vink H (2006) Large-deformation analysis of the elastic recoil of fibre layers in a brinkman medium with application to the endothelial glycocalyx. J Fluid Mech 554:217–235CrossRefGoogle Scholar
  16. Hellums JD (1977) The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue. Microvasc Res 13:131–136CrossRefGoogle Scholar
  17. Ke H, Ye S, Carroll RL, Showalter K (2010) Motion analysis of self-propelled Pt-silica particles in hydrogen peroxide solutions. J Phys Chem A 114: 5462–5467CrossRefGoogle Scholar
  18. Keh HJ, Weng JC (2001) Diffusiophoresis of colloidal spheres in nonelectrolyte gradients at small but finite péclet numbers. Colloid Polymer Sci 279:305–311CrossRefGoogle Scholar
  19. Kiaer T, Kristensen KD (1988) Intracompartmental pressure, PO2, PCO2 and blood flow in the human skeletal muscle. Arch Orthop Trauma Surg 107:114–116CrossRefGoogle Scholar
  20. Kindig CA, Poole DC (1998) A comparison of the microcirculation in the rat spinotrapezius and diaphragm muscles. Microvasc Res 57:144–152CrossRefGoogle Scholar
  21. Kindig CA, Richardson TE, Poole DC (2002) Skeletal muscle capillary hemodynamics from rest to contractions: implications for oxygen transfer. J Appl Physiol 92:2513–2520CrossRefGoogle Scholar
  22. Klitzman B, Duling BR (1979) Microvascular hematocrit and red cell flow in resting and contracting striated muscle. Am J Physiol 237:H481–H490PubMedGoogle Scholar
  23. Klitzman B, Damon DN, Gorczynski RJ, Duling BR (1982) Augmented tissue oxygen supply during striated muscle contraction in the hamster. relative contributions of capillary recruitment, functional dilation, and reduced tissue PO2. Circ Res 51:711–721CrossRefGoogle Scholar
  24. Krogh A (1919a) The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue. J Physiol 52:409–415CrossRefGoogle Scholar
  25. Krogh A (1919b) The supply of oxygen to the tissue and the regulation of the capillary circulation. J Physiol 52:457–474CrossRefGoogle Scholar
  26. Lecoq J, Tiret P, Najac M, Shepherd GM, Greer CA, Charpak S (2009) Odor-evoked oxygen consumption by action potential and synaptic transmission in the olfactory bulb. J Neurosci 29:1424–1433CrossRefGoogle Scholar
  27. Lecoq J, Parpaleix A, Roussakis E, Ducros M, Houssen YG, Vinogradov SA, Charpak S (2011) Simultaneous two-photon imaging of oxygen and blood flow in deep cerebral vessels. Nat Med 17:893–899CrossRefGoogle Scholar
  28. Linderkamp O, Meiselman HJ (1982) Geometric, osmotic, and membrane mechanical properties of density-separated human red cells. Blood 59: 1121–1127PubMedGoogle Scholar
  29. Martini P, Pierach A, Schreyer E (1930) Die Strömung des Blutes in engen Gefässen. eine Abweichung vom Poiseuille’schen Gesetz. Deutsches Archiv für klinische Medizin 169:212–222Google Scholar
  30. Ndubuizu O, LaManna JC (2007) Brain tissue oxygen concentration measurements. Antioxid Redox Signal 9:1207–1219CrossRefGoogle Scholar
  31. Paxton WF, Kistler KC, Olmeda CC, Sen A, St. Angelo SK, Cao Y, Mallouk TE, Lammert PE, Crespi VH (2004) Catalytic nanomotors: autonomous movement of striped nanorod. J Am Chem Soc 126:13425–13431CrossRefGoogle Scholar
  32. Paxton WF, Sundararajan S, Mallouk TE,  Sen A (2006) Minireview: chemical locomotion. Angew Chem 45:5420 –5429CrossRefGoogle Scholar
  33. Poiseuille JLM (1830) Recherches sur les causes du mouvement du sang dans les veines. J Physiol Exp Pathol 10:277–295Google Scholar
  34. Poiseuille JLM (1840a) Recherches expérimentales sur ie mouvement des liquides dans les tubes de très petits diamètres; i. influence de la pression sur la quantité de liquide qui traverse les tubes de très petits diamètres. C R Acad Sci 11:961–67Google Scholar
  35. Poiseuille JLM (1840b) Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamètres; ii.influence de la longueur sur la quantité de liquide qui traverse les tubes de très petits diamètres; iii. influence du diamètre sur la quantité de liquide qui traverse les tubes de très petits diamètres. C R Acad Sci 11:1041–1048Google Scholar
  36. Poiseuille JLM (1841) Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamètres; iv. influence de la température sur la quantité de liquide qui traverse les tubes de très petits diamètres. C R Acad Sci 12:112–115Google Scholar
  37. Polwaththe-Gallage HN, Saha SC, Sauret E, Flower RL, Gu Y (2015) Numerical inventigation of motion and deformation of a single red blood cell in a stenosed capillary. Int J Comput Methods 12:1540003CrossRefGoogle Scholar
  38. Poole DC, Musch TI, Kindig CA (1997) In vivo microvascular structural and functional consequences of muscle length changes. Am J Physiol 272:H2107–H2114PubMedGoogle Scholar
  39. Poole DC, Copp SW, Hirai DM, Musch TI (2011) Dynamics of muscle microcirculatory and blood–myocyte O2 flux during contractions. Acta Physiol (Oxf) 202:293–310CrossRefGoogle Scholar
  40. Poole DC, Copp SW, Ferguson SK, Musch TI (2013) Skeletal muscle capillary function: contemporary observations and novel hypotheses. Exp Physiol 98:1645–1658CrossRefGoogle Scholar
  41. Pozrikidis C (2010) Computational hydrodynamics of capsules and biological cells. CRC Press, Boca RatonCrossRefGoogle Scholar
  42. Pries AR, Ley K, Gaehtgens P (1986) Generalization of the Fahraeus principle for microvessel networks. Am J Physiol 251(6):H1324–32PubMedGoogle Scholar
  43. Pries AR, Secomb TW, Gaehtgens P (1996) Biophysical aspects of blood flow in the microvasculature. Cardiovasc Res 32:654–667CrossRefGoogle Scholar
  44. Ruckenstein E (1981) Can phoretic motion be treated as an interfacial tension gradient driven phenomena? J Colloid Interface Sci 77:83Google Scholar
  45. Sabass BC (2012) Active, phoretic motion. Phd dissertation, University of Stuttgart, Department of Physics and MathematicsGoogle Scholar
  46. Sarelius IH, Duling BR (1982) Direct measurement of microvessel hematocrit, red cell flux, velocity and transit time. Am J Physiol 243:H1018–1026PubMedGoogle Scholar
  47. Sharan M, Popel AS (2001) A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 38: 415–428PubMedGoogle Scholar
  48. Shi L, Pan T-W, Glowinski R (2012) Deformation of a single red blood cell in bounded poiseuille flows. Phys Rev E 85:016307CrossRefGoogle Scholar
  49. Shi N, Nery-Azevedo R, Abdel-Fattah AI, Squires TM (2016) Diffusiophoretic focusing of suspended colloids. Phys Rev Lett 117:258001CrossRefGoogle Scholar
  50. Skalak R, Branemark P-I (1969) Deformation of red blood cells in capillaries. Science 164(3880):717–719CrossRefGoogle Scholar
  51. Secomb TW (2003) Mechanics of RBCs and blood flow in narrow tubes. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  52. Secomb TW, Styp-Rekowska B, Pries AR (2007) Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann Biomed Eng 35:755–765CrossRefGoogle Scholar
  53. Snyder GK, Sheafor BA (1999) RBCs: centerpiece in the evolution of the vertebrate circulatory system. Am Zool 39:189–198CrossRefGoogle Scholar
  54. Velegol D, Garg A, Guha R, Kar A, Kumar M (2016) Origins of concentration gradients for diffusiophoresis. Soft Matter CrossRefGoogle Scholar
  55. Vink H, Duling BR (1996) Identification of distinct luminal domains for macromolecules, erythrocytes and leucocytes within mammalian capillaries. Circ Res 79:581–589CrossRefGoogle Scholar
  56. von Reuss FF (1809) Notice sur un nouvel effet de l’électricité galvanique. Mémoires de la Société Impériale des Naturalistes de l’Université Impériale de Moscou 2:327Google Scholar
  57. Weinbaum S, Zhang X, Han Y, Vink H, Cowin SC (2003) Mechanotransduction and flow across the endothelial glycocalyx. Proc Natl Acad Sci USA 100:7988–7995CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bernal InstituteUniversity of LimerickLimerickIreland
  2. 2.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations