Article thumbnail
Location of Repository

Shock formation and non-linear dispersion in a microvascular capillary network

By S.R. Pop, Giles Richardson, S.L. Waters and O.E. Jensen


Temporal and spatial fluctuations are a common feature of blood flow in microvascular networks. Among many possible causes, previous authors have suggested that the non-linear rheological properties of capillary blood flow (notably the Fåhræus effect, the Fåhræus–Lindqvist effect and the phase-separation effect at bifurcations) may be sufficient to generate temporal fluctuations even in very simple networks. We have simulated blood flow driven by a fixed pressure drop through a simple arcade network using coupled hyperbolic partial differential equations (PDEs) that incorporate well-established empirical descriptions of these rheological effects, accounting in particular for spatially varying haematocrit distributions; we solved the PDE system using a characteristic-based method. Our computations indicate that, under physiologically realistic conditions, there is a unique steady flow in an arcade network which is linearly stable and that plasma skimming suppresses the oscillatory decay of perturbations. In addition, we find that non-linear perturbations to haematocrit distributions can develop shocks via the Fåhræus effect, providing a novel mechanism for non-linear dispersion in microvascular networks. <br/><br/

Year: 2007
OAI identifier:
Provided by: e-Prints Soton
Sorry, our data provider has not provided any external links therefore we are unable to provide a link to the full text.

Suggested articles


  1. 3, 234–258.An asymptotic analysis of the buckling of a highly shear-resistant vesicle 517 L a n d a u
  2. (1987). A comparison of the postbuckling behavior of plates and shells. doi
  3. (1998). A thick hollow sphere compressed by equal and opposite concentrated axial loads: An asymptotic solution. doi
  4. (1985). An investigation of the complete postbuckling behavior of axisymmetrical spherical-shells.
  5. (2001). Analysis of large deflection equilibrium states of composite shells of revolution. Part 1. General model and singular perturbation analysis. doi
  6. (1986). Bendings of Surfaces and Stability of Shells.
  7. (2001). Buckling of actin-coated membranes under application of a local force. doi
  8. (2008). Buckling of an axisymmetric vesicle under compression: The effects of resistance to shear. doi
  9. (2005). Buckling of spherical shells adhering onto a rigid substrate. doi
  10. (1987). Compression of a capsule: Mechanical laws of membranes with negligible bending stiffness. doi
  11. (2001). Computational modeling of RBC and neutrophil transit through the pulmonary capillaries. doi
  12. (2003). Constitutive equation for elastic indentation of a thin-walled bio-mimetic microcapsule by an atomic force microscope tip. Colloids Surf. doi
  13. (1977). Elastic deformations of red blood cells. doi
  14. (2008). Experimental and theoretical studies on buckling of thin spherical shells under axial loads. doi
  15. F e r y ,A .&W e i n k a m e r ,R .(2007) Mechanical properties of micro- and nanocapsules: Single-capsule measurements. doi
  16. (1997). L i d m a r ,J . ,M i r n y ,L .&N e l s o n ,D .R .(2003) Virus shapes and buckling transitions in spherical shells. doi
  17. (2008). Localized and extended deformations of elastic shells. doi
  18. (2007). M o n l l o r ,P . ,B o n e t ,M .A .&C a s e s ,F doi
  19. (1980). Mechanics and Thermodynamics doi
  20. (2001). Microencapsulation: Its application in nutrition. doi
  21. (2000). Nano and microparticles as controlled drug delivery devices.
  22. (1980). On large axisymmetrical deflection states of spherical shells. doi
  23. (1998). On uniquely determining cell-wall material properties with the compression experiment. doi
  24. (1993). P a m p l o n a ,D .C .&C a l l a d i n doi
  25. (1984). P a r k e r doi
  26. P a r k e r ,K .H .&W i n l o v e ,C .P .(1999) The deformation of spherical vesicles with permeable, constant-area membranes: Application to the red blood cell. doi
  27. P a u c h a r d ,L .&R i c a ,S .(1998) Contact and compression of elastic spherical shells: The physics of a ping-pong ball. doi
  28. (1961). r r a y ,F .J .&W r i g h t doi
  29. (2005). Shape transitions of fluid vesicles and red blood cells in capillary flows. doi
  30. (2003). Shell theory for capsules and cells. doi
  31. (2007). Soft matters in cell adhesion: Rigidity sensing on soft elastic substrates. doi
  32. (2004). Solution space of axisymmetric capsules enclosed by elastic membranes. doi
  33. (2005). The buckling of spherical liposomes. doi
  34. (1980). The dimpling of spherical caps. doi
  35. (1970). The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. doi
  36. W i t t e n ,T .A .(2007) Stress focusing in elastic sheets. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.