Modeling arteriolar flow and mass transport using the immersed boundary method

Kayne M. Arthurs, Leon C. Moore, Charles Peskin, E. Bruce Pitman, H. E. Layton

Research output: Contribution to journalArticle

Abstract

Flow in arterioles is determined by a number of interacting factors, including perfusion pressure, neural stimulation, vasoactive substances, the intrinsic contractility of arteriolar walls, and wall shear stress. We have developed a two-dimensional model of arteriolar fluid flow and mass transport. The model includes a phenomenological representation of the myogenic response of the arteriolar wall, in which an increase in perfusion pressure stimulates vasoconstriction. The model also includes the release, advection, diffusion, degradation, and dilatory action of nitric oxide (NO), a potent, but short-lived, vasodilatory agent. Parameters for the model were taken primarily from the experimental literature of the rat renal afferent arteriole. Solutions to the incompressible Navier-Stokes equations were approximated by means of a splitting that used upwind differencing for the inertial term and a spectral method for the viscous term and incompressibility condition. The immersed boundary method was used to include the forces arising from the arteriolar walls. The advection of NO was computed by means of a high-order flux-corrected transport scheme; the diffusion of NO was computed by a spectral solver. Simulations demonstrated the efficacy of the numerical methods employed, and grid refinement studies confirmed anticipated first-order temporal convergence and demonstrated second-order spatial convergence in key quantities. By providing information about the effective width of the immersed boundary and sheer stress magnitude near that boundary, the grid refinement studies indicate the degree of spatial refinement required for quantitatively reliable simulations. Owing to the dominating effect of NO advection, relative to degradation and diffusion, simulations indicate that NO has the capacity to produce dilation along the entire length of the arteriole.

Original languageEnglish (US)
Pages (from-to)402-440
Number of pages39
JournalJournal of Computational Physics
Volume147
Issue number2
DOIs
StatePublished - Dec 10 1998

Fingerprint

Nitric oxide
nitric oxide
arterioles
Mass transfer
Advection
advection
vasoconstriction
degradation
Degradation
incompressibility
simulation
spectral methods
two dimensional models
stimulation
Navier-Stokes equation
Navier Stokes equations
shear stress
rats
fluid flow
Rats

Keywords

  • Blood vessel
  • Computational biofluiddynamics
  • Myogenic autoregulation
  • Nitric oxide
  • Renal microvasculature

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Arthurs, K. M., Moore, L. C., Peskin, C., Pitman, E. B., & Layton, H. E. (1998). Modeling arteriolar flow and mass transport using the immersed boundary method. Journal of Computational Physics, 147(2), 402-440. https://doi.org/10.1006/jcph.1998.6097

Modeling arteriolar flow and mass transport using the immersed boundary method. / Arthurs, Kayne M.; Moore, Leon C.; Peskin, Charles; Pitman, E. Bruce; Layton, H. E.

In: Journal of Computational Physics, Vol. 147, No. 2, 10.12.1998, p. 402-440.

Research output: Contribution to journalArticle

Arthurs, KM, Moore, LC, Peskin, C, Pitman, EB & Layton, HE 1998, 'Modeling arteriolar flow and mass transport using the immersed boundary method', Journal of Computational Physics, vol. 147, no. 2, pp. 402-440. https://doi.org/10.1006/jcph.1998.6097
Arthurs, Kayne M. ; Moore, Leon C. ; Peskin, Charles ; Pitman, E. Bruce ; Layton, H. E. / Modeling arteriolar flow and mass transport using the immersed boundary method. In: Journal of Computational Physics. 1998 ; Vol. 147, No. 2. pp. 402-440.
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