### Abstract

In this paper, we present a one-dimensional model for blood flow in arteries, without assuming an a priori shape for the velocity profile across an artery (Azer, Ph.D. thesis, Courant Institute, New York University, 2006). We combine the one-dimensional equations for conservation of mass and momentum with the Womersley model for the velocity profile in an iterative way. The pressure gradient of the one-dimensional model drives the Womersley equations, and the velocity profiles calculated then feed back into both the friction and nonlinear parts of the one-dimensional model. Besides enabling us to evaluate the friction correctly and also to use the velocity profile to correct the nonlinear terms, having the velocity profile available as output should be useful in a variety of applications. We present flow simulations using both structured trees and pure resistance models for the small arteries, and compare the resulting flow and pressure waves under various friction models. Moreover, we show how to couple the one-dimensional equations with the Taylor diffusion limit (Azer, Int J Heat Mass Transfer 2005;48:2735-40; Taylor, Proc R Soc Lond Ser A 1953;219:186-203) of the convection-diffusion equations to drive the concentration of a solute along an artery in time.

Original language | English (US) |
---|---|

Pages (from-to) | 51-73 |

Number of pages | 23 |

Journal | Cardiovascular Engineering |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2007 |

### Fingerprint

### Keywords

- Compliance
- Hypertension
- MRI
- One-dimensional blood flow
- Shear stress
- Structured tree
- Taylor diffusion
- Velocity profile
- Womersley

### ASJC Scopus subject areas

- Cardiology and Cardiovascular Medicine
- Medicine (miscellaneous)

### Cite this

*Cardiovascular Engineering*,

*7*(2), 51-73. https://doi.org/10.1007/s10558-007-9031-y

**A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile.** / Azer, Karim; Peskin, Charles.

Research output: Contribution to journal › Article

*Cardiovascular Engineering*, vol. 7, no. 2, pp. 51-73. https://doi.org/10.1007/s10558-007-9031-y

}

TY - JOUR

T1 - A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile

AU - Azer, Karim

AU - Peskin, Charles

PY - 2007/6

Y1 - 2007/6

N2 - In this paper, we present a one-dimensional model for blood flow in arteries, without assuming an a priori shape for the velocity profile across an artery (Azer, Ph.D. thesis, Courant Institute, New York University, 2006). We combine the one-dimensional equations for conservation of mass and momentum with the Womersley model for the velocity profile in an iterative way. The pressure gradient of the one-dimensional model drives the Womersley equations, and the velocity profiles calculated then feed back into both the friction and nonlinear parts of the one-dimensional model. Besides enabling us to evaluate the friction correctly and also to use the velocity profile to correct the nonlinear terms, having the velocity profile available as output should be useful in a variety of applications. We present flow simulations using both structured trees and pure resistance models for the small arteries, and compare the resulting flow and pressure waves under various friction models. Moreover, we show how to couple the one-dimensional equations with the Taylor diffusion limit (Azer, Int J Heat Mass Transfer 2005;48:2735-40; Taylor, Proc R Soc Lond Ser A 1953;219:186-203) of the convection-diffusion equations to drive the concentration of a solute along an artery in time.

AB - In this paper, we present a one-dimensional model for blood flow in arteries, without assuming an a priori shape for the velocity profile across an artery (Azer, Ph.D. thesis, Courant Institute, New York University, 2006). We combine the one-dimensional equations for conservation of mass and momentum with the Womersley model for the velocity profile in an iterative way. The pressure gradient of the one-dimensional model drives the Womersley equations, and the velocity profiles calculated then feed back into both the friction and nonlinear parts of the one-dimensional model. Besides enabling us to evaluate the friction correctly and also to use the velocity profile to correct the nonlinear terms, having the velocity profile available as output should be useful in a variety of applications. We present flow simulations using both structured trees and pure resistance models for the small arteries, and compare the resulting flow and pressure waves under various friction models. Moreover, we show how to couple the one-dimensional equations with the Taylor diffusion limit (Azer, Int J Heat Mass Transfer 2005;48:2735-40; Taylor, Proc R Soc Lond Ser A 1953;219:186-203) of the convection-diffusion equations to drive the concentration of a solute along an artery in time.

KW - Compliance

KW - Hypertension

KW - MRI

KW - One-dimensional blood flow

KW - Shear stress

KW - Structured tree

KW - Taylor diffusion

KW - Velocity profile

KW - Womersley

UR - http://www.scopus.com/inward/record.url?scp=34447132809&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34447132809&partnerID=8YFLogxK

U2 - 10.1007/s10558-007-9031-y

DO - 10.1007/s10558-007-9031-y

M3 - Article

C2 - 17566860

AN - SCOPUS:34447132809

VL - 7

SP - 51

EP - 73

JO - Cardiovascular Engineering

JF - Cardiovascular Engineering

SN - 1567-8822

IS - 2

ER -