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Incorporating vessel taper and compliance properties in Navier-Stokes based blood flow models

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Abstract

A popular and useful technique used to model blood flow in cardiovascular simulations is to divide each blood vessel into a series of segments, each with its own lumped resistance, intertance, and compliance parameters. The values of these parameters are usually obtained through a simplification of the Navier-Stokes equations for fluid flow. However, the simplification often ignores the nonlinear and convective terms of the equations, resulting in errors in the parameter values, especially in the value found for resistance per unit length. We report a new method for the calculation of vessel resistance per unit length which takes into account the effects of vessel taper and wall compliance. It is shown that these effects can be addressed by the addition of two time-varying terms to the calculation of resistance per unit length. One term, due to vessel taper, is proportional to volumetric flow rateQ. The other term, due to vessel compliance, is proportional to ∂p/∂t. These variables are readily available in computer simulations of blood flow in lumped parameter systems. Using data for the descending aorta, the new parameter values, when averaged over a cardiac cycle, compare favorably with results in the literature.

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Abbreviations

i:

class number of parent element

j:

class number of daughter element

k :

branching number

m :

daughter element number at one branching

n :

number of pathlength group

z :

generation number

d z,i :

diameter of zth-generation and i-class element

len(i):

length of i-class element

N i,j :

observed number of j-class from i-class

Nt:

total number of branching

N el(i):

element number of i-class element

N tr(i):

tree number of i-class element

TNEEt :

total number of the exits of the model of tree

TNEE(n):

total number of the exit elements of group-n

R:

resistance

Rp:

peripheral resistance from one exit to left atrium

Rt:

total resistance from the entrance to left atrium

Rt(n):

Rt when the Rp ofn-group is infinite

Rc:

the imaginary resistance of the model of tree

C 1(n):

the imaginary conductance of one exit vessel of n-group

r :

random disit

E i,j :

the matrix of mathematical expectation of branching

a :

coefficient of becoming narrow

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Authors and Affiliations

  1. Biomedical Engineering and Science Institute, Drexel University, 19104, Philadelphia, PA

    Guo-Fan Ye, Thomas W. Moore & Dov Jaron

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  1. Guo-Fan Ye
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  2. Thomas W. Moore
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  3. Dov Jaron
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Ye, GF., Moore, T.W. & Jaron, D. Incorporating vessel taper and compliance properties in Navier-Stokes based blood flow models. Ann Biomed Eng 21, 97–106 (1993). https://doi.org/10.1007/BF02367605

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  • DOI: https://doi.org/10.1007/BF02367605

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