Numerical analysis of blood flow in the heart

Charles S. Peskin

doi:10.1016/0021-9991(77)90100-0

Numerical analysis of blood flow in the heart

Charles S. Peskin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The flow pattern of blood in the heart is intimately connected with the performance of the heart valves. This paper extends previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid. The boundary representation now includes the muscular heart wall. The fixed topology of the boundary representation is exploited in the solution of the nonlinear equations which implicitly define the boundary forces. An improved numerical representation of the δ-function is introduced. A fast Laplace-solver is used. The results of calculations with a natural valve and with a prosthetic valve are presented.

Original language	English (US)
Pages (from-to)	220-252
Number of pages	33
Journal	Journal of Computational Physics
Volume	25
Issue number	3
DOIs	https://doi.org/10.1016/0021-9991(77)90100-0
State	Published - Nov 1977

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/0021-9991(77)90100-0

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title = "Numerical analysis of blood flow in the heart",

abstract = "The flow pattern of blood in the heart is intimately connected with the performance of the heart valves. This paper extends previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid. The boundary representation now includes the muscular heart wall. The fixed topology of the boundary representation is exploited in the solution of the nonlinear equations which implicitly define the boundary forces. An improved numerical representation of the δ-function is introduced. A fast Laplace-solver is used. The results of calculations with a natural valve and with a prosthetic valve are presented.",

author = "Peskin, {Charles S.}",

note = "Funding Information: The author is deeply indebted to Alexandre Chorin, Edward Yellin, and Olof Widlund, who have participated in this project and whose research has made this project possible. This work was supported in part by a research grant from the National Institutes of Health, HL-17859. Computation was supported by the US ERDA under Contract EY-76-C-02-3077*000 at New York University.",

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AU - Peskin, Charles S.

N1 - Funding Information: The author is deeply indebted to Alexandre Chorin, Edward Yellin, and Olof Widlund, who have participated in this project and whose research has made this project possible. This work was supported in part by a research grant from the National Institutes of Health, HL-17859. Computation was supported by the US ERDA under Contract EY-76-C-02-3077*000 at New York University.

PY - 1977/11

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N2 - The flow pattern of blood in the heart is intimately connected with the performance of the heart valves. This paper extends previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid. The boundary representation now includes the muscular heart wall. The fixed topology of the boundary representation is exploited in the solution of the nonlinear equations which implicitly define the boundary forces. An improved numerical representation of the δ-function is introduced. A fast Laplace-solver is used. The results of calculations with a natural valve and with a prosthetic valve are presented.

AB - The flow pattern of blood in the heart is intimately connected with the performance of the heart valves. This paper extends previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid. The boundary representation now includes the muscular heart wall. The fixed topology of the boundary representation is exploited in the solution of the nonlinear equations which implicitly define the boundary forces. An improved numerical representation of the δ-function is introduced. A fast Laplace-solver is used. The results of calculations with a natural valve and with a prosthetic valve are presented.

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Numerical analysis of blood flow in the heart

Abstract

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