A quasi-lumped model for the peripheral distortion of the arterial pulse
As blood circulates through the arterial tree, the flow and pressure pulse distort. Principal factors to this distortion are reflections form arterial bifurcations and the viscous character of the flow of the blood. Both of them are expounded in the literature and included in our analysis. The nonli...
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AIMS Press
2011-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.175 |
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| author | Panagiotes A. Voltairas Antonios Charalambopoulos Dimitrios I. Fotiadis Lambros K. Michalis |
| author_facet | Panagiotes A. Voltairas Antonios Charalambopoulos Dimitrios I. Fotiadis Lambros K. Michalis |
| author_sort | Panagiotes A. Voltairas |
| collection | DOAJ |
| description | As blood circulates through the arterial tree, the flow and pressure pulse distort. Principal factors to this distortion are reflections form arterial bifurcations and the viscous character of the flow of the blood. Both of them are expounded in the literature and included in our analysis. The nonlinearities of inertial effects are usually taken into account in numerical simulations, based on Navier-Stokes like equations. Nevertheless, there isn't any qualitative, analytical formula, which examines the role of blood's inertia on the distortion of the pulse. We derive such an analytical nonlinear formula. It emanates from a generalized Bernoulli's equation for an an-harmonic, linear, viscoelastic, Maxwell fluid flow in a linear, viscoelastic, Kelvin-Voigt, thin, cylindrical vessel. We report that close to the heart, convection effects related to the change in the magnitude of the velocity of blood dominate the alteration of the shape of the pressure pulse, while at remote sites of the vascular tree, convection of vorticity, related to the change in the direction of the velocity of blood with respect to a mean axial flow, prevails. A quantitative comparison between the an-harmonic theory and related pressure measurements is also performed. |
| format | Article |
| id | doaj-art-e749f0254fe945578edf774edf036d68 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e749f0254fe945578edf774edf036d682025-01-24T02:05:22ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-11-019117519810.3934/mbe.2012.9.175A quasi-lumped model for the peripheral distortion of the arterial pulsePanagiotes A. Voltairas0Antonios Charalambopoulos1Dimitrios I. Fotiadis2Lambros K. Michalis3Department of Materials Science, University of Ioannina, GR 451 10, IoanninaDepartment of Materials Science, University of Ioannina, GR 451 10, IoanninaDepartment of Materials Science, University of Ioannina, GR 451 10, IoanninaDepartment of Materials Science, University of Ioannina, GR 451 10, IoanninaAs blood circulates through the arterial tree, the flow and pressure pulse distort. Principal factors to this distortion are reflections form arterial bifurcations and the viscous character of the flow of the blood. Both of them are expounded in the literature and included in our analysis. The nonlinearities of inertial effects are usually taken into account in numerical simulations, based on Navier-Stokes like equations. Nevertheless, there isn't any qualitative, analytical formula, which examines the role of blood's inertia on the distortion of the pulse. We derive such an analytical nonlinear formula. It emanates from a generalized Bernoulli's equation for an an-harmonic, linear, viscoelastic, Maxwell fluid flow in a linear, viscoelastic, Kelvin-Voigt, thin, cylindrical vessel. We report that close to the heart, convection effects related to the change in the magnitude of the velocity of blood dominate the alteration of the shape of the pressure pulse, while at remote sites of the vascular tree, convection of vorticity, related to the change in the direction of the velocity of blood with respect to a mean axial flow, prevails. A quantitative comparison between the an-harmonic theory and related pressure measurements is also performed.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.175fluid-structure interactionviscoelasticityklein-gordon equationarterial pulse modelingvascular disease.wave propagation |
| spellingShingle | Panagiotes A. Voltairas Antonios Charalambopoulos Dimitrios I. Fotiadis Lambros K. Michalis A quasi-lumped model for the peripheral distortion of the arterial pulse Mathematical Biosciences and Engineering fluid-structure interaction viscoelasticity klein-gordon equation arterial pulse modeling vascular disease. wave propagation |
| title | A quasi-lumped model for the peripheral distortion of the arterial pulse |
| title_full | A quasi-lumped model for the peripheral distortion of the arterial pulse |
| title_fullStr | A quasi-lumped model for the peripheral distortion of the arterial pulse |
| title_full_unstemmed | A quasi-lumped model for the peripheral distortion of the arterial pulse |
| title_short | A quasi-lumped model for the peripheral distortion of the arterial pulse |
| title_sort | quasi lumped model for the peripheral distortion of the arterial pulse |
| topic | fluid-structure interaction viscoelasticity klein-gordon equation arterial pulse modeling vascular disease. wave propagation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.175 |
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