Flow optimization in vascular networks
The development of mathematical models for studying phenomena observed in vascular networks is very useful for its potential applications in medicine and physiology. Detailed $3$D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence redu...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590056969207808 |
|---|---|
| author | Radu C. Cascaval Ciro D'Apice Maria Pia D'Arienzo Rosanna Manzo |
| author_facet | Radu C. Cascaval Ciro D'Apice Maria Pia D'Arienzo Rosanna Manzo |
| author_sort | Radu C. Cascaval |
| collection | DOAJ |
| description | The development of mathematical models for studying phenomena observed in vascular networks is very useful for its potential applications in medicine and physiology. Detailed $3$D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence reduced models are often used, both for the constitutive laws and the spatial domain. In order to capture the major features of the phenomena under study, such as variations in arterial pressure and flow velocity, the resulting PDE models on networks require appropriate junction and boundary conditions. Instead of considering an entire network, we simulate portions of the latter and use inflow and outflow conditions which realistically mimic the behavior of the network that has not been included in the spatial domain. The resulting PDEs are solved numerically using a discontinuous Galerkin scheme for the spatial and Adam-Bashforth method for the temporal discretization. The aim is to study the effect of truncation to the flow in the root edge of a fractal network, the effect of adding or subtracting an edge to a given network, and optimal control strategies on a network in the event of a blockage or unblockage of an edge or of an entire subtree. |
| format | Article |
| id | doaj-art-74cd885b99534526b9a3c2af54b35be8 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-74cd885b99534526b9a3c2af54b35be82025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114360762410.3934/mbe.2017035Flow optimization in vascular networksRadu C. Cascaval0Ciro D'Apice1Maria Pia D'Arienzo2Rosanna Manzo3Department of Mathematics, University of Colorado Colorado Springs, Colorado Springs, CO 80919, USADipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, ItalyDipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, ItalyDipartimento di Ingegneria dell'Informazione ed Elettrica e Matematica Applicata, Universita degli Studi di Salerno, Fisciano (SA), 84084, ItalyThe development of mathematical models for studying phenomena observed in vascular networks is very useful for its potential applications in medicine and physiology. Detailed $3$D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence reduced models are often used, both for the constitutive laws and the spatial domain. In order to capture the major features of the phenomena under study, such as variations in arterial pressure and flow velocity, the resulting PDE models on networks require appropriate junction and boundary conditions. Instead of considering an entire network, we simulate portions of the latter and use inflow and outflow conditions which realistically mimic the behavior of the network that has not been included in the spatial domain. The resulting PDEs are solved numerically using a discontinuous Galerkin scheme for the spatial and Adam-Bashforth method for the temporal discretization. The aim is to study the effect of truncation to the flow in the root edge of a fractal network, the effect of adding or subtracting an edge to a given network, and optimal control strategies on a network in the event of a blockage or unblockage of an edge or of an entire subtree.https://www.aimspress.com/article/doi/10.3934/mbe.2017035blood flownetwork optimizationdiscontinuous galerkin scheme |
| spellingShingle | Radu C. Cascaval Ciro D'Apice Maria Pia D'Arienzo Rosanna Manzo Flow optimization in vascular networks Mathematical Biosciences and Engineering blood flow network optimization discontinuous galerkin scheme |
| title | Flow optimization in vascular networks |
| title_full | Flow optimization in vascular networks |
| title_fullStr | Flow optimization in vascular networks |
| title_full_unstemmed | Flow optimization in vascular networks |
| title_short | Flow optimization in vascular networks |
| title_sort | flow optimization in vascular networks |
| topic | blood flow network optimization discontinuous galerkin scheme |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017035 |
| work_keys_str_mv | AT raduccascaval flowoptimizationinvascularnetworks AT cirodapice flowoptimizationinvascularnetworks AT mariapiadarienzo flowoptimizationinvascularnetworks AT rosannamanzo flowoptimizationinvascularnetworks |