### Abstract

Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity fields are nearly divergence-free. The two most commonly used types of vector field representation are piece-wisecontinuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-free vector fields are approximated, i.e. they are not exactly divergence-free and both representation types require a relatively large number of degrees freedom. We showed that a continuous, divergence-free vector field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of freedom. The divergence-free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.

Original language | English (US) |
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Title of host publication | Proceedings - 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009 |

Pages | 891-894 |

Number of pages | 4 |

DOIs | |

State | Published - 2009 |

Event | 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009 - Boston, MA, United States Duration: Jun 28 2009 → Jul 1 2009 |

### Other

Other | 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009 |
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Country | United States |

City | Boston, MA |

Period | 6/28/09 → 7/1/09 |

### Fingerprint

### Keywords

- Divergence-free
- Incompressibility
- Vector field representation

### ASJC Scopus subject areas

- Biomedical Engineering
- Radiology Nuclear Medicine and imaging

### Cite this

*Proceedings - 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009*(pp. 891-894). [5193196] https://doi.org/10.1109/ISBI.2009.5193196

**A divergence-free vector field model for imaging applications.** / Škrinjar, O.; Bistoquet, A.; Oshinski, J.; Sundareswaran, K.; Frakes, David; Yoganathan, A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009.*, 5193196, pp. 891-894, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009, Boston, MA, United States, 6/28/09. https://doi.org/10.1109/ISBI.2009.5193196

}

TY - GEN

T1 - A divergence-free vector field model for imaging applications

AU - Škrinjar, O.

AU - Bistoquet, A.

AU - Oshinski, J.

AU - Sundareswaran, K.

AU - Frakes, David

AU - Yoganathan, A.

PY - 2009

Y1 - 2009

N2 - Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity fields are nearly divergence-free. The two most commonly used types of vector field representation are piece-wisecontinuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-free vector fields are approximated, i.e. they are not exactly divergence-free and both representation types require a relatively large number of degrees freedom. We showed that a continuous, divergence-free vector field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of freedom. The divergence-free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.

AB - Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity fields are nearly divergence-free. The two most commonly used types of vector field representation are piece-wisecontinuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-free vector fields are approximated, i.e. they are not exactly divergence-free and both representation types require a relatively large number of degrees freedom. We showed that a continuous, divergence-free vector field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of freedom. The divergence-free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.

KW - Divergence-free

KW - Incompressibility

KW - Vector field representation

UR - http://www.scopus.com/inward/record.url?scp=70449341645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449341645&partnerID=8YFLogxK

U2 - 10.1109/ISBI.2009.5193196

DO - 10.1109/ISBI.2009.5193196

M3 - Conference contribution

SN - 9781424439324

SP - 891

EP - 894

BT - Proceedings - 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009

ER -