### Abstract

We propose a computational technique to reconstruct internal physiological flows described by sparse point-wise MRI velocity measurements. Assuming that the viscous forces in the flow are negligible, the incompressible flow field can be obtained from a velocity potential that satisfies Laplace's equation. A set of basis functions each satisfying Laplace's equation with appropriately defined boundary data is constructed using the finite-element method. An inverse problem is formulated where higher resolution boundary and internal velocity data are extracted from the point-wise MRI velocity measurements using a least-squares method. From the results we obtained with ∼100 internal measurement points, the proposed reconstruction method is shown to be effective in filtering out the experimental noise at levels as high as 30%, while matching the reference solution within 2%. This allows the reconstruction of a high-resolution velocity field with limited MRI encoding.

Original language | English (US) |
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Pages (from-to) | 1100-1103 |

Number of pages | 4 |

Journal | Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings |

Volume | 26 II |

State | Published - Dec 1 2004 |

Event | Conference Proceedings - 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2004 - San Francisco, CA, United States Duration: Sep 1 2004 → Sep 5 2004 |

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### Keywords

- Inverse Laplace problem
- Magnetic resonance imaging
- Potential flow
- Velocity reconstruction

### ASJC Scopus subject areas

- Bioengineering

### Cite this

*Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings*,

*26 II*, 1100-1103.