### 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 |

### Fingerprint

### 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.

**An inverse problem for reduced-encoding MRI velocimetry in potential flows.** / Raguin, L. Guy; Kodali, Anil K.; Rovas, Dimitrios V.; Georgiadis, John G.

Research output: Contribution to journal › Conference article

*Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings*, vol. 26 II, pp. 1100-1103.

}

TY - JOUR

T1 - An inverse problem for reduced-encoding MRI velocimetry in potential flows

AU - Raguin, L. Guy

AU - Kodali, Anil K.

AU - Rovas, Dimitrios V.

AU - Georgiadis, John G.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - 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.

AB - 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.

KW - Inverse Laplace problem

KW - Magnetic resonance imaging

KW - Potential flow

KW - Velocity reconstruction

UR - http://www.scopus.com/inward/record.url?scp=11144264085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11144264085&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:11144264085

VL - 26 II

SP - 1100

EP - 1103

JO - Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference

JF - Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference

SN - 1557-170X

ER -