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) |
|---|---|
| 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
An inverse problem for reduced-encoding MRI velocimetry in potential flows. / Raguin, L. Guy; Kodali, Anil K.; Rovas, Dimitrios V.; Georgiadis, John G.
In: Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, Vol. 26 II, 01.12.2004, p. 1100-1103.Research output: Contribution to journal › Conference article
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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 -