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

L. Guy Raguin, Anil K. Kodali, Dimitrios V. Rovas, John G. Georgiadis

Research output: Contribution to journalConference article

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 languageEnglish (US)
Pages (from-to)1100-1103
Number of pages4
JournalAnnual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings
Volume26 II
StatePublished - Dec 1 2004
EventConference Proceedings - 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2004 - San Francisco, CA, United States
Duration: Sep 1 2004Sep 5 2004

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Rheology
Potential flow
Inverse problems
Velocity measurement
Magnetic resonance imaging
Laplace equation
Incompressible flow
Least-Squares Analysis
Noise
Flow fields
Finite element method

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 journalConference article

Raguin, L. Guy ; Kodali, Anil K. ; Rovas, Dimitrios V. ; Georgiadis, John G. / An inverse problem for reduced-encoding MRI velocimetry in potential flows. In: Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings. 2004 ; Vol. 26 II. pp. 1100-1103.
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