Flow measurement of incompressible fluid using divergence-free constraint
AssigneeThe Board of Trustees of the Leland Stanford Junior University
InventorsSamuel M. Song, Sandy A. Napel, Norbert J. Pelc
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Abstract
A method and apparatus to reduce the noise in three-dimensional phase contrast magnetic resonance velocity measurements exploits the property that blood is incompressible and therefore the velocity field describing its flow must be divergence-free. The divergence-free condition can be incorporated by the projection operation on Hilbert space where the velocity measurements are projected onto the space of divergence-free velocity fields. The reduction of noise is achieved since the projection operation eliminates the noise component that is not divergence-free. Higher quality angiograms are produced due to the noise reduction in the velocity measurement signals.
Claims29
A method of enhancing a measured velocity field with non-zero divergence comprising the steps of:
- (a) defining a space of divergence-free velocity fields;
- (b) projecting said measured velocity field onto said space of divergence-free fields to find the divergence-free field which is closest to the measured velocity field.
A method of improving signal to noise ratio of three-dimensional phase contrast magnetic resonance imaging signals from an incompressible medium such as blood flowing in vessels comprising the steps of:
- (a) obtaining signals representative of the velocity of motion at a plurality of voxels, and
- (b) applying a divergence-free constraint to said signals by a vector projection operation, whereby noise components of said signals are reduced.
Apparatus for producing an angiogram of the flow of blood in vessels of a body comprising:
- (a) means for obtaining phase contrast magnetic resonance signals indicative of flow velocity,
- (b) means for projecting said signals onto a space of divergence-free fields,
- (c) means for extracting from said space signal components in which noise is reduced, and
- (d) means for producing an angiogram of flow based on said signal components.
Apparatus for enhancing a measured velocity field with non-zero divergence comprising
- (a) means for defining a space of divergence-free velocity fields, and
- (b) means for projecting said measured velocity field onto said space of divergence-free fields to find a divergence-free field which is closest to said measured velocity field.
Apparatus for improving signal to noise ratio of three-dimensional phase contrast magnetic resonance imaging signals from an incompressible medium such as blood flowing in vessels comprising
- (a) means for obtaining signals representative of the velocity of motion at a plurality of voxels, and
- (b) means for applying a divergence-free constraint to said signals by a vector projection operation, whereby noise components of said signals are reduced.
Dependencies are inferred from the claim text.