US 12,481,012 B2
Methods and systems for improved reconstruction of magnetic resonance velocimetry data and a method of compressing flow data of a fluid
Matthew Juniper, Cambridge (GB); and Alexandros Kontogiannis, Cambridge (GB)
Assigned to CAMBRIDGE ENTERPRISE LIMITED, Cambridge (GB)
Appl. No. 18/291,138
Filed by CAMBRIDGE ENTERPRISE LIMITED, Cambridge (GB)
PCT Filed Aug. 2, 2022, PCT No. PCT/GB2022/052027
§ 371(c)(1), (2) Date Jan. 22, 2024,
PCT Pub. No. WO2023/012467, PCT Pub. Date Feb. 9, 2023.
Claims priority of application No. 2111141 (GB), filed on Aug. 2, 2021; and application No. 2207201 (GB), filed on May 17, 2022.
Prior Publication US 2025/0004084 A1, Jan. 2, 2025
Int. Cl. G01V 3/00 (2006.01); G01R 33/56 (2006.01); G01R 33/561 (2006.01)
CPC G01R 33/5611 (2013.01) [G01R 33/5608 (2013.01)] 20 Claims
OG exemplary drawing
 
1. A computer implemented method for reconstruction of magnetic resonance velocimetry, MRV, data, the method comprising the steps of:
(a) receiving MRV data encoding information relating to a fluid velocity field, u*, within a subset of the MRV data forming a region, Ω, enclosed by a boundary, ∂Ω, the boundary including at least a physical boundary portion, Γ, and optionally further including an inlet portion, Γi, and/or an outlet portion, Γo; and
wherein the region Ω is a subset of an imaging region, I, over which the MRV data encodes information;
(b) receiving initial values for a set of unknown parameters, {x}, including at least:
a shape of the boundary, ∂Ω, within which the fluid is located;
a kinematic viscosity of the fluid, v; and optionally
an inlet boundary condition for the fluid, gi where an inlet portion exists; and/or
an outlet boundary condition for the fluid, go where an outlet portion exists;
(c) calculating a model fluid velocity field, uo, using the initial values as inputs to a Navier-Stokes problem, and solving for the velocity field within and at the boundary;
(d) constructing an error functional, J, of the form:

OG Complex Work Unit Math
in which E is a penalty term which penalises deviations in uo from the received MRV data; R is a penalty term which penalises outcomes for in uo which arise from statistically unlikely values for the parameters in the set of unknown parameters, {x}, and M is a penalty term which penalises deviations in uo from the Navier Stokes problem;
(e) determining a generalised gradient of J with respect to each of the unknown parameters in the set {x};
(f) for each of the unknown parameters in the set {x}, using the generalised gradient for that parameter, evaluated at the initial value of all of the parameters, to determine a direction in which perturbing each parameter reduces the magnitude of J and thereby determining improved values for each of the unknown parameters in the set {x}; and
(g) reconstructing the MRV data by outputting the improved values from step (f) and calculating the reconstructed velocity, u, across at least the region Ω.