US 12,578,291 B1Granted

Magnetic resonance methods and devices for characterizing a pattern of flow of a fluid

AssigneeUniversity of New Brunswick

InventorsBruce J. Balcom, Michael M. B. Ross, Jiangfeng Guo, Benedict Newling

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Abstract

A magnetic resonance method and device for characterizing the pattern of flow of a flowing fluid including the steps of flowing the fluid through a conduit, wherein a segment of the conduit defines a measurement volume, subjecting the flowing fluid in the measurement volume to a magnetic field gradient generally in the direction of flow of the fluid, wherein the magnetic field gradient in the direction of flow comprises a generally fixed value in the measurement volume, and a magnetic resonance pulse, acquiring at least one odd echo from the magnetic resonance pulse, wherein the echo comprises signals from streamlines in the flowing fluid in the measurement volume, processing the signals to determine a flow behaviour index for the flowing fluid, determining an average velocity of the flowing fluid, and calculating velocity as a function of the radius of the conduit using the flow behaviour index and the average velocity and relating the function to a pattern of flow to characterize the pattern of flow exhibited by the flowing fluid.

Claims8

Dependent claims

A magnetic resonance method for characterizing a pattern of flow of a flowing fluid comprising the steps of:

flowing the fluid through a conduit wherein the fluid comprises a direction of flow and a central axis of the direction of flow, wherein a segment of the conduit defines a measurement volume and the conduit comprises a radius;
subjecting the flowing fluid in the measurement volume to
a magnetic field gradient in the direction of flow of the fluid, wherein
the magnetic field gradient in the direction of flow comprises a fixed value in the measurement volume and
the magnetic field gradient is generated by at least two opposing non-parallel permanent magnets equally inclined with respect to the central axis of the direction of flow;
and
radio frequency excitation pulses generating a signal comprising a series of echoes having an echo time;
acquiring at least one odd echo from the series of echoes, wherein the at least one odd echo comprises signals from streamlines in the flowing fluid in the measurement volume;
determining an average velocity of the flowing fluid;
processing the signals from the streamlines to determine a flow behaviour index for the flowing fluid;
and
calculating velocity as a function of the radius of the conduit using the flow behaviour index and the average velocity and relating the function to the pattern of flow to characterize the pattern of flow exhibited by the flowing fluid
wherein the average velocity is calculated using the equation
ϕ
odd
=
∫
∫
ϕ
⁢
rdrd
⁢
θ
∫
∫
rdrd
⁢
θ
=
∫
0
R
ϕ
⁢
rdr
∫
0
R
rdr
=
∫
0
R
(
γ
⁢
Gv
⁡
(
r
)
⁢
τ
2
)
⁢
rdr
∫
0
R
rdr
=
γ
⁢
G
⁢
τ
2
⁢
∫
0
R
(
v
max
⁢
(
1
-
r
m
R
m
)
)
⁢
rdr
∫
0
R
rdr
=
m
m
+
2
⁢
v
max
⁢
γ
⁢
G
⁢
τ
2
=
γ
⁢
Gv
avg
⁢
τ
2
,
wherein
r is the radial position;
φ are phase accumulation;
φodd is the net phase accumulation of odd echoes;
γ is the gyromagnetic ratio;
v(r) is the flow velocity on a radial position r,
vavg is the average velocity;
vmax is the maximum flow velocity;
R is the radius of a circular pipe;
rdrdθ is differential of cross-sectional area;
m is a laminar flow parameter;
τ is the time interval between pulses;
G is a constant magnetic field gradient in the direction of flow;
and the flow behavior index is determined by fitting to the equation
M
ϕ
=
(
S
Re
)
2
+
(
S
Im
)
2
=
2
mX
2
m
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
wherein
Mφ is the normalized magnitude of odd echoes;
SRe is the normalized real signal;
SIm is the imaginary signal;
Γ is a gamma distribution function according to the equation
Γ
⁢
(
a
,
x
)
=
∫
x
∞
w
a
-
1
⁢
e
-
w
⁢
dw
;
and
X is determined by the equation
X
=
m
+
2
m
⁢
γ
⁢
Gv
avg
⁢
τ
2
.

227 more elements

A computer-implemented method for characterizing a pattern of flow of a flowing fluid in a conduit comprising a radius, wherein the fluid comprises a direction of flow and a central axis of the direction of flow, comprising:

using a processor for
processing at least one odd echo acquired from radio frequency pulses of a measurement volume containing the flowing fluid, wherein the radio frequency pulses are applied as part of an echo train measurement,
and wherein the flowing fluid is subjected to a magnetic field gradient generated by
at least two opposing non-parallel permanent magnets equally inclined with respect to the central axis of the direction of flow, or
a switched magnetic field that is turned on with a stable value, and left on for the duration of the echo train measurement,
and wherein the echo includes signals from streamlines in the flowing fluid in the measurement volume;
processing the signals to determine a flow behaviour index for the flowing fluid;
and,
determining an average velocity of the flowing fluid, and calculating velocity as a function of the radius of the conduit using the flow behaviour index and the average velocity and relating the function to a pattern of flow to characterize the pattern of flow exhibited by the flowing fluid,
wherein the average velocity is calculated using the equation
ϕ
odd
=
∫
∫
ϕ
⁢
rdrd
⁢
θ
∫
∫
rdrd
⁢
θ
=
∫
0
R
ϕ
⁢
rdr
∫
0
R
rdr
=
∫
0
R
(
γ
⁢
Gv
⁡
(
r
)
⁢
τ
2
)
⁢
rdr
∫
0
R
rdr
=
γ
⁢
G
⁢
τ
2
⁢
∫
0
R
(
v
max
⁢
(
1
-
r
m
R
m
)
)
⁢
rdr
∫
0
R
rdr
=
m
m
+
2
⁢
v
max
⁢
γ
⁢
G
⁢
τ
2
=
γ
⁢
Gv
avg
⁢
τ
2
,
wherein
r is the radial position;
φ are phase accumulation;
φodd is the net phase accumulation of odd echoes;
γ is the gyromagnetic ratio;
v(r) is the flow velocity on a radial position r;
vavg is the average velocity;
vmax is the maximum flow velocity;
R is the radius of a circular pipe;
rdrdθ is differential of cross-sectional area;
m is a laminar flow parameter;
τ is the time interval between pulses;
G is a constant magnetic field gradient in the direction of flow;
and the flow behavior index is determined by fitting to the equation
M
ϕ
=
(
S
Re
)
2
+
(
S
Im
)
2
=
2
mX
2
m
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
wherein
Mφ is the normalized magnitude of odd echoes;
SRe is the normalized real signal;
SIm is the imaginary signal;
Γ is a gamma distribution function according to the equation
Γ
⁢
(
a
,
x
)
=
∫
x
∞
w
a
-
1
⁢
e
-
w
⁢
dw
;
and
X is determined by the equation
X
=
m
+
2
m
⁢
γ
⁢
Gv
avg
⁢
τ
2
.

224 more elements

A magnetic resonance method for characterizing a pattern of flow of a flowing fluid comprising the steps of:

flowing the fluid through a conduit wherein the fluid comprises a direction of flow and a central axis of the direction of flow, wherein a segment of the conduit defines a measurement volume and the conduit comprises a radius;
subjecting the flowing fluid in the measurement volume to
a magnetic field gradient in the direction of flow of the fluid, wherein the magnetic field gradient in the direction of flow comprises a fixed value in the measurement volume;
and
radio frequency excitation pulses generating a signal comprising a series of echoes having an echo time, wherein the radio frequency excitation pulses are applied as part of an echo train measurement;
and wherein the magnetic field gradient is generated by a switched magnetic field that is turned on with a stable value, and left on for the duration of the echo train measurement;
acquiring at least one odd echo from the series of echoes, wherein the at least one odd echo comprises signals from streamlines in the flowing fluid in the measurement volume;
determining an average velocity of the flowing fluid;
processing the signals from the streamlines to determine a flow behaviour index for the flowing fluid;
and
calculating velocity as a function of the radius of the conduit using the flow behaviour index and the average velocity and relating the function to the pattern of flow to characterize the pattern of flow exhibited by the flowing fluid,
wherein the step of calculating the velocity further comprises calculating the average velocity is calculated using the equation
ϕ
odd
=
∫
∫
ϕ
⁢
rdrd
⁢
θ
∫
∫
rdrd
⁢
θ
=
∫
0
R
ϕ
⁢
rdr
∫
0
R
rdr
=
∫
0
R
(
γ
⁢
Gv
⁡
(
r
)
⁢
τ
2
)
⁢
rdr
∫
0
R
rdr
=
γ
⁢
G
⁢
τ
2
⁢
∫
0
R
(
v
max
⁢
(
1
-
r
m
R
m
)
)
⁢
rdr
∫
0
R
rdr
=
m
m
+
2
⁢
v
max
⁢
γ
⁢
G
⁢
τ
2
=
γ
⁢
Gv
avg
⁢
τ
2
,
wherein
r is the radial position;
φ are phase accumulation;
φodd is the net phase accumulation of odd echoes;
γ is the gyromagnetic ratio;
v(r) is the flow velocity on a radial position r,
vavg is the average velocity;
vmax is the maximum flow velocity;
R is the radius of a circular pipe;
rdrdθ is differential of cross-sectional area;
m is a laminar flow parameter;
τ is the time interval between pulses;
G is a constant magnetic field gradient in the direction of flow;
and the flow behavior index is determined by fitting to the equation
M
ϕ
=
(
S
Re
)
2
+
(
S
Im
)
2
=
2
mX
2
m
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
⁢
(
Γ
⁢
(
2
m
)
-
Γ
⁢
(
2
m
,
-
Xi
)
)
wherein
Mφ is the normalized magnitude of odd echoes;
SRe is the normalized real signal;
SIm is the imaginary signal;
Γ is a gamma distribution function according to the equation
Γ
⁢
(
a
,
x
)
=
∫
x
∞
w
a
-
1
⁢
e
-
w
⁢
dw
;
and
X is determined by the equation
X
=
m
+
2
m
⁢
γ
⁢
Gv
avg
⁢
τ
2
.

226 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/728,063Filed 25 Apr 2022 · us provisional application
Priority: 23 Apr 2021
Granted: 17 Mar 2026
Term ends: Not estimatedThe source records don’t support an estimate.

Classification9 codes

G01F 1/716
Measuring the time taken to traverse a fixed distance: using electron paramagnetic resonance [EPR] or nuclear magnetic resonance [NMR]
G01N 24/082
By using nuclear magnetic resonance: measurement of solid, liquid or gas content
G01F 1/74
Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow: devices…
G01R 33/383
Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field: using permanent magnets