US 12,560,665 B1 · Magnetic resonance methods and devices for characterizing rheological properties of a fluid

Abstract

A magnetic resonance method and device for method for characterizing the pattern of flow of a flowing fluid including processing at least one odd echo acquired from radio frequency pulses of a measurement volume containing a flowing fluid, wherein the echo includes signals from streamlines in the flowing fluid in the measurement volume, processing the signals to concurrently determine a signal magnitude and a net phase accumulation and using the signal magnitude and the net phase accumulation to determine a flow behaviour index and an average velocity 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 a pattern of flow to characterize the pattern of flow exhibited by the flowing fluid.

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 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 fixed value in the measurement volume and
radio frequency excitation pulses generating a signal in the form of a series of echoes, wherein the radio frequency excitation pulses are applied as part of an echo train measurement;
and wherein the magnetic field gradient is generated by at least two opposing non-parallel permanent magnets equally inclined with respect to a central axis of the direction of flow, or by a switched magnetic field that is turned on with a stable value for a 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;
processing the signals from the streamlines to concurrently determine a signal magnitude and a net phase accumulation and using the signal magnitude and the net phase accumulation to determine a flow behaviour index and an average velocity for the flowing fluid;
and
calculating velocity as a function of a 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,
where the step of concurrently determining the signal magnitude and the net phase accumulation is determined using the equations:
M
ϕ
′
=
❘
"\[LeftBracketingBar]"
S
ϕ
′
❘
"\[RightBracketingBar]"
=
S
ϕ
′
⁢
S
_
ϕ
′
=
{
Γ
⁡
(
2
n
′
-
1
)
⁢
2
⁢
C
2
n
′
n
′
⁢
[
0
D
t
=
1
C
-
2
n
′
+
1
⁢
(
(
1
-
e
-
1
t
)
⁢
(
1
C
-
t
)
⁢
e
-
iAt
)
]
⁢
[
0
D
t
=
1
C
-
2
n
′
+
1
⁢
(
(
1
-
e
-
1
t
)
⁢
(
1
C
-
t
)
⁢
e
-
iAt
)
]
,
C
⁢
[
0
N
t
=
1
C
⁢
(
e
-
1
t
⁢
e
-
iAt
)
]
[
0
N
t
=
1
C
⁢
(
e
-
1
t
⁢
e
-
iAt
)
]
,
Γ
⁢
(
2
n
′
)
⁢
2
⁢
C
2
n
′
n
′
⁢
[
0
D
t
=
1
C
-
2
n
′
⁢
(
(
1
-
e
-
1
t
)
⁢
e
-
iAt
)
]
⁢
[
0
D
t
=
1
C
-
2
n
′
⁢
(
(
1
-
e
-
1
t
)
⁢
e
-
iAt
)
]
,
⁢
1
<
n
′
<
2
n
′
=
2
n
′
>
2
⁢
and
ϕ
′
a
⁢
d
⁢
d
=
arctan
⁡
(
S
′
ϕ
,
Im
S
ϕ
,
Re
′
)
=
{
arctan
⁡
(
0
D
t
=
1
C
-
2
n
′
+
1
⁢
(
(
1
-
e
-
1
t
)
⁢
(
1
C
-
t
)
⁢
sin
⁡
(
At
)
)
0
D
t
=
1
C
-
2
n
′
+
1
⁢
(
(
1
-
e
-
1
t
)
⁢
(
1
C
-
t
)
⁢
cos
⁡
(
At
)
)
)
,
1
<
n
′
<
2
arctan
⁡
(
0
N
t
=
1
C
⁢
(
e
-
1
t
⁢
sin
⁡
(
At
)
)
0
N
t
=
1
C
⁢
(
e
-
1
t
⁢
cos
⁡
(
At
)
)
)
,
n
′
=
2
arctan
⁡
(
0
D
t
=
1
C
-
2
n
′
⁢
(
(
1
-
e
-
1
t
)
⁢
sin
⁡
(
At
)
)
0
D
t
=
1
C
-
2
n
′
⁢
(
(
1
-
e
-
1
t
)
⁢
cos
⁡
(
At
)
)
)
,
n
′
>
2
wherein
M′ϕ is a normalized signal magnitude;
S′ϕ is a normalized odd echo signal due to phase shift;
ϕ′add is a net phase accumulation of odd echoes;
S′ϕ,Im is an imaginary signal component of the measurement;
S′ϕ,Re is a real signal component of the measurement
Γ is a gamma distribution function according to the equation
Γ
⁡
(
x
)
=
∫
0
∞
w
x
-
1
⁢
e
-
w
⁢
d
⁢
w
⁡
(
x
>
0
)
;
n′ is a flow behaviour index;
C is determined using the equation
C
=
L
pol
T
1
⁢
v
max
Lpol is effective polarization length;
T1 is a spin lattice relaxation time of a fluid;
Vmax is the maximum flow velocity of the fluid;
D is a Riemann-Liouville fractional integral;
A is determined using the equation
A=γGvmaxτ2C
γ is the gyromagnetic ratio;
G is a constant magnetic field gradient in the direction of flow;
τ is the time interval between pulses;
X is determined by the equation
n
′
+
2
n
′
X
=
m
+
2
m
⁢
γ
⁢
G
⁢
v
a
⁢
v
⁢
g
⁢
τ
2
;
and
m is a laminar flow parameter;
and
N is a function defined by the equation
a
N
x
⁢
f
⁡
(
x
)
=
∫
a
x
f
⁡
(
w
)
⁢
dw
.

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Magnetic resonance methods and devices for characterizing rheological properties of a fluid

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Magnetic resonance methods and devices for characterizing rheological properties of a fluid

Life of this patent

Abstract

Claims14