Method and apparatus for estimating fat
Disclosed herein are methods, non-transitory computer-readable medium, and systems for determining an estimate of fat within a volume of a subject by determining a parameter α from the signal intensities of at least three echo signals emitted from a region of the volume of a subject imaged by a magnetic resonance image scanner in response to an applied RF pulse, wherein the three echo signals are taken at a first opposing-phase echo time, a second opposing-phase echo time and an in-phase echo time; and determining a fat volume fraction, f, from the parameter α.
1. A method for determining an estimate of fat within a volume of a subject comprising the steps of:
a) generating a magnetic resonance image scan with a magnetic resonance image scanner that acquires the signal intensities of at least three echo signals emitted from a region of the volume, using a flip angle of 30°-70° or 70°-90°, and in response to an applied RF pulse, wherein the three echo signals are taken at a first opposing-phase echo time, a second opposing-phase echo time, and an in-phase echo time;
b) determining a parameter α from the acquired signal intensities, a reflecting a fat signal fraction within the volume; and
c) determining a fat volume fraction, f from the parameter α, using equation (3)
α
=
kf
(
1
+
kf
-
f
)
(
Equation
3
)
where k is a constant greater than 1 and f is less than 1.
2. A method according to claim 1 and further comprising selecting k when the rate of change of α with respect to the fat volume fraction, f, is maximized to optimize the rate of change of α with respect to the fat volume fraction.
3. A method according to claim 2 wherein k is less than or equal to 10.
4. A method according to claim 1 wherein said scan was generated using a flip angle of 30°-70°.
5. A method according to claim 1 wherein a is determined by means of equation (1):
α
=
IP
-
OP
1
[
exp
(
TE
1
-
TE
2
T
2
*
)
]
2
IP
where T2* is determined according to equation (2):
T
2
*
=
(
TE
3
-
TE
1
)
ln
(
OP
1
OP
2
)
and where TE1 is the first opposing-phase echo time, TE2 the in-phase echo time, TE3 the second opposing-phase echo time, OP1 and OP2 are the signal intensities measured at the first and second opposing-phase echo times, TE1 and TE3, and IP is the signal intensity measured at the in-phase echo time.
6. A method according to claim 1 further comprising the step of correcting the signal intensities for background noise.
7. A method according to claim 6 wherein the signal intensities are corrected by subtracting the background noise signal intensities in quadrature.
8. A method according to claim 6 wherein the signal intensities are corrected for background noise by determining the parameter α by means of equation (1′):
α
=
IP
T
-
OP
1
T
[
exp
(
TE
1
-
TE
2
T
2
*
)
]
2
IP
T
where T2* is determined according to equation (2′):
T
2
*
=
(
TE
3
-
TE
1
)
ln
(
OP
1
T
OP
2
T
)
and OP1 T , IP T and OP2 T are the true signal intensities in the absence of noise in regions-of-interest in the first opposed-phase, in-phase and second opposed-phase images, wherein the true signal intensity, S T , is determined as follows:
S T =√{square root over ( S M 2 −N M 2 )}
where:
S T is the true signal intensity within the region-of-interest corrected for background noise levels, S M is the measured signal intensity within the region-of-interest in the magnitude MR image and N M is the measurement of the background noise levels in the magnitude image in an area free of image artefacts and structured noise.
9. A method according to claim 6 wherein the background noise signal is determined by one or more of (i) the statistical mean of the signal intensities within the background region-of-interest of the magnitude image; (ii) the statistical mean plus an offset of one standard deviation of the background noise intensity levels; (iii) the mean of a probability density function fitted to the distribution of the signal intensities within the background region-of-interest; (iv) the mean plus one standard deviation of a probability density function fitted to the distribution of the background noise intensity levels.
10. A method according to claim 9 wherein the probability density function is selected from the group comprising: a Gaussian distribution, a Rician distribution and a Poisson distribution.
11. A method according to claim 1 wherein a is determined as the average of three consecutive axial image slices along an axis.
12. A method according to claim 1 wherein the volume of the subject comprises an organ, or part of an organ.
13. A method according to claim 12 wherein the organ is a liver, kidney, or pancreas.
14. A method according to claim 1 , wherein a computer program is used to determine the parameter α and
determine the fat volume fraction, f, from the parameter α, using equation (3)
α
=
kf
(
1
+
kf
-
f
)
(
Equation
3
)
where k is a constant greater than 1 and f is less than 1.
15. A method according to claim 1 , which comprises using a computer system comprising: a processor, and a non-transitory computer-readable medium comprising instructions stored thereon, that when executed by the processor, performs steps b) and c).
16. A system for determining an estimate of fat within a volume of a subject, the system comprising: a magnetic resonance imaging scanner that acquires signal intensities of at least three echo signals emitted from a region of the volume, using a flip angle of 30°-70° or 70°-90°, and in response to an applied RF pulse, wherein the three echo signals are taken at a first opposing-phase echo time, a second opposing-phase echo time, and an in-phase echo time; and a computing device comprising a processor, and a non-transitory computer-readable medium comprising instructions stored thereon, that when executed by the processor, performs the steps of:
a) generating a magnetic resonance image scan with the magnetic resonance image scanner, and determining, from the magnetic resonance image scan, a parameter α from the acquired signal intensities of at least three echo signals emitted from a region of the volume, using a flip angle of 30°-70° or 70°-90°, and in response to an applied RF pulse, a reflecting a fat signal fraction within the volume, wherein the three echo signals are taken at a first opposing-phase echo time, a second opposing-phase echo time and an in-phase echo time; and
b) determining a fat volume fraction, f from the parameter α, using equation (3)
α
=
kf
(
1
+
kf
-
f
)
(
Equation
3
)
where k is a constant greater than 1 and f is less than 1.