Fat/water separation and fat minimization magnetic resonance imaging systems and methods

• US 7,099,499 B2
• Filed: 08/15/2002
• Issued: 08/29/2006
• Est. Priority Date: 08/15/2002
• Status: Active Grant

• Current Assignee: General Electric Company
• Original Assignee: General Electric Company
• Inventors: Blezek, Daniel, Dhawale, Paritosh, Dixon, William
• Primary Examiner(s): Dang, Duy M.
• Application Number:
  US10/219,637
• Publication Number:
  US 20040032977A1
• Time in Patent Office: 1,475 Days
• Field of Search: 382/128, 382/130, 382/228, 128/922, 600/409, 356/39, 377/10, 324/309
• US Class Current: 382/128
• CPC Class Codes: G01R 33/4828 Resolving the MR signals of different chemical species, e.g. water-fat imaging
• CPC Class Codes: G01R 33/5607 by reducing the NMR signal of a particular spin species, e.g. of a chemical species for fat suppression, or of a moving spin species for black-blood imaging
• CPC Class Codes: G01R 33/56563 caused by a distortion of the main magnetic field B0, e.g. temporal variation of the magnitude or spatial inhomogeneity of B0 G01R33/56509, G01R33/56518, G01R33/56536 take precedence

Abstract

Systems and methods for identifying the relative contribution of fat and water signals in a magnetic resonance (“MR”) image including an algorithm operable for selecting an image signal model, selecting a scan parameter, forming a bias field estimate, applying a bias correction to a phase image, estimating the signal fraction of fat and water at each of a plurality of voxels, and forming a fat-suppressed image, a water-suppressed image, or a combination of a fat-based image and a water-based image. The (“MRI”) fat suppression systems and methods requiring only a single image acquisition including an algorithm operable for selecting a relative phase of approximately θ=π/2 or another suitable relative phase, employing an expectation maximization algorithm to classify the phase of the complex image, and projecting complex vectors into fat and water components to obtain fat and water images.

Claims

1. A method for identifying the relative contributions of signals of a first substance and a second substance in a magnetic resonance (“

MR”

) image, the method comprising;

selecting an image signal model;

selecting a scan parameter;

forming a bias field estimate;

applying a bias correction to a phase image;

estimating a signal fraction of the first substance and the second substance at each of a plurality of voxels; and

forming a suppressed image with respect to the first substance or the second substance.

2. The method of claim 1, wherein the image signal model comprises the following equations:

I_observed=(I_water+I_fate<sup>−

i2π

ω</sup>

_f^TE)β

′

β

′

=β

_(x,y)e<sup>−

iφ</sup>

_(x,y),

wherein β

′

=β

_(x,y)e<sup>−

iφ</sup>

_(x,y) is a spatially-dependent bias field.

3. The method of claim 2, wherein the image signal model further comprises the following equations:

∠

I_observed=∠

(β

′

I_water+β

′

I_fate<sup>−

i2π

ω</sup>

_f^TE)

∠

I_observed=θ

=θ

_object+φ

_(x,y),

wherein θ and

θ

_object are observed and true phases, respectively.

4. The method of claim 3, further comprising estimating and removing φ

(x,y) to recover the true phase.

5. The method of claim 4, further comprising using the true phase to decouple the signals of the first substance and the second substance from the image into individual components.

6. The method of claim 1, wherein choosing a scan parameter comprises choosing an echo time, TE.

7. The method of claim 1, further comprising calculating a chemical shift between the first substance and the second substance.

8. The method of claim 1, further comprising acquiring the image using a pulse sequence comprising a pulse sequence selected from the group consisting of gradient recalled echo pulse sequence, a spin echo pulse sequence, and a fast spin echo pulse sequence.

9. The method of claim 1, further comprising unwrapping the phase of the image.

10. The method of claim 9, wherein unwrapping the phase of the image comprises implementing a minimum spanning tree (“

MST”

)-based phase unwrapping algorithm.

11. The method of claim 10, wherein unwrapping the phase of the image further comprises determining the minimum edge weight of a border pixel and adding the border pixel, p_i, to the MST.

12. The method of claim 11, wherein unwrapping the phase of the image further comprises calculating the unwrapped phase of the border pixel.

13. The method of claim 12, wherein unwrapping the phase of the image further comprises terminating the MST-based phase unwrapping algorithm when each of a plurality of pixels have been added to the MST.

14. The method of claim 1, further comprising modeling observed phases as Gaussian distributions according to the following equations:

p(θ

_i|Γ

_water,β

_i)=G(θ

_i−

μ

_water−

β

_i,φ

_water)

p(θ

_i|Γ

_fat,β

_i)=G(θ

_i−

μ

_fat−

β

_i,φ

_fat),

wherein θ

_i is the unwrapped, observed phase at pixel i, Γ

ε

[water, fat] is a tissue class, μ

_water, φ

_water and μ

_fat, φ

_fat are class means and variances of water and fat classes, respectively, and G(x,φ

) is a Gaussian distribution function with zero mean and φ

variance, evaluated at x.

15. The method of claim 14, further comprising using a conditional probability of observed phase given a bias field β

;

$\begin{array}{c}p<br><br>\left({\mathrm{\theta <br><br>}}_i❘<br><br>{\mathrm{\beta <br><br>}}_i\right)=<br><br>{\mathrm{\Sigma <br><br>}}_{\mathrm{\Gamma <br><br>}<br><br><br><br>i}<br><br>p<br><br>\left({\mathrm{\theta <br><br>}}_i,{\mathrm{\Gamma <br><br>}}_i❘<br><br>{\mathrm{\beta <br><br>}}_i\right)\\ =<br><br>{\mathrm{\Sigma <br><br>}}_{\mathrm{\Gamma <br><br>}<br><br><br><br>i}<br><br>p<br><br>\left({\mathrm{\theta <br><br>}}_i❘<br><br>{\mathrm{\Gamma <br><br>}}_i,{\mathrm{\beta <br><br>}}_i\right)<br><br>p<br><br>\left({\mathrm{\Gamma <br><br>}}_i\right),\end{array}\hspace{1em}<br><br>$

wherein p(Γ

_i) is a stationary prior probability distribution on the tissue class.

16. The method of claim 15, further comprising introducing a uniformly distributed “

other”

class, Γ

other, producing the following equations;

p(θ

_i|β

_i)=p(θ

_water|Γ

_water)+p(Γ

_water)+p(θ

_fat|Γ

_fat)p(Γ

_fat)+p(Γ

_other)

W_ij=(p(θ

_i|Γ

_j,β

_i)p(Γ

_i))/(Σ

_rjp(θ

_i|Γ

_j,β

_i)p(Γ

_j))

R_i=W_i,j=water(θ

_i−

μ

_water)φ

_water+W_i,j=fat(θ

_i−

μ

_fat)φ

_fat

β

=H R,

wherein p(Γ

_other) is a uniform distribution.

17. The method of claim 16, further comprising estimating class parameters using the following equations:

μ

_j=(Σ

_ip(Γ

_i=j|θ

_i)(θ

_i−

β

_i))/(Σ

_ip(Γ

_i=j|θ

_i))

φ

_j=(Σ

_ip(Γ

_i=j|θ

_i)(θ

_i−

μ

_j−

β

_i)²)/(Σ

_ip(Γ

_i=j|θ

_i)),

wherein j ε

[water, fat].

18. The method of claim 1, further comprising generating images associated with the first substance and the second substance by calculating the intensity contributions of the signals of the first substance and the second substance.

19. The method of claim 1, further comprising generating images associated with the first substance and the second substance by correcting complex image data and re-projecting a vector field into the images associated with the first substance and the second substance.

20. The method of claim 1, further comprising forming an image that represents a combination of the first substance and the second substance.

21. A system operable for identifying the relative contributions of signals of a first substance and a second substance in a magnetic resonance (“

MR”

) image, the system comprising;

an algorithm operable for;

selecting an image signal model;

selecting a scan parameter;

forming a bias field estimate;

applying a bias correction to a phase image;

estimating a signal fraction of the first substance and the second substance at each of a plurality of voxels; and

forming a suppressed image with respect to the first substance or the second substance.

22. The system of claim 21, wherein the image signal model comprises the following equations:

I_observed=(I_water+I_fate<sup>−

i2π

ω</sup>

_f^TE)β

′

β

′

=β

_(x,y)e<sup>−

iφ</sup>

_(x,y),

wherein β

′

=β

_(x,y)e<sup>−

iφ</sup>

_(x,y) is a spatially-dependent bias field.

23. The system of claim 22, wherein the image signal model further comprises the following equations:

∠

I_observed=∠

(β

′

I_water+β

′

I_fate<sup>−

i2π

ω</sup>

_f^TE)

∠

I_observed=θ

=θ

_object+φ

_(x,y),

wherein θ and

θ

_object are observed and true phases, respectively.

24. The system of claim 23, wherein the algorithm is further operable for estimating and removing φ

(x,y) to recover the true phase.

25. The system of claim 24, wherein the algorithm is further operable for using the true phase to decouple the signals of the first substance and the second substance from the image into individual components.

26. The system of claim 21, wherein choosing a scan parameter comprises choosing an echo time, TE.

27. The system of claim 21, wherein the algorithm is further operable for calculating a chemical shift between the first substance and the second substance.

28. The system of claim 21, wherein the algorithm is further operable for acquiring the image using a pulse sequence comprising a pulse sequence selected from the group consisting of a gradient recalled echo pulse sequence, a spin echo pulse sequence, and a fast spin echo pulse sequence.

29. The system of claim 21, wherein the algorithm is further operable for unwrapping the phase of the image.

30. The system of claim 29, wherein unwrapping the phase of the image comprises implementing a minimum spanning tree (“

MST”

)-based phase unwrapping algorithm.

31. The system of claim 30, wherein unwrapping the phase of the image further comprises determining the minimum edge weight of a border pixel and adding the border pixel, p_i, to the MST.

32. The system of claim 31, wherein unwrapping the phase of the image further comprises calculating the unwrapped phase of the border pixel.

33. The system of claim 32, wherein unwrapping the phase of the image further comprises terminating the MST-based phase unwrapping algorithm when each of a plurality of pixels have been added to the MST.

34. The system of claim 21, wherein the algorithm is further operable for modeling observed phases as Gaussian distributions according to the following equations:

p(θ

_i|Γ

_water,β

_i)=G(θ

_i−

μ

_water−

β

_i,φ

_water)

p(θ

_i|Γ

_fat,β

_i)=G(θ

_i−

μ

_fat−

β

_i,φ

_fat),

wherein θ

_i is the unwrapped, observed phase at pixel i, Γ

ε

[water, fat] is a tissue class, μ

_water, φ

_water and μ

_fat, φ

_fat are class means and variances of water and fat classes, respectively, and G(x,φ

) is a Gaussian distribution function with zero mean and φ

variance, evaluated at x.

35. The system of claim 34, wherein the algorithm is further operable for using a conditional probability of observed phase given a bias field β

;

$\begin{array}{c}p<br><br>\left({\mathrm{\theta <br><br>}}_i❘<br><br>{\mathrm{\beta <br><br>}}_i\right)=<br><br>{\mathrm{\Sigma <br><br>}}_{\mathrm{\Gamma <br><br>}<br><br><br><br>i}<br><br>p<br><br>\left({\mathrm{\theta <br><br>}}_i,{\mathrm{\Gamma <br><br>}}_i❘<br><br>{\mathrm{\beta <br><br>}}_i\right)\\ =<br><br>{\mathrm{\Sigma <br><br>}}_{\mathrm{\Gamma <br><br>}<br><br><br><br>i}<br><br>p<br><br>\left({\mathrm{\theta <br><br>}}_i❘<br><br>{\mathrm{\Gamma <br><br>}}_i,{\mathrm{\beta <br><br>}}_i\right)<br><br>p<br><br>\left({\mathrm{\Gamma <br><br>}}_i\right),\end{array}\hspace{1em}<br><br>$

wherein p(Γ

_i) is a stationary prior probability distribution on the tissue class.

36. The system of claim 35, wherein the algorithm is further operable for introducing a uniformly distributed “

other”

class, other, producing the following equations;

p(θ

_i|β

_i)=p(θ

_water|Γ

_water)p(Γ

_water)+p(θ

_fat|Γ

_fat)p(Γ

_fat)+p(Γ

_other)

W_ij=(p(θ

_i|Γ

_j,β

_i)p(Γ

_j))/(Σ

_rjp(θ

_i|Γ

_j,β

_i)p(Γ

_j))

R_i=W_i,j=water(θ

_i−

μ

_water)φ

_water+W_i,j=fat(θ

_i−

μ

_fat)φ

_fat

β

=H R,

wherein p(Γ

_other) is a uniform distribution.

37. The system of claim 36, wherein the algorithm is further operable for estimating class parameters using the following equations:

μ

_j=(Σ

_ip(Γ

_i=j|θ

_i)(θ

_i−

β

_i))/(Σ

_ip(Γ

_i=j|θ

_i))

φ

_j=(Σ

_ip(Γ

_i=j|θ

_i)(θ

_i−

μ

_i−

β

_i)²)/(Σ

_ip(Γ

_i=j|θ

_i)),

wherein j ε

[water, fat].

38. The system of claim 21, wherein the algorithm is further operable for generating images associated with the first substance and the second substance by calculating the intensity contributions of the signals of the first substance and the second substance.

39. The system of claim 21, wherein the algorithm is further operable for generating images associated with the first substance and the second substance by correcting complex image data and re-projecting a vector field into the images associated with the first substance and the second substance.

40. The system of claim 21, wherein the algorithm is further operable for forming an image that represents a combination of the first substance and the second substance.