RU2544387C1 - Separation of water from fat at magnetic resonance tomography - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: produced are two complex images I₁ and I₂ with different echo times wherein signals from fat and water are in phase and in counter phase, respectively. Phase 2φ of complex vector $$I^2={(I_2{I}_1^{*}/|I_1|)}^2$$

for every pixel of image matrix is calculated. Constructed is the matrix of developed phase 2φ and in the range of main magnitudes -180°…180° and defined is the sign of complex vector Ie^-iφu in matrix every pixel. Imaging for water is performed as the half-sum of absolute magnitude of image in phase and counter phase multiplied by sign Ie^-iφu, imaging of fat is made as half-difference of absolute magnitude of images of fat in phase and image in counter phase multiplied by the sign Ie^-iφu. Note here that estimated are averaged gradients of changes in phases of fat and water images by the formulae: G_F=(|I₁|-|I₂|)²/N_F at Ie^-iφu<0 G_W=(|I₁|-|I₂|)²/N_W at Ie^-iφu<0. Magnitudes G_F and G_W are compared. In case G_F<G_W, pixels of fat and water images are changed in places.

EFFECT: higher correctness of classification.

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Description

The invention relates to the field of medicine, more specifically to methods for diagnosing the state of an organism with magnetic resonance imaging based on the separation of images of water and fat.

All methods for separate acquisition of images of fat and water are based on the phenomenon of chemical shift, namely, that the hydrogen nuclei from which the signal is recorded in a magnetic resonance imager have different resonance frequencies ω in free water molecules and in water molecules associated with organic fat . The frequency difference Δω is known in advance and depends on the magnetic field strength.

So, for example, for a tomograph with a magnet 0.3 T Δω = 45 Hz, for a tomograph with a superconducting magnet 1.5 T Δω = 225 Hz.

The idea of separating fat and water is to obtain several images with different signal acquisition times t _i , in which fat and water are summed up in different known phases depending on time t _i :

where I _i - ie image,

W is the signal from the water,

F is the signal from fat,

φ _i = Δω * t _i is the phase of the signal from fat relative to the signal from water, accumulated over time t _i .

It can be seen from (1) that for known φ _i theoretically, two measurements of I ₁ and I ₂ are sufficient for separating fat and water. The corresponding method is called the Two point Dixon method and is the most effective in terms of time costs. In the simplest version, according to the Dickson method, 2 images are collected, in one of which fat and water are in phase (φ ₁ = 0 °), and in the second - in antiphase (φ ₂ = 180 °) (Fig. 1).

To obtain these two images in tomography, the pulse sequence shown in Fig. 2 is used.

In figure 2:

1 - exciting radio pulse,

2 - gradient selection layer

3 - reading gradient,

4 - an echo signal with an echo time TE1, forming an image of I ₁ (fat and water in phase),

5 - an echo signal with an echo time TE2 forming an image of I ₂ (fat and water in antiphase).

Substituting in (1) the values of φ _i respectively 0 ° and 180 °, we have:

From (2), fat and water are easily separated:

However, in practice, everything is much more complicated, since the phase accumulation in the I ₂ signal occurs not only due to a chemical shift, but also due to other factors, the main of which is the nonuniformity of the magnet field, which is expressed in the fact that at different points in space, occupied by the object, the value of the field of the magnet B0 and, accordingly, the resonance frequency are different.

In this case, equations (2) take the form:

where φ0 is the initial phase of the vectors W and F accumulated by water and fat due to field inhomogeneity during the time between excitation of the system by the radio pulse and the first charge, φ is the phase incursion accumulated due to field inhomogeneity during the time between two charges

It turns out 2 equations with 4 unknowns W, F, φ0, φ.

However, given that I ₁ and I ₂ are complex numbers, the number of equations expands to 4 and the system is basically solvable.

A number of methods have been proposed to solve the problem.

A known method of separating images of water and fat [1], in which 2 candidates for a real phase incursion — φ ₁ and φ ₂ — are considered for each pixel of the generated images. The choice between them is made using the estimation of two components of the measured signals — large B and small S. For φ _1, it is assumed that component B is water, and component S is fat, and for φ ₂ , vice versa. The choice of two options is carried out according to the criterion of smoothness of the nature of the phase change φ [1].

There is also a method of separating images of water and fat [2], based on a priori knowledge of the magnetic field inhomogeneity map (B0 map). The field map is constructed in advance, for example, using a homogeneous object, and then the phase shift associated with the field inhomogeneity is corrected taking into account the obtained inhomogeneity map [2].

Closest to the proposed method is the separation of water and fat images by the Dixon point-to-point method [3], which includes obtaining two complex images I ₁ and I ₂ with different echo times, in which the signals from water and fat are in phase and out of phase, respectively, and calculating the values phase 2φ of the complex vector I ² = (I ₂ I * ₁ / | I ₁ |) ² for each pixel of the image matrix, the construction of the matrix of the “expanded” phase 2φ _u in the range of principal values - 180 ° ... 180 °, for example, by the method of merging regions complex vector sign definition and Ie- ^iφu in each pixel of the matrix and the formation of an image by water as a half-sum of the absolute value of the image in phase and the image in antiphase multiplied by the sign Ie ^-iφu and the image of fat as the half-difference of the absolute value of the image in phase and the image in antiphase multiplied by the sign Ie ^-iφu [3].

The disadvantage of this method is the high likelihood of "confusion" of the resulting pixels containing water and fat, under the conditions of the heterogeneity of the magnet field and the presence of measurement noise when determining the phase of complex numbers I ² = (I ₂ I * ₁ / | I ₁ |) ² .

The aim of the proposed method is to increase the reliability of the correct classification of images by water and fat. To achieve this goal, in a method for separating images of water and fat in magnetic resonance imaging, including obtaining two complex images I ₁ and I ₂ with different echo times, in which the signals from water and fat are respectively in phase and out of phase, the calculation of the phase values 2φ of the complex vector I ² = (I ₂ I * ₁ / | I ₁ |) ² for each pixel of the image matrix, the construction of the matrix of the “expanded” phase 2φ _u in the range of principal values - 180 ° ... 180 °, for example, by the method of region fusion, determination of the sign of the complex vector Ie- ^iφu in each m of the matrix pixel and the formation of water images as half sums of the absolute value of the image in phase and the image in antiphase multiplied by the sign of Ie- ^iφu and the image of fat as the half-difference of the absolute value of the image in phase and the image in antiphase multiplied by the sign of Ie- ^iφu phase change gradients of the obtained images of fat and water according to the formulas:

G _F = (| I ₁ | - | I ₂ |) ² / N _F for Ie ^-iφu <0

G _w = (| I ₁ | - | I ₂ |) ² / N _W for Ie ^-iφu > 0,

comparing the values of G _F and G _W and, if G _F <G _W , the pixels of the images of fat and water are swapped.

The essence of the proposed method for separating images of fat and water is as follows. Using the pulse sequence shown in figure 2 receive 2 complex image:

I ₁ = (W + F) e ^iφ0 fat and water in phase

and I ₂ = (WF) e ^{i (φ0 + φ)} fat and water in antiphase

where φ0 is the initial phase of the vectors W and F accumulated by water and fat due to field inhomogeneity during the time between excitation of the system by the radio pulse and the first charge, φ is the phase incursion accumulated due to field inhomogeneity during the time between two charges

To solve the system of equations for W and F, an auxiliary complex quantity is introduced

where * is the sign of complex conjugation

It is impossible to determine unambiguously the desired phase φ as the phase of the complex number I due to the uncertainty of the W-F sign, since it is not known in advance whether a given pixel contains more water or fat. This ambiguity is eliminated by squaring both sides of (6):

In principle, the phase is now defined as

However, expression (8) is valid only under the condition that all values of the angle 2φ lie in the range -180 ° <2φ <180 °, which in reality is unlikely in the presence of field inhomogeneity and noise measurements of echo signals.

This situation for a one-dimensional case is illustrated in FIG.

As can be seen from figure 3, when passing through 180 °, the phase experiences a jump, which must be smoothed out before determining the phase φ and solving equation (6).

There are a number of methods for two-dimensional “unfolding” of the phase, among which one can use, for example, the method of merging regions [4].

Figure 4 presents an example of the two-dimensional phase of the complex image I for the axial section of the knee joint obtained by the pulse program shown in figure 2.

Figure 4 on the left shows the image of phase 2φ calculated by the formula (8), and on the right - the image of the "expanded" phase φ _u obtained by the method of merging regions.

Having determined the phase estimate φ _u , from (6) we can obtain the estimate of the difference WF

Since the left-hand side of (9) is a real number, the phase of the complex number Ie ^-iφu theoretically can take only 2 values 0 ° or 180 °.

Therefore, (9) can be rewritten in the form:

where g takes values ± 1 depending on the sign of Ie ^-iφu

The sum of water and fat is also valid and positive:

From (10) and (11) we find the desired images W and F:

In reality, due to the presence of noise, the coefficient g is not obtained strictly equal to 1 or -1. Therefore, an approximation gives a smoother solution:

As can be seen from (12), with an error in determining the sign of the coefficient g, water and fat are mixed up, which with a probability close to 50% occurs under conditions of an inhomogeneous field and measurement noise.

In order to increase the likelihood of correct classification of images of water and fat, the obtained images are corrected according to the averaged phase gradients G _F and G _W in pixels related to fat and water, respectively. It uses the statistical fact that the rate of change of phase (phase gradient) in areas with a predominance of fat is higher than in areas with a predominance of water.

The averaged phase change gradients are estimated from the original image matrices “in phase” I ₁ and in “antiphase” I ₂ and the matrix of coefficients g:

Illustration to (14) is presented in figure 5.

The order of the actions of the proposed method is schematically represented in Fig.6.

Fig. 7 shows separate images of water and fat obtained in the described manner using an example of an axial section of a knee joint.

7:

and - the total image of water and fat in antiphase,

b is the total image of water and fat in phase,

c is the image of water,

d is the image of fat.

The experience of using the proposed method in traumatology showed its reliability and high diagnostic information content.

Information sources

[1] Patent EP 2414860 B1, "TWO-POINT DIXON TECHNIQUE WITH FLEXIBLE CHOICE OF ECHO TIMES".

[2] Patent EP 2610632 A1, "MRI with Dixon-type water / fat separation and prior knowledge about inhomogeneity of the main magnetic field".

[3] Bernstein, Zhou, King "Handbook-of-MRI-Pulse-Sequence". Part 17.3.1 Two point Dixon, ELSEVIER ACADEMIC PRESS, 2004.

[4] Salah Karout "Two-Dimensional Phase Unwrapping", General Engineering Research Institute (GERI), Liverpool John Moores University, 2007.

Claims (1)

A method for separating images of water and fat in magnetic resonance imaging, including obtaining two complex images I ₁ and I ₂ with different echo times, in which the signals from water and fat are respectively in phase and in antiphase, calculating phase values 2φ of the complex vector I ² = (I ₂ I * ₁ / | I ₁ |) ² for each pixel of the image matrix, building the matrix of the “expanded” phase 2φ and in the range of principal values -180 ° ... 180 °, determining the sign of the complex vector I e ^-iφu in each pixel matrices and imaging over water as a half ummahs of the absolute value of the image in phase and the image in antiphase multiplied by the sign I e ^-iφu , and the image of fat as a half difference of the absolute value of the image in phase and the image in antiphase multiplied by the sign I e ^-iφu , characterized in that the average variation gradients are estimated phases of the obtained images of fat and water according to the formulas:
G _F = (| I ₁ | - | I ₂ |) ² / N _F for I e ^-iφu <0
G _W = (| I ₁ | - | I ₂ |)) ² / Ν _W for I e ^-iφu > 0, the values of G _F and G _{W are} compared and, if G _F <G _W , the pixels of the images are fat and water exchange places.

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