Patent Grant
7141972
This invention generally relates to Magnetic Resonance Imaging (MRI) and, in particular, to a method and apparatus for water-fat image separation in MRI.
Fast spin echo (FSE) imaging offers fast acquisition with long repetition times (TR). FSE can be used to improve contrast of long transverse relaxation time (T2) image components with respect to short transverse T2 image components. In clinical applications, where water signals are chiefly of interest, it is desirable to attenuate or eliminate MR signals from lipids (the terms “lipid” and “fat” are used interchangeably) which tend to reduce image contrast especially in the extremities and abdominal sections of a patient. The loss of water image contrast due to lipids is also exasperated by the natural behavior of the FSE sequence to enhance the lipid signal by partial averaging the scalar J-coupling of the lipid protons. The J-coupling signal enhancement becomes progressively worse as refocusing pulses are repeatedly applied during the FSE imaging echo train. Lipid signal levels tend to be relatively intense because of partial averaging in FSE sequences especially when they have long effective echo times (TE) and short echo spacing.
Conventional approaches to attenuate lipid signals include: chemically selective radio frequency (RF) preparation, saturation, and excitation pulses, inversion recovery preparation pre-pulse such as in short tau inversion recovery (STIR) and multipoint Dixon techniques. Chemically selective RF pulses are dependent on the homogeneity of the main magnetic field. For successful application of chemically selective RF pulses, magnetic field homogeneity of one (1) part per million [ppm] or better is typically needed to effectively attenuate lipids during image acquisition. Such high levels of main field homogeneity are not always achievable over the entire field of view (FOV) being imaged. Even where shimming of the main magnetic field provides field homogeneity under 1 ppm, small field inhomogeneities can occur in certain anatomical areas being imaged. For example, a discontinuity of magnetic susceptibility of several ppm can occur at tissue-to-tissue and tissue-to-air interfaces. Furthermore, at mid and low magnetic field strengths, the actual frequency difference between water and lipid signals is so small that impractically long RF pulse lengths are needed to discriminate between the water and lipid signals.
An inversion recovery preparation pre-pulse, e.g., STIR, to prepare the subject region for acquisition is simple and easy to implement. A difficulty with STIR is the loss of signals from tissues that have longitudinal relaxation times (T1) which are similar to the T1 of the attenuated lipids. At mid-field strengths, typical values of T1 for muscle, brain, cerebrospinal fluid (CSF) and lipids are: 450, 600, 3500 and 220 milliseconds (ms) respectively. Although lipids have the fastest relaxations, the recovery curve after an inversion pre-pulse at an evolution time of about 100 to 150 ms removes significant amounts of signal from the water components which reduces the overall conspicuity of many features of clinical importance.
Phase sensitive methods have been applied to distinguish water and lipid signals. These methods rely on the phase increment of the water signals relative to lipid signals in a homogeneous field. Within the small volume of a single image volume element (voxel) the main field can be treated as uniform even though it is not so over the entire image field of view. The phase increment α is given in radians by the following relationship (1):
α=2π*ΔF0*Δt (1)
where ΔF0 is the water-lipid chemical shift in hertz (Hz) and Δt is the evolution time in seconds (sec). The evolution time is measured from the echo formation to a point where the first order interactions are canceled out, such as at the nominal time TE or at a multiple of TE for each echo in the sampling window. In a typical fast spin echo sequence, TE is also the time distance between refocusing pulses and TE/2 is the time between the 90 degree excitation and the first refocusing pulse.
When echo formation occurs at a time different from the mid-point between the refocusing pulses, a water-lipid phase difference is generated for every voxel in the imaging volume. The water-lipid phase difference may be used to distinguish the water and lipid signals, and thereby facilitate attenuation of the lipid signals. The water-lipid phase difference may be relatively small or be obscured by inhomogeneties in the static magnetic field. In the past, identifying and using the water-lipid phase difference to attenuate lipid signals has been problematic. There remains a long felt need for improved phase sensitive methods to suppress lipid signals and thereby improve MR images.
A standard fast spin echo sequence (FSE) has been modified to obtain substantial phase increments between water and lipid signals. This modification is applicable to two-dimensional (2D) sequences, three-dimensional (3D) or higher dimension FSE sequences. The Carr Purcell Meiboom Gill Sequence (CPMG) phase condition is preserved by maintaining symmetry such that all echoes (direct and indirect) are spatially phase encoded in the same manner for the entirety of the echo train. Symmetry may be accomplished by moving the set of gradient waveforms that are composed of the readout sampling and the surrounding phase encoding (imaging) gradient pulses solidly between the refocusing RF pulses. With this approach, the point of echo formation varies to the same degree for all echoes. This approach preserves the echo train symmetry for all possible refocusing angles.
Progressive encoding is performed by shifting all echoes in a FSE sequence by various time differentials to gather water-lipid phase encoding information. An algorithm has been developed to calculate water and lipid images based on a least-squares solution space for magnetic field inhomogeneity, which may be treated as a two-point field space. Because inhomogeneities in the field tend to change slowly from voxel to voxel, the most smooth least squares solution space is chosen of all available solution spaces. The chosen solution space may further be smoothed by fitting a polynomial curve to the solution space. This approach is suitable for water-lipid image separation where the induced error varies with the phase increment between water and lipid signals.
The invention may be embodied as a method for magnetic resonance imaging of a subject separating two moieties of differing chemical shift in the presence of a non-uniform magnetic field comprising the steps of: (i) acquiring at least three complete sets of MRI data using a series of fast spin echo (FSE) sequences in which the readout gradient waveform is shifted to produce sets of MRI data that are similarly spatially encoded, and wherein each of the three sets has different signal timing to produce three different phase shifts between two chemically shifted signals and wherein one of the phase differences (α0) is substantially zero; (ii) generating at least three complex image data sets by reconstructing images from the at least three data sets; (iii) using the at least three complex image data sets, two at a time, to generate two solutions for a separate image of w and f signals having different chemical shifts according to the following model:
|w+f*exp(iαn)|=|In|, n=0,1, . . . , N−1,
where αn is the induced phase shift between the w and f signals for each set (n) from which the two pairs of solutions for w and f may be determined; (iv) from the two pairs (with n={0, n1} and n={0, n2}) of solutions for w and f and from the following equations
cos(αnβ)*w+cos [αn(1+β)]*f=real(In)
sin(αnβ)*w+sin [αn(1+β)]*f=imaginary(In),
determine two pairs of solutions ({β11, β12} and {β21, β22}) for the main magnetic field inhomogeneity (β) wherein solution {β11, β12} is determined using the set of in-phase data and a data set having the largest α and the solution {β21, β22} is determined using the in-phase data set and a data set having the second largest α; (v) selecting a unique solution for β from {β11, β12} and {β21, β22}; (vi) select one of β11 and β12 having a minimum distance among the following:
|β11−β21|, |β11−β22|, |β12−β21|, |β12−β22|,
and, (vii) applying the selected β to determine a final solution for w and f.
The method described above may also use MRI data to solve for β from more than three data sets, e.g., four or five sets, and the method is not limited to only three data sets (which are the two sets with the largest phase shifts and an in-phase set).
The method may be applied using three rapidly acquired echoes within one scan, and if the echoes are closely spaced they can all be acquired between each 180 degree pulse. For example, the may be applied using a gradient echo readout sequence and rapidly reversing the readout gradient to produce the requisite phase shifted echoes. In addition, rapid readout reversals may be applied to produce the phase shifted echoes within a conventional spin echo or field echo sequence.
In addition, the method may be applied using three separate MRI scans. Further the method may be performed on three or more image data sets that are three dimensional (3D) image data sets.
The invention may also be embodied as a method to separate two chemically-shifted signal components w and f comprising: (i) estimating a main magnetic field inhomogeneity (β) using a heavy spatially low-pass filtered input signal (In) applied to the following equations:
cos(αnβ)*w+cos [αn(1+β)]*f=real(In)
sin(αnβ)*w+sin [αn(1+β)]*f=imaginary(In)
assuming that for the heavy low-pass filtered input signal the w to f ratio is approximately constant and applying the estimated field inhomogeneity (β) to separate the w and f signals in a non-filtered MRI input signal.
A first series of readout gradients (ro1) 30 is applied to collect in-phase image data (s1) 32. The first series of readout gradients are applied centered at a mid-point (TE/2) of the period (TE) between each pair of refocusing pulses. The effects of background magnetic field inhomogeneity in the in-phase data (s1) cancel out at the time TE/2, which is measured from the center of the preceding refocusing pulse (π). The readout gradient (ro2) for the shifted FSE is applied centered at a time TE/2 plus a certain time difference (Δt). The period of the time difference (Δt) progressively increases for each successive scan. Various order of varying Δt may be applied.
The time shifted readout gradients (ro2) 34 collect out of phase image data (s2) 36. This data (s2) has a certain water-lipid phase increment and a corresponding background inhomogeneity error associated with a time difference (Δt) relative to the corresponding echo point of the in-phase (s1) image data. The time difference (Δt) is the period between the in-phase data signal (s1) and the out-of-phase data signal (s2). To ensure the same global RF phase at the beginning of each scan, the sequence runs in a mode that effectively locks the phase for all N scans used to generate the images. Each of the N scans has a level of phase increment value directly proportional to the time differential (Δt). By altering the time differential for successive dynamic scans (0,1,2, . . . N−1), a series of water-lipid signals with different phase increment angles is obtained.
After standard FSE-2D processing, the complex voxel image data (In) is subjected to post processing. This post-processed image data is a heavy spatially low-filtered input signal that is acquired as three image data sets which are in turn processed to determine solutions for the main magnetic field inhomogeneity (β). The FSE water-fat imaging is based on the mathematical model (2) presented below:
(w+f*exp(iαn))*exp(iαnβ)=In, where n=0, 1, 2, . . . , N-1 (2)
The image data parameter In is the complex input MR image data generated in the current voxel for the current phase angle, w is the MR part of the image data from the water component in the current image voxel, f is the part of the image data from the fat component of the current voxel, αn is the n-th phase increment angle, and β is the scalar magnetic field inhomogeneity coefficient. The scalar magnetic field inhomogeneity coefficient (β) is represented by ΔB0/ΔF0, where ΔB0 is field inhomogeneity in hertz (Hz) and ΔF0 is the chemical shift between water and fat in Hz.
For each given inhomogeneity coefficient β, the real-valued least-squares solution {w,f} of the model (2) may be represented by the Moore-Penrose pseudo inverse of the system using the following system (3, 4):
cos(αnβ)*w+cos [αn(1+β)]*f=real(In) (3)
sin(αnβ)*w+sin [αn(1+β)]*f=imaginary(In) (4)
The residual of the Moore-Penrose solution of the system (3, 4) over a series of phase increment values (0, 1, 2, . . . N−1) for a given β is R(β). Values for w, f and β can be found by minimization of R(β) over an interval (βmin, βmax). If w does not equal f, the function R(β) has two close local minima which may cause the minimization process to be unstable. In particular, it is easy to select the wrong value for R(β) minimum, especially in the presence of noise in the input data (In) and where the water/fat component ratio is small.
The difficulty in selecting the proper R(β) minimum is illustrated by
To mitigate the problem of noise in the input data (In), a less precise but more robust and direct method is proposed to select a minimum value for R(β). For purposes of this direct method, assume first that N≧3 and α0=0. Applying equation (5).
|w+f*exp(iαn)|=|In| (5)
with n={0, n1} and n={0, n2}, two pairs of solutions for w and f may be determined. From these two pairs of solutions for w and f and applying equations 3 and 4, solutions for β may be determined as {β11, β12} and {β21, β22}.
To select a unique solution for β from {β11, β12} and {β21, β22 }, suppose that the first pair {β11, β12} corresponds to the largest phase increment angle between αn1 and αn2. From β11 and β12, chose the one with the minimum distance among the following:
|β11−β21|, |β11−β22|, |β12−β21|, |β12−β22| (6)
Again, as for minimization of R(β) with the presence of noise, there is a certain possibility that the chosen solution for β is wrong for a particular image data voxel. Since β represents the magnetic field inhomogeneity, it should change very slowly from voxel to voxel and can be approximated with enough precision by a low order function, for example a cubic polynomial function, of the voxel position. The chosen solution for β is fitted with a cubic polynomial over the whole slice or volume being imaged. In the case of N=2, there is only one pair of equations (5). In this case, between β11 and β12, choose the solution which minimizes the average residual of the Moore-Penrose solution of equation (2) in the neighborhood of the corresponding voxel. As for N≧3, the chosen solution can be further fitted to a low order polynomial equation.
Numerical experiments for the two methods of selecting the local solution for β described above found that the tedious process of searching for two local minima in R(β) in the presence of In noise yields results similar to the direct solution (such as shown by equations 5 and 6). The direct solution was used for further experiments. Even for the 2D-FSE sequence described herein, where efforts are made to decrease the fat signal, the fat signal is still sometimes 4–5 times stronger than the water signal. A 2D model test object was created comprising four similar squares with different ratios of the fat and water signal amplitudes. In relative units, the average water signal is 5,000, the average fat signal is 20,000 and the global average signal is 12,500.
The algorithm of water/fat separation can be described as follows: (i) Initially create a magnitude mask M(x,y) and β-mask B(x,y). These masks are initialized to one (1) at the points where the magnitude of the signal is above a selected multiple of the noise level, and to zero (0) where the signal is below that noise threshold level. (ii) For all points where M(x, y) equals 1, β(x,y) is calculated using a direct method. For those points where there are no positive solutions for w and f or where the solution for β is complex, the β-mask B(x, y) is set to 0. (iii) The function β(x,y) is least squares approximated by a cubic polynomial β˜(x,y) over the points where B(x,y) equals 1. Assuming that the number of such points is more than the number of coefficients of a 2D cubic polynomial, e.g., 10, a system of 10 linear equations must be solved. (iv) For all points, where M(x,y) equals one 1, the water and fat images w(x,y) and f(x,y) are determined using β˜(x,y) by the Moore-Penrose solution (of EQ. 2 and 3 above) with the restrictions that w and f are greater than zero.
The test object water and fat image data used in all numerical experiments are depicted in
A white noise of a certain level was added to In(x,y) to test the effects of noise on the images. The field inhomogeneity coefficient was modeled by the following cubic polynomial:
β(x,y)=a0+a1x+a2y+a3xy+a4x2+a5y2+a6x2y+a7xy2+a8x3+a9y3,
where ai={−2, 0.02368, 0.2368, 0, −0.000185, −0.000185, 0, 0, 4.81645e−7, 4.81645e−7}.
On the rectangle x⊂[0,255], y⊂[0,255], the value of β changes between −2 and 2.
The results of the water/fat separation for αmax=60° are presented in Table 1 and
The water/fat separation quality depends on the noise level in the input data and the values of increment angles and on the water/fat ratio. Table 1 and
With αn={0°,30°,60°,90°,120°} the results of the water/fat separation are acceptable with the noise level up to 2.5%. The larger the water are component in the total signal the better is the water/fat separation with respect to the water estimate. For areas 2–4 in Tables 1 and 2, the results of the water/fat separation are acceptable with the noise level in the input water signal up to 5%.
In a second series of experiments, the distribution of increment angles (α) was varied. To normalize the results of experiments with different numbers (N) of increment angles, the effect of total acquisition time was fixed. The acquisition time is proportional to N and to the number of the signal repetitions NAQ. The signal to noise ratio (SNR) of the input signal is proportional to the square root of NAQ. To make the results of the second series experiments with different N comparable, the level of noise added to the input signal was altered. For N=5 10% noise was added; for N=4, 8.9% noise was added (square root of 4/5 times 10%); and for N=3, 7.7% noise was added (square root of 3/5 times 10%). The N=2 case was skipped because it requires a different algorithm of calculation.
The results of these experiments are presented in Tables 3, 4, and 5 below:
Tables 3–5 show that for the model in
In
As before, β(x,y) can be further fit by a low order polynomial, and used in the solution of equations 2,3. In particular, to separate the two chemically-shifted signal components w and f, the following image collection and process steps are performed: (i) acquire a heavy spatially low-filtered input signal (In) generated by applying a fast spin echo (FSE) sequence to an object, wherein the input signal has a relatively small and non-zero phase difference between the w and f signal components, (ii) estimating a main magnetic field inhomogeneity (β) using the heavy spatially low-pass filtered input signal (In) applied to equations B and C:
cos(αnβ)*w+cos [αn(1+β)]*f=real(In) (B)
sin(αnβ)*w+sin [αn(1+β)]*f=imaginary(In) and (C)
(iii) apply the estimated inhomogeneity (β) to separate the w and f signals in a non-filtered MRI input signal. This method assumes that for heavy spatially low-pass filtered input signal, the w to f signal components ratio has relatively small variation over the whole input signal space.
The invention has been described in connection with what is presently considered to be the most practical and preferred embodiments. The invention is not to be limited to the disclosed embodiments, but, on the contrary, covers various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
This application claims is a continuation of and claims priority of U.S. provisional application Ser. No. 60/520,321 filed on Nov. 17, 2003, the entirety of which is incorporated by reference.
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