Magnetic resonance imaging apparatus and sampling pattern determination method

Abstract

To provide a sampling pattern suitable for image reconfiguration of high-speed imaging using a sensitivity distribution difference of a reception coil and sparsity of measurement data, and capable of generating an image free of noise and artifacts.SOLUTION: An MRI apparatus includes a measurement point determination part for determining each measurement point of three-dimensional k space data. With a kx direction of a three-dimensional k space as a lead-out direction, the measurement point determination part adjusts a first condition that an angle of straight lines connecting the measurement points and the center of a plane changes at a golden angle (α), and a distance (r) from the center point of the plane increases monotonously on a plurality of measurement points in the ky-kz plane, and determines the measurement point to satisfy a second condition that a change in the position of the measurement point is made aperiodic.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present invention relates to a magnetic resonance imaging (hereinafter referred to as MRI) apparatus, and in particular to a technique for controlling sampling of k-space. [Background technology]

[0002] One high-speed MRI imaging method is a technique that thins out and samples k-space, and reconstructs an image from k-space data that includes unmeasured sampling points. This high-speed imaging reconstruction method includes parallel imaging, which uses the sensitivity difference of coils to perform reconstruction, and compressed sensing, which uses the sparsity of images to perform sequential reconstruction. In addition, a method has been proposed that estimates and reconstructs signals at unmeasured points using both the sensitivity distribution difference of coils and the sparsity of images (such as L1-SPIRiT, the method described in Patent Document 1: hereinafter referred to as the third reconstruction method).

[0003] There are various sampling patterns for the k-space thinning method, i.e., sampling patterns that indicate which points in k-space are sampled, such as an equal-interval pattern that thins out the phase encoding at equal intervals and a random pattern that thins out randomly, and an appropriate sampling pattern is used depending on the reconstruction method. For example, parallel imaging reconstruction such as SENSE and GRAPPA only supports equal-interval patterns, and some compressed sensing methods only support random patterns. In addition, reconstruction methods that use sensitivity distribution differences and image sparsity support both equal-interval and random patterns.

[0004] In three-dimensional imaging, phase encoding is performed in two dimensions excluding the frequency encoding direction (readout direction), so thinning can be performed in two directions (ky direction, kz direction), and various ky-kz sampling patterns have been proposed (Patent Document 2, Patent Document 3). Patent Document 2 proposes a method of sampling points obtained by rotating a straight line passing through the center of the ky-kz plane by a golden angle (Fig. 20), and a sampling pattern in which a spiral trajectory is rotated multiple times (Fig. 21). In addition, Patent Document 3 proposes a sampling pattern in which a spiral phyllotaxis is arranged at a certain angle (golden angle) in order to solve the problem that it is difficult to process MR data when dividing it into regions or interleaving it with a pseudo-random pattern used in compressed sensing. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2023-69890 A [Patent Document 2] JP 2022-019354 A [Patent Document 3] U.S. Patent No. 8,848,993 Summary of the Invention [Problem to be solved by the invention]

[0006] The reconstruction method using the above-mentioned sensitivity distribution difference and image sparsity is said to be compatible with any sampling pattern, but issues remain such as noise and artifacts when using conventional sampling patterns.

[0007] For example, in the case of an equal interval pattern, unmeasured signals around the measurement points are estimated mainly due to the sensitivity distribution difference, so the number of speed-ups is limited by the number of coils, and reconstruction is not possible at a speed-up number (thinning-out rate) greater than the number of coils, or large noise and artifacts occur. Also, in the case of a random pattern, the center of the k-space data is generally dense, and high frequencies are estimated due to sparsity, but there are regions where the distance between measurement points is unevenly wide, and estimation based on the sensitivity distribution difference is not possible, which also causes noise and artifacts.

[0008] In the sampling pattern described in Patent Document 2, the sampling pattern in which a straight line is rotated has measurement points on one straight line adjacent to each other, but the distance between the measurement points on the other straight lines is large, and the density difference between the measurement points in the direction of distance from the center and the direction of rotation is large, which makes it easy for noise and artifacts to occur. In addition, in a pattern in which multiple spiral trajectories are arranged, it is difficult to adjust the arrangement of multiple trajectories so that the measurement turns are not too close. The sampling pattern described in Patent Document 3 compensates for the shortcomings of the conventional sampling pattern described above, but since the spiral phyllotaxis of the central measurement point is arranged at a certain golden angle, there is a regularity inherent in the pattern, and artifacts due to this regularity occur.

[0009] In order to solve these problems, the present invention proposes a pattern in which the density of measurement points spreading radially from the center of k-space is controlled, while the measurement points are locally spaced equally and the regularity of their arrangement is reduced, thereby reducing noise and artifacts during reconstruction. [Means for solving the problem]

[0010] In order to solve the above problems, the present invention provides a means for arranging sampling points while controlling the density of measurement points and varying the distance from the k-space origin to the measurement points and the angle of the line connecting the origin and the measurement points, and at that time, setting a sampling pattern by adding slight variations (non-periodicity) to at least one of the distance and angle.

[0011] That is, the MRI apparatus of the present invention includes an imaging unit that collects nuclear magnetic resonance signals from a subject and obtains three-dimensional k-space data, a calculation unit that reconstructs an image of the subject using the three-dimensional k-space data, and a measurement point determination unit that determines each measurement point of the three-dimensional k-space data. The measurement point determination unit is characterized in that, when the kx direction of the three-dimensional k-space is the readout direction, for a plurality of measurement points on a ky-kz plane, the measurement points are determined so as to satisfy a first condition that the angle of the straight line connecting the measurement point and the center of the plane changes at the golden angle (α) and the distance (r) from the center point of the plane increases monotonically, and the measurement points are determined so as to satisfy a second condition that the change in the position of the measurement point is made non-periodic.

[0012] The present invention also provides a method for determining a sampling pattern for arranging measurement data in three-dimensional k-space in three-dimensional imaging, characterized in that when the kx direction of three-dimensional k-space is the readout direction, for multiple measurement points on the ky-kz plane, the first condition is adjusted so that the angle of the straight line connecting the measurement point and the center of the plane changes by the golden angle (α) and the distance (r) from the center point of the plane increases monotonically, and the measurement points are determined so as to satisfy the second condition that the change in the position of the measurement point is made non-periodic. Effect of the Invention

[0013] According to the present invention, it is possible to restore measurement data by utilizing sparsity in the high frequency region, and it is possible to estimate unmeasured points by utilizing differences in sensitivity distribution, and it is also possible to perform high-speed imaging using a sampling pattern that can suppress the occurrence of artifacts due to the regularity of the sampling pattern. [Brief description of the drawings]

[0014] [Figure 1] Diagram showing the overall outline of an MRI device [Diagram 2] Functional block diagram of a computer according to the first embodiment [Diagram 3] FIG. 1 is a diagram showing an imaging procedure of the MRI apparatus of the first embodiment. [Figure 4] A diagram showing the three-dimensional k-space in which measurement data from three-dimensional imaging is arranged. [Diagram 5]FIG. 1 is a diagram for explaining conditions for setting a sampling pattern according to the first embodiment; [Figure 6] (a) and (b) are diagrams showing the fitting of sampling patterns to k-space with different matrix sizes. [Figure 7] FIG. 1 is a diagram for explaining the difference in effect between a first condition (keeping the golden angle constant) of the sampling pattern in the first embodiment and a second condition (giving a slight variation to the golden angle) obtained by adjusting the first condition. [Figure 8] FIG. 10 is a diagram for explaining an algorithm for determining a sampling pattern used in the second embodiment. [Figure 9] FIG. 13 is a diagram for explaining sampling pattern determination (addition of slight variations) in the second embodiment. [Figure 10] FIG. 11 is a diagram for explaining sampling pattern determination (aspect ratio and speed correction) in the second embodiment. [Figure 11] FIG. 11 is a diagram showing a process flow of a measurement point determination unit according to the second embodiment. [Figure 12] Functional block diagram of a computer according to a third embodiment [Figure 13] FIG. 1 is a diagram for explaining evaluation of a sampling pattern by a sampling evaluation unit. [Figure 14] FIG. 1 is a diagram for explaining evaluation of a sampling pattern by a sampling evaluation unit. [Figure 15] FIG. 11 is a diagram for explaining a procedure for setting a sampling pattern according to the third embodiment. [Figure 16] Functional block diagram of a computer according to a fourth embodiment [Figure 17] Diagram explaining the difference in PSF due to sampling density distribution [Figure 18] FIG. 13 is a diagram showing the process flow of the fourth embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] Hereinafter, an embodiment of an MRI apparatus of the present invention will be described with reference to the drawings.

[0016] <Embodiment 1> First, the configuration of an MRI apparatus to which the present invention is applied will be described. As shown in Fig. 1, the MRI apparatus 1 of this embodiment is roughly divided into an imaging section 10 and a computer 20 having the functions of an arithmetic section and a control section. The configuration of the imaging section 10 is the same as that of a general MRI apparatus, and includes a static magnetic field magnet 11 that generates a uniform static magnetic field in an examination space in which a subject 50 is placed, a gradient magnetic field coil 12 that applies gradient magnetic fields in three axial directions to the static magnetic field space formed by the static magnetic field magnet 11, a transmitting radio frequency (RF) coil 13 that applies a high frequency magnetic field in a pulsed form to the subject 50, and a receiving RF coil 14 that receives a nuclear magnetic resonance signal (echo signal) generated from the subject 50 by applying an RF pulse. In some cases, one RF coil serves as both the transmitting RF coil 13 and the receiving RF coil 14.

[0017] The gradient magnetic field coil 12, the transmitting RF coil 13 and the receiving RF coil 14 are connected to a gradient magnetic field power supply 15, a transmitter 16 and a receiver 17, and imaging is performed by a sequencer 18 driving these gradient magnetic field power supply 15, transmitter 16 and receiver 17 according to a pulse sequence determined according to the imaging.

[0018] The receiver 17 samples the echo signals and digitizes them into measurement data. The measurement data is used for image reconstruction as k-space data of a specified matrix size. When imaging each specified cross section (slice), two-dimensional k-space data is obtained, and when imaging a specified volume, three-dimensional k-space data is obtained. There are two-dimensional pulse sequences that select a slice in one excitation and collect echo signals, and three-dimensional pulse sequences that excite a specified volume in one excitation and collect echo signals using phase encoding in two directions.

[0019] There are various pulse sequences depending on the imaging method, and the sequencer 18 calculates the pulse sequence to be used for imaging using the pulse sequence type and imaging conditions selected by the user or determined in advance by the examination protocol. The imaging conditions include imaging parameters such as the repetition time TR of the pulse sequence, the timing TE for measuring the nuclear magnetic resonance signal (echo signal), and the flip angle FA of the excitation RF pulse, as well as conditions related to the k-space, such as the matrix size of the k-space, the thinning rate of the k-space, i.e., the speed ratio, and the sampling pattern of the k-space in the case of thinning. When performing thinning measurement, the MRI apparatus 1 of this embodiment determines the sampling pattern of the k-space according to a predetermined condition, and collects echo signals with the sampling pattern.

[0020] The calculator 20 can be configured as a general-purpose calculator equipped with a CPU, GPU, and memory, and realizes a function of controlling the operation of each part of the imaging unit 10 described above, and a function of reconstructing an image using measurement data collected by the receiver 17 (function of the calculation unit). Specifically, as shown in Fig. 2, the calculator 20 includes an imaging control unit 21, an image reconstruction unit 22, a measurement point determination unit 23, a display control unit 24, and other functions. The imaging control unit 21 controls the entire imaging via the sequencer 18.

[0021] The image reconstruction unit 22 performs image reconstruction calculations using the k-space data. As described above, there are various image reconstruction methods, such as parallel imaging reconstruction, compressed sensing, and sequential reconstruction using the sensitivity distribution difference of the receiving coils and the sparsity of the data, and reconstruction is performed using a predetermined method or a method specified by the user. The measurement point determination unit 23 determines which measurement points are to be measured among the measurement points on the k-space matrix. The measurement points are determined to determine a sampling pattern of the k-space. In this embodiment, a sampling pattern suitable for compressed sensing and sequential reconstruction is determined in high-speed imaging at a predetermined speed ratio. The details of the measurement point determination will be described in detail in a later embodiment.

[0022] In FIG. 2, only four functions are shown as the main functions of the calculator 20, but it goes without saying that the calculator 20 may be provided with other known functions, such as calculation of quantitative values, and body movement correction.

[0023] Each function of the computer 20 is stored in advance as a program in the memory of the computer 20 or in an external storage device, and is realized by uploading the program to a CPU or the like.

[0024] Furthermore, as shown in Fig. 2, the computer 20 is connected to a UI unit 30 and an external storage device 40 for user operation. The UI unit 30 is equipped with a display and an input device that display the processing results of the computer 20, such as a reconstructed image, and a GUI operated by the user. The computer 20 can also be connected to an intranet or cloud within a facility as necessary, and can share data with other devices or realize some of its functions using other devices. Some of the functions of the computer 20 may also be realized using a programmable IC.

[0025] As shown in FIG. 3, the flow of imaging by the MRI apparatus of this embodiment is as follows: when imaging conditions are set in the imaging control unit 21 (S1), the measurement point determination unit 23 uses imaging conditions such as imaging parameters and speed ratio to determine measurement points to be actually measured among all measurement points determined by the matrix size of k-space (S2). The arrangement pattern of the determined measurement points is the sampling pattern. The imaging control unit 21 controls the operation of the imaging unit 10 according to the imaging conditions and the determined sampling pattern, and the imaging unit 10 collects echo signals and samples k-space data (S3). The image reconstruction unit 22 reconstructs an image by a predetermined image reconstruction method using the collected k-space data (S4), and performs image processing such as a predetermined correction process as necessary to generate a diagnostic image. The display control unit 24 displays the generated image on the display of the UI unit 30 (S5). The image is transferred to a medical image management system such as PACS as necessary.

[0026] The processes other than the determination of the sampling pattern (S2) are the same as those of a general MRI device. The sampling pattern is an arrangement of sampling points to be measured among all measurement points (lattice points) in the k-space where the measurement data collected by imaging is arranged, and the sampling pattern is determined by determining the sampling points. In this embodiment, in three-dimensional imaging, a sampling pattern is determined in which the measurement points in the ky-kz plane of the three-dimensional k-space are thinned out at a predetermined thinning rate.

[0027] In the three-dimensional k-space in which the measurement data collected by three-dimensional imaging is arranged, measurement points are arranged in the kx, ky, and kz directions as shown in Fig. 4. If the kx direction is the readout direction, the ky and kz directions are phase encoding directions. The measurement points on the ky-kz plane, which is determined by the combination of these two phase encodings, are determined to form a predetermined sampling pattern.

[0028] Specifically, a sampling pattern is provided in which sampling points are arranged while changing the distance from the k-space origin to the measurement point and the angle of the line connecting the origin and the measurement point, and the coordinates of each sampling point are slightly changed. This makes it possible to obtain measurement data that has appropriate sparsity, has high estimation accuracy of the measurement points using the sensitivity distribution difference, and can reduce the occurrence of artifacts.

[0029] Specifically, for multiple measurement points on the ky-kz plane, the angle of the line connecting the measurement point and the center of the plane changes by the golden angle, and the distance (r) from the center point of the plane increases monotonically (first condition). Based on this condition, the first condition is adjusted to determine the measurement points so as to satisfy the second condition that the change in the position of the measurement point is non-periodic.

[0030] The first condition is, when determining N measurement points, as shown on the left side of FIG. 5, when point P0 (corresponding to the origin of the ky-kz plane) is set as the starting point, point P0 and point Pn (n=1 to N) are connected by a straight line Ln that connects P0 and Pn, and the distance between P0 and Pn is rn. The angle between Ln and Ln+1 is the golden angle (α=137.507…), and The difference (increment) Δr between rn+1 and rn is positive, that is, the distance r between the starting point and the measurement point increases monotonically. The following is a description of an example in which Δr is constant, which is the easiest case to process.

[0031] By satisfying this first condition, the density of sampling points is high near the center of k-space, i.e., in the low-frequency region, and the density is moderately reduced in the high-frequency region, resulting in highly sparse data, which is suitable for reconstruction using the sensitivity distribution difference and sparsity. However, this first condition has a certain regularity, and artifacts are likely to occur due to the regularity in images reconstructed from k-space data acquired with a sampling pattern that satisfies the first condition.

[0032] In this embodiment, an adjustment is made to condition 1 to give irregularity (non-periodicity) to the regularity. As an adjustment method for giving non-periodicity, for example, as shown on the right side of Fig. 5, there is a method of adding (moving) non-periodic fluctuations (Δz, Δy) in the z and y directions to the coordinates of each point. Other methods include changing the increment value Δr between the origin and the measurement point, which increases monotonically, rather than making it constant, changing the angle α by a small amount non-periodically, or a combination of these. Specific adjustment methods and procedures will be described in detail in the embodiments described later.

[0033] Finally, P0 to PN are determined so as to satisfy these conditions. The sampling pattern formed by the points determined in this way is a roughly circular pattern, which is applied to the rectangular ky-kz to determine the measurement points. At this time, by varying the increment value Δr according to the matrix size, sampling patterns that apply to k-spaces (ky-kz planes) of different matrix sizes can be obtained. For example, if the k-space has a matrix size of 256×256, sampling pattern A as shown in FIG. 6(a) is obtained, and if the k-space has a matrix size of 128×128, sampling pattern B with a smaller number of measurement points N than sampling pattern A is obtained as shown in FIG. 6(b).

[0034] When the sampling pattern is determined in this way, the imaging control unit 21 controls the imaging unit 10 according to the sampling pattern to collect measurement data of the measurement points with the set pulse sequence and speed rate of 3D imaging (S3). That is, the application strength and application order of the gradient magnetic fields in the three axial directions included in the imaging sequence are controlled to obtain 3D k-space data for image reconstruction (S4).

[0035] The image reconstruction unit 22 creates an image from the three-dimensional k-space data using a predetermined reconstruction method. The reconstruction method is not limited, but the sampling pattern of this embodiment can suitably adopt sequential reconstruction using the sensitivity distribution of the receiving coil and the sparsity of the measurement data. Specifically, the sampling pattern is suitable for a reconstruction method (Patent Document 1) that repeats denoising using L1-SPIRiT (Murphy M, Alley M, Demmel J, et al., Fast L1-SPIRiT Compressed Sensing Parallel Imaging MRI: Scalable Parallel Implementation and Clinically Feasible Runtime. IEEE Trans Med Imaging 2012; 31:1250-1262.), sparsity, CNN, etc., and reconstruction using the sensitivity distribution.

[0036] According to this embodiment, by using a sampling pattern that satisfies the second condition obtained by adjusting the first condition, it is possible to obtain an effect that could not be achieved by conventional methods, namely, it is possible to utilize the sensitivity distribution difference of the receiving coil even in the high frequency range while maintaining randomness, and to eliminate the regularity that causes artifacts. As a result, it is possible to obtain good quality images without noise or artifacts in various reconstruction methods including compressed sensing.

[0037] Figure 7 shows images reconstructed using a sampling pattern with no variation and a sampling pattern with variation. The left side of the figure shows the case where no variation was applied, and the right side shows the case where minute variation was applied. Although it is difficult to see from the figure, stripe-like artifacts have occurred at the position indicated by the arrow in the image on the left, but it can be confirmed that the stripe-like artifacts have been reduced in the image on the right.

[0038] Note that in FIG. 5, a case where non-periodic fluctuations (Δz, Δy) are added in the z and y directions is described; however, the second condition can be achieved by applying a small fluctuation to the increment value Δr or the angle α (golden angle) between the two measurement points, which will produce the same effect.

[0039] Hereinafter, a description will be given of an embodiment of specific processing of the measurement point determination unit 23. In the following embodiment, configurations and processing common to the first embodiment shown in Figs. 1 to 3 will be omitted from the description, and differences will be mainly described.

[0040] <Embodiment 2> First, the algorithm for determining the measurement points performed by the measurement point determining unit 23 of this embodiment will be described.

[0041] The measurement point determination unit 23 first generates a series of point clouds consisting of N points on a plane (S11). Here, the plane is virtual, and later, a process is performed to fit the point clouds generated on the plane to the ky-kz plane of the three-dimensional k-space. The number of point clouds N is a number that can be changed depending on the matrix size of the matrix to which the point clouds are fitted and the speed ratio of high-speed imaging.

[0042] In generating the point group, the coordinates of the nth point are determined by the following formula: [Number 1] y(n)=r(n)·cos(αn) z(n) = r(n) sin(αn) r(n)=(n-1) / N

[0043] The nth points are arranged in ascending order of distance r from the origin, i.e., the distance r increases monotonically, and the angular difference from the next point (the angular difference between the line connecting the origin and the nth point and the line connecting the origin and the (n+1)th point) is the golden angle α.

[0044] If the coordinates of the origin are (0,0), the coordinates (y,z) of the point cloud are -1 ≤ y ≤ 1, -1 ≤ z ≤ 1 Therefore, by multiplying y and z by a coefficient, it can be applied to k-space (ky, kz) of any size (matrix size). Specifically, as shown in the following equations (2-1) and (2-2), the coordinates of each point multiplied by the coefficient (A / 2·y, B / 2·z) (A is the matrix size in the y direction, and B is the matrix size in the z direction) are taken as the coordinates of that point.

[0045] [Number 2] ky(n)=round(A / 2 y(n)) (2-1) kz(n)=round(B / 2 z(n)) (2-2)

[0046] At this time, fluctuations Δy and Δz are added to the coordinates of each point as shown in the following equation. [Number 3] ky(n)=round(A / 2·y(n)+Δy) (3-1) kz(n)=round(B / 2 z(n)+Δz) (3-2)

[0047] By adding such variations, it is possible to impart non-periodicity to the sampling pattern determined by equations (2-1) and (2-2), thereby reducing artifacts after reconstruction. Δy and Δz can be generated by varying at least one of the distance from the center and the golden angle between the lines connecting the two points and the center.

[0048] A specific method for adjusting the fluctuation amounts Δy and Δz in this embodiment will be further described. In this method, the fluctuation amounts Δy and Δz are calculated by correcting the fluctuation amount according to the distance r (distance correction), as well as correcting it according to the aspect ratio of the matrix to which the point cloud is applied and the target speed ratio. Specifically, as shown in the following formula, the aspect ratio (A / B or B / A) and the target speed ratio (R IP ) and the "distance correction term" which includes the square root of the distance r.

[0049]

number

[0050]

number

[0051] In equations (4-1) and (4-2), the real and imaginary parts of the complex function f(n) are used to generate the fluctuations in two directions, and the magnitude of the fluctuations is then adjusted using a distance correction term and an aspect ratio / speed correction term. These corrections prevent degradation of image quality caused by the fluctuations being excessively large or small compared to the interval between the measurement points.

[0052] The distance correction term is derived from the following idea. As shown in Figure 9, if we imagine a ring-shaped region of width w outside a circle with radius r, the number of measurement points included in this ring-shaped region is w / Δr. Therefore, when Δr is constant, the density of the measurement points is proportional to 1 / r, so the measurement points become denser toward the center and the fluctuation becomes relatively larger. The distance correction term in equations (4-1) and (4-2) prevents the fluctuation from becoming relatively large at the center by making the amount of fluctuation in both the z and y directions proportional to √r.

[0053] The aspect ratio correction is a correction term introduced to keep the magnitude of the variation in the vertical and horizontal t the same when fitting a point cloud to a ky-kz plane with a different aspect ratio. Also, the speed-up correction is a correction term to prevent the variation from becoming relatively large compared to the overall thinning ratio. For example, as shown in Figure 10, a square sampling pattern (a) on the ky-kz plane is multiplied by a speed-up ratio R IP When the aspect ratio is changed to make the sampling pattern (b) with a vertical matrix size of B and a horizontal matrix size of A while keeping the size the same, the average intervals σz and σy between the measurement points satisfy the following relationship.

[0054]

number

[0055] By using σz and σy as coefficients, it is possible to maintain a constant ratio of the magnitude of the fluctuation with respect to the distance between measurement points, which differs depending on the aspect ratio and the speed factor. However, in order to ensure appropriate correction even in the case of extreme aspect ratios, the following restriction is added to the aspect ratio and speed factor correction.

[0056]

number

[0057] Next, based on the above-mentioned measurement point determination process, the flow of the process of the measurement point determination unit 23 of this embodiment will be described with reference to the flow shown in FIG.

[0058] When imaging conditions such as the total number of points M in the measurement range, the desired thinning rate p, the phase encoding number Y, and the slice encoding number Z are set, the measurement point determination unit 23 generates a point cloud according to the above-mentioned point cloud generation method. In this embodiment, as an example, the measurement range is an elliptical region, and the total number of measurement points within this region is M.

[0059] In point group generation, first, an initial value of the increment value Δr in the radial direction of the points (the difference between the distance r(n) of the n-th point and the distance r(n+1) of the (n+1)-th point) is determined (S21). The initial value of Δr is set to Δr = 1 / (M / p). This is equivalent to dividing the normalized radius r (0 to 1) into N / p (N is the number of points to be generated).

[0060] Next, each point from the 1st to the N-th is determined starting from the origin (cz, cy) (S22). Specifically, according to the algorithm expressed by the following formula, the coordinates (z, y) of the points in the normalized plane are sequentially determined. In the following formula, Δz and Δy are the amounts of variation calculated by the aforementioned formulas (4-1) and (4-2). s[Z][Y] is a two-dimensional array representing the sampling pattern, where the measurement point is 1 and the non-measurement point is 0.

[0061] [Equation 8] r = 0; θ = 0, s[Z][Y] = 0 while r <= 1 z = cz + round(r * cos(θ) * Z / 2 + Δz) y = cy + round(r * sin(θ) * Y / 2 + Δy) if z, y are within the measurement range and s[z][y] == 0 s[z][y] = 1 θ = θ + α (α: Golden Angle) r = r + Δr

[0062] If N point groups are determined, the actual decimation rate p’ is calculated by the following formula (S23). [Equation 9] p’ = Σs / N

[0063] If the actual decimation rate p’ is within a predetermined allowable range with respect to the target decimation rate p, that is, if p - Δp < p’ < p + Δp, the process ends (S24). Δp is a parameter indicating the allowable range and a value such as a few percent of p is set in advance.

[0064] On the other hand, if the actual thinning rate p' is outside the predetermined allowable range, the increment value Δr is updated by a binary search as shown in the following equation, and the above-mentioned steps S22 to S24 are repeated (S25). [Number 10] p' <p → Δr = Δr - |Δr - Δr old | / 2 p'>p → Δr = Δr + |Δr - Δr old | / 2

[0065] In this process, for example, if the initially assumed number of points N is smaller than the target thinning rate, the number is increased, and if the initially assumed number of points N is larger, the number is decreased.

[0066] The sampling pattern is determined by the above processes (S21 to S25). Thereafter, as shown in Fig. 3, the image reconstruction unit 22 reconstructs an image using echo signals (measurement data) collected by the imaging unit 10 in the sampling pattern (processing after S4 in Fig. 3), which is the same as in the first embodiment.

[0067] According to this embodiment, as in the first embodiment, it is possible to obtain a sampling pattern that can utilize the sensitivity distribution differences of the receiving coils even in the high frequency range while maintaining randomness, and that eliminates the regularity that causes artifacts.

[0068] <Embodiment 3> In the second embodiment, the measurement point determination unit 23 generated a sampling pattern that matched the desired speed ratio and matrix size using the imaging conditions set by the user, but in the present embodiment, a function is added to evaluate the generated sampling pattern and adjust the sampling pattern based on the results.

[0069] 12, the MRI apparatus of this embodiment adds a sampling evaluation unit 25 that evaluates a sampling pattern to a computer 20. Other configurations of the imaging unit 10 and computer 20 are the same as those of the first and second embodiments, and the method of the measurement point determination unit 23 that determines the sampling pattern is also the same as that of the second embodiment. The following describes this embodiment, focusing on the differences from the second embodiment.

[0070] As described in the second embodiment, the measurement point determination unit 23 determines a sampling pattern by applying fluctuations Δz and Δy to the coordinates of the measurement points determined by the first condition when determining each measurement point. The sampling evaluation unit 25 evaluates the sampling pattern determined by the measurement point determination unit 23 from the viewpoint of randomness. In general, artifacts occurring in an image can be estimated by analyzing a point spread function (PSF) convoluted with the image, and there are few artifacts if the side lobes of the point spread function are small and random.

[0071] Fig. 13 shows the PSF obtained by Fourier transforming two types of sampling patterns. As shown in the figure, in the sampling pattern (left) in which the measurement point position is changed by the golden angle and the distance increment value Δr is constant, the maximum value of the side lobe is small, but the side lobe occurs in a ring shape, and artifacts due to regularity are expected. In contrast, in the sampling pattern (right) in which variation is added to the sampling pattern on the left, the side lobe is even smaller and the regularity disappears.

[0072] The sampling evaluation unit 25 of this embodiment utilizes this fact to generate a PSF by Fourier transforming the determined sampling pattern, and evaluates the maximum value of the area excluding the center (for example, about 1 / 8 of the whole). The closer the maximum value is to 0, the fewer the artifacts. As shown in Fig. 14, evaluation using the PSF may use the error between the intensity histogram of the area excluding the center and the maximum likelihood estimate (Rayleigh distribution) of the random noise (left side of Fig. 14), or the error between the cumulative distribution function of the PSF and the maximum likelihood estimate of the random noise (right side of Fig. 14). In either case, the closer the error is to 0, the more the artifacts are reduced.

[0073] The measurement point determination unit 23 performs the measurement point determination process again using the evaluation result of the sampling evaluation unit 25. As shown in FIG. 15, the flow of the process is as follows: after setting the initial value of the parameter (for example, the coefficient D in Equations 4-1 and 4-2) for adjusting the variation (for example, D=1) and determining the sampling pattern in the same manner as in the first embodiment (S32: including S22 to S25 in FIG. 11), when the error value resulting from the sampling evaluation (S33) becomes equal to or less than a preset threshold value, the measurement point is determined as the sampling pattern, and otherwise the parameter is updated with another value (S34, S35). For example, the updating may be a method of sequentially selecting from several candidate values. Then, the process is repeated until the error becomes equal to or less than the threshold value. Alternatively, when the number of repetitions reaches a predetermined number, the sampling pattern with the smallest error value in the multiple processes may be adopted.

[0074] According to this embodiment, the sampling pattern is evaluated and the sampling pattern is adjusted based on the evaluation result, thereby making it possible to further reduce artifacts.

[0075] <Embodiment 4> This embodiment is characterized by the addition of a function (density adjustment unit) for adjusting the density of measurement points according to the imaging target or the user's preference. The configuration of the computer 20 of this embodiment is shown in Fig. 15. Note that Fig. 15 shows a configuration in which a density adjustment unit 26 is added to the configuration of the computer 20 of the first embodiment shown in Fig. 2, but the computer 20 may also be provided with a sampling evaluation function (sampling evaluation unit 25) included in the computer 20 of the third embodiment.

[0076] In the principle (first condition) for determining the sampling pattern in the first embodiment, the density of the measurement points is inversely proportional to the distance r, so that the density is high at the center and low in the high frequency region. On the other hand, depending on the purpose of imaging, there are cases where it is better to improve the imaging ability of fine structures, or conversely, cases where it is better to expand the range of the central region where the density is high. In addition, the suitable density differs depending on the type of imaging sequence, for example, T1 weighted imaging or T2 weighted imaging. In this embodiment, the density of the measurement points is adjusted based on the imaging sequence or imaging parameters specified by the user, or by accepting a user specification regarding the density.

[0077] Specifically, the radius of the nth measurement point is defined by the following equation, which includes an adjustment value “γ”. [Number 11] r(n)=(n / N) ∧ Gamma

[0078] In this formula, as shown in Fig. 17, when γ = 0.5, the density is uniform, and when γ = 1, the density is proportional to 1 / r (sampling pattern according to the first condition). The density can be varied by arbitrarily changing the adjustment value γ between 0.5 and 1. The adjustment value γ may be specified by the user via the UI unit 30 (Fig. 2), or may be automatically determined according to the imaging conditions specified by the user by storing values ​​suitable for the imaging sequence and imaging parameters in advance as a table in the calculator 20.

[0079] The measurement point determination process of this embodiment is shown in Fig. 18. First, the measurement point determination unit 23 determines a sampling pattern in the same manner as in the first or second embodiment (S1, S2). The density adjustment unit 26 adjusts the density using γ specified by the user or γ determined from the set imaging conditions (S2-3), and then passes the adjusted sampling pattern to the imaging control unit 21 and starts imaging (S3-S5). Note that it is also possible to reverse the order of S2 and S2-3, have the density adjustment unit 26 accept or determine γ (S2-3), and obtain a sampling pattern with adjusted density by calculating the radius using γ when determining the sampling pattern (S2).

[0080] According to this embodiment, by adding a function for adjusting the density of measurement points according to imaging conditions or user designation, it is possible to reduce the occurrence of artifacts and provide an image suited to the imaging purpose.

[0081] Although each embodiment of the present invention has been described above, the present invention is not limited to each embodiment. For example, among the methods described in the embodiments, a publicly known method may be replaced with another publicly known method. Furthermore, multiple embodiments may be combined as long as there is no technical contradiction. [Explanation of symbols]

[0082] 1: MRI device, 10: imaging unit, 20: computer, 21: imaging control unit, 22: image reconstruction unit, 23: measurement point determination unit, 24: display control unit, 25: sampling evaluation unit, 30: UI unit

Claims

1. an imaging unit that collects nuclear magnetic resonance signals from a subject and obtains three-dimensional k-space data, a calculation unit that reconstructs an image of the subject using the three-dimensional k-space data, and a measurement point determination unit that determines each measurement point of the three-dimensional k-space data, The measurement point determination unit determines measurement points on a ky-kz plane so as to satisfy a first condition that, when the kx direction of three-dimensional k-space is the readout direction, the angle of a straight line connecting the measurement point and the center of the plane changes by the golden angle (α) and the distance (r) from the center point of the plane increases monotonically, and to satisfy a second condition that the change in the position of the measurement point is made non-periodic.

2. 2. The magnetic resonance imaging apparatus according to claim 1, The magnetic resonance imaging apparatus according to claim 1, wherein the measurement point determination unit determines measurement points for a predetermined region on the ky-kz plane so that the number of measurement points is a predetermined number.

3. 3. The magnetic resonance imaging apparatus according to claim 2, A magnetic resonance imaging apparatus, characterized in that the number of measurement points is determined using a matrix size of a ky-kz plane and a thinning rate of thinning measurement performed by an imaging section.

4. 3. The magnetic resonance imaging apparatus according to claim 2, A magnetic resonance imaging apparatus, wherein the predetermined region is any one of a rectangle, a circle, and an ellipse.

5. 2. The magnetic resonance imaging apparatus according to claim 1, the measurement point determination unit fits a series of points conforming to the first condition onto a ky-kz plane, and determines measurement points so as to satisfy the second condition by adding variation to coordinates of each point of the point cloud; A magnetic resonance imaging apparatus comprising:

6. 6. The magnetic resonance imaging apparatus according to claim 5, the measurement point determination unit corrects the magnitude of the slight fluctuation in accordance with at least one of a distance from a center of a plane, an aspect ratio of a matrix size, and a target speed ratio; A magnetic resonance imaging apparatus comprising:

7. 2. The magnetic resonance imaging apparatus according to claim 1, The magnetic resonance imaging apparatus according to claim 1, wherein the measurement point determination unit controls a density of the measurement points based on at least one of an imaging condition set in the imaging unit and an imaging part in addition to the second condition.

8. 2. The magnetic resonance imaging apparatus according to claim 1, A magnetic resonance imaging apparatus further comprising a sampling evaluation unit that evaluates the arrangement of measurement points (sampling pattern) determined by the measurement point determination unit using an index of randomness.

9. 9. The magnetic resonance imaging apparatus according to claim 8, 4. A magnetic resonance imaging apparatus according to claim 1, wherein the sampling evaluation unit uses, as the index of randomness, a maximum value of a side lobe of a point spread function or an error between the point spread function and a Rayleigh distribution.

10. 1. A method for determining a sampling pattern for arranging measurement data in a three-dimensional k-space in three-dimensional imaging, comprising: A method for determining a sampling pattern, characterized in that, when the kx direction of three-dimensional k-space is the readout direction, for a plurality of measurement points on a ky-kz plane, a first condition is adjusted such that the angle of a straight line connecting the measurement point and the center of the plane changes by the golden angle (α) and the distance (r) from the center point of the plane increases monotonically, and measurement points are determined so as to satisfy a second condition that the change in the position of the measurement point is made non-periodic.

11. A method for determining a sampling pattern according to claim 10, comprising the steps of: A step (1) of generating a point group consisting of N points, in which the coordinates of the n-th point in the zy plane satisfy the following equation: [Number 1] y(n) = r(n) · cos(αn) z(n) = r(n) sin(αn) r(n)=(n-1) / N, -1≦y≦1, -1≦z≦1 (In the formula, α is the golden angle, n is an integer between 1 and N, and r(n) is the distance from the center point of the zy plane (z,y=0,0) to the nth point.) Step (2) of fitting the points generated in step (1) to the ky-kz plane using the following equation; [Number 3] ky(n)=round(A / 2・y(n)+Δy) kz(n) = round(B / 2 z(n) + Δz) (In the formula, A and B represent the matrix sizes in the ky and kz directions of the ky-kz plane, and Δy and Δz represent the amounts of variation that give irregularity, respectively.) A method for determining a sampling pattern, comprising:

12. A method for determining a sampling pattern according to claim 10, comprising the steps of: A method for determining a sampling pattern, comprising the further step of evaluating, after determining the measurement points, the randomness of a sampling pattern determined by the arrangement of the measurement points, and adjusting the sampling pattern based on the evaluation results.

13. A method for determining a sampling pattern according to claim 10, comprising the steps of: A method for determining a sampling pattern, further comprising a step of adjusting a parameter that determines an increment value of a radius of the measurement points under the second condition, thereby adjusting a density of the measurement points.

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