H-1 sampling trajectory navigation Na-23 MRI pulse sequence method

Abstract

The invention discloses a method for navigating a Na-23MRI (Magnetic Resonance Imaging) pulse sequence by an H-1 sampling track, which comprises the following steps of: designing a pulse sequence sequentially comprising an H-1 navigation echo module and a Na-23 ultra-short echo time pulse sequence module, and reconstructing an actually-measured H-1 sampling track by utilizing an H-1 sampling signal corresponding to the H-1 navigation echo module, so as to obtain an actually-measured Na-23 sampling track; and finally, performing image reconstruction on the Na-23 sampling signal based on the actually measured Na-23 sampling track to obtain a Na-23 reconstructed image, thereby remarkably reducing the reconstruction artifacts of the Na-23 image and realizing the optimization of the image quality.

Description

Technical Field

[0001] This invention belongs to the field of multi-nuclear magnetic resonance imaging (MRI) pulse sequence methods, and particularly relates to a method for navigating Na-23 MRI pulse sequences using an H-1 sampling trajectory. This method obtains a Na-23 sampling trajectory based on the H-1 navigator echo, guiding Na-23 data sampling and reconstruction. This method can be used for sampling trajectory measurement and sampling signal reconstruction in multi-nuclear MRI, optimizing image reconstruction quality. Background Art

[0002] Magnetic resonance imaging uses strong magnetic fields and radio frequency pulses to excite atomic nuclei (such as hydrogen H-1 or sodium Na-23) in human tissue, collects their magnetic resonance signals, and reconstructs high-resolution images through a computer.

[0003] Currently, magnetic resonance imaging (MRI) is primarily based on proton (hydrogen H-1) signals. Hydrogen H-1 is a spin-1 / 2 nucleus with advantages such as a high gyromagnetic ratio (42.577 MHz / T) and high tissue concentration, making it the most sensitive nuclide for in vivo detection. Sodium Na-23 is the second most abundant MRI-detectable nucleus in the human body, after hydrogen H-1, and its MRI signal is closely related to ion balance and energy metabolism. However, sodium Na-23 is a spin-3 / 2 nucleus with short T2 and T2* relaxation times, a low gyromagnetic ratio (11.232 MHz), and a much lower tissue concentration (on the order of 10 millimolar) than hydrogen H-1. Therefore, sodium Na-23 MRI generally utilizes an ultrashort echo time design based on non-Cartesian sampling. In non-Cartesian sampling methods, gradient delays in the encoding gradient and eddy current effects significantly affect image reconstruction results, resulting in severe image reconstruction artifacts.

[0004] By measuring the k-space sampling trajectory corresponding to the actual measurement of the encoding gradient and filling the sampling signal in the k-space according to the measured sampling trajectory, the reconstruction artifacts caused by gradient delay and eddy current effect can be eliminated, significantly improving the image quality. At present, the non-Cartesian sampling pulse sequence method based on hydrogen H-1 can measure the sampling trajectory before sampling. It is mainly based on the layer selection measurement method and related improved methods proposed by Duyn et al. [Simple correction method for k-space trajectory deviations in MRI [J]. Journal of Magnetic Resonance, 1998, 132 (1): 150-153]. The sampling trajectory measurement method based on hydrogen H-1 also includes the trajectory measurement method based on time-space coding proposed by Zhou et al. [A magnetic resonance k-space trajectory measurement method based on time-space coding, invention patent, ZL 202410149995.1]. However, the T2 relaxation time and T2* relaxation time of sodium Na-23 in tissue are short and the concentration is low, making it difficult to measure the sampling trajectory based on the sodium Na-23 signal. Therefore, it is currently impossible to directly obtain the k-space sampling trajectory of sodium Na-23 using non-Cartesian sampling sodium Na-23 pulse sequence methods. The measured sampling trajectory is inconsistent with the theoretical sampling trajectory used for image reconstruction, introducing artifacts into the image reconstruction of the sodium Na-23 pulse sequence sampling signal. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems existing in the prior art and provide a method for navigating the Na-23 MRI pulse sequence using the H-1 sampling trajectory, thereby realizing the k-space trajectory measurement of the Na-23 pulse sequence and reducing the Na-23 image reconstruction artifacts.

[0006] The above-mentioned purpose of the present invention is achieved by the following technical means:

[0007] The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory comprises the following steps:

[0008] Step 1: Design a pulse sequence, which includes an H-1 navigation echo module and a Na-23 ultra-short echo time pulse sequence module.

[0009] Step 2: Scan and sample the test object based on the designed pulse sequence, and obtain the H-1 sampling signal corresponding to the H-1 navigation echo module and the Na-23 sampling signal corresponding to the Na-23 ultra-short echo time pulse sequence module in sequence;

[0010] Step 3: reconstruct the actual k-space sampling trajectory corresponding to the H-1 sampling signal to obtain the measured H-1 sampling trajectory;

[0011] Step 4: Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory, the k-space sampling trajectory corresponding to the Na-23 sampling signal is reconstructed to obtain the measured Na-23 sampling trajectory;

[0012] Step 5: Reconstruct the Na-23 sampling signal based on the measured Na-23 sampling trajectory to obtain a Na-23 reconstructed image.

[0013] As described above, the Na-23 ultrashort echo time pulse sequence module includes Ns Na-23 excitation sampling units, the number of excitations Ns ≥ 2, and each Na-23 excitation sampling unit sequentially realizes Na-23 signal excitation and Na-23 signal sampling, and during the Na-23 signal sampling, a Na-23 encoding gradient is simultaneously applied and the analog-to-digital converter ADC for Na-23 signal sampling is turned on.

[0014] As described above, the H-1 navigator echo module includes a plurality of slice selection excitation sampling units in sequence, each slice selection excitation sampling unit corresponds to a k-space coordinate axis direction, and the k-space coordinate axis directions corresponding to different slice selection excitation sampling units are perpendicular to each other;

[0015] In each layer selection excitation sampling unit, an H-1 excitation pulse and a layer selection gradient are first applied simultaneously; then the layer selection refocusing gradient is applied. After the layer selection refocusing gradient is completed, the H-1 encoding gradient is applied simultaneously and the analog-to-digital converter ADC for H-1 signal sampling is turned on;

[0016] The H-1 encoding gradient, slice selection gradient, and slice selection refocusing gradient in the same slice selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 encoding gradient is the same as the Na-23 encoding gradient when pointing to the same k-space coordinate axis direction.

[0017] The preset k-space sampling trajectory corresponding to the Na-23 ultrashort echo time pulse sequence module is recorded as the preset Na-23 sampling trajectory. The k value of the sampling point in the preset Na-23 sampling trajectory meets the following requirements:

[0018] The preset Na-23 sampling trajectory is a straight radial trajectory from the center to the periphery in the three-dimensional k-space;

[0019] The k value of the sampling point in the preset Na-23 sampling trajectory is proportional to the integral of the Na-23 encoding gradient in the same k-space direction over time. The Na-23 signal sampling after a pulse excitation corresponds to a spoke in the preset Na-23 sampling trajectory, and the corresponding Na-23 encoding gradient has a different direction. The Na-23 signal is collected in the entire k-space through multiple pulse excitations and spatial encoding of the encoding gradient. The steps for setting the k-space direction of the Na-23 encoding gradient are as follows:

[0020] Determine the encoding gradient corresponding to the preset Na-23 sampling trajectory when it is completely along a k-space coordinate axis direction;

[0021] Then, a k-space coordinate value on a three-dimensional sphere is generated through a Fibonacci grid. A k-space coordinate value on the three-dimensional sphere corresponds to the k-space direction of the Na-23 encoding gradient during the pulse excitation of a Na-23 excitation pulse.

[0022] The above step 3 specifically includes the following steps:

[0023] Step 3.1, extract the phase value of the H-1 sampling signal at each sampling time point;

[0024] Step 3.2: Deconvolution is performed on the phase value to obtain the deconvolution phase value at each sampling time point. The variation of the deconvolution phase value with sampling time is recorded as

[0025] Step 3.3: Changes of the deconvolution phase value corresponding to each k-space coordinate axis direction with sampling time The corresponding actual H-1 sampling trajectory is reconstructed to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis.

[0026] The above step 3.3 specifically includes the following steps:

[0027] The trajectory of H-1 sampling trajectory is reconstructed based on the following objective function and constraints:

[0028]

[0029] st-γ H ·G s ·T p / 2≤k enc (t)≤γ H ·G s ·T p / 2

[0030] k enc represents the k value of the H-1 sampling trajectory; k enc (t) represents the change of k value of H-1 sampling trajectory with sampling time, which is the quantity to be calculated; It's about k enc The numerical minimization function, st represents the constraint condition of the objective function, abs represents the absolute value, L w is the thickness of the layer selected for excitation by the H-1 excitation pulse, G s is the intensity of the layer selection gradient, T p is the duration of the H-1 excitation pulse, L offis the bias distance of the H-1 excitation pulse selection layer, γ H is the gyromagnetic ratio of H-1; t is the duration of the encoding gradient during sampling.

[0031] The above-mentioned step 4 specifically includes the following steps:

[0032] Step 4.1. Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory in each k-space coordinate axis direction, calculate the k value of the measured Na-23 sampling trajectory corresponding to each k-space coordinate axis when the Na-23 encoding gradient is completely pointed in the direction of each k-space coordinate axis according to the following formula:

[0033]

[0034] Among them, γ Na is the gyromagnetic ratio of Na-23, The k value represents the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely directed toward the k-space coordinate axis M. The k-space coordinate axis M∈{x-axis direction, y-axis direction, z-axis direction}, where the x-axis direction, y-axis direction, and z-axis direction are mutually perpendicular to each other. represents the k value of the H-1 sampling trajectory in the k-space coordinate axis direction M;

[0035] Step 4.2: Based on the k-values of the measured Na-23 sampling trajectories corresponding to the Na-23 encoding gradients fully pointing in the directions of the k-space coordinate axes, the k-values of the measured spokes corresponding to each pulse excitation and spatial encoding are calculated using the following formula:

[0036]

[0037] Among them, k n (t) represents the k-space trajectory corresponding to the n-th spatial encoding, 1≤n≤Ns; k n (t) is the k value of the measured spoke corresponding to the nth pulse excitation and spatial encoding, 1≤n≤Ns;

[0038] x n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the x-axis direction, denoted as the unit vector projection in the x-axis direction at the n-th pulse excitation;

[0039] y n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the y-axis direction, denoted as the unit vector projection in the y-axis direction at the n-th pulse excitation;

[0040] z nis the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the z-axis direction, and is the projection of the unit vector in the z-axis direction at the n-th pulse excitation;

[0041] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the x-axis direction;

[0042] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the y-axis direction;

[0043] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointed in the z-axis direction;

[0044] In step 4.3, the measured spokes of Ns excitations together constitute the measured Na-23 sampling trajectory in the complete k-space.

[0045] As mentioned above, the unit vector projection y in the y-axis direction during the n-th pulse excitation is n The calculation is based on the following formula:

[0046] y n =1-2(n-1) / (Ns-1)

[0047] The unit vector projection x in the x-axis direction during the nth pulse excitation n The calculation is based on the following formula:

[0048]

[0049] The unit vector projection z in the z-axis direction during the nth pulse excitation n The calculation is based on the following formula:

[0050]

[0051] The above step 5 specifically includes the following steps:

[0052] The measured Na-23 sampling trajectory and the corresponding Na-23 sampling signal are input into a three-dimensional non-uniform Fourier transform function for image reconstruction to obtain a Na-23 reconstructed image based on the measured Na-23 sampling trajectory.

[0053] As mentioned above, the Na-23 excitation pulse is a rectangular pulse, and the H-1 excitation pulse is a swept frequency pulse.

[0054] Compared with the existing methods, the present invention has the following beneficial effects:

[0055] A method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory includes an H-1 navigator echo module and a Na-23 ultra-short echo time pulse sequence module. The H-1 navigator echo module is used to obtain a measured Na-23 sampling trajectory, and the Na-23 ultra-short echo time pulse sequence module is used to acquire three-dimensional Na-23 image data. Image reconstruction using the measured Na-23 sampling trajectory significantly reduces Na-23 image reconstruction artifacts. Furthermore, three-dimensional data acquisition based on ultra-short echo time helps reduce signal attenuation due to T2 / T2* relaxation time, improves the imaging signal-to-noise ratio, and optimizes image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of the method of the present invention.

[0057] Figure 2 This is the pulse sequence diagram designed by the method of the present invention. Wherein, Ns represents the number of excitations. The Na-23 encoding gradient has components in the x-axis direction, the y-axis direction, and the z-axis direction. If the Na-23 encoding gradient is completely directed to a certain k-space coordinate axis, then only the component of the Na-23 encoding gradient in the k-space coordinate axis direction is non-zero. If the components of the Na-23 encoding gradient in the x-axis direction, the y-axis direction, and the z-axis direction are non-zero, then the amplitudes in the three directions are small, such as Figure 2 The Na-23 encoding gradient curve is shown as a solid line.

[0058] Figure 3 It is the coding gradient corresponding to the density adaptive radial sampling trajectory used by both the Na-23 coding gradient and the H-1 coding gradient in the method of the present invention.

[0059] Figure 4 This is a comparison diagram of the measured Na-23 sampling trajectory and the theoretical Na-23 sampling trajectory in the method of the present invention.

[0060] Figure 5 It is a comparison between the image reconstructed by the measured trajectory and the image reconstructed by the theoretical trajectory using the method of the present invention. DETAILED DESCRIPTION

[0061] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to the embodiments. The embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0062] Example 1:

[0063] The method of navigating Na-23 MRI pulse sequence using H-1 sampling trajectory, such as Figure 1 As shown, the following steps are included:

[0064] Step 1: Design the pulse sequence

[0065] Pulse sequence such as Figure 2 As shown, it includes the H-1 navigation echo module and the Na-23 ultra-short echo time pulse sequence module. The H-1 navigation echo module is applied before the Na-23 ultra-short echo time pulse sequence module. The H-1 navigation echo module is used to obtain the measured sampling trajectory, and the Na-23 ultra-short echo time pulse sequence module is used for Na-23 data sampling. The design rules of the H-1 navigation echo module and the Na-23 ultra-short echo time pulse sequence module are as follows:

[0066] (1)Na-23 ultra-short echo time pulse sequence module

[0067] The Na-23 ultra-short echo time pulse sequence module includes Ns Na-23 excitation sampling units. A pulse excitation is performed in each Na-23 excitation sampling unit, and the number of excitations Ns ≥ 2. Each Na-23 excitation sampling unit sequentially implements Na-23 signal excitation and Na-23 signal sampling. During the Na-23 signal excitation, a Na-23 excitation pulse is applied. During the Na-23 signal sampling, a Na-23 encoding gradient is simultaneously applied and an analog-to-digital converter ADC for Na-23 signal sampling is turned on. The preset k-space sampling trajectory corresponding to the Na-23 ultra-short echo time pulse sequence module is recorded as a preset Na-23 sampling trajectory. In this embodiment, the k value of the sampling point in the preset Na-23 sampling trajectory meets the following requirements:

[0068] The preset Na-23 sampling trajectory points from the center to the periphery in three-dimensional k-space, specifically, it radiates linearly from the center to the periphery. Therefore, the Na-23 encoding gradient has components in the x-axis direction, the y-axis direction, and the z-axis direction. The k value of the sampling point in the preset Na-23 sampling trajectory is proportional to the integral of the Na-23 encoding gradient in the same k-space direction over time. The Na-23 signal sampling after a pulse excitation corresponds to a spoke in the preset Na-23 sampling trajectory (that is, the direction of the Na-23 encoding gradient corresponding to each Na-23 signal sampling is different). The Na-23 signal is collected in the entire k-space through multiple pulse excitations and spatial encoding of the encoding gradient. The steps for setting the k-space direction of the Na-23 encoding gradient are as follows:

[0069] First, determine the encoding gradient corresponding to the preset Na-23 sampling trajectory when it is completely along one k-space coordinate axis direction (the three-dimensional k-space coordinate axis direction includes the x-axis direction, the y-axis direction, and the z-axis direction. In this embodiment, the x-axis direction is selected). The Na-23 encoding gradient used in this embodiment is the encoding gradient corresponding to the density-adapted radial sampling trajectory, such as Figure 3 As shown;

[0070] A spherical Fibonacci grid is then used to generate k-space coordinates on a three-dimensional sphere. Each k-space coordinate on the three-dimensional sphere corresponds to the k-space direction of the Na-23 encoding gradient during a single Na-23 signal sampling event. The k-space directions of the corresponding Na-23 encoding gradients differ between different Na-23 excitation sampling units. In this embodiment, after each Na-23 excitation pulse, the Na-23 encoding gradient is rotated using the k-space coordinates on the three-dimensional sphere, simultaneously sampling a line of Na-23 k-space sampling data. A line of Na-23 k-space sampling data includes the Na-23 sampling signals at each Na-23 sampling point on the corresponding spoke. The Na-23 ultrashort echo time pulse sequence module achieves Na-23 signal sampling throughout the entire three-dimensional k-space through multiple pulse excitations, sampling, and direction changes.

[0071] (2) H-1 Navigation Echo Module

[0072] In order to obtain the actual Na-23 k-space sampling trajectory, an H-1 navigator echo module is set before the Na-23 ultrashort echo time pulse sequence module. The H-1 navigator echo module includes multiple slice selection excitation sampling units in sequence. Each slice selection excitation sampling unit corresponds to a k-space coordinate axis direction. The k-space coordinate axes corresponding to different slice selection excitation sampling units are perpendicular to each other. In this embodiment, three slice selection excitation sampling units are set.

[0073] In each slice selection excitation sampling unit, an H-1 excitation pulse and a slice selection gradient in the direction of the corresponding k-space coordinate axis are first applied simultaneously; then a slice selection refocusing gradient is applied, and the area of the slice selection refocusing gradient is half the area of the slice selection gradient; after the slice selection refocusing gradient is completed, an H-1 encoding gradient is applied simultaneously and the analog-to-digital converter ADC for H-1 signal sampling is turned on;

[0074] The H-1 encoding gradient, slice selection gradient, and slice selection refocusing gradient in the same slice selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 encoding gradient is the same as the Na-23 encoding gradient when pointing to the same k-space coordinate axis direction.

[0075] The H-1 navigator echo module uses the layer selection gradient to perform corresponding excitation and sampling in the three k-space coordinate axis directions (i.e., the x-axis direction, the y-axis direction, and the z-axis direction) in sequence, and uses the spatiotemporal encoding principle of the H-1 excitation pulse to measure the H-1 k-space sampling trajectory in the x-axis direction, the y-axis direction, and the z-axis direction, respectively, to obtain the measured H-1 sampling trajectory, thereby obtaining the components of the measured Na-23 sampling trajectory in the three k-space coordinate axis directions, and further calculating the measured Na-23 sampling trajectory through the measured H-1 sampling trajectory for subsequent image reconstruction of the Na-23 sampling signal.

[0076] In this embodiment, the Na-23 ultrashort echo time pulse sequence module includes three Na-23 excitation sampling units, each of which realizes Na-23 signal excitation and Na-23 signal sampling in turn. The Na-23 excitation pulse is a rectangular pulse. After the Na-23 excitation pulse ends, the three-dimensional Na-23 encoding gradient (that is, the Na-23 encoding gradient includes components in the x-axis direction, the y-axis direction and the z-axis direction) is immediately turned on simultaneously to perform spatial encoding of the signal, and the analog-to-digital converter ADC for Na-23 signal sampling is also turned on; then the Na-23 encoding gradient and the analog-to-digital converter ADC for Na-23 signal sampling are turned off simultaneously; at this time, the echo time TE is half the length of the Na-23 excitation pulse; the k-space direction of the Na-23 encoding gradient corresponding to different Na-23 excitation sampling units is changed based on the k-space coordinate value on the three-dimensional sphere generated by the Fibonacci grid.

[0077] In this embodiment, an H-1 excitation pulse (in this embodiment, the H-1 excitation pulse adopts a swept frequency pulse) and a slice selection gradient in the direction of the corresponding k-space coordinate axis are first synchronously applied to each slice selection excitation sampling unit in the H-1 navigator echo module, and then a slice selection refocusing gradient is applied, wherein the area of the slice selection refocusing gradient is half the area of the slice selection gradient; after the slice selection refocusing gradient is completed, an H-1 encoding gradient in the same k-space coordinate axis direction is applied once, and the H-1 encoding gradient is the same as the Na-23 encoding gradient when pointing in the same k-space coordinate axis direction, so as to facilitate the subsequent calculation of the measured Na-23 sampling trajectory and be used for the subsequent image reconstruction of the Na-23 sampling signal. Taking the x-axis direction as an example, first, an H-1 excitation pulse and a layer selection gradient in the x-axis direction are synchronously applied (the analog-to-digital converter ADC for H-1 signal sampling and the H-1 encoding gradient are turned on and off at the same time) to selectively excite and phase modulate the H-1 signal; then, a layer selection refocusing gradient in the x-axis direction is applied, where the area of the layer selection refocusing gradient is half the area of the layer selection gradient; after the layer selection refocusing gradient is completed, an H-1 encoding gradient in the x-axis direction is applied once, and the H-1 encoding gradient in the x-axis direction is consistent with the Na-23 encoding gradient when it is completely pointed in the x-axis direction; when the H-1 signal is sampled, the .... The analog-to-digital converter ADC of the sample is synchronously turned on and off once with the H-1 coding gradient, that is, sampling is performed once; for the layer selection excitation sampling units in the y-axis direction and the z-axis direction in the H-1 navigation echo module, the H-1 excitation pulse is consistent with the H-1 excitation pulse in the layer selection excitation sampling unit in the x-axis direction, only the direction of the corresponding layer selection gradient, layer selection refocusing gradient, and H-1 coding gradient is adjusted to the y-axis direction or the z-axis direction, and the H-1 coding gradient, the analog-to-digital converter ADC for H-1 signal sampling, and the analog-to-digital converter ADC for H-1 signal sampling are also synchronously turned on and off.

[0078] Step 2: Scan and sample the test object based on the designed pulse sequence

[0079] This embodiment scans and samples the sample based on the pulse sequence designed in step 1, and sequentially obtains the H-1 sampling signal corresponding to the H-1 navigation echo module and the Na-23 sampling signal corresponding to the Na-23 ultra-short echo time pulse sequence module.

[0080] This embodiment was carried out on a Bruker 400M magnetic resonance microimager (model: AVANCE 400), and a saturated sodium chloride solution was used to fill a 10mm nuclear magnetic sample tube for testing. A H-1 / Na-23 dual-channel body coil with an inner diameter of 10mm was used for pulse emission and reception, and the sample temperature was maintained at 298K. In the H-1 navigation echo module of the pulse sequence of this embodiment, the H-1 excitation pulse used a WURST swept pulse with a duration of 10ms, the sweep range was set to 5000Hz, and the intensity of the layer selection gradient was set to 46.97mT / m (converted to a proton frequency of 2000Hz / mm). The layer thickness L of the layer selection excitation by the H-1 excitation pulse is w is 2.5mm; the bias frequency of the H-1 excitation pulse is set to 8000Hz, then the bias distance L of the H-1 excitation pulse selection layer is off The pulse width is 4 mm; the corresponding flip angle is 90°, and the repetition time TR is 3000 ms. In the Na-23 ultrashort echo time pulse sequence module of this embodiment, the parameters used are: Na-23 excitation pulse duration is 0.5 ms, the corresponding flip angle is 60°, the echo time TE is 0.25 ms, the field of view FOV is 20 mm × 20 mm × 20 mm, the sampling matrix MATRIX is 64 × 64 × 64, the repetition time TR is 100 ms, and the average number is 1; the number of excitations Ns is 3217, which is 1 / 4 of the full sampling (the full sampling number is 64 × 64 × π, i.e., 12868 times).

[0081] Based on the above pulse sequence parameters, the pulse sequence of the method of the present invention is used to sample a sodium chloride solution sample, and the obtained sampling signals include an H-1 sampling signal and a Na-23 sampling signal.

[0082] Step 3: Reconstruct the actual k-space sampling trajectory of the H-1 navigation echo module

[0083] The actual k-space sampling trajectory corresponding to the H-1 sampling signal is reconstructed to obtain the measured H-1 sampling trajectory. Since the H-1 navigator echo module of the pulse sequence of this embodiment uses H-1 encoding gradients in the three k-space coordinate axis directions of x, y, and z respectively during sampling, the measured H-1 sampling trajectory includes k-space sampling trajectories in the three k-space coordinate axis directions (i.e., the x-axis direction, the y-axis direction, and the z-axis direction). The following steps are illustrated using the x-axis direction as an example:

[0084] Step 3.1, extract the phase value of the H-1 sampling signal at each sampling time point;

[0085] Taking the x-axis direction as an example, sampling is performed when the H-1 coding gradient in the x-axis direction is enabled. The sampled H-1 sampling signal is a complex signal that changes with the sampling time. The argument of the complex signal is the phase of the H-1 sampling signal. In this embodiment, the H-1 sampling signal obtained by the H-1 navigation echo module is calculated using the phase angle (angle) function in MATLAB to obtain the phase value of the H-1 sampling signal at each sampling time point.

[0086] Step 3.2, deconvolution is performed on the phase value to obtain the deconvolution phase value at each sampling time point;

[0087] Phase wrapping will occur when the phase value exceeds 2π. In this embodiment, the phase value of the H-1 sampling signal is further unwrapped by the MATLAB unwrap function to obtain the unwrapped phase value at each sampling time point; the unwrapped phase value is recorded as The change of the phase value after deconvolution with the sampling time is recorded as

[0088] Step 3.3: Changes of the deconvolution phase value corresponding to each k-space coordinate axis direction with sampling time The corresponding actual H-1 sampling trajectory is reconstructed to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis.

[0089] When filling the H-1 sampling signal into the k-space, the k value of the H-1 sampling trajectory in each k-space coordinate axis direction is proportional to the integral of the H-1 encoding gradient in the corresponding k-space coordinate axis direction over time, which can be expressed as:

[0090]

[0091] Among them, G enc (τ) is the change of H-1 coding gradient over time, k enc represents the k value of the H-1 sampling trajectory, k enc(t) is the change of k value of H-1 sampling trajectory with sampling time, t is the duration of the coding gradient at sampling time, t∈{0,Δt,2*Δt,3*Δt,…,T}, one sampling point corresponds to the duration t of the coding gradient at sampling time, Δt represents the interval between two sampling points, and T represents the total duration of the entire coding gradient; γ H is the gyromagnetic ratio of H-1; τ represents time.

[0092] According to the principle of space-time coding, when the H-1 excitation pulse is used for layer-selective excitation, the H-1 sampling signal presents a quadratic phase distribution, and the H-1 coding gradient will change the phase of the H-1 sampling signal; during the sampling period, the phase value after deconvolution changes with the sampling time. The k value of the H-1 sampling trajectory pointing to the same k-space direction changes with the sampling time k enc (t) is expressed as:

[0093]

[0094] Among them, L w is the thickness of the layer selected for excitation by the H-1 excitation pulse, G s is the intensity of the layer selection gradient, T p is the duration of the H-1 excitation pulse, L off is the bias distance of the H-1 excitation pulse selection layer. According to this formula, this embodiment uses the MATLAB single variable minimization function (fminbnd function) to calculate the k value k of the corresponding H-1 sampling trajectory according to the deconvolved phase value of the H-1 sampling signal. enc That is, the measured H-1 sampling trajectory is obtained. Specifically, for each k-space coordinate axis direction, the k value of the corresponding H-1 sampling trajectory is calculated based on the following objective function and constraints:

[0095]

[0096] st-γ H ·G s ·T p / 2≤k enc (t)≤γ H ·G s ·T p / 2

[0097] It's about k enc The numerical minimization function, st represents the constraint of the objective function, and abs represents the absolute value. Based on the above objective function and constraint conditions, according to the change of the phase value after deconvolution with the sampling time Calculate the change of k value of H-1 sampling trajectory over time enc(t), and thus the measured H-1 sampling trajectory is reconstructed.

[0098] Step 4: Reconstruct the actual k-space sampling trajectory of the Na-23 sampling signal

[0099] Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory in each k-space coordinate axis direction, the k-space sampling trajectory corresponding to the Na-23 sampling signal is reconstructed to obtain the measured Na-23 sampling trajectory;

[0100] Step 4.1: Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory in each k-space coordinate axis direction, obtain the k value of the measured Na-23 sampling trajectory corresponding to each k-space coordinate axis direction when the Na-23 encoding gradient is completely pointed. The specific process is as follows:

[0101] Since the k value of the k-space sampling trajectory is proportional to the gyromagnetic ratio, the corresponding Na-23 sampling trajectory pointing to the same k-space coordinate axis and with the same encoding gradient can be calculated according to the following formula based on the measured H-1 sampling trajectory pointing to the k-space coordinate axis:

[0102]

[0103] Among them, γ Na is the gyromagnetic ratio of Na-23, It represents the k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointed to the k-space coordinate axis direction M, the k-space coordinate axis direction M∈{x-axis direction, y-axis direction, z-axis direction}, and the x-axis direction, y-axis direction and z-axis direction are mutually perpendicular to the k-space coordinate axis direction, that is, is the k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the x-axis direction, is the k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the y-axis direction, The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointed in the z-axis direction; The k value represents the H-1 sampling trajectory in the k-space coordinate axis direction M. The comparison between the measured Na-23 sampling trajectory and the theoretical Na-23 sampling trajectory is as follows: Figure 4 As shown in the figure, due to gradient delay and other reasons, the measured Na-23 sampling trajectory climbs significantly slower than the Na-23 sampling trajectory in the initial stage.

[0104] Step 4.2: Based on the k-values of the measured Na-23 sampling trajectories corresponding to the Na-23 encoding gradients fully pointing in the directions of the k-space coordinate axes, the k-values of the measured spokes corresponding to each pulse excitation and spatial encoding are calculated using the following formula:

[0105]

[0106] k n (t) is the k value of the measured spoke corresponding to the nth pulse excitation and spatial encoding, 1≤n≤Ns;

[0107] x n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the x-axis direction, denoted as the unit vector projection in the x-axis direction at the n-th pulse excitation;

[0108] y n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the y-axis direction, denoted as the unit vector projection in the y-axis direction at the n-th pulse excitation;

[0109] z n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the z-axis direction, and is the projection of the unit vector in the z-axis direction at the n-th pulse excitation;

[0110] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the x-axis direction;

[0111] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the y-axis direction;

[0112] The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointed in the z-axis direction.

[0113] In the Na-23 ultrashort echo time pulse sequence module of this embodiment, the Na-23 encoding gradient undergoes a spatial rotation after each pulse excitation. This spatial rotation is achieved by the k-space coordinate values on the three-dimensional sphere generated by the spherical Fibonacci grid. One k-space coordinate value on the three-dimensional sphere corresponds to a unit vector in the k-space direction of the Na-23 encoding gradient. The total number of k-space coordinate values on the three-dimensional sphere is equal to the total number of excitations Ns.

[0114] Then, the unit vector projection y in the y-axis direction during the nth pulse excitation is n The calculation is based on the following formula:

[0115] yn =1-2(n-1) / (Ns-1)

[0116] The unit vector projection x in the x-axis direction during the nth pulse excitation n The calculation is based on the following formula:

[0117]

[0118] The unit vector projection z in the z-axis direction during the nth pulse excitation n The calculation is based on the following formula:

[0119]

[0120] In step 4.3, the measured spokes of Ns excitations together constitute the measured Na-23 sampling trajectory in the complete k-space.

[0121] Step 5: Na-23 image reconstruction

[0122] The measured Na-23 sampling trajectory of the Na-23 sampling signal obtained in step 4 and the corresponding Na-23 sampling signal are input into the three-dimensional non-uniform Fourier transform function (i.e., nufft3d function) for image reconstruction, thereby obtaining the Na-23 reconstructed image of the sample corresponding to the measured Na-23 sampling trajectory. For comparison, the Na-23 sampling signal and the theoretical sampling trajectory are input into the three-dimensional non-uniform Fourier transform (nufft3d) function for image reconstruction, and the Na-23 reconstructed image reconstructed based on the theoretical sampling trajectory is obtained, as shown in FIG. Figure 5 As shown in Figure 2, it can be seen that the reconstruction artifacts of the Na-23 reconstructed image based on the true sampling trajectory are significantly reduced.

[0123] It should be noted that the embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory, characterized in that: The following steps are involved: Step 1: Design a pulse sequence, which includes an H-1 navigation echo module and a Na-23 ultra-short echo time pulse sequence module. Step 2: Scan and sample the test object based on the designed pulse sequence, and obtain the H-1 sampling signal corresponding to the H-1 navigation echo module and the Na-23 sampling signal corresponding to the Na-23 ultra-short echo time pulse sequence module in sequence; Step 3: reconstruct the actual k-space sampling trajectory corresponding to the H-1 sampling signal to obtain the measured H-1 sampling trajectory; Step 4: Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory, the k-space sampling trajectory corresponding to the Na-23 sampling signal is reconstructed to obtain the measured Na-23 sampling trajectory; Step 5: Reconstruct the Na-23 sampling signal based on the measured Na-23 sampling trajectory to obtain a Na-23 reconstructed image.

2. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 1, characterized in that: The Na-23 ultrashort echo time pulse sequence module includes Ns Na-23 excitation sampling units, the number of excitations Ns ≥ 2, each Na-23 excitation sampling unit sequentially realizes Na-23 signal excitation and Na-23 signal sampling, and during the Na-23 signal sampling, a Na-23 encoding gradient is simultaneously applied and an analog-to-digital converter ADC for Na-23 signal sampling is turned on.

3. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 2, characterized in that: The H-1 navigator echo module includes a plurality of slice selection excitation sampling units in sequence, each slice selection excitation sampling unit corresponds to a k-space coordinate axis direction, and the k-space coordinate axis directions corresponding to different slice selection excitation sampling units are perpendicular to each other; In each layer selection excitation sampling unit, an H-1 excitation pulse and a layer selection gradient are first applied simultaneously; then the layer selection refocusing gradient is applied. After the layer selection refocusing gradient is completed, the H-1 encoding gradient is applied simultaneously and the analog-to-digital converter ADC for H-1 signal sampling is turned on; The H-1 encoding gradient, slice selection gradient, and slice selection refocusing gradient in the same slice selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 encoding gradient is the same as the Na-23 encoding gradient when pointing to the same k-space coordinate axis direction.

4. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 2, characterized in that: The preset k-space sampling trajectory corresponding to the Na-23 ultrashort echo time pulse sequence module is recorded as a preset Na-23 sampling trajectory, and the k value of the sampling point in the preset Na-23 sampling trajectory meets the following requirements: The preset Na-23 sampling trajectory is a straight radial trajectory from the center to the periphery in the three-dimensional k-space; The k value of the sampling point in the preset Na-23 sampling trajectory is proportional to the integral of the Na-23 encoding gradient in the same k-space direction over time. The Na-23 signal sampling after a pulse excitation corresponds to a spoke in the preset Na-23 sampling trajectory, and the corresponding Na-23 encoding gradient has a different direction. The Na-23 signal is collected in the entire k-space through multiple pulse excitations and spatial encoding of the encoding gradient. The steps for setting the k-space direction of the Na-23 encoding gradient are as follows: Determine the encoding gradient corresponding to the preset Na-23 sampling trajectory when it is completely along a k-space coordinate axis direction; Then, a k-space coordinate value on a three-dimensional sphere is generated through a Fibonacci grid. A k-space coordinate value on the three-dimensional sphere corresponds to the k-space direction of the Na-23 encoding gradient during the pulse excitation of a Na-23 excitation pulse.

5. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 3, characterized in that: The step 3 specifically includes the following steps: Step 3.1, extract the phase value of the H-1 sampling signal at each sampling time point; Step 3.2: Deconvolution is performed on the phase value to obtain the deconvolution phase value at each sampling time point. The variation of the deconvolution phase value with sampling time is recorded as Step 3.3: Changes of the deconvolution phase value corresponding to each k-space coordinate axis direction with sampling time The corresponding actual H-1 sampling trajectory is reconstructed to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis.

6. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 5, characterized in that: The step 3.3 specifically includes the following steps: The trajectory of H-1 sampling trajectory is reconstructed based on the following objective function and constraints: s.t.-γ H ·G s ·T p / 2≤k enc (t)≤γ H ·G s ·T p / 2 k enc represents the k value of the H-1 sampling trajectory; k enc (t) represents the change of k value of H-1 sampling trajectory with sampling time, which is the quantity to be calculated; It's about k enc The numerical minimization function, st represents the constraint condition of the objective function, abs represents the absolute value, L w is the thickness of the layer selected for excitation by the H-1 excitation pulse, G s is the intensity of the layer selection gradient, T p is the duration of the H-1 excitation pulse, L off is the bias distance of the H-1 excitation pulse selection layer, γ H is the gyromagnetic ratio of H-1; t is the duration of the encoding gradient during sampling.

7. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 2, characterized in that: The step 4 specifically includes the following steps: Step 4.

1. Based on the gyromagnetic ratio of Na-23, the gyromagnetic ratio of H-1, and the measured H-1 sampling trajectory in each k-space coordinate axis direction, calculate the k value of the measured Na-23 sampling trajectory corresponding to each k-space coordinate axis when the Na-23 encoding gradient is completely pointed in the direction of each k-space coordinate axis according to the following formula: Among them, γ Na is the gyromagnetic ratio of Na-23, The k value represents the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely directed toward the k-space coordinate axis M. The k-space coordinate axis M∈{x-axis direction, y-axis direction, z-axis direction}, where the x-axis direction, y-axis direction, and z-axis direction are mutually perpendicular to each other. represents the k value of the H-1 sampling trajectory in the k-space coordinate axis direction M; Step 4.2: Based on the k-values of the measured Na-23 sampling trajectories corresponding to the Na-23 encoding gradients fully pointing in the directions of the k-space coordinate axes, the k-values of the measured spokes corresponding to each pulse excitation and spatial encoding are calculated using the following formula: Among them, k n (t) represents the k-space trajectory corresponding to the n-th spatial encoding, 1≤n≤Ns; k n (t) is the k value of the measured spoke corresponding to the nth pulse excitation and spatial encoding, 1≤n≤Ns; x n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the x-axis direction, denoted as the unit vector projection in the x-axis direction at the n-th pulse excitation; y n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the y-axis direction, denoted as the unit vector projection in the y-axis direction at the n-th pulse excitation; z n is the projection of the unit vector in the k-space direction corresponding to the Na-23 encoding gradient at the n-th pulse excitation on the z-axis direction, and is the projection of the unit vector in the z-axis direction at the n-th pulse excitation; The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the x-axis direction; The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointing in the y-axis direction; The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely pointed in the z-axis direction; In step 4.3, the measured spokes of Ns excitations together constitute the measured Na-23 sampling trajectory in the complete k-space.

8. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 7, characterized in that: The unit vector projection y in the y-axis direction during the n-th pulse excitation n The calculation is based on the following formula: y n =1-2(n-1) / (Ns-1) The unit vector projection x in the x-axis direction during the nth pulse excitation n The calculation is based on the following formula: The unit vector projection z in the z-axis direction during the nth pulse excitation n The calculation is based on the following formula:

9. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 2, characterized in that: The step 5 specifically includes the following steps: The measured Na-23 sampling trajectory and the corresponding Na-23 sampling signal are input into a three-dimensional non-uniform Fourier transform function for image reconstruction to obtain a Na-23 reconstructed image based on the measured Na-23 sampling trajectory.

10. The method for navigating a Na-23 MRI pulse sequence using an H-1 sampling trajectory according to claim 2, characterized in that: The Na-23 excitation pulse is a rectangular pulse, and the H-1 excitation pulse is a swept frequency pulse.

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