H-1 sampling trajectory navigation method for Na-23 MRI pulse sequences

Abstract

This invention discloses a method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory. The method involves designing a pulse sequence that sequentially includes an H-1 navigation echo module and a Na-23 ultrashort echo time pulse sequence module. The measured H-1 sampling trajectory is reconstructed using the H-1 sampling signal corresponding to the H-1 navigation echo module, thereby obtaining the measured Na-23 sampling trajectory. Finally, the Na-23 sampling signal is reconstructed based on the measured Na-23 sampling trajectory to obtain a reconstructed Na-23 image. This invention can significantly reduce Na-23 image reconstruction artifacts and optimize image quality.

Description

Technical Field

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

[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 tissues, acquire their magnetic resonance signals, and reconstruct high-resolution images using computers.

[0003] Currently, magnetic resonance imaging (MRI) is primarily based on proton (H-1) signals. 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 nuclide with the highest detection sensitivity in vivo. Sodium (Na-23) is the second most abundant magnetic resonance-detectable nucleus in the human body after H-1, and its magnetic resonance 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 relatively low gyromagnetic ratio (11.232 MHz), and a tissue concentration (on the order of 10 millimoles) far lower than that of H-1. Therefore, sodium (Na-23) MRI generally employs an ultrashort echo time design based on non-Cartesian sampling. In non-Cartesian sampling methods, gradient delay and eddy current effects of the encoded gradient significantly affect image reconstruction results, producing severe image reconstruction artifacts.

[0004] By measuring the k-space sampling trajectory corresponding to the measured coded gradient, the sampling signal is filled into the k-space according to the measured sampling trajectory, which can eliminate the reconstruction artifacts caused by gradient delay and eddy current effect, and significantly improve 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 slice measurement method and related improvement 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 spatiotemporal coding proposed by Zhou et al. [A magnetic resonance k-space trajectory measurement method based on spatiotemporal 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 sodium Na-23 signal. Therefore, the sodium Na-23 pulse sequence method based on non-Cartesian sampling cannot currently directly obtain the k-space sampling trajectory information of sodium Na-23. 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 this invention is to address the problems existing in the prior art by providing a method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory information. This method utilizes H-1 navigation echo information to achieve k-space trajectory measurement of Na-23 pulse sequences, thereby reducing artifacts in Na-23 image reconstruction.

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

[0007] The method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectories includes the following steps:

[0008] Step 1: Design the pulse sequence, which includes the H-1 navigation echo module and the Na-23 ultra-short echo time pulse sequence module in sequence;

[0009] Step 2: Scan and sample the test object based on the designed pulse sequence to 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, reconstruct the k-space sampling trajectory corresponding to the Na-23 sampling signal to obtain the measured Na-23 sampling trajectory.

[0012] Step 5: Based on the measured Na-23 sampling trajectory, perform image reconstruction on the Na-23 sampling signal to obtain the Na-23 reconstructed image.

[0013] As described above, the Na-23 ultrashort echo time pulse sequence module includes Ns Na-23 excitation sampling units, with Ns≥2 excitation times. Each Na-23 excitation sampling unit sequentially performs Na-23 signal excitation and Na-23 signal sampling. During Na-23 signal sampling, the Na-23 encoding gradient and the analog-to-digital converter (ADC) that enables Na-23 signal sampling are applied simultaneously.

[0014] As described above, the H-1 navigation echo module includes multiple layer-selective excitation sampling units, each of which corresponds to a k-space coordinate axis direction. The k-space coordinate axis directions corresponding to different layer-selective excitation sampling units are perpendicular to each other.

[0015] Within each selected layer excitation sampling unit, an H-1 excitation pulse and a selected layer gradient are applied simultaneously; then, a selected layer refocusing gradient is applied; after the selected layer refocusing gradient ends, an H-1 encoding gradient and an analog-to-digital converter (ADC) that enables H-1 signal sampling are applied simultaneously.

[0016] The H-1 coding gradient, layer selection gradient, and layer re-aggregation gradient within the same layer selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 coding gradient and the Na-23 coding gradient pointing to the same k-space coordinate axis direction are the same.

[0017] As described above, the preset k-space sampling trajectory corresponding to the Na-23 ultrashort echo time pulse sequence module is denoted 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 radiates outwards in a straight line from the center in three-dimensional k-space;

[0019] The k-value of a 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. Each Na-23 signal sampled after a single pulse excitation corresponds to a spoke in the preset Na-23 sampling trajectory, and the directions of the corresponding Na-23 encoding gradients are all different. The acquisition of Na-23 signals in the entire k-space is achieved through multiple pulse excitations and spatial encoding of the encoding gradients. 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;

[0021] Then, k-space coordinates on a three-dimensional sphere are generated using a Fibonacci grid. A k-space coordinate on a 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] As described above, step 3 specifically includes the following steps:

[0023] Step 3.1: Extract the phase value of the H-1 sampled signal at each sampling time point;

[0024] Step 3.2: Deconvolve the phase values ​​to obtain the deconvoluted phase values ​​at each sampling time point. The change of the deconvoluted phase value with sampling time is denoted as...

[0025] Step 3.3: The change of the deconvoluted phase value with sampling time based on the directions of each k-space coordinate axis. Trajectory reconstruction is performed on the corresponding actual H-1 sampling trajectory to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis.

[0026] As described above, step 3.3 specifically includes the following steps:

[0027] Trajectory reconstruction of the H-1 sampled trajectory is performed 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 The k value represents the H-1 sampling trajectory; k enc (t) represents the change of the k value of the H-1 sampling trajectory with the sampling time, which is a quantity to be calculated; It's about k enc The numerical minimization function, where st represents the constraints on the objective function, abs represents the absolute value, and L... w G represents the layer thickness for H-1 excitation pulse selective excitation. s T represents the intensity of the gradient at each selected layer. p L is the duration of the H-1 excitation pulse. offThe offset distance for H-1 excitation pulse selection, γ H t is the gyromagnetic ratio of H-1; t is the duration of the encoded gradient during sampling.

[0031] As described above, 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 trajectories along each k-space coordinate axis, calculate the k-values ​​of the measured Na-23 sampling trajectories corresponding to when the Na-23 encoding gradient is completely aligned with each k-space coordinate axis according to the following formula:

[0033]

[0034] Where, γ Na The gyromagnetic ratio of Na-23 The value of k represents the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with 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 k-space coordinate axis directions. The k value represents the H-1 sampling trajectory along the direction M of the k-space coordinate axis;

[0035] Step 4.2: Based on the measured k values ​​of the Na-23 sampling trajectories corresponding to each k spatial coordinate axis when the Na-23 encoding gradient is completely aligned, calculate the measured k values ​​of the spokes corresponding to each pulse excitation and spatial encoding using the following formula:

[0036]

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

[0038] x n It is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the x-axis direction during the nth pulse excitation, denoted as the unit vector projection in the x-axis direction during the nth pulse excitation;

[0039] y n It is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the y-axis direction during the nth pulse excitation, denoted as the unit vector projection in the y-axis direction during the nth pulse excitation;

[0040] z nIt is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the z-axis direction during the nth pulse excitation, and the projection of the unit vector in the z-axis direction during the nth pulse excitation.

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

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

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

[0044] Step 4.3 and the measured spokes of Ns excitations together form the measured Na-23 sampling trajectory in the complete k-space.

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

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

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

[0048]

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

[0050]

[0051] As described 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, resulting in 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 existing methods, the present invention has the following advantages:

[0055] A method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory guidance includes an H-1 navigation echo module and a Na-23 ultrashort echo time pulse sequence module. The H-1 navigation echo module obtains the measured Na-23 sampling trajectory, while the Na-23 ultrashort echo time pulse sequence module acquires three-dimensional Na-23 image data. Using the measured Na-23 sampling trajectory for image reconstruction significantly reduces Na-23 image reconstruction artifacts. Simultaneously, three-dimensional data acquisition based on ultrashort echo time helps reduce signal attenuation due to T2 / T2* relaxation time, improving the imaging signal-to-noise ratio and optimizing image quality. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method of the present invention.

[0057] Figure 2 This is a pulse sequence diagram designed by the method of this invention. Here, Ns represents the number of excitations. The Na-23 coding gradient has components in the x-axis, y-axis, and z-axis directions. If the Na-23 coding gradient points completely to a certain k-space coordinate axis, then only the component of the Na-23 coding gradient in that k-space coordinate axis direction is non-zero. If the components of the Na-23 coding gradient in the x-axis, y-axis, and z-axis directions are all non-zero, then the amplitude in these three directions is relatively small. Figure 2 The solid line represents the Na-23 coding gradient curve.

[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 this 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 this invention.

[0060] Figure 5 This is a comparison between the image of the actual trajectory reconstructed by the method of the present invention and the image of the theoretical trajectory reconstructed. Detailed Implementation

[0061] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. The embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0062] Example 1:

[0063] The method of H-1 sampling trajectory navigation for Na-23 MRI pulse sequences, such as Figure 1 As shown, it includes the following steps:

[0064] Step 1: Design the pulse sequence

[0065] Pulse sequences such as Figure 2 As shown, the system comprises, in sequence, an H-1 navigation echo module and a Na-23 ultrashort echo time pulse sequence module. The H-1 navigation echo module is applied before the Na-23 ultrashort echo time pulse sequence module. The H-1 navigation echo module is used to acquire the measured sampling trajectory, while the Na-23 ultrashort echo time pulse sequence module is used for Na-23 data sampling. The design rules for the H-1 navigation echo module and the Na-23 ultrashort echo time pulse sequence module are as follows:

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

[0067] The Na-23 ultrashort echo time pulse sequence module includes Ns Na-23 excitation sampling units. One pulse excitation is performed in each Na-23 excitation sampling unit, with the number of excitations Ns≥2. Each Na-23 excitation sampling unit sequentially performs Na-23 signal excitation and Na-23 signal sampling. During Na-23 signal excitation, a Na-23 excitation pulse is applied. During Na-23 signal sampling, a Na-23 encoding gradient and an analog-to-digital converter (ADC) that enables Na-23 signal sampling are simultaneously applied. The preset k-space sampling trajectory corresponding to the Na-23 ultrashort echo time pulse sequence module is denoted as the preset Na-23 sampling trajectory. In this embodiment, the k-value of the sampling point in the preset Na-23 sampling trajectory satisfies the following requirements:

[0068] The preset Na-23 sampling trajectory points from the center outwards in three-dimensional k-space, specifically radiating outwards in a straight line. Therefore, the Na-23 encoding gradient has components in the x, y, and z axes. Furthermore, the k-value of each sampling point in the preset Na-23 sampling trajectory is proportional to the integral of the Na-23 encoding gradient over time in the same k-space direction. Each pulse excitation of the Na-23 signal corresponds to a spoke in the preset Na-23 sampling trajectory (i.e., the direction of the Na-23 encoding gradient is different for each Na-23 signal sampling). By using multiple pulse excitations and spatial encoding of the encoding gradient, the Na-23 signal is acquired throughout the entire k-space. 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 being completely along a k-space coordinate axis (the three-dimensional k-space coordinate axis includes the x-axis, y-axis, and z-axis; in this embodiment, the x-axis is chosen). In this embodiment, the Na-23 encoding gradient used is the encoding gradient corresponding to the density-adapted radial sampling trajectory, such as... Figure 3 As shown;

[0070] Then, k-space coordinates on a three-dimensional sphere are generated using a spherical Fibonacci grid. Each k-space coordinate corresponds to the k-space direction of the Na-23 encoding gradient during a single Na-23 signal sampling. The k-space directions of the Na-23 encoding gradient differ in 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, and a single Na-23 k-space sampling data point is sampled. This single Na-23 k-space sampling data point 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 across the entire three-dimensional k-space through multiple pulse excitations, sampling, and direction changes.

[0071] (2) H-1 navigation echo module

[0072] To obtain the actual k-space sampling trajectory of Na-23, an H-1 navigation echo module is set in front of the Na-23 ultrashort echo time pulse sequence module. The H-1 navigation echo module includes multiple layer-selective excitation sampling units, each of which corresponds to a k-space coordinate axis direction. The k-space coordinate axis directions corresponding to different layer-selective excitation sampling units are perpendicular to each other. In this embodiment, three layer-selective excitation sampling units are set.

[0073] Within each selected layer excitation sampling unit, an H-1 excitation pulse and the corresponding k-space coordinate axis direction are applied simultaneously; then, a selected layer refocusing gradient is applied, the area of ​​which is half the area of ​​the selected layer gradient; after the selected layer refocusing gradient ends, an H-1 encoding gradient and an analog-to-digital converter (ADC) that enables H-1 signal sampling are applied simultaneously.

[0074] The H-1 coding gradient, layer selection gradient, and layer re-aggregation gradient within the same layer selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 coding gradient and the Na-23 coding gradient pointing to the same k-space coordinate axis direction are the same.

[0075] The H-1 navigation echo module utilizes layer-selective gradients to sequentially excite and sample along the three k-space coordinate axes (x-axis, y-axis, and z-axis). Using the spatiotemporal coding principle of the H-1 excitation pulse, the module measures the k-space sampling trajectory of H-1 along the x-axis, y-axis, and z-axis, obtaining the measured H-1 sampling trajectory. This yields the components of the measured Na-23 sampling trajectory along the three k-space coordinate axes. Furthermore, the measured Na-23 sampling trajectory is calculated from the measured H-1 sampling trajectory and used 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 Na-23 excitation sampling unit sequentially performs Na-23 signal excitation and Na-23 signal sampling. The Na-23 excitation pulse is a rectangular pulse. After the Na-23 excitation pulse ends, the three-dimensional Na-23 encoding gradient (i.e., the Na-23 encoding gradient includes components in the x-axis, y-axis, and z-axis directions) is immediately and simultaneously activated for spatial encoding of the signal. At the same time, the analog-to-digital converter (ADC) for Na-23 signal sampling is also activated. Then, the Na-23 encoding gradient and the ADC for Na-23 signal sampling are simultaneously deactivated. At this time, the echo time TE is half the duration 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 values ​​on the three-dimensional sphere generated by the Fibonacci grid.

[0077] In this embodiment, each layer-selection excitation sampling unit in the H-1 navigation echo module first synchronously applies an H-1 excitation pulse (in this embodiment, the H-1 excitation pulse is a swept-frequency pulse) and a layer-selection gradient in the corresponding k-space coordinate axis direction, and then applies a layer-selection refocusing gradient, wherein the area of ​​the layer-selection refocusing gradient is half the area of ​​the layer-selection gradient; after the layer-selection refocusing gradient ends, an H-1 encoding gradient in the same k-space coordinate axis direction is applied once. The H-1 encoding gradient is the same as the Na-23 encoding gradient pointing in the same k-space coordinate axis direction, so as to calculate the measured Na-23 sampling trajectory and use it for image reconstruction of the subsequent Na-23 sampling signal. Taking the x-axis direction as an example, firstly, an H-1 excitation pulse and a layer-selective gradient in the x-axis direction are applied simultaneously (the analog-to-digital converter (ADC) for H-1 signal sampling and the H-1 encoding gradient are simultaneously turned on and off) for selective excitation and phase modulation of the H-1 signal; then, a layer-selective refocusing gradient in the x-axis direction is applied, where the area of ​​the layer-selective refocusing gradient is half the area of ​​the layer-selective gradient; after the layer-selective refocusing gradient ends, 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 pointing in the x-axis direction; when the H-1 signal is sampled... The analog-to-digital converter (ADC) is turned on and off synchronously with the H-1 coding gradient once, which is equivalent to one sampling. For the layer selection excitation sampling units in the y-axis and z-axis directions 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 directions of the corresponding layer selection gradient, layer refocusing gradient, and H-1 coding gradient are adjusted to the y-axis or z-axis direction. The H-1 coding gradient, the ADC for H-1 signal sampling, and the ADC for H-1 signal sampling are also turned on and off synchronously.

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

[0079] In this embodiment, the sample is scanned and sampled based on the pulse sequence designed in step 1, and the H-1 sampling signal corresponding to the H-1 navigation echo module and the Na-23 sampling signal corresponding to the Na-23 ultrashort echo time pulse sequence module are obtained in sequence.

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

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

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

[0083] Trajectory reconstruction is performed on the actual k-space sampling trajectory corresponding to the H-1 sampling signal to obtain the measured H-1 sampling trajectory. Since the H-1 navigation echo module of the pulse sequence in this embodiment uses H-1 encoded gradients in the x, y, and z k-space coordinate axes respectively during sampling, the measured H-1 sampling trajectory includes k-space sampling trajectories in three k-space coordinate axis directions (i.e., x-axis, y-axis, and z-axis). 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 sampled signal at each sampling time point;

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

[0086] Step 3.2: Deconvolve the phase values ​​to obtain the deconvoluted phase values ​​at each sampling time point;

[0087] Phase wrapping occurs when the phase value exceeds 2π. In this embodiment, the phase value of the H-1 sampled signal is further dewrapped using MATLAB's unwrap function to obtain the dewrapped phase value at each sampling time point; the dewrapped phase value is denoted as... The change in phase value after de-folding with sampling time is denoted as .

[0088] Step 3.3: The change of the deconvoluted phase value with sampling time based on the directions of each k-space coordinate axis. Trajectory reconstruction is performed on the corresponding actual H-1 sampling trajectory to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis.

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

[0090]

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

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

[0093]

[0094] Among them, L w G represents the layer thickness for H-1 excitation pulse selective excitation. s T represents the intensity of the gradient at each selected layer. p L is the duration of the H-1 excitation pulse. off The offset distance for H-1 excitation pulse selection is given. Based on this formula, this embodiment uses MATLAB's univariate minimization function (fminbnd function) to calculate the corresponding H-1 sampling trajectory value k based on the deconvoluted phase value of the H-1 sampling signal. enc This yields the measured H-1 sampling trajectory. Specifically, for each k-space coordinate axis direction, based on the following objective function and constraints, the k value of the corresponding H-1 sampling trajectory is calculated:

[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 is defined by `st`, where `st` represents the constraints of the objective function, and `abs` represents the absolute value. Based on the above objective function and constraints, the change in phase value after deconvolution with sampling time is considered. Calculate the change of the k value of the H-1 sampling trajectory over time. enc(t), thus reconstructing the measured H-1 sampling trajectory.

[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 trajectories along each k-space coordinate axis, 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 trajectories along each k-space coordinate axis, obtain the k values ​​of the measured Na-23 sampling trajectories corresponding to when the Na-23 encoding gradient is completely pointed to each k-space coordinate axis. The specific process is as follows:

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

[0102]

[0103] Where, γ Na The gyromagnetic ratio of Na-23 This represents the value of k in the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with the k-space coordinate axis direction M. The k-space coordinate axis direction M ∈ {x-axis direction, y-axis direction, z-axis direction}, where the x-axis, y-axis, and z-axis directions are mutually perpendicular k-space coordinate axis directions. The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with the x-axis direction. The k value of the measured Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with the y-axis direction. The measured k value of the Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with the z-axis direction; The value of k represents the H-1 sampling trajectory along the direction M of the k-space coordinate axis. A comparison between the measured Na-23 sampling trajectory and the theoretical Na-23 sampling trajectory is shown below. Figure 4 As shown, 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 measured k values ​​of the Na-23 sampling trajectories corresponding to each k spatial coordinate axis when the Na-23 encoding gradient is completely aligned, calculate the measured k values ​​of the spokes corresponding to each pulse excitation and spatial encoding using the following formula:

[0105]

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

[0107] x n It is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the x-axis direction during the nth pulse excitation, denoted as the unit vector projection in the x-axis direction during the nth pulse excitation;

[0108] y n It is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the y-axis direction during the nth pulse excitation, denoted as the unit vector projection in the y-axis direction during the nth pulse excitation;

[0109] z n It is the projection of the unit vector in the k-space direction representing the corresponding Na-23 coding gradient in the z-axis direction during the nth pulse excitation, and the projection of the unit vector in the z-axis direction during the nth pulse excitation.

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

[0111] The measured k value of the Na-23 sampling trajectory when the Na-23 encoding gradient is completely aligned with 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 of 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 along the y-axis direction during the nth pulse excitation... n The calculation is based on the following formula:

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

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

[0117]

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

[0119]

[0120] Step 4.3 and the measured spokes of Ns excitations together form 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, along with the corresponding Na-23 sampling signal, is input into a three-dimensional non-uniform Fourier transform function (i.e., the nufft3d function) for image reconstruction, thereby obtaining the Na-23 reconstructed image of the sample based on the measured Na-23 sampling trajectory. For comparison, the Na-23 sampling signal and the theoretical sampling trajectory are input into a three-dimensional non-uniform Fourier transform (nufft3d) function for image reconstruction, obtaining a Na-23 reconstructed image based on the theoretical sampling trajectory, as shown below. Figure 5 As shown, the reconstruction artifacts in the Na-23 reconstructed image based on the real sampling trajectory are significantly reduced.

[0123] It should be noted that the embodiments described in this invention are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains can make various modifications or additions to the described embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectories, characterized in that, Includes the following steps: Step 1: Design the pulse sequence, which includes the H-1 navigation echo module and the Na-23 ultra-short echo time pulse sequence module in sequence; Step 2: Scan and sample the test object based on the designed pulse sequence to 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, reconstruct the k-space sampling trajectory corresponding to the Na-23 sampling signal to obtain the measured Na-23 sampling trajectory. Step 5: Based on the measured Na-23 sampling trajectory, perform image reconstruction on the Na-23 sampling signal to obtain the Na-23 reconstructed image; The Na-23 ultrashort echo time pulse sequence module includes Ns Na-23 excitation sampling units, with Ns≥2 excitation times. Each Na-23 excitation sampling unit sequentially performs Na-23 signal excitation and Na-23 signal sampling. During Na-23 signal sampling, Na-23 encoding gradient and analog-to-digital converter (ADC) that enables Na-23 signal sampling are applied simultaneously. Step 3 specifically includes the following steps: Step 3.1: Extract the phase value of the H-1 sampled signal at each sampling time point; Step 3.2: Deconvolve the phase values ​​to obtain the deconvoluted phase values ​​at each sampling time point. The change of the deconvoluted phase value with sampling time is denoted as... ; Step 3.3: The change of the deconvoluted phase value with sampling time based on the directions of each k-space coordinate axis. Trajectory reconstruction is performed on the corresponding actual H-1 sampling trajectory to obtain the measured H-1 sampling trajectory in the direction of the corresponding k-space coordinate axis; Step 3.3 specifically includes the following steps: Trajectory reconstruction of the H-1 sampled trajectory is performed based on the following objective function and constraints: The k value represents the H-1 sampling trajectory; The value of k representing the H-1 sampling trajectory varies with sampling time and is a quantity to be calculated. It is about The numerical minimization function, The constraints represent the objective function. Represents absolute value. The layer thickness for H-1 excitation pulse selective excitation. The strength of the gradient for the selected layer, The duration of the H-1 excitation pulse. The offset distance for H-1 excitation pulse selection. The gyromagnetic ratio of H-1; The duration of the encoded gradient during sampling; 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 trajectories along each k-space coordinate axis, calculate the k-values ​​of the measured Na-23 sampling trajectories corresponding to when the Na-23 encoding gradient is completely aligned with each k-space coordinate axis according to the following formula: in, The gyromagnetic ratio of Na-23 This indicates that the Na-23 encoding gradient is completely aligned with the k-space coordinate axis. The k value of the measured Na-23 sampling trajectory, where the k-space coordinate axis direction M∈ , Axial direction, Axial direction and The axes are perpendicular to each other in the k-space coordinate system. The k value represents the H-1 sampling trajectory along the direction M of the k-space coordinate axis; Step 4.2: Based on the measured k values ​​of the Na-23 sampling trajectories corresponding to each k spatial coordinate axis when the Na-23 encoding gradient is completely aligned, calculate the measured k values ​​of the spokes corresponding to each pulse excitation and spatial encoding using the following formula: in, This represents the k-space trajectory corresponding to the nth spatial encoding, where 1 ≤ n ≤ Ns; Let k be the measured value of the spokes corresponding to the nth pulse excitation and spatial encoding, where 1 ≤ n ≤ Ns; It is the unit vector in the k-space direction representing the corresponding Na-23 encoding gradient during the nth pulse excitation. The projection along the axial direction is denoted as the projection during the nth pulse excitation. Projection of a unit vector along an axis; It is the unit vector in the k-space direction representing the corresponding Na-23 encoding gradient during the nth pulse excitation. The projection along the axial direction is denoted as the projection during the nth pulse excitation. Projection of a unit vector along an axis; It is the unit vector in the k-space direction representing the corresponding Na-23 encoding gradient during the nth pulse excitation. Projection along the axial direction, during the nth pulse excitation Projection of a unit vector along an axis; The gradient for encoding Na-23 is completely aligned. The k value of the measured Na-23 sampling trajectory in the axial direction; The gradient for encoding Na-23 is completely aligned. The k value of the measured Na-23 sampling trajectory in the axial direction; The gradient for encoding Na-23 is completely aligned. The k value of the measured Na-23 sampling trajectory in the axial direction; Step 4.3 and the measured spokes of Ns excitations together form the measured Na-23 sampling trajectory in the complete k-space.

2. The method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory according to claim 1, characterized in that, The H-1 navigation echo module includes multiple layer-selective excitation sampling units, each of which corresponds to a k-space coordinate axis direction. The k-space coordinate axis directions corresponding to different layer-selective excitation sampling units are perpendicular to each other. Within each selected layer excitation sampling unit, an H-1 excitation pulse and a selected layer gradient are applied simultaneously; then, a selected layer refocusing gradient is applied; after the selected layer refocusing gradient ends, an H-1 encoding gradient and an analog-to-digital converter (ADC) that enables H-1 signal sampling are applied simultaneously. The H-1 coding gradient, layer selection gradient, and layer re-aggregation gradient within the same layer selection excitation sampling unit all point to the same k-space coordinate axis direction. The H-1 coding gradient and the Na-23 coding gradient pointing to the same k-space coordinate axis direction are the same.

3. The method for navigating Na-23 MRI pulse sequences using 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 denoted 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: The preset Na-23 sampling trajectory radiates outwards in a straight line from the center in three-dimensional k-space; The k-value of a 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. Each Na-23 signal sampled after a single pulse excitation corresponds to a spoke in the preset Na-23 sampling trajectory, and the directions of the corresponding Na-23 encoding gradients are all different. The acquisition of Na-23 signals in the entire k-space is achieved through multiple pulse excitations and spatial encoding of the encoding gradients. 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; Then, k-space coordinates on a three-dimensional sphere are generated using a Fibonacci grid. A k-space coordinate on a 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.

4. The method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory according to claim 1, characterized in that, During the nth pulse excitation Unit vector projection along the axis The calculation is based on the following formula: During the nth pulse excitation Unit vector projection along the axis The calculation is based on the following formula: During the nth pulse excitation Unit vector projection along the axis The calculation is based on the following formula: 。 5. The method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory according to claim 2, characterized in that, Step 1 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, resulting in a Na-23 reconstructed image based on the measured Na-23 sampling trajectory.

6. The method for navigating Na-23 MRI pulse sequences using H-1 sampling trajectory according to claim 1, 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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