Na-23 density-adapted multi-echo pulse sequence design and method of use

Abstract

The application discloses a density self-adaptive multi-echo pulse sequence design and use method of Na-23, designs a Na-23 density self-adaptive multi-echo pulse sequence, and performs nuclear magnetic resonance scanning, obtains sampling data, image reconstruction and T2* relaxation curve fitting, and the Na-23 density self-adaptive multi-echo pulse sequence comprises a plurality of multi-echo pulse sub-sequences in sequence, each multi-echo pulse sub-sequence comprises a Na-23 excitation pulse and a return unit in sequence, each return unit comprises components of three axis direction encoding gradients which are synchronously turned on; the signal of Na-23 is collected in the whole k space corresponding to each return unit; and the encoding gradient comprises a density self-adaptive encoding gradient unit and a gradient compensation unit in sequence. The application can disperse motion artifacts and background noise, improve the signal-to-noise ratio SNR, reduce aliasing artifacts, improve image resolution and finely fit the T2* relaxation curve.

Description

Technical Field

[0001] This invention belongs to the field of Na-23 magnetic resonance imaging (MRI) methods, and specifically relates to the design and use of density-adaptive multi-echo pulse sequences for Na-23, enabling fine fitting of T2* relaxation curves in Na-containing tissue MRI. This invention can be used for high signal-to-noise ratio, high-quality Na-23 MRI and fine fitting of T2 relaxation curves in Na-containing tissue, achieving information acquisition and related quantitative studies of Na-containing tissue. Background Technology

[0002] Sodium (Na-23), as the most abundant monovalent cation in living organisms, is used in magnetic resonance imaging (MRI) for non-invasive detection of intracellular and extracellular sodium ion distribution and dynamic balance, providing a unique visualization tool for studying tissue metabolic abnormalities, pathological changes, and functional states. Compared to conventional proton (H-1) MRI, Na-23 MRI faces several technical challenges: its gyromagnetic ratio is only 11.232 MHz (approximately 26.5% of H-1), and its physiological concentration in tissues is in the range of 10-100 mmol / L (4-5 orders of magnitude lower than H-1). These characteristics lead to a dual dilemma of limited signal-to-noise ratio (SNR) and increased motion sensitivity in traditional imaging sequences. Furthermore, Na-23, as a quadrupole nucleus, exhibits complex double-exponential relaxation characteristics (T2 and T2* are both <40 ms), requiring the acquisition of different echo times. The echo signal is used to distinguish signals from different sodium sources.

[0003] To address the aforementioned technical bottlenecks, current Na-23 magnetic resonance imaging (MRI) commonly employs ultrashort echo time (UTE) and multiple gradient echo (MGRE) sequence designs. This approach acquires echo signals from multiple echo times within a single repetition time (TR), covering the entire T2* decay range of sodium. However, due to the inherent limitation of signal-to-noise ratio (SNR), this method often requires multiple signal averaging operations for compensation, significantly extending the scan time. Furthermore, this approach acquires fewer signal points and struggles to separate parameters such as T1 and T2, resulting in significant disadvantages in quantitative studies such as relaxation analysis and multi-parameter analysis. Summary of the Invention

[0004] To address the aforementioned problems in the prior art, this invention proposes a method for designing and using density-adaptive multi-echo pulse sequences for Na-23.

[0005] The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions:

[0006] The method for designing density-adaptive multi-echo pulse sequences for Na-23 includes the following steps:

[0007] The Na-23 density-adaptive multi-echo pulse sequence sequentially comprises multiple multi-echo pulse sub-sequences, each multi-echo pulse sub-sequence sequentially comprising a Na-23 excitation pulse and... Number of echo units Each echo unit includes components of the encoded gradient in the x-axis direction, the y-axis direction, and the z-axis direction, which are synchronously activated. The x-axis, y-axis, and z-axis directions are mutually perpendicular k-space coordinate axes. Each echo unit uses an analog-to-digital converter to acquire the Na-23 signal in the entire k-space.

[0008] The coding gradient includes a density-adaptive coding gradient unit and a gradient compensation unit.

[0009] As described above, the density-adaptive coding gradient unit consists of four temporal stages: a linear ascent stage, a gradient steady-state stage, a density adaptation stage, and a linear descent stage. The gradient magnitude of the encoded gradient in the density-adaptive coding gradient unit satisfies the following formula:

[0010] ,

[0011] in, This represents the change in the magnitude of the encoded gradient over time. Indicates time;

[0012] The cutoff time of the linear ascent phase is also equal to the start time of the gradient steady-state phase, denoted as time t. ; Indicates the maximum switching rate;

[0013] The cutoff time for the gradient steady-state phase is also equal to the start time of the density adaptation phase, denoted as time t. ;time The corresponding k value satisfies , Indicates the value of k. express The value of k at time t, The critical radius of the central region of k-space is denoted as the critical radius. ; This represents the gradient magnitude during the steady-state phase.

[0014] This is the cutoff time of the density adaptation phase, which is also equal to the start time of the linear descent phase. It is the gyromagnetic ratio; The gradient magnitude of the encoded gradient at the cutoff point of the density adaptation phase;

[0015] ,

[0016] The cutoff time for the linear descent phase satisfies the following relationship:

[0017] ,

[0018] The gradient magnitude based on the encoded gradient is continuous from the linear ascent phase to the steady-state phase, at time... The following relationship must be satisfied:

[0019] ,

[0020] The gradient magnitude during the steady-state phase Based on the following formula, the maximum switching rate With critical radius Decide:

[0021] ,

[0022] Critical radius Based on the following formula, the k-space is pre-defined by a certain proportion. The absolute value of the maximum amplitude in k-space Decide:

[0023] ,

[0024] Absolute value of the maximum amplitude in k-space Based on the following formula, determined by preset pulse series parameters: imaging field of view (FOV) and matrix size (Matrix),

[0025] ,

[0026] in, Let be the value of the first dimension of the matrix Matrix. The value representing the first dimension of the field of view (FOV) is... It represents the product.

[0027] The waveform of the gradient compensation module described above is as follows:

[0028] like A trapezoidal waveform is used;

[0029] like A triangular waveform is used;

[0030] in, , To determine the critical value of the waveform, This represents the maximum gradient magnitude. , The k value at the end of the density adaptively encoded gradient unit, It is the gyromagnetic ratio. Represents the residual gradient moment. This represents the magnitude of the residual gradient moment;

[0031] For a compensation mechanism using a trapezoidal waveform, the magnitude of the corresponding coding gradient satisfies the following formula:

[0032] ,

[0033] This represents the cutoff time of the linearly decreasing phase of the gradient magnitude in the trapezoidal waveform, satisfying... ;

[0034] This represents the cutoff time of the gradient sustaining phase in the trapezoidal waveform, satisfying... ;

[0035] This indicates the moment when the gradient magnitude of the encoded gradient in the trapezoidal waveform returns to 0, satisfying the condition... ;

[0036] For the compensation mechanism of the triangular waveform, the magnitude of the corresponding coding gradient satisfies the following formula:

[0037] ,

[0038] in, The cutoff time for the linear decrease of the gradient magnitude in the triangular waveform satisfies... ;

[0039] The cutoff time for the linearly increasing gradient magnitude in the triangular waveform satisfies... ;

[0040] To achieve the optimal gradient magnitude, .

[0041] As mentioned above, the components of the coding gradient in the x-axis direction, the y-axis direction, and the z-axis direction change synchronously according to the following rules:

[0042] ,

[0043] ,

[0044] ,

[0045] in, This represents the change in the magnitude of the encoded gradient over time. Indicates time; This represents the magnitude of the components of the encoded gradient along the x-axis. This represents the magnitude of the component of the encoded gradient along the y-axis. The magnitude of the component of the encoded gradient along the z-axis, the first angle. With the second angle It is derived from the direction of the radial line formed by the Fibonacci spherical distribution.

[0046] The gradient magnitudes of the encoded gradients in two adjacent echo units of each of the multi-echo pulse subsequences have opposite signs.

[0047] A time delay is set between the Na-23 excitation pulse in each of the multi-echo pulse subsequences and the first echo unit of the same multi-echo pulse subsequence. Delay , , Indicates the sequence number of the multi-echo pulse sub-sequence. Indicates the number of multi-echo pulse subsequences. It is a time delay parameter. , It is the number of pulse repetitions, which is equal to the number of multi-echo pulse subsequences. ; It is the echo interval.

[0048] The method for using the density-adaptive multi-echo pulse sequence of Na-23 includes the following steps:

[0049] Nuclear magnetic resonance scanning of the sample was performed using a Na-23 density-adaptive multi-echo pulse sequence to obtain sampling data;

[0050] Image reconstruction is performed on the sampled data;

[0051] On the reconstructed image corresponding to the first echo unit of the first multi-echo pulse subsequence, the outline of the irregular region of interest (ROI) is freely drawn. The coordinate mask of the ROI corresponding to the first echo unit of the first multi-echo pulse subsequence is applied frame by frame to the images corresponding to other different echo units.

[0052] Calculate the average gray value of the pixels within the region of interest (ROI) for each image, and denot it as the average gray value.

[0053] The average gray value of each region of interest (ROI) is normalized to obtain the corresponding normalized average gray value of the ROI.

[0054] The T2 relaxation curve is fitted based on the set of average gray values ​​of each normalized region of interest (ROI) and the corresponding effective echo time.

[0055] The fitting equation for the T2 relaxation curve is:

[0056] ,

[0057] in To normalize the transverse magnetization vector intensity, the effective echo times are used during fitting. The corresponding normalized average gray value of the region of interest (ROI) is input. ; The equilibrium magnetization vector intensity, For the lateral relaxation time, This is the baseline offset. Indicates the effective echo time.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The Na-23 density-adaptive multi-echo pulse sequence used in this invention is a density-adaptive multi-echo design sequence for radial radial trajectories. Repeated sampling at the k-space center disperses motion artifacts and background noise, improving the signal-to-noise ratio (SNR). A single excitation acquires multiple echo signals, each echo corresponding to independent k-space filling, giving the sequence significant advantages in quantitative studies such as accurate parameter calculation and multi-parameter joint analysis of multi-echo signals. Furthermore, variable density sampling increases the density of peripheral sampling points, compensating for high-frequency signal attenuation, reducing aliasing artifacts, and improving image detail and resolution. Additionally, the use of a variable delay parameter... This invention enables interpolation, resulting in a more precise fit to the T2* relaxation curve. Compared to existing technologies, this invention addresses the low signal-to-noise ratio and motion sensitivity issues of Na-23 through three-dimensional radial linear density adaptive sampling. It also mitigates systemic errors in actual sampling using variable time-delay interpolation and waveform flipping modes, achieving sub-millisecond-level accurate fitting of the relaxation curve. This lays the foundation for further quantitative research. Furthermore, the dynamic gradient compensation module design maximizes scanning efficiency within hardware limitations. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0061] Figure 2This is a timing structure diagram of the waveforms of the density adaptive coding gradient unit and gradient compensation unit designed in this invention; the horizontal axis is the duration of the gradient, and the vertical axis is the magnitude of the coding gradient.

[0062] Figure 3 This is a complete schematic diagram of the Na-23 density-adaptive multi-echo pulse sequence designed in this invention; the horizontal axis represents the running time, and the vertical axis represents the gradient intensity in each direction. It is a variable delay parameter.

[0063] Figure 4 This is a schematic diagram of two different working modes of the Na-23 density adaptive multi-echo pulse sequence designed in this invention, which are divided into waveform non-flipping mode and waveform flipping mode.

[0064] Figure 5 The image is reconstructed using data collected in the embodiments of the present invention. In this embodiment, a multi-echo pulse subsequence contains six echo units, where (a) to (f) correspond to the reconstructed images corresponding to the first to sixth echo units in the first multi-echo pulse subsequence, respectively.

[0065] Figure 6 The region of interest (ROI) is selected in the image reconstructed in the example to fit the T2 relaxation curve.

[0066] Figure 7 It is a trend graph of the average gray value change corresponding to the selected region of interest (ROI). Groups 1 to 3 correspond to the first to third multi-echo pulse sub-sequences in the embodiment.

[0067] Figure 8 This is a graph showing the fitting results of the T2 relaxation curve; y represents the normalized transverse magnetization vector intensity in the fitted T2 relaxation curve, and x represents the effective echo time in the fitted T2 relaxation curve. This represents the lateral relaxation time. Detailed Implementation

[0068] 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.

[0069] Example 1:

[0070] The density-adaptive multi-echo pulse sequence design method for Na-23, such as Figure 1 As shown, it includes the following steps:

[0071] Design of Na-23 density-adaptive multi-echo pulse sequences:

[0072] The design of the Na-23 density-adaptive multi-echo pulse sequence includes the design of the waveform of the coding gradient in the Na-23 density-adaptive multi-echo pulse sequence to achieve density-adaptive coding gradient and gradient compensation; as well as the overall design of the Na-23 density-adaptive multi-echo pulse sequence.

[0073] (1) Design of the waveform of the coding gradient

[0074] The waveform of the encoded gradient in the Na-23 density-adaptive multi-echo pulse sequence is as follows: Figure 2 As shown, the coding gradient includes a density-adaptive coding gradient unit and a gradient compensation unit in sequence.

[0075] (1.1) Density-adaptive encoding gradient unit

[0076] The density-adaptive coding gradient unit consists of four temporal stages: a linear ascent stage, a gradient steady-state stage, a density adaptation stage, and a linear descent stage. The gradient magnitude of the encoded gradient in the density-adaptive coding gradient unit satisfies the following formula:

[0077] ,

[0078] in, This represents the change in the magnitude of the encoded gradient over time. Indicates time;

[0079] The cutoff time of the linear ascent phase is also equal to the start time of the gradient steady-state phase, denoted as time t. ; This indicates the maximum switching rate, which is determined by the magnetic resonance imaging system itself.

[0080] The cutoff time for the gradient steady-state phase is also equal to the start time of the density adaptation phase, denoted as time t. ;time The corresponding k value satisfies , Indicates the value of k. express The value of k at time t, express The modulus of k at time t. The critical radius of the central region of k-space is denoted as the critical radius. ; This represents the gradient magnitude during the steady-state phase.

[0081] This is the cutoff time of the density adaptation phase, which is also equal to the start time of the linear descent phase. It is the gyromagnetic ratio; The gradient magnitude of the encoded gradient at the cutoff point of the density adaptation phase;

[0082] ,

[0083] The cutoff time for the linear descent phase satisfies the following relationship:

[0084] ,

[0085] The gradient magnitude based on the encoded gradient is continuous from the linear ascent phase to the steady-state phase, at time... The following relationship must be satisfied:

[0086] ,

[0087] The gradient magnitude during the steady-state phase Based on the following formula, the maximum switching rate With critical radius Decide:

[0088] ,

[0089] Critical radius Based on the following formula, the k-space is pre-defined by a certain proportion. (Generally 20%-30%) and the absolute value of the maximum amplitude in k-space. Decide:

[0090] ,

[0091] Absolute value of the maximum amplitude in k-space Based on the following formula, determined by preset pulse series parameters: imaging field of view (FOV) and matrix size (Matrix),

[0092] ,

[0093] in, Let be the value of the first dimension of the matrix Matrix. The value representing the first dimension of the field of view (FOV) is... It represents the product.

[0094] From the above formula, we can see that:

[0095] (1.1.1) Linear Ascent Phase: The magnitude of the encoded gradient rises from zero at the maximum slew rate. The gradient magnitude increases linearly to the steady-state phase. And then enter the next gradient steady state stage;

[0096] (1.1.2) Gradient steady state phase: The magnitude of the encoded gradient is maintained at the gradient magnitude during the gradient steady state phase. To achieve the central region of k-space ( ( ) routine sampling;

[0097] (1.1.3) Density adaptation stage: The magnitude of the encoding gradient is dynamically adjusted according to the radius of the k-space spherical coordinates. The sampling point density within a unit volume of the spherical shell satisfies , This indicates the number of sampling points within the volume of the spherical shell. It is a constant;

[0098] (1.1.4) Linear descent phase: The magnitude of the encoded gradient decreases at the maximum switching rate. Return to zero to complete the readout cycle.

[0099] It should be specifically noted that the maximum gradient magnitude (denoted as) The physical limitations of the slew rate (determined by the magnetic resonance imaging system itself) and the switching rate, when hour( (The critical radius is determined by hardware performance), so the system cannot achieve ideal density adaptation. Therefore, the conventional linear gradient coding strategy is adopted in this region, namely the linear rising phase and the gradient steady-state phase.

[0100] (1.2) Gradient compensation unit

[0101] Employing a time-optimal control strategy, the maximum gradient magnitude is achieved within the physical limits of the hardware. and maximum switching rate Under constraints, the fastest possible return of the residual gradient moment to zero is achieved by dynamically selecting the waveform structure. The specific design of the gradient compensation unit is as follows:

[0102] like It adopts a trapezoidal waveform (three-stage structure);

[0103] like It adopts a triangular waveform (two-stage structure);

[0104] in, , The threshold value for waveform determination is determined by hardware. , The k value at the end of the density adaptively encoded gradient unit, It is the gyromagnetic ratio. Represents the residual gradient moment. This represents the magnitude of the residual gradient moment; the gradient moment to be compensated is equal to... The negative sign indicates that reverse gradient compensation is required;

[0105] For the compensation mechanism using a trapezoidal waveform: after calculating the time required for the gradient maintenance phase, the gradient magnitude of the encoded gradient is set at the maximum switching rate. The maximum gradient magnitude that decreases linearly from zero to negative Then maintains a negative maximum gradient magnitude Finally, the gradient magnitude is at the maximum switching rate. From the negative maximum gradient magnitude As the gradient increases linearly to zero, the magnitude of the corresponding coding gradient satisfies the following formula:

[0106] ,

[0107] This represents the cutoff time of the linearly decreasing phase of the gradient magnitude in the trapezoidal waveform, satisfying... ;

[0108] This represents the cutoff time of the gradient sustaining phase in the trapezoidal waveform, satisfying... ;

[0109] This indicates the moment when the gradient magnitude of the encoded gradient in the trapezoidal waveform returns to 0, satisfying the condition... ;

[0110] The compensation mechanism for the triangular waveform is as follows: after calculating the optimal gradient magnitude, the gradient strength is adjusted at the maximum switching rate. The gradient decreases linearly from zero to the optimal gradient magnitude, and then the gradient magnitude decreases at the maximum switching rate. As the optimal gradient magnitude increases linearly to zero, the magnitude of the corresponding encoded gradient satisfies the following formula:

[0111] ,

[0112] in, The cutoff time for the linear decrease of the gradient magnitude in the triangular waveform satisfies... ;

[0113] The cutoff time for the linearly increasing gradient magnitude in the triangular waveform satisfies... ;

[0114] To achieve the optimal gradient magnitude, .

[0115] This design achieves time-optimal control within the physical limits of the gradient system by dynamically switching waveform structures.

[0116] (2) Overall design of Na-23 density adaptive multi-echo pulse sequence

[0117] The Na-23 density-adaptive multi-echo pulse sequence sequentially comprises multiple multi-echo pulse sub-sequences, each multi-echo pulse sub-sequence sequentially comprising a Na-23 excitation pulse and... Number of echo units In this embodiment, the number of echo units Each echo unit includes components of the encoded gradient in the x-axis direction, the encoded gradient in the y-axis direction, and the encoded gradient in the z-axis direction, which are synchronously activated. The x-axis, y-axis, and z-axis directions are mutually perpendicular k-space coordinate axes. For each echo unit, an analog-to-digital converter is used to acquire the signal of Na-23 in the entire k-space.

[0118] The Na-23 density adaptive multi-echo pulse sequence designed in this embodiment is shown in Figure 3. The Na-23 excitation pulse is a rectangular radio frequency pulse, and there are 6 echo signals in one multi-echo pulse subsequence to more accurately reflect the signal characteristics. In this embodiment, the Na-23 density adaptive multi-echo pulse sequence adopts a 3D radial line k-space filling method. That is, after the Na-23 excitation pulse is excited, the encoding gradients in the x, y, and z axes are simultaneously activated. To achieve a radial trajectory, the components of the encoding gradient in the x-axis direction, the amplitude of the encoding gradient in the y-axis direction, and the components of the encoding gradient in the z-axis direction are all based on the aforementioned constructed encoding gradient, and the amplitudes change synchronously according to a specific ratio. , , ,in, This represents the magnitude of the components of the encoded gradient along the x-axis. This represents the magnitude of the component of the encoded gradient along the y-axis. The magnitude of the component of the encoded gradient along the z-axis, the first angle. With the second angle (The direction is derived from the radial lines formed by the Fibonacci spherical distribution). This synchronous activation method enables precise encoding of spatial information, giving NMR signals from different locations unique spatial characteristics. Simultaneously, the analog-to-digital converter is strictly synchronized with the timing of the triaxial encoding gradient. This strict timing synchronization mechanism ensures complete acquisition of the NMR signal during gradient application, avoiding signal loss and distortion, thus guaranteeing signal quality and spatial resolution.

[0119] Furthermore, to increase the sampling density of the relaxation decay curve, a time delay parameter is introduced. In other words, a time delay is set between the Na-23 excitation pulse of each multi-echo pulse subsequence in the Na-23 density adaptive multi-echo pulse sequence and the first echo unit of the same multi-echo pulse subsequence. Delay , , Indicates the sequence number of the multi-echo pulse sub-sequence. This indicates the number of multi-echo pulse subsequences; this time delay parameter It was carefully calculated and set to a fixed echo spacing (Echo SpacingPeriod). )of One-third, that is ,in It is the number of pulse repetitions, which is equal to the number of multi-echo pulse subsequences. In this embodiment, Through this delay parameter Supplementary data collection was performed to allow for the acquisition of data with different effective echo times. The echo sampling point sequence was expanded from 6 to In this embodiment, the final echo sampling point sequence is increased to 18, forming an interval of [number missing]. High-density sampling sequences. For example: fixed echo intervals. Equal to 3ms (milliseconds), the effective echo time corresponding to each echo unit in the first multi-echo pulse subsequence. The effective echo times are 2ms, 5ms, 8ms, 11ms, 14ms, and 17ms, respectively. Effective echo times are particularly important in sodium magnetic resonance imaging research. For data within 5ms, a delay parameter is introduced. The effective echo time corresponding to each echo unit in the second multi-echo pulse subsequence The effective echo times for each echo unit in the third multi-echo pulse subsequence are 3ms, 6ms, 9ms, 12ms, 15ms, and 18ms, respectively. The effective echo times were obtained in total after three multi-echo pulse subsequences: 4ms, 7ms, 10ms, 13ms, 16ms, and 19ms. The echo sampling point sequence, corresponding to the effective echo time The durations are 2ms, 3ms, 4ms, 5ms, 6ms, 7ms, 8ms, 9ms, 10ms, 11ms, 12ms, 13ms, 14ms, 15ms, 17ms, 18ms, and 19ms respectively, which not only increases the effective echo time. The sampling data within 5ms was increased, and the data beyond 5ms was also added, meaning that more sampling points were obtained for the entire scan. Furthermore, multi-parameter image data, including sodium ion density weighted, T1 weighted, and T2 weighted images, was acquired, which is a significant advantage in quantitative studies. This phased expansion strategy is crucial; it achieves this through… Sub-data interpolation can effectively cover the characteristic processes in the bi-exponential relaxation model. The bi-exponential relaxation model is commonly used to describe the decay process of Na-23 NMR signals, including rapid initial decay and slow later decay. High-density sampling sequences can more accurately capture the details of these two processes, providing a high-quality data foundation for subsequent model fitting and parameter extraction.

[0120] Furthermore, the Na-23 density-adaptive multi-echo pulse sequence operates in two gradient modes: a waveform-unflipped mode and a waveform-flipped mode. Figure 3 The waveform shown is in the non-flipped mode, meaning the sign of the encoded gradient is the same in all echo units; as shown... Figure 4 As shown, this embodiment employs a waveform reversal mode. In the sequence of echo units corresponding to the encoded gradient, the phase coding accuracy is jointly affected by the gradient pulse polarity, gradient moment, and timing parameters. The waveform reversal mode simultaneously suppresses gradient error (hardware level) and phase error (signal level) through a unified physical mechanism. Its core lies in alternately applying the positive coding gradient (… ) and negative coding gradient ( This means that the gradient magnitudes of the encoded gradients in two adjacent echo units have opposite signs, and that the integral areas of the two gradients over time are strictly equal (i.e., the absolute values ​​of the gradient moments are the same). For gradient errors (such as field strength deviations caused by gradient amplifier delay or eddy current effects)... Due to the symmetry of the hardware response, the error introduced by the forward encoding gradient... Error introduced by negative encoding gradient They will cancel each other out, reducing the total gradient error. This improves the stability of the gradient field. As for the phase error (i.e., the phase shift of Na-23 ions due to the accumulated gradient error)... Since the phase shift is the integral result of the gradient error ( , The deviation between the actual applied gradient field (G) and the ideal gradient field; the phase shift generated by the forward encoded gradient. With the generation of inverse encoding gradient They will also cancel each other out, ultimately causing a net phase shift. This avoids the formation of cumulative artifacts during repeated encoding. Furthermore, this mode is naturally compatible with the symmetry of radial k-space trajectories, ensuring the integrity of spatial encoding during alternating positive and negative gradients and preventing missing k-space coverage due to flipping operations.

[0121] Example 2:

[0122] The method for using the density-adaptive multi-echo pulse sequence of Na-23 includes the following steps:

[0123] Step 1: Setting parameters for the Na-23 density-adaptive multi-echo pulse sequence and scanning the sample;

[0124] 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 10 mm NMR sample tube. A 10 mm inner diameter H-1 / Na-23 dual-channel body coil was used for transmission and reception, and the sample temperature was maintained at 298 K. In the pulse sequence parameters of this embodiment, the Na-23 excitation pulse duration was 0.5 ms, the corresponding flip angle was 60°, and the effective echo time corresponding to the first echo unit in the first multi-echo pulse subsequence was... The effective echo time for subsequent echo units can be obtained by combining the echo interval ESP with the 2.5ms interval. The repetition time (TR) is 100ms, the number of echo units in a single excitation is 6, the interpolation cycle excitation is 3 times, the echo interval (ESP) is 3.3ms, the adjacent excitation delays are 0ms, 1.1ms, and 2.2ms, the imaging field of view (FOV) is 20 mm × 20 mm × 20 mm, the matrix size (MATRIX) is 64 × 64 × 64, the average number of excitations is 1, and the number of excitations is the total number of full samples, which is 64 × 64 × π, or 12868 times. The working mode is waveform flipping mode.

[0125] Based on the above pulse sequence parameters, the pulse sequence of the method of the present invention is used to sample sodium chloride solution samples to obtain sampling data.

[0126] Step 2: Reconstruct the image from the sampled data of the multi-echo pulse sequence;

[0127] In MATLAB, the actual k-space trajectory of the sampling data during the imaging process, as well as the acquired image data, are input into the three-dimensional non-uniform Fourier transform (nufft3d) function for image reconstruction, thereby obtaining a three-dimensional Na-23 image of the sample based on the sampling trajectory reconstruction.

[0128] The cross-sectional images of the six echoes obtained from the first complete multi-echo pulse subsequence (this set of multi-echo pulse subsequences without inserted delays) are compared, as follows: Figure 5As shown in the image, the white bright spots have clear boundaries, indicating that the sequence can effectively distinguish the difference between the saturated NaCl solution and the background, without significant edge blurring, motion artifacts, or background noise. The six bright spots are uniformly symmetrical in shape, without radial stripes or distortions (traditional Cartesian trajectories are prone to Gibbs artifacts). The results of the six imaging studies are highly consistent (arranged in two rows and three columns), indicating that the algorithm maintains stability even under rapid scanning and is suitable for dynamic or large-scale sodium imaging studies. The average gray value of the six imaging results decreases in degree of primary and secondary reduction, which is consistent with the theory of T2 relaxation.

[0129] Step 3: Relaxation time curve analysis;

[0130] Step 3.1: Fit and analyze the relaxation time curve in MATLAB. Use the `imfreehand` function to find the first echo unit (corresponding to the first group of effective echo times) in the first multi-echo pulse subsequence. On the corresponding reconstructed image, freely draw the outline of the irregular region of interest (ROI), such as... Figure 6 As shown, the coordinate mask of the region of interest (ROI) corresponding to the first echo unit of the first multi-echo pulse subsequence is applied frame by frame to the images corresponding to all other different echo units, ensuring that the ROIs sampled at different time points are completely consistent. This operation eliminates the positional deviation introduced by manual repetition of selection, ensuring the spatial comparability of time series data;

[0131] Step 3.2: Calculate the average gray value of pixels within the Region of Interest (ROI) for each image (denoted as the average gray value). The variation of the average gray value of the selected ROIs for each group is as follows: Figure 7 As shown, this mean-averaging process effectively suppresses single-pixel noise interference while preserving the overall relaxation characteristics of the tissue, providing high signal-to-noise ratio input data for subsequent fitting.

[0132] Step 3.3: Normalize the average grayscale value of each Region of Interest (ROI) (i.e.) , This represents the average grayscale value of the region of interest (ROI). This represents the maximum average gray value of the region of interest (ROI). This represents the normalized average gray value of the region of interest (ROI), resulting in a set of normalized average gray values ​​for the ROI.

[0133] Step 3.4: Call the lsqcurvefit function, a nonlinear least squares fitting tool in MATLAB, and use the set of normalized average gray values ​​of the region of interest (ROI) and their corresponding effective echo times. The key parameters for fitting the T2 relaxation curve are set as follows:

[0134] (1) The maximum number of function evaluations is 10,000 to avoid iteration non-convergence;

[0135] (2) Tolerance is 1×10 -5 To ensure the accuracy of parameter estimation;

[0136] (3) Set according to the signal attenuation trend The initial value is used to accelerate convergence, where, The equilibrium magnetization vector intensity, The lateral relaxation time (a core parameter to be solved). This is the baseline offset, used to correct zero-point drift or background signal in magnetic resonance micro-imagers.

[0137] The sample used in this embodiment is a saturated sodium chloride solution (single-exponential relaxation characteristic), therefore, the fitting equation for its T2 relaxation curve is:

[0138] ,

[0139] in To normalize the transverse magnetization vector intensity, the effective echo times are used during fitting. The corresponding normalized average gray value of the region of interest (ROI) is input. .

[0140] By introducing ( (For a fixed echo interval), the original 6 valid echo times The corresponding high-density sampling points are expanded to 18 effective echo times. Corresponding high-density sampling points. This design refines the sampling interval to... This significantly improves the ability to distinguish relaxation decay curves (especially the rapid initial decay phase in the double exponential model).

[0141] The relaxation curve fitting result in this embodiment is as follows: Figure 8 As shown, the T2 relaxation time of the saturated sodium chloride solution used in this embodiment is 40.9 ms, which is highly consistent with the theoretical expectation (the transverse relaxation time of the sodium chloride solution). Typically located in the 30–50 ms range. High-density sampling data covers the inflection point and plateau region of the decay curve, resulting in significantly better fit (R² > 0.99) and parameter confidence intervals compared to traditional sparse sampling.

[0142] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific 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 of designing a density-adapted multi-echo pulse sequence for Na-23, characterized in that The following steps are included in designing the Na-23 density-adaptive multi-echo pulse sequence: The Na-23 density self-adaptive multi-echo pulse sequence comprises a plurality of multi-echo pulse sub-sequences in sequence, each multi-echo pulse sub-sequence comprises an Na-23 excitation pulse and a plurality of echo units Each echo unit comprises a component of an x-axis direction encoding gradient, a component of a y-axis direction encoding gradient and a component of a z-axis direction encoding gradient which are synchronously turned on, and the x-axis direction, the y-axis direction and the z-axis direction are mutually perpendicular k-space coordinate axis directions; an analog-to-digital converter is used to complete the collection of the Na-23 signal in the whole k-space corresponding to each echo unit; The coding gradient includes a density-adaptive coding gradient unit and a gradient compensation unit in sequence. The density-adaptive coding gradient unit comprises four temporal stages: a linear ascent stage, a gradient steady-state stage, a density adaptation stage, and a linear descent stage. The gradient magnitude of the encoded gradient in the density-adaptive coding gradient unit satisfies the following formula: ， wherein denotes the gradient magnitude of the encoding gradient, denotes time; The time instant at which the linear increase phase ends, also equal to the time instant at which the gradient steady state phase starts, is denoted as time instant ; denotes the maximum switching rate; The cutoff time of the gradient steady state phase, which is also the starting time of the density adaptation phase, is denoted as time ; time The corresponding k value satisfies , The k value is denoted as k The k value at time is denoted as k The critical radius of the central region of k space is denoted as critical radius ; The gradient amplitude of the gradient steady state phase is denoted as is the end time of the density adaptation phase, which is also the start time of the linear ramp-down phase; is the gyromagnetic ratio; is the gradient amplitude of the encoding gradient at the end time of the density adaptation phase; ， The cut-off time for the linear decrease phase is met by the relation: ， The gradient amplitude based on the coding gradient is continuous from the linear rising stage to the gradient steady stage, and the time satisfies the following relationship: ， the gradient amplitude of the gradient steady state phase based on the following equation from the maximum slew rate with the critical radius determined: ， Critical radius Based on the following formula, the k-space preset ratio The absolute value of the maximum amplitude of k-space Decide: ， absolute value of k-space maximum amplitude Based on the following formula, the imaging field of view FOV and the matrix size Matrix are determined from the preset pulse series parameters: ， wherein is a value of a first dimension of a matrix size Matrix, is a value of a first dimension of an imaging field of view FOV, denotes a product; The waveform of the gradient compensation module is as follows: If , a trapezoidal waveform is used; If , a triangular waveform is used; wherein , is a waveform decision threshold, is a maximum gradient amplitude; , is a k value at the end of the density adaptive encoding gradient unit, is a gyromagnetic ratio, denotes a residual gradient matrix, denotes a modulus of the residual gradient matrix; For a compensation mechanism using a trapezoidal waveform, the magnitude of the corresponding coding gradient satisfies the following formula: ， denotes the cut-off time of the linearly decreasing phase of the gradient amplitude in the trapezoidal waveform, satisfying ; denotes the cut-off time of the gradient sustain phase in the trapezoidal waveform, and satisfies ; The time at which the gradient amplitude of the encoded gradient in the trapezoidal waveform returns to 0 is represented by t2, and satisfies ; For the compensation mechanism of the triangular waveform, the magnitude of the corresponding coding gradient satisfies the following formula: ， wherein is the cut-off time for the linearly decreasing gradient amplitude in the triangular waveform, satisfying ; The cut-off time for the triangular waveform in which the gradient amplitude linearly increases is satisfied by ; for the optimal gradient magnitude, .

2. The method of claim 1, wherein the Na-23 density-adapted multi-echo pulse sequence design is characterized by, The synchronous change pattern of the components of the coding gradient in the x-axis direction, the y-axis direction, and the z-axis direction is as follows: ， ， ， wherein, denotes a gradient amplitude of the encoding gradient, denotes time; denotes an amplitude of a component of the encoding gradient in the x-axis direction, denotes an amplitude of a component of the encoding gradient in the y-axis direction, denotes an amplitude of a component of the encoding gradient in the z-axis direction, a first angle a second angle is derived from the direction of a radial line formed by a Fibonacci spherical distribution.

3. The method of claim 1, wherein the Na-23 density-adapted multi-echo pulse sequence design is characterized by, The gradient magnitudes of the encoded gradients in two adjacent echo units of each of the multi-echo pulse subsequences have opposite signs.

4. The method of claim 1, wherein the Na-23 density-adapted multi-echo pulse sequence design is characterized by, a time delay is provided between the Na-23 excitation pulse in each of the multiple echo pulse sub-sequences and the first echo element of the same multiple echo pulse sub-sequence , the time delay , , denotes the number of the multiple echo pulse sub-sequence, denotes the number of the multiple echo pulse sub-sequences, is a time delay parameter, , is the number of pulse repetitions, which is equal to the number of multiple echo pulse sub-sequences ; is the echo interval.

5. The method for using the Na-23 density-adapted multi-echo pulse sequence generated by the Na-23 density-adapted multi-echo pulse sequence design method of claim 1, wherein, Includes the following steps: Nuclear magnetic resonance scanning of the sample was performed using a Na-23 density-adaptive multi-echo pulse sequence to obtain sampling data; Image reconstruction is performed on the sampled data; On the reconstructed image corresponding to the first echo unit of the first multi-echo pulse subsequence, the outline of the irregular region of interest (ROI) is freely drawn. The coordinate mask of the ROI corresponding to the first echo unit of the first multi-echo pulse subsequence is applied frame by frame to the images corresponding to other different echo units. Calculate the average gray value of pixels within the region of interest (ROI) for each image, and denot it as the average gray value. The average gray value of each region of interest (ROI) is normalized to obtain the corresponding normalized average gray value of the ROI. The T2 relaxation curve is fitted based on the set of average gray values ​​of each normalized region of interest (ROI) and the corresponding effective echo time.

6. The method of using the density-adapted multi-echo pulse sequence of Na-23 of claim 5, wherein, The fitting equation for the T2 relaxation curve is: ， wherein is the normalized transverse magnetization vector strength, each effective echo time corresponding normalized region of interest (ROI) average gray value is brought into ; is the equilibrium magnetization vector strength, is the transverse relaxation time, is the baseline offset, denotes the effective echo time.

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