A variable rate radio frequency pulse design method for sodium magnetic resonance imaging

Abstract

The present invention discloses a variable-rate radio frequency pulse design method for sodium magnetic resonance imaging. In response to the requirement for radio frequency pulses to reduce the radio frequency special absorption rate (SAR) value and pulse duration in sodium magnetic resonance imaging, when the pulse duration remains unchanged, the SAR value of the variable-rate radio frequency pulse is optimized to minimize the SAR value of the radio frequency pulse; when the SAR value of the pulse remains unchanged, the duration of the variable-rate radio frequency pulse is optimized to minimize the pulse duration of the radio frequency pulse; and during the optimization process, the maximum gradient intensity and maximum climbing rate constraints are met. By optimizing the SAR pulse, the applicability of sodium magnetic resonance imaging is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-nuclear magnetic resonance imaging (MRI), and in particular relates to a variable rate radio frequency pulse design method for sodium element magnetic resonance imaging. Background Art

[0002] Sodium ions are a vital electrolyte in the human body, playing a key role in maintaining electrochemical equilibrium inside and outside cells, regulating cell function, and maintaining fluid balance. The sodium-potassium pump (Na+ / K+ pump) actively transports sodium ions out of cells and potassium ions into cells, maintaining the resting potential of cell membranes and nerve impulse conduction. This is crucial for processes such as muscle contraction and nerve signaling.

[0003] Conventional magnetic resonance imaging is mainly based on hydrogen atoms ( 1 H) signals, enabling high-resolution imaging of tissue structure and function. 23 Na is the 1 The most abundant endogenous element detected by magnetic resonance besides H is 23 Na magnetic resonance imaging has the ability to detect sodium ion concentration in the human body without invasion or radiation, providing a new means to explore scientific issues such as the regulation of sodium-potassium pump function, quantitative evaluation of sodium concentration, and sodium channel signal transduction. 23 The concentration of Na in the body is low (tens to hundreds of millimolar), and the gyromagnetic ratio is about 1 One quarter of H. Therefore, 23 The signal-to-noise ratio of Na MRI is low, and it is often necessary to increase the signal strength through multiple accumulation. In addition, the repetition time (TR) of its imaging method is short, and the frequency of application of radio frequency pulses is higher, thereby increasing the specific absorption ratio (SAR) value of radio frequency during the sampling process. Excessive SAR value may cause tissue overheating, especially in high-field MRI (3T and above). On the other hand, 23 The T2 relaxation time of Na is short, so the sampling echo time (TE) needs to be shortened, and the duration of the RF pulse needs to be further shortened. The RF specific absorption rate value and pulse duration become 23 Key considerations for Na RF pulse design. The overall RF SAR value of an RF pulse is typically evaluated based on the following formula.

[0004]

[0005] Where σ is the conductivity of the tissue, ρ is the tissue density, B1 is the amplitude of the RF pulse, and B1 2Proportional to the overall RF pulse power, t is the pulse duration. Conventional RF pulses typically maintain a constant slice gradient strength during slice-selective excitation, while B1 is determined by the pulse waveform, duration, and flip angle. Highly selective RF pulses, such as SINC pulses, have significantly higher overall RF SAR values ​​than rectangular pulses with the same flip angle. Summary of the Invention

[0006] The present invention provides a variable rate radio frequency pulse design method for sodium magnetic resonance imaging, which effectively reduces the overall radio frequency specific absorption rate value or pulse duration of the radio frequency pulse.

[0007] The above-mentioned purpose of the present invention is achieved by the following technical means:

[0008] A variable rate radio frequency pulse design method for sodium magnetic resonance imaging comprises the following steps:

[0009] Step 1: Design the waveform of the initial radio frequency pulse and the waveform of the initial slice selection gradient;

[0010] Step 2: Constructing an objective function and constraints for RF pulse optimization based on a time axis scaling factor; the time axis scaling factor is used to scale the waveform of the initial RF pulse and the waveform of the initial layer selection gradient on the time axis; the objective function is to minimize the sum of the overall RF specific absorption rate value of the RF pulse and a regularization term, or the objective function is to minimize the sum of the pulse duration and the regularization term, the regularization term is used to smooth the waveform of the RF pulse and the waveform of the layer selection gradient, and the constraints are that the waveform of the layer selection gradient meets the maximum gradient strength and maximum climbing rate limits;

[0011] Step 3: Set the initial value of the time axis scaling factor corresponding to each time segment in the initial value distribution of the time axis scaling factor, construct an optimization algorithm for variable rate radio frequency pulse optimization, and optimize the initial value distribution of the time axis scaling factor in combination with the objective function and the constraint conditions to obtain the final optimized time axis scaling factor value distribution;

[0012] Step 4: Based on the final optimized time axis scaling factor value distribution, the initial RF pulse and the initial layer selection gradient are scaled by the time axis scaling factor in the final optimized time axis scaling factor value distribution to obtain the scaled RF pulse and the scaled layer selection gradient.

[0013] The above-mentioned step 1 specifically includes the following steps:

[0014] Determine the type of initial RF pulse, pulse duration, stopband ripple amplitude, passband ripple amplitude, selected layer thickness, time-bandwidth product, and number of time segments;

[0015] The waveform of the initial radio frequency pulse is designed based on the type of the initial radio frequency pulse, the pulse duration, the stopband ripple amplitude, the passband ripple amplitude, and the selected layer thickness. The waveform of the initial radio frequency pulse represents the change of the amplitude of the initial radio frequency pulse over time.

[0016] The waveform of the initial layer selection gradient is determined based on the product of the layer selection thickness and the time-bandwidth. The waveform of the initial layer selection gradient represents the change of the intensity of the initial layer selection gradient over time. The intensity of the initial layer selection gradient is:

[0017]

[0018] Where γ is the gyromagnetic ratio, T p is the pulse duration of the initial RF pulse, d is the slice thickness, TBP is the time-bandwidth product, and G is the strength of the initial slice gradient;

[0019] The amplitude of the initial radio frequency pulse and the intensity of the initial slice selection gradient are both divided into multiple time segments according to the number of time segments, and the segment durations corresponding to the various time segments are equal.

[0020] Step 2 as described above specifically includes the following steps:

[0021] Step 2.1: Set the time axis scaling factor to perform scaling operations:

[0022] The amplitude of the i-th time segment of the initial RF pulse is recorded as B 1i , the time axis scaling factor of the i-th time segment is recorded as S i , the segment length of each time segment before scaling is recorded as Δt; then the amplitude of the i-th time segment of the RF pulse after scaling is B 1i / S i , the intensity of the i-th time segment of the scaled layer selection gradient is G / S i , the length of the i-th time segment after scaling is Δt·S i ;

[0023] The overall RF specific absorption rate value of the initial RF pulse is calculated based on the following formula:

[0024]

[0025] Where SAR0 is the overall radiofrequency specific absorption rate value of the initial radiofrequency pulse, σ is the conductivity of the tissue, ρ is the tissue density, N is the number of time segments of the initial radiofrequency pulse, ∝ means proportional to, i is the sequence number of the time segment, i∈{1,2,…N};

[0026] Set the SAR threshold for radio frequency specific absorption rate th , when the overall radio frequency specific absorption rate value SAR0 of the initial radio frequency pulse is greater than the radio frequency specific absorption rate threshold SARth When the overall radio frequency special absorption rate value SAR0 of the initial radio frequency pulse is less than or equal to the set radio frequency special absorption rate threshold SAR th When , execute step 2.3;

[0027] Step 2.2: Keeping the pulse duration constant, based on minimizing the sum of the overall RF specific absorption rate value of the RF pulse and the regularization term, construct the following objective function and constraints:

[0028]

[0029] Among them, lamda is the parameter for adjusting the smoothness, diff represents the difference function of the corresponding calculation formula of two adjacent time segments, G is the intensity of the initial layer selection gradient, G max is the maximum gradient strength, SR max is the maximum climbing rate of the layer selection gradient; st represents the constraint condition;

[0030] Step 2.3: Keeping the overall RF special absorption rate of the RF pulse unchanged, minimize the sum of the pulse duration and the regularization term. The objective function and constraints are as follows:

[0031]

[0032] Step 3 as described above includes the following steps:

[0033] Set the initial value distribution of the time axis scaling factor. The initial value distribution of the time axis scaling factor includes the initial value of the time axis scaling factor corresponding to each time segment. Substitute the initial value distribution of the time axis scaling factor into the objective function constructed in step 2. Perform iterative calculation based on the corresponding constraints and the selected optimization algorithm to obtain the corresponding iteratively optimized time axis scaling factor value distribution as the final optimized time axis scaling factor value distribution.

[0034] Step 3 as described above includes the following steps:

[0035] Set multiple groups of time axis scaling factor initial value distributions, each group of time axis scaling factor initial value distributions includes the time axis scaling factor initial value corresponding to each time segment, and each group of time axis scaling factor initial value distributions is in a different value range;

[0036] Each set of time axis scaling factor initial value distributions is substituted into the objective function constructed in step 2, and iterative calculations are performed based on the corresponding constraints and the selected optimization algorithm to obtain the corresponding iteratively optimized time axis scaling factor value distributions;

[0037] From all iteratively optimized timeline scaling factor value distributions, a set of iteratively optimized timeline scaling factor value distributions whose corresponding objective function values ​​are minimized is selected as the final optimized timeline scaling factor value distribution.

[0038] The iterative calculation mentioned above specifically includes the following steps:

[0039] The initial value distribution of the time axis scaling factor is substituted into the objective function constructed in step 2, and the optimized time axis scaling factor value distribution of the first round of iteration is obtained based on the corresponding constraints and the selected optimization algorithm. Then, the optimized time axis scaling factor value distribution of the first round of iteration is used as the input of the objective function in the second round of iteration, and the selected optimization algorithm is continued to be used to calculate the optimized time axis scaling factor value distribution of the second round of iteration. Similarly, the optimized time axis scaling factor value distribution of the previous round of iteration is used as the input of the objective function in this round of iteration, and the optimized time axis scaling factor value distribution of this round of iteration is calculated by the optimization algorithm until the change in the value of the objective function in two adjacent rounds of iteration is less than the set tolerance, or the number of completed iterations reaches the iteration number threshold. The corresponding optimized time axis scaling factor value distribution is used as the iterative optimized time axis scaling factor value distribution corresponding to the initial value distribution of the time axis scaling factor.

[0040] As mentioned above, the type of the initial RF pulse is an SLR pulse. The inverse SLR algorithm is used to design the waveform of the initial RF pulse. The Parks-McClellan algorithm is used as a filter for the inverse SLR algorithm. The selected layer thickness, pulse duration, stopband ripple amplitude, and passband ripple amplitude are input to the inverse SLR algorithm to calculate the waveform of the initial RF pulse.

[0041] As mentioned above, the optimization algorithm is a sequential quadratic programming algorithm.

[0042] As described above, the time axis scaling factor initial value in the time axis scaling factor initial value distribution is linearly distributed.

[0043] Step 4 as described above also includes the following steps:

[0044] The scaled radio frequency pulses and the scaled slice selection gradients are interpolated and resampled to obtain variable rate radio frequency pulses and corresponding slice selection gradients with equal time interval distribution.

[0045] Compared with the existing methods, the present invention has the following beneficial effects:

[0046] 1. Based on the design concept of variable-rate RF pulses, the present invention scales the RF pulse waveform on the time axis, and the slice selection gradient is also scaled synchronously. Without changing the pulse duration of the RF pulse, the RF pulse amplitude can be stretched in a larger range and compressed in other ranges during the scaling process, thereby optimizing the RF special absorption rate value of the variable-rate RF pulse and minimizing the RF special absorption rate value of the RF pulse;

[0047] 2. When the pulsed radio frequency specific absorption rate value remains unchanged, the pulse duration of the variable rate radio frequency pulse is optimized to minimize the duration of the radio frequency pulse, and the maximum gradient intensity and maximum climbing rate constraints are met during the optimization process.

[0048] 3. It does not affect the layer selection performance of radio frequency pulses and meets the requirements of low radio frequency specific absorption rate and short duration of radio frequency pulses in sodium magnetic resonance imaging.

[0049] The present invention can be used for optimizing the design of radio frequency pulses, reducing the radio frequency specific absorption rate value of the pulses, thereby improving the clinical applicability of sodium element magnetic resonance imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of the method of the present invention;

[0051] Figure 2 The waveforms of the initial RF pulse and initial slice selection gradient used in the method of the present invention are shown below. (a) shows the amplitude of the initial RF pulse over time, with the maximum amplitude of the initial RF pulse set to 100; (b) shows the intensity of the initial slice selection gradient over time, with the intensity of the initial slice selection gradient set to 1.

[0052] Figure 3 Figure 3 is a waveform diagram of the variable-rate RF pulse and layer selection gradient designed by the method of the present invention for minimizing the RF special absorption rate (solid line, marked as scaled), compared with the initial RF pulse and initial layer selection gradient (dashed line, marked as initial); (a) is a comparison of the amplitude of the variable-rate RF pulse (solid line) for minimizing the RF special absorption rate and the amplitude of the initial RF pulse (dashed line); (b) is a comparison of the intensity of the layer selection gradient (solid line) for minimizing the RF special absorption rate and the intensity of the initial layer selection gradient (dashed line).

[0053] Figure 4Figure 3 is a waveform diagram of the variable-rate RF pulse and layer selection gradient designed by the method of the present invention (solid line, marked as scaled), compared with the initial RF pulse and initial layer selection gradient (dashed line, marked as initial); (a) is a comparison of the amplitude of the variable-rate RF pulse with the pulse duration minimized (solid line) and the amplitude of the initial RF pulse (dashed line); (b) is a comparison of the intensity of the layer selection gradient with the pulse duration minimized (solid line) and the intensity of the initial layer selection gradient (dashed line).

[0054] Figure 5 3. The graph of the selected layer position excitation of the variable rate radio frequency pulse designed by the method of the present invention (solid line, marked as optimized) is compared with the graph of the selected layer position excitation of the initial radio frequency pulse (dashed line, marked as initial). DETAILED DESCRIPTION

[0055] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to the embodiments. The embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0056] Example 1:

[0057] A variable rate radio frequency pulse design method for sodium magnetic resonance imaging comprises the following steps:

[0058] Step 1: Determine the parameters of the initial RF pulse and the initial layer selection gradient, and design the waveform of the initial RF pulse and the waveform of the initial layer selection gradient.

[0059] Determine the type of initial RF pulse, pulse duration, stopband ripple amplitude, passband ripple amplitude, selected layer thickness, time-bandwidth product (TBP), and number of time segments;

[0060] The waveform of the initial radio frequency pulse is designed based on the type of the initial radio frequency pulse, the pulse duration, the stopband ripple amplitude, the passband ripple amplitude, and the selected layer thickness. The waveform of the initial radio frequency pulse represents the change of the amplitude of the initial radio frequency pulse over time.

[0061] The waveform of the initial layer selection gradient is determined based on the product of the layer selection thickness and the time-bandwidth. The waveform of the initial layer selection gradient represents the change of the intensity of the initial layer selection gradient over time. The intensity of the initial layer selection gradient is:

[0062]

[0063] Where γ is the gyromagnetic ratio, T p is the pulse duration of the initial RF pulse, d is the slice thickness, TBP is the time-bandwidth product, and G is the strength of the initial slice gradient;

[0064] The amplitude of the initial radio frequency pulse and the intensity of the initial slice selection gradient are both divided into multiple time segments according to the number of time segments, and the segment durations corresponding to the various time segments are equal.

[0065] In this embodiment, the type of initial RF pulse is an SLR pulse. The corresponding initial RF pulse is designed using the inverse SLR (Shinnar–Le Roux) algorithm, and the Parks-McClellan algorithm is used as the filter of the inverse SLR algorithm. The selected layer thickness, pulse duration, stopband ripple amplitude, and passband ripple amplitude are input to the inverse SLR algorithm to calculate the waveform of the initial RF pulse. The amplitude of each initial RF pulse is divided into discrete values ​​at equal time intervals according to the number of time segments. In this embodiment, an excitation pulse with a pulse duration of 5 milliseconds is used as an example. The number of time segments corresponding to the amplitude of the initial RF pulse and the intensity of the initial layer selection gradient is set to 500, the segment duration of each time segment is 0.01 milliseconds, the time-bandwidth product (TBP) is 8, the stopband ripple amplitude is 1%, and the passband ripple amplitude is 1%. The Parks-McClellan algorithm is used as the filter of the inverse SLR algorithm to calculate the waveform of the amplitude of the initial RF pulse changing with time, as shown in FIG. Figure 2 shown.

[0066] Step 2: Construct the objective function and constraints for RF pulse optimization

[0067] The time axis scaling factor is used to construct the objective function and constraint conditions of RF pulse optimization. The time axis scaling factor is used to scale the waveform of the initial RF pulse and the waveform of the initial layer selection gradient designed in step 1 on the time axis, so as to generate variable rate RF pulses. The objective function is to minimize the sum of the overall RF special absorption rate value of the RF pulse and the regularization term, or the objective function is to minimize the sum of the pulse duration and the regularization term. The regularization term is used to smooth the waveform of the RF pulse and the waveform of the layer selection gradient. The constraint condition is that the waveform of the layer selection gradient meets the maximum gradient strength and maximum climbing rate limits. The specific process is as follows:

[0068] Step 2.1: Set the timeline scaling factor to perform scaling operations

[0069] The amplitude of the i-th time segment of the initial RF pulse is recorded as B 1i , the time axis scaling factor of the i-th time segment is recorded as S i , the segment duration of each time segment before scaling is recorded as Δt, Δt is equal to the segment duration of the time segment corresponding to the initial RF pulse and the initial layer selection gradient; then the amplitude of the i-th time segment of the RF pulse after scaling is B 1i / S i, the intensity of the i-th time segment of the scaled layer selection gradient is G / S i , the length of the i-th time segment after scaling is Δt·S i .

[0070] The waveform of the initial RF pulse is discrete, and each time segment occupies a certain duration. The effect achieved by using the time axis scaling factor of each time segment to scale the pulse duration of the corresponding time segment, the amplitude of the initial RF pulse, and the intensity of the initial layer selection gradient is as follows: i When it is 2, the segment duration of the i-th time segment is multiplied by 2. At the same time, the amplitude of the i-th time segment of the scaled RF pulse is 1 / 2 of the amplitude of the i-th time segment of the initial RF pulse, and the intensity of the i-th time segment of the scaled layer selection gradient is 1 / 2 of the intensity of the initial layer selection gradient.

[0071] The overall RF specific absorption rate value of the initial RF pulse is calculated based on the following formula:

[0072]

[0073] Where SAR0 is the overall radiofrequency specific absorption rate value of the initial radiofrequency pulse, σ is the conductivity of the tissue, ρ is the tissue density, N is the number of time segments of the initial radiofrequency pulse, ∝ means proportional to, i is the sequence number of the time segment, i∈{1,2,…N};

[0074] Set the SAR threshold for radio frequency specific absorption rate th , compare the overall radio frequency special absorption rate value SAR0 of the initial radio frequency pulse with the radio frequency special absorption rate threshold SAR th , when the overall radio frequency specific absorption rate value SAR0 of the initial radio frequency pulse is greater than the radio frequency specific absorption rate threshold SAR th When the overall radio frequency special absorption rate value SAR0 of the initial radio frequency pulse is less than or equal to the set radio frequency special absorption rate threshold SAR th , proceed to step 2.3.

[0075] Step 2.2: Keep the pulse duration unchanged and minimize the RF specific absorption rate by scaling the amplitude of the initial RF pulse.

[0076] The objective function aims to minimize the overall RF special absorption rate value of the RF pulse. At the same time, the total variation (TV) regularization term is introduced to constrain the waveform of the generated RF pulse and the waveform of the layer selection gradient, making the waveform of the RF pulse and the waveform of the layer selection gradient smoother.

[0077] To ensure that the total pulse duration of the scaled RF pulse remains unchanged from the pulse duration of the initial RF pulse, we have:

[0078]

[0079] N is the time segment number of the initial RF pulse, S i is the time axis scaling factor of the i-th time segment. Therefore, the overall RF SAR value of the scaled RF pulse is expressed as:

[0080]

[0081] ∝ means proportional to.

[0082] Since the intensity of the layer selection gradient and the amplitude of the radio frequency pulse are also scaled by the time axis scaling factor, the intensity of the layer selection gradient in each time segment must meet the maximum gradient intensity and maximum climbing rate limits (that is, the waveform of the layer selection gradient must meet the maximum gradient intensity and maximum climbing rate limits).

[0083] Therefore, the goal is to minimize the overall RF special absorption rate of the RF pulse, while also constraining the smoothness of the RF pulse waveform and the layer selection gradient waveform to solve the overfitting problem. The layer selection gradient waveform meets the maximum gradient and maximum climbing rate constraints. The objective function constructed is to minimize the sum of the overall RF special absorption rate of the RF pulse and the regularization term. The objective function and constraints are as follows:

[0084]

[0085] Among them, lamda is a parameter for adjusting the smoothness, and diff represents the difference function of the corresponding calculation formulas of two adjacent time segments. By reducing the difference between the corresponding calculation formulas of adjacent time segments, the smoothness of the change of the time axis scaling factor is increased. max is the maximum gradient strength, G is the strength of the initial layer selection gradient, and the strength of the initial layer selection gradient G cannot exceed the maximum gradient strength G during scaling. max Δt is the duration of each time segment before scaling. After scaling, the change in the intensity of the layer selection gradient cannot exceed the maximum climbing rate SR of the layer selection gradient. max , st represents the constraint condition. Among them, S i+1 Indicates the time axis scaling factor for the i+1th time segment.

[0086] Step 2.3: Keep the overall RF special absorption rate of the RF pulse unchanged, minimize the sum of the pulse duration and the regularization term, and ensure that the waveform of the layer selection gradient meets the maximum gradient intensity and maximum climbing rate constraints.

[0087] The constructed objective function and constraints are as follows:

[0088]

[0089] The definition of each parameter is consistent with formula (5). In this embodiment, the lamda value used in the objective function is 0.05.

[0090] Step 3: Construct an optimization algorithm for variable rate RF pulse optimization. The optimization algorithm optimizes the initial value distribution of the time axis scaling factor by combining the objective function and the constraint conditions to obtain the final optimized time axis scaling factor value distribution.

[0091] Set the initial value distribution of the time axis scaling factor. The initial value distribution of the time axis scaling factor includes the initial value of the time axis scaling factor corresponding to each time segment. Substitute the initial value distribution of the time axis scaling factor into the objective function constructed in step 2. Perform iterative calculation based on the corresponding constraints and the selected optimization algorithm to obtain the corresponding iteratively optimized time axis scaling factor value distribution as the final optimized time axis scaling factor value distribution.

[0092] The iterative calculation specifically includes the following steps:

[0093] The initial value distribution of the time axis scaling factor is substituted into the objective function constructed in step 2, and the optimized time axis scaling factor value distribution of the first round of iteration is obtained based on the corresponding constraints and the selected optimization algorithm. Then, the optimized time axis scaling factor value distribution of the first round of iteration is used as the input of the objective function in the second round of iteration, and the selected optimization algorithm is continued to be used to calculate the optimized time axis scaling factor value distribution of the second round of iteration. Similarly, the optimized time axis scaling factor value distribution of the previous round of iteration is used as the input of the objective function in this round of iteration, and the optimized time axis scaling factor value distribution of this round of iteration is calculated by the optimization algorithm until the change in the value of the objective function in two adjacent rounds of iteration is less than the set tolerance, or the number of completed iterations reaches the iteration number threshold. The corresponding optimized time axis scaling factor value distribution is used as the iterative optimized time axis scaling factor value distribution corresponding to the initial value distribution of the time axis scaling factor.

[0094] Since the objective function constructed in step 2 is a nonlinear programming problem, a constrained nonlinear optimization algorithm is used to optimize the pulse. This embodiment uses MATLAB's fmincon function to optimize the initial value of the time axis scaling factor in the time axis scaling factor initial value distribution, using a sequential quadratic programming (SQP) algorithm, which is suitable for nonlinear problems with nonlinear constraints.

[0095] Step 4: Interpolate and smooth to obtain variable rate RF pulses and layer selection gradients

[0096] Based on the final optimized time axis scaling factor value distribution obtained in step 3, the initial RF pulse and initial layer selection gradient are scaled using the time axis scaling factor in the final optimized time axis scaling factor value distribution. The time segments corresponding to the scaled RF pulse (i.e., the variable rate RF pulse) and the scaled layer selection gradient are not of equal duration. The scaled RF pulse and the scaled layer selection gradient are interpolated and resampled to equalize the duration, resulting in a variable rate RF pulse and corresponding layer selection gradient with equal time interval distribution.

[0097] This embodiment uses Smoothing Spline in MATLAB to fit the waveform and resample it to obtain variable rate radio frequency pulses and corresponding slice selection gradients with equal time interval distribution. The waveform of the variable rate radio frequency pulse and the corresponding slice selection gradient obtained based on the minimization of the radio frequency special absorption rate value is shown in the figure below. Figure 3 As shown in the figure, the waveform of the variable rate RF pulse and the corresponding slice selection gradient obtained by minimizing the pulse duration is shown in Figure 4 shown.

[0098] The performance of the optimized variable-rate RF pulse was evaluated, including a comparison of the overall RF special absorption rate value and pulse duration of the RF pulse, as well as the layer-selective excitation capability. The overall RF special absorption rate value of the RF pulse was calculated using formula (4). After calculation, the overall RF special absorption rate value of the variable-rate RF pulse obtained by minimizing the RF special absorption rate value in this embodiment was 23.82% of the overall RF special absorption rate value of the initial RF pulse. The pulse duration of the variable-rate RF pulse obtained by minimizing the pulse duration was 52.01% of the pulse duration of the initial RF pulse.

[0099] The forward SLR algorithm is used to evaluate the selective excitation capability of variable rate RF pulses, that is, the precession and nutation of the excitation signal corresponding to different selected layer positions in each discrete time segment are calculated, and finally the excitation signal intensity at different selected layer positions is obtained. This embodiment calculates the pulse duration to minimize the selective excitation effect under the combined action of variable rate RF pulses and layer selection gradients, such as Figure 5 As shown in the figure, the variable-rate RF pulse designed in this embodiment shortens the pulse duration to 52.01% of the initial RF pulse duration while maintaining the overall RF SAR value of the RF pulse. Furthermore, the signal excitation intensity of the variable-rate RF pulse at different layer selection positions is nearly consistent with that of the initial RF pulse, maintaining good layer selection excitation capability.

[0100] Furthermore, when there are many variables, the quadratic programming algorithm runs slowly in step 3. Therefore, in step 1, the number of time segments of the initial RF pulse is reduced, and the initial RF pulse is resampled based on the reduced number of time segments. The initial RF pulse is resampled into 200 time segments using spline interpolation in the interp1 function in MATLAB to reduce the overall computational overhead. Then, the initial value of the time axis scaling factor in the initial value distribution of the time axis scaling factor is optimized according to the objective function.

[0101] Furthermore, in step 3, multiple groups of different time axis scaling factor initial value distributions are set, each group of time axis scaling factor initial value distributions includes the time axis scaling factor initial value corresponding to each time segment, each group of time axis scaling factor initial value distributions is located in a different numerical range, and the time axis scaling factor initial value in each group of time axis scaling factor initial value distributions are all linearly distributed. In this embodiment, the three different groups of time axis scaling factor initial value distributions are: 0.5 to 1.5, 200 time segments; 1.5 to 0.5, 200 time segments; all 1,200 time segments. For each group of time axis scaling factor initial value distributions, first substitute them into the objective function constructed in step 2, and then use the optimization algorithm (the optimization algorithm in this embodiment is the quadratic programming algorithm) based on the corresponding constraints to iteratively calculate the corresponding iteratively optimized time axis scaling factor value distribution. An iteratively optimized time axis scaling factor value distribution is calculated under each set of time axis scaling factor initial value distributions. From all iteratively optimized time axis scaling factor value distributions, the iteratively optimized time axis scaling factor value distribution with the smallest corresponding objective function value is selected as the final optimized time axis scaling factor value distribution.

[0102] It should be noted that the embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A variable rate radio frequency pulse design method for sodium magnetic resonance imaging, characterized in that: The following steps are involved: Step 1: Design the waveform of the initial radio frequency pulse and the waveform of the initial slice selection gradient; Step 2: construct the objective function and constraints for RF pulse optimization based on the time axis scaling factor; The time axis scaling factor is used to scale the waveform of the initial radio frequency pulse and the waveform of the initial slice selection gradient on the time axis; The objective function is to minimize the sum of the overall RF special absorption rate value of the RF pulse and the regularization term, or the objective function is to minimize the sum of the pulse duration and the regularization term. The regularization term is used to smooth the waveform of the RF pulse and the waveform of the layer selection gradient. The constraint condition is that the waveform of the layer selection gradient meets the maximum gradient strength and maximum climbing rate limits. Step 3: Set the initial value of the time axis scaling factor corresponding to each time segment in the initial value distribution of the time axis scaling factor, construct an optimization algorithm for variable rate radio frequency pulse optimization, and optimize the initial value distribution of the time axis scaling factor in combination with the objective function and the constraint conditions to obtain the final optimized time axis scaling factor value distribution; Step 4: Based on the final optimized time axis scaling factor value distribution, the initial RF pulse and the initial layer selection gradient are scaled by the time axis scaling factor in the final optimized time axis scaling factor value distribution to obtain the scaled RF pulse and the scaled layer selection gradient.

2. A variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 1, characterized in that: The step 1 specifically includes the following steps: Determine the type of initial RF pulse, pulse duration, stopband ripple amplitude, passband ripple amplitude, selected layer thickness, time-bandwidth product, and number of time segments; The waveform of the initial radio frequency pulse is designed based on the type of the initial radio frequency pulse, the pulse duration, the stopband ripple amplitude, the passband ripple amplitude, and the selected layer thickness. The waveform of the initial radio frequency pulse represents the change of the amplitude of the initial radio frequency pulse over time. The waveform of the initial layer selection gradient is determined based on the product of the layer selection thickness and the time-bandwidth. The waveform of the initial layer selection gradient represents the change of the intensity of the initial layer selection gradient over time. The intensity of the initial layer selection gradient is: Where γ is the gyromagnetic ratio, T p is the pulse duration of the initial RF pulse, d is the slice thickness, TBP is the time-bandwidth product, and G is the strength of the initial slice gradient; The amplitude of the initial radio frequency pulse and the intensity of the initial slice selection gradient are both divided into multiple time segments according to the number of time segments, and the segment durations corresponding to the various time segments are equal.

3. The variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 2, characterized in that: The step 2 specifically includes the following steps: Step 2.1: Set the time axis scaling factor to perform scaling operations: The amplitude of the i-th time segment of the initial RF pulse is recorded as B 1i , the time axis scaling factor of the i-th time segment is recorded as S i , the segment length of each time segment before scaling is recorded as Δt; then the amplitude of the i-th time segment of the RF pulse after scaling is B 1i / S i , the intensity of the i-th time segment of the scaled layer selection gradient is G / S i , the length of the i-th time segment after scaling is Δt·S i ; The overall RF specific absorption rate value of the initial RF pulse is calculated based on the following formula: Where SAR0 is the overall radiofrequency specific absorption rate value of the initial radiofrequency pulse, σ is the conductivity of the tissue, ρ is the tissue density, N is the number of time segments of the initial radiofrequency pulse, ∝ means proportional to, i is the sequence number of the time segment, i∈{1,2,…N}; Set the SAR threshold for radio frequency specific absorption rate th , when the overall radio frequency specific absorption rate value SAR0 of the initial radio frequency pulse is greater than the radio frequency specific absorption rate threshold SAR th When the overall radio frequency special absorption rate value SAR0 of the initial radio frequency pulse is less than or equal to the set radio frequency special absorption rate threshold SAR th When , execute step 2.3; Step 2.2: Keeping the pulse duration constant, based on minimizing the sum of the overall RF specific absorption rate value of the RF pulse and the regularization term, construct the following objective function and constraints: Among them, lamda is the parameter for adjusting the smoothness, diff represents the difference function of the corresponding calculation formula of two adjacent time segments, G is the intensity of the initial layer selection gradient, G max is the maximum gradient strength, SR max is the maximum climbing rate of the layer selection gradient; st represents the constraint condition; Step 2.3: Keeping the overall RF special absorption rate of the RF pulse unchanged, minimize the sum of the pulse duration and the regularization term. The objective function and constraints are as follows:

4. The variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 1, characterized in that: The step 3 comprises the following steps: Set the initial value distribution of the time axis scaling factor. The initial value distribution of the time axis scaling factor includes the initial value of the time axis scaling factor corresponding to each time segment. Substitute the initial value distribution of the time axis scaling factor into the objective function constructed in step 2. Perform iterative calculation based on the corresponding constraints and the selected optimization algorithm to obtain the corresponding iteratively optimized time axis scaling factor value distribution as the final optimized time axis scaling factor value distribution.

5. The variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 1, characterized in that: The step 3 comprises the following steps: Set multiple groups of time axis scaling factor initial value distributions, each group of time axis scaling factor initial value distributions includes the time axis scaling factor initial value corresponding to each time segment, and each group of time axis scaling factor initial value distributions is in a different value range; Each set of time axis scaling factor initial value distributions is substituted into the objective function constructed in step 2, and iterative calculations are performed based on the corresponding constraints and the selected optimization algorithm to obtain the corresponding iteratively optimized time axis scaling factor value distributions; From all iteratively optimized timeline scaling factor value distributions, a set of iteratively optimized timeline scaling factor value distributions whose corresponding objective function values ​​are minimized is selected as the final optimized timeline scaling factor value distribution.

6. A variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 4 or 5, characterized in that: The iterative calculation specifically includes the following steps: The initial value distribution of the time axis scaling factor is substituted into the objective function constructed in step 2, and the optimized time axis scaling factor value distribution of the first round of iteration is obtained based on the corresponding constraints and the selected optimization algorithm. Then, the optimized time axis scaling factor value distribution of the first round of iteration is used as the input of the objective function in the second round of iteration, and the selected optimization algorithm is continued to be used to calculate the optimized time axis scaling factor value distribution of the second round of iteration. Similarly, the optimized time axis scaling factor value distribution of the previous round of iteration is used as the input of the objective function in this round of iteration, and the optimized time axis scaling factor value distribution of this round of iteration is calculated by the optimization algorithm until the change in the value of the objective function in two adjacent rounds of iteration is less than the set tolerance, or the number of completed iterations reaches the iteration number threshold. The corresponding optimized time axis scaling factor value distribution is used as the iterative optimized time axis scaling factor value distribution corresponding to the initial value distribution of the time axis scaling factor.

7. The variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 2, characterized in that: The type of the initial RF pulse is an SLR pulse. The waveform of the initial RF pulse is designed using an inverse SLR algorithm. The Parks-McClellan algorithm is used as a filter for the inverse SLR algorithm. The selected layer thickness, pulse duration, stopband ripple amplitude, and passband ripple amplitude are input to the inverse SLR algorithm to calculate the waveform of the initial RF pulse.

8. A variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 4 or 5, characterized in that: The optimization algorithm is a sequential quadratic programming algorithm.

9. A variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 4 or 5, characterized in that: The time axis scaling factor initial values ​​in the time axis scaling factor initial value distribution are distributed linearly.

10. The variable rate radio frequency pulse design method for sodium magnetic resonance imaging according to claim 1, characterized in that: The step 4 further comprises the following steps: The scaled radio frequency pulses and the scaled slice selection gradients are interpolated and resampled to obtain variable rate radio frequency pulses and corresponding slice selection gradients with equal time interval distribution.

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