A magnetic resonance sequence parameter joint optimization method based on Cramer-Rao lower bound

Abstract

The application discloses a magnetic resonance sequence parameter joint optimization method based on Cramer-Rao lower bound, which comprises two parts of multilayer perception network construction and joint loss function setting. The Cramer-Rao lower bound is obtained based on preset biological tissue parameters and network output optimization parameters to form a CRLB loss term, and a time penalty term related to the total time length of sequence acquisition is constructed based on the recovery interval time. The network is iteratively trained by minimizing the joint loss function composed of the CRLB loss term and the time penalty term, and the optimization parameters finally output by the network model are combined for scanner sequence setting to complete imaging. The application realizes efficient joint optimization of flip angles and key timing parameters without a large number of physical scanning tests, reduces the acquisition time length while ensuring or improving the accuracy of quantitative parameter maps, and the optimized parameters can reduce the number of readout sections of the magnetic resonance sequence, thereby realizing the reduction of the scanning time.

Description

Technical Field

[0001] This invention belongs to the field of magnetic resonance imaging sequence optimization technology, specifically involving a joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound. Background Technology

[0002] Quantitative magnetic resonance imaging (QMRI) is an advanced medical imaging technique that provides intrinsic tissue physical parameters such as longitudinal relaxation time (T1), transverse relaxation time (T2), and proton density (PD). It has significant applications in the early diagnosis and pathological assessment of diseases such as Alzheimer's disease, multiple sclerosis, and brain tumors. Among these, the 3D-QALAS (3D-quantification using an interleaved Look-Locker acquisition sequence with T2 preparation pulse) sequence has attracted considerable attention because it can simultaneously acquire high-resolution T1, T2, and PD parameter maps of the entire brain in a single scan. This sequence typically includes multiple interleaved Turbo FLASH readout segments and a T2 preparation module, encoding different relaxation information through specific timing design.

[0003] However, traditional 3D-QALAS sequences have significant limitations in parameter settings. Current sequence parameters, including the flip angle (FA) of the Turbo FLASH readout segment, the recovery interval (GAP) between readout segments, and the echo time (TE) of the T2 preparation module, are mostly set based on experience. This non-optimized parameter configuration often fails to achieve the best signal-to-noise ratio and parameter estimation accuracy for specific biological tissues (such as gray and white matter), and also results in longer scan times, limiting its widespread clinical application.

[0004] To address the parameter configuration problem, researchers have proposed optimization strategies based on the Cramer-Rao Lower Bound (CRLB). For example, existing studies have used automatic differentiation techniques to find schemes that minimize the flip angle of the CRLB, such as the literature [Arefeen, Y., Gagoski, B., Jun, Y., Bilgic, B., & Adalsteinsson, E. (2023). Improved T1 and T2 mapping in 3D-QALAS using temporal subspaces and flip angle optimization enabled by auto-differentiation. In Proceedings of the International Society for Magnetic Resonance in Medicine Annual Meeting] and the literature [Lee, PK, Watkins, LE, Anderson, TI, Buonincontri, G. & Hargreaves, BA Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations. Magn. Reson. Med. 82, 1438-1451 (2019)]. While these methods perform reasonably well in optimizing single flip angles, their search efficiency and convergence performance are often insufficient when faced with the complex combination optimization of hundreds or thousands of flip angles in a Turbo FLASH echo chain. More importantly, most existing methods only focus on optimizing flip angles, neglecting the joint adjustment of sequence timing parameters (such as TE and GAP), and it is difficult to effectively reduce the number of readout segments to shorten scan time while ensuring image quality.

[0005] Therefore, how to achieve efficient and joint optimization of the flip angle sequence and key timing parameters in the sequence through theoretical model guidance without requiring a large number of physical scanning tests, and how to use the powerful nonlinear expression capabilities of deep learning models (such as multilayer perceptrons) to overcome the limitations of traditional gradient descent methods, thereby significantly reducing scanning time while improving the accuracy of quantitative parameter maps, is a key challenge that urgently needs to be solved in the field of quantitative magnetic resonance sequence design. Summary of the Invention

[0006] To address the problems of existing quantitative magnetic resonance imaging (MRI) sequence parameters, such as those in 3D-QALAS, which rely heavily on empirical settings and struggle to balance quantitative accuracy with scan time, and the low efficiency and insufficient convergence of existing CRLB-based gradient optimization methods in high-dimensional parameter searches, often focusing only on the flip angle while neglecting the joint adjustment of key timing parameters, this invention provides a joint optimization method for MRI sequence parameters based on the Cramer-Rhodes lower bound. This method eliminates the need for extensive physical scanning tests and can achieve efficient joint optimization of the flip angle and key timing parameters under the guidance of theoretical models. This reduces the total sequence acquisition time while ensuring or improving the quantitative accuracy of T1, T2, and PD, thereby enhancing the clinical usability and scalability of quantitative MRI.

[0007] A joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound includes the following steps: (1) Determine the initial parameters to be optimized in the magnetic resonance sequence, including the flip angle FA of the readout segment, the echo time TE of the T2 preparation module, and the recovery interval time GAP between readout segments; (2) Construct a self-supervised MLP (Multilayer Perceptron) network and use the initial parameters as the input of the network; (3) The CRLB loss is calculated using the optimization parameters output by the MLP network and the preset biological tissue parameters to evaluate the accuracy of the optimization parameters; (4) Calculate the time penalty term loss based on the recovery interval time in the output optimization parameters of the MLP network, which is used to constrain the total scan duration of the sequence; (5) Construct a joint loss function that includes CRLB loss and time penalty term loss, and iteratively train the MLP network by minimizing the joint loss function; (6) Apply the optimized parameters generated by the final output of the MLP network after training to the sequence settings of the magnetic resonance scanner for imaging.

[0008] Furthermore, in step (2), the initial flip angle FA, recovery interval time GAP, and echo time TE are concatenated into a one-dimensional vector, which is used as the input data of the MLP network.

[0009] Furthermore, the MLP network consists of an input layer, a hidden layer with a size of 300×100×300, and an output layer connected in sequence. The output layer outputs three optimized parameter variables: optimized flip angle oFA, optimized recovery interval time oGAP, and optimized echo time oTE. During the optimization process of the MLP network, numerical constraints need to be applied to the output parameters. Specifically, the constraints are: the range of oFA is limited to 2° to 6°, and the range of oGAP is limited to 750ms to 1000ms.

[0010] Furthermore, in step (3), representative brain tissue parameters are selected as targets when calculating CRLB loss. The brain tissue parameters include white matter and gray matter. The white matter parameters are set to T1=700ms, T2=70ms, M0=1; the gray matter parameters are set to T1=1300ms, T2=80ms, M0=1, where M0 represents the proton density-weighted longitudinal equilibrium magnetization. At the same time, different weights are assigned according to different parameters to be measured (T1, T2, PD) to prioritize optimizing the estimation accuracy of tissue parameters with shorter T1 and T2 values.

[0011] Furthermore, the time penalty term loss in step (4) is calculated by summing the optimized recovery interval time oGAP between all readout segments output by the MLP network, aiming to reduce the acquisition time of the sequence while ensuring image quality.

[0012] Furthermore, the joint loss function expression in step (5) is as follows: in: Indicates the first i The weights corresponding to each organizational parameter CRLB i To calculate the value of the first parameter based on the optimized parameters i The lower bound of the Cramé-Röhler parameter for each organization. TimePenalty Loss due to time penalty item It is a balancing coefficient, whose value ensures that the two loss values ​​are on similar orders of magnitude.

[0013] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rao lower bound.

[0014] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rao lower bound.

[0015] This invention achieves efficient joint optimization of the flip angle and key timing parameters without requiring extensive physical scanning tests, reducing acquisition time while ensuring or improving the accuracy of quantitative parametric maps. Applying the optimized parameters of this invention can reduce the number of readout segments in the magnetic resonance imaging sequence, thereby reducing scan time. Furthermore, this method can be extended to the simultaneous optimization of multiple parameters in various magnetic resonance imaging sequences, such as 3D-QALAS and MR Fingerprinting sequences. Attached Figure Description

[0016] Figure 1This is a schematic diagram of the overall process of the magnetic resonance sequence parameter joint optimization method based on the Cramer-Rhodes lower bound of the present invention.

[0017] Figure 2 This is a schematic diagram of a multilayer perceptron network.

[0018] Figure 3 This is an ablation experiment diagram of a multilayer perceptron network structure.

[0019] Figure 4 The figure shows a comparison of simulation experiments of the unoptimized method, the traditional optimized method, and the optimized method of this invention.

[0020] Figure 5 The images show the quantitative results of real-world water model scanning under the unoptimized, conventionally optimized, and optimized methods of this invention.

[0021] Figure 6 for Figure 5 The numerical analysis graph shows the quantitative results of the actual scanning water model.

[0022] Figure 7 Images show the actual quantitative results of brain scans under the gold standard, unoptimized, traditionally optimized, and the optimized method of this invention. Detailed Implementation

[0023] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] Example: This embodiment provides a joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound, such as... Figure 1 As shown, the core process of this method mainly includes two parts: multilayer perceptron network construction and joint loss function setting.

[0025] (1) Construction and parameter initialization of multilayer perceptron network.

[0026] Parameter Initialization and Input: First, determine the initial parameters of the 3D-QALAS sequence to be optimized. In a preferred embodiment, the initial parameters are set as follows: flip angle FA = 4°, length 640, echo time TE of the T2 preparation module = 109.7 ms, recovery interval time GAP between readout segments = 900 ms, and length 5. The initial parameters FA, GAP, and TE are concatenated into a one-dimensional vector, which serves as the input data for the neural network.

[0027] Network initialization: A self-supervised multilayer perceptron network is used to optimize and model the sequence parameters, such as... Figure 2As shown, the network consists of one input layer, one hidden layer, and one output layer. Ablation experiments validated that the preferred hidden layer structure has dimensions of 300×100×300 (i.e., three consecutive hidden layers with 300, 100, and 300 nodes respectively), and the activation function is ReLU. Compared to traditional gradient descent methods, this deep network structure can more effectively capture the complex nonlinear relationships and deep feature representations within the input vector.

[0028] Output and Constraints: The network's output layer corresponds to three optimized parameter variables: optimized flip angle oFA, optimized recovery interval time oGAP, and optimized echo time oTE. To ensure that the output sequence parameters are within the hardware limits of the magnetic resonance scanner and conform to the physical laws of imaging, numerical constraints are applied to the network output: , This constraint limits the search space for the flip angle and time interval, ensuring the feasibility of the optimization results.

[0029] (2) Setting the joint loss function.

[0030] Cramer-Robb lower bound loss: This loss term is used to evaluate the lower bound of the theoretical accuracy of the tissue parameter (T1, T2, PD) estimation under optimized parameters. To make the optimized sequence closer to actual clinical needs, this embodiment selects two representative brain tissue parameters as optimization targets: white matter parameters are set as [T1=700ms, T2=70ms, M0=1]; gray matter parameters are set as [T1=300ms, T2=80ms, M0=1]. When calculating the CRLB value, weights are assigned according to different parameters to be measured (T1, T2, PD) [1 / T1...]. 2 , 1 / T2 2 [1], in order to prioritize the quantification accuracy of short T1 and T2 tissues.

[0031] Time penalty term: In order to achieve the goal of shortening the scan time, a time penalty term is introduced. This term is calculated by summing the output recovery interval time oGAP. Minimizing this term can drive the network to find the parameter combination with a shorter total scan time in the solution space.

[0032] The final joint loss function expression is: in: tissues This indicates the number of representative brain tissue parameters mentioned above (in this embodiment, it is taken as 2, corresponding to gray matter and white matter). Indicates the first i The weights corresponding to each organizational parameter CRLB i To calculate the value of the first parameter based on the optimized parameters iThe lower bound of the Cramé-Röhler parameter for each organization. TimePenalty For time penalty items, This is a balancing coefficient, whose value ensures that the two loss values ​​are on similar orders of magnitude. In this embodiment, it is taken as... .

[0033] The Cramer-Rao lower bound is a theoretical limit used to assess the accuracy of an estimator. The variance of any unbiased estimator must be greater than or equal to the CRLB value, expressed as: in: X The signal was acquired during the scan sequence. E For mathematical expectation, For the parameters to be optimized (e.g., FA, GAP, TE), For Kramer-Lo's lower realm, Indicates in the parameter The signal to be measured X The probability density function of occurrence.

[0034] Using the aforementioned loss function, the MLP network is iteratively updated via backpropagation, with the Adam optimizer selected and the iteration count set to 1000. After optimization, the network output parameters are applied to 3D-QALAS sequence acquisition.

[0035] Experimental results show that the optimized parameters of this invention can reduce the number of Turbo FLASH readout segments from the traditional 5 to 3 or 4. Specifically, the optimized sequences with 3 and 4 readout segments achieved a 40% and 20% reduction in scan time, respectively, and the generated T1 and T2 quantitative maps were comparable to those of the traditional 5-readout-segment sequence in terms of error level, effectively solving the problem of long scan time in the traditional method.

[0036] Verification example: This verification example is divided into two parts: a simulation experiment and a real experiment. The simulation experiment part is as follows: Figure 3 and Figure 4 As shown, a brain digital model was constructed, and ablation experiments with different MLP network structures and comparative experiments with traditional optimization methods and unoptimized sequences were carried out using this model.

[0037] exist Figure 3 In the ablation experiments, the 300×100×300 network structure outperformed both the 300×300 and 100×100 network structures. Furthermore, the complexity of the network structure affects the sequence optimization speed; therefore, considering both optimization performance and speed, the 300×100×300 network structure was chosen. Additionally, a mask was selected to extract the region of interest, and the deviation between this region and the ground truth was calculated. ,in and These represent the true quantitative value of the parameters and the quantitative simulation results, respectively.

[0038] exist Figure 4 In the comparative experiments, we compared five unoptimized readout sequences (5 minutes), four conventionally optimized readout sequences with the optimization method described in this invention (4 minutes), and three conventionally optimized readout sequences with the optimization method described in this invention (3 minutes). The results show that the optimization method of this invention can still achieve the original or higher quantitative accuracy with fewer readouts, i.e., less scan time.

[0039] Real experimental section: Figure 5 The results of the actual scanned water model experiment are shown. The experiment compares: five unoptimized readout sequences (5 minutes), four unoptimized readout sequences, conventional optimization, and the optimization method described in this invention (4 minutes), and three unoptimized readout sequences, conventional optimization, and the optimization method described in this invention (3 minutes).

[0040] Figure 6 Showing Figure 5 Numerical analysis showed that the four readouts of the optimized sequence of this invention can achieve better quantitative results than the first five readouts. That is, the present invention can reduce the scanning time by about 20% and obtain higher accuracy.

[0041] Figure 7 The image shows the quantitative results of a real brain scan, with a magnified region of interest. The results indicate that the optimization method of this invention can improve the signal-to-noise ratio of the image and obtain better image contrast, especially in T2 quantitative maps.

[0042] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound, characterized in that, Includes the following steps: (1) Determine the initial parameters to be optimized in the magnetic resonance sequence, including the flip angle FA of the readout segment, the echo time TE of the T2 preparation module, and the recovery interval time GAP between readout segments; (2) Construct a self-supervised MLP network, using the initial parameters as the input to the network; (3) The CRLB loss is calculated using the optimization parameters output by the MLP network and the preset biological tissue parameters to evaluate the accuracy of the optimization parameters; (4) Calculate the time penalty term loss based on the recovery interval time in the output optimization parameters of the MLP network, which is used to constrain the total scan duration of the sequence; (5) Construct a joint loss function that includes CRLB loss and time penalty term loss, and iteratively train the MLP network by minimizing the joint loss function; (6) Apply the optimized parameters generated by the final output of the MLP network after training to the sequence settings of the magnetic resonance scanner for imaging.

2. The method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound according to claim 1, characterized in that: In step (2), the initial flip angle FA, recovery interval time GAP, and echo time TE are concatenated into a one-dimensional vector, which is used as the input data of the MLP network.

3. The method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound according to claim 1, characterized in that: The MLP network consists of an input layer, a hidden layer with dimensions of 300×100×300, and an output layer connected in sequence. The output layer outputs three optimized parameter variables: optimized flip angle oFA, optimized recovery interval time oGAP, and optimized echo time oTE. During the optimization process of the MLP network, numerical constraints need to be applied to the output parameters. Specifically, the range of oFA is limited to 2° to 6°, and the range of oGAP is limited to 750ms to 1000ms.

4. The method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound according to claim 1, characterized in that: In step (3), representative brain tissue parameters are selected as targets when calculating CRLB loss. The brain tissue parameters include white matter and gray matter. The white matter parameters are set to T1=700ms, T2=70ms, M0=1; the gray matter parameters are set to T1=1300ms, T2=80ms, M0=1, where M0 represents the proton density-weighted longitudinal equilibrium magnetization. At the same time, different weights are assigned according to different parameters to be measured, so as to prioritize the optimization of the estimation accuracy of tissue parameters with shorter T1 and T2 values.

5. The method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound according to claim 3, characterized in that: The time penalty term loss in step (4) is calculated by summing the optimized recovery interval time oGAP between all readout segments output by the MLP network, aiming to reduce the acquisition time of the sequence while ensuring image quality.

6. The method for joint optimization of magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound according to claim 1, characterized in that, The joint loss function expression in step (5) is as follows: in: Indicates the first i The weights corresponding to each organizational parameter CRLB i To calculate the value of the first parameter based on the optimized parameters i The lower bound of the Cramé-Röhler parameter for each organization. TimePenalty Loss due to time penalty item It is a balancing coefficient, whose value ensures that the two loss values ​​are on similar orders of magnitude.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: The processor is used to execute the computer program to implement the joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rhodes lower bound as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the joint optimization method for magnetic resonance sequence parameters based on the Cramer-Rao lower bound as described in any one of claims 1 to 6.

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