System and method of creating and using automated system for physics control

Abstract

Systems and methods are described that utilize a generalized physics-guided self-supervised learning (GPS) artificial intelligence (AI) system that can be applied to design magnetic resonance imaging (MRI) radiofrequency (RF) pulses. The AI system may also compensate for experimental and scanner imperfections using online adaptation.

Description

Atty. Dkt. No.125141.04843.MGH2024-359 SYSTEM AND METHOD OF CREATING AND USING AUTOMATED SYSTEM FOR PHYSICS CONTROL Cross Reference to Related Applications

[0001] The present application is based on, claims priority to, and incorporates herein by reference in its entirety for all purposes, US Provisional Application Serial No.63 / 665,204, filed June 27, 2024. Statement of Government Support

[0002] This invention was made with government support under 1R56AR081017, 5R01AR081344-03, 5R21EB031185-03, and 5R01AR079442-03 awarded by the National Institutes of Health. The government has certain rights in the invention. Background

[0003] Deep learning (DL) has profoundly influenced many fields of physics, including but not limited to the field of medical imaging. It has been successfully applied in medical image analysis, such as image segmentation, registration, synthesis, and computer-aided diagnosis. Recently, DL leveraging convolutional neural networks (CNNs) to extract image features using data-driven approaches has also gained considerable interest and popularity in MRI acquisition and reconstruction. Varying implementations of DL have been shown to enable proficient networks to identify and remove artifacts and noise that arise from undersampled k-space in accelerated MRI.

[0004] On the acquisition side of the MRI process, learning-based methods have been applied in designing RF pulses. Early studies used a machine learning approach to design RF shimming where models characterize features from simulation data using numerical phantoms and in vivo subjects to achieve patient-tailored and calibration-free shimming. More recently, DL has also been investigated for RF pulse design. Several works have used supervised deep learning to generate RF pulses based on learning on the training datasets.

[0005] Reinforcement learning (RL) is another DL paradigm that uses an agent to act in an environment. Instead of using a traditional data-driven approach, RL assigns the objective of maximizing a reward based on environmental feedback. Work has also been shown to use RL in designing RF pulses, where a Bloch simulator was treated as an environment, and theAtty. Dkt. No.125141.04843.MGH2024-359 corresponding reward was used to minimize differences between the target RF excitation profile and the estimated profile in design. Although supervised learning and reinforcement learning have both shown great capabilities in designing various RF pulses, they are not without challenges. Supervised learning typically relies on a large amount of labeled data for adequate training, which can be challenging to access in MRI. Although researchers have made creative efforts, such as using extensive natural image databases and numerical simulations, to augment training data size, there is no guarantee that the trained model will behave optimally when facing severe data discrepancy between training and testing in real applications. Reinforcement learning is also known to be challenging to implement. Its utilization has been limited because of the non- trivial design of a suitable state space, action space, and reward function for MRI applications. Overall, supervised learning and reinforcement learning both require substantial training effort for the model to converge.

[0006] Thus, there is a need to develop a DL approach in the design and control of systems for physics control, such as MRI. As one non-limiting example, there is a need to develop a DL approach for the design of RF pulses for MRI that does not require vast amounts of labeled data and retains high performance on testing data. Summary

[0007] The present disclosure provides systems and methods that overcome the aforementioned drawbacks by providing a method that integrates a physics model into a self-supervised learning framework as a means of guiding and enforcing the learning process for control of physics control systems. A system may be provided that forms a generalized physics-guided self- supervised learning (GPS) system. When applied to the example of MRI, Bloch equations can be leveraged as the physics model to enable various RF design applications. GPS’s generalizability by designing 1D selective, B1-insensitive, saturation, and multidimensional RF pulses, each of which conventionally requires separate dedicated design algorithms. By integrating online adaptation in GPS, scanner imperfections such as ^^^^0 / ^^^^1+inhomogeneity can be accounted for, often occurring in real-time applications. By employing a self-supervised learning framework instead of relying on large, labeled datasets, the systems and methods described herein can use the Bloch equations as a physics model to generate supervisory signals during training. This approach leverages the intrinsic physical properties of MRI to guide the learning process.Atty. Dkt. No.125141.04843.MGH2024-359

[0008] In one aspect of the present disclosure, a radiofrequency (RF) pulse design system is provided. The system comprises a processor comprising a self-supervised artificial intelligence (AI) system including a neural network module (^^^^^^^^^^^^(^^^^)) and a physics module (^^^^(∙)) based on Bloch equations, configured to (a) receive a target RF excitation profile (^^^^^^^^^^^^^^^^), (b) in^^^^^^^^^^^^^^^^^^^^put the ^^^^^^^^^^^^into the neural network module to generate an RF pulse (^^^^^^^^∗), and (c) input the ^^^^^^^^∗into the ^^^^(∙) to generate a Bloch-simulated RF excitation profile (^^^^^∗^^^^^^^).

[0009] In another aspect of the present disclosure, a method of designing a radiofrequency (RF) is provided. The method comprises (a) receiving, via a processor including a self-supervised artificial intelligence (AI) system including a neural network module (^^^^^^^^^^^^(^^^^)) and a physics module (^^^^(∙)) based on Bloch equations, a target RF excitation profile (^^^^^^^^^^^^^^^^^^^^^^^^), (b) inputting, via the processor, the ^^^^^^^^^^^^^^^^^^^^^^^^into the ^^^^^^^^^^^^(^^^^) to generate a RF pulse (^^^^^^^^∗), and (c) inputting, via the processor, the ^^^^^^^^∗into the ^^^^(∙) to generate a Bloch-simulated RF excitation profile (^^^^^∗^^^^^^^).

[0010] In another aspect of the present disclosure, a system for creating a pulse sequence for magnetic resonance imaging (MRI) is provided. The system comprises a neural network configured to generate a radiofrequency (RF) pulse for an MRI pulse sequence based on an input target RF excitation profile, a physics simulator configured to simulate the generated RF pulse to produce a simulated RF excitation profile, and a processor. The processor is configured to iteratively minimize a difference between the simulated RF excitation profile and the input target RF excitation profile to select a desired RF pulse for the MRI pulse sequence, and deliver the desired RF pulse for use by an RF system of an MRI system when performing the MRI pulse sequence.

[0011] In another aspect of the present disclosure, a method for creating a pulse sequence for magnetic resonance imaging (MRI) is provided. The method comprises generating, using a neural network, an RF pulse for an MRI pulse sequence based on an input target RF excitation profile, simulating, using a physics simulator, the generated RF pulse to produce a simulated RF excitation profile, iteratively minimizing, using a processor, a difference between the simulated RF excitation profile and the input target RF excitation profile to select a desired RF pulse for the MRI pulse sequence and delivering, using the processor, the desired RF pulse for use by an RF system of an MRI system when performing the MRI pulse sequence.

[0012] These aspects are nonlimiting. Other aspects and features of the systems and methods described herein will be provided below.Atty. Dkt. No.125141.04843.MGH2024-359 Brief Description of the Drawings

[0013] The foregoing features of embodiments will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which:

[0014] FIG.1 is a block diagram of an MRI system.

[0015] FIG.2 is a block diagram of an RF system of and MRI system.

[0016] FIG.3A is an exemplary architecture of generalized physics-guided self-supervised learning (GPS) consisting of a neural network module and a physics module for offline use, according to aspects of the present disclosure.

[0017] FIG.3B is an exemplary architecture of generalized physics-guided self-supervised learning (GPS) consisting of a neural network module and a physics module for online use on an MRI system, according to aspects of the present disclosure.

[0018] FIG.4A is an example method for designing an RF pulse, according to aspects of the present disclosure.

[0019] FIG.4B is an example method for creating a pulse sequence for MRI, according to aspects of the present disclosures.

[0020] FIG.5 is a diagram of an example GPS architecture consisting of a neural network module and a physics module. The neural network module takes the target profile ^^^^tgtPFas input and generates an RF pulse ^^^^RF(^^^^tgtPF|^^^^) as output. ^^^^RF(^^^^tgtPF|^^^^) is subsequently loaded into the physics module, which outputs the corresponding Bloch-simulated profile ^^^^P∗F = ^^^^(^^^^RF(^^^^tgtPF|^^^^)). The network parameters are trained by minimizing the difference between ^^^^tgt ∗PFand ^^^^PF. For online adaptation, scanner imperfections such as ^^^^0 / ^^^^1+inhomogeneity is included in the physics module. Using the parameters obtained from offline learning as initial values, the neural network module uses methods such as low-rank adaptation to expedite the learning process.

[0021] FIG.6A shows plots of one-dimensional selective RF pulse amplitude and phase designed using the Shinnar-Le Roux (SLR) algorithm overlaid with generalized RF pulse design using GPS design (left). Plots of both simulation and phantom experiment results (right) exhibit that the profiles generated by both pulses agree well.

[0022] FIG.6B shows plots of amplitude and phase modulation functions of the HS1 pulse overlaid with GPS-designed ^^^^1-insensitive pulse (left). Inversion profiles obtained fromAtty. Dkt. No.125141.04843.MGH2024-359 sweeping ^^^^1maxfrom 2.35 to 28.2 μT in both simulations and phantom experiments (right) show excellent agreement in addition to showing ^^^^1insensitivity for ^^^^1maxvalues beyond 18.8 μT.

[0023] FIG.7 shows plots of the learning dynamics of the generalized RF pulse design using GPS framework using 1D selective pulse design as an example. After the first iteration, the RF pulse already starts to take a single-lobe Gaussian-like shape. Through the supervision of the physics module, the neural network module learns to design the side lobes, resulting in a profile selectivity that starts to resemble the target (iteration 7). Further down, the overall and relative amplitudes of the 5 lobes are learned (iteration 37), which produces a profile that closely matches the target. In the latter stages of the design process, the pulse is fine-tuned so that its output optimally matches its target (iteration 114), which describes the low rate of the loss curve's decrease and Euclidean distance measurement (EDM) curve's increase.

[0024] FIG.8A shows a 0 Hz spectral excitation spectral-spatial (SPSP) pulse designed using conventional method overlaid with generalized RF pulse design using GPS design (left column). As shown in the zoom-in, in the gradient ramp regions, the pulse is 0 in the conventional design, whereas the GPS design is not. Despite these differences, simulation results obtained using both pulses (center column) show good agreement in terms of spectral and spatial selectivity. This was further confirmed through phantom experiments (right column).

[0025] FIG.8B shows a 440 Hz spectral excitation SPSP pulse designed using the conventional method overlaid with GPS design (left column). Similar to the 0 Hz case in FIG.8A, the GPS design differs from the conventional design in that it is not 0 in gradient ramp regions (zoom-in). The simulation (center column) and phantom experiment (right column) results obtained from both pulses agree well.

[0026] FIG.9 shows a 2D target profile composed of the letters “AI” (top left) input as a target profile to the generalized RF pulse design using GPS framework, which designed a 2D selective RF pulse (top right) using predefined spiral trajectory gradients (bottom right) designed to meet scanner gradient specifications. The simulated 2D profile obtained from Bloch simulations (bottom left) exhibits some blur because of the limited extent to which excitation k-space is sampled, but otherwise agrees well with the target profile.

[0027] FIG.10 shows anatomical knee images acquired using generalized RF pulse design using GPS 1D selective pulse (left column top) and Shinnar-Le Roux (SLR) (left column bottom), spectral-spatial (SPSP) selective pulse for 0 Hz (center column) and 440 Hz (right column) usingAtty. Dkt. No.125141.04843.MGH2024-359 both GPS and conventional. For the 1D selective images, both GPS and SLR agree well, with no noticeable difference. For 0 Hz water selective SPSP (center column), in both GPS (top row) and conventional (bottom row) images, the muscle and cartilage, indicated by arrows, appear bright, whereas bone marrow, infrapatellar fat pad, and other fatty tissue are dark, demonstrating that both pulse designs achieve good spectral selectivity at 0 Hz. The same can be said for the 440 Hz fat selective case (right column), whereby in both GPS (top row) and conventional (bottom row) images, bone marrow, infrapatellar fat pad, and other fatty tissue, indicated by arrows, appear bright whereas the muscle and cartilage appear dark.

[0028] FIG.11 depicts phantom ^^^^0 / ^^^^1+inhomogeneity online adaptation results. The left is the offline generalized RF pulse design using GPS-designed 2D selective RF pulse and its corresponding excitation profile in the presence ^^^^0 / ^^^^1+inhomogeneity. Experiment results show that the letters “A” and “I” are not well resolved, which was also confirmed by Bloch simulations. The online adapted GPS-designed 2D selective RF pulse and its corresponding excitation profile are shown on the right. Compared with the offline design, the online adapted RF pulse has a lower overall amplitude, which reflects the high relative values of the ^^^^1+map it has adapted to. Experiment results show both letters are now well resolved, which was also verified through simulations.

[0029] FIG.12 depicts in vivo ^^^^0 / ^^^^1+inhomogeneity online adaptation results. Offline generalized RF pulse design using GPS-designed 2D selective RF pulse and its corresponding excitation profile in the presence ^^^^0 / ^^^^1+inhomogeneity (left). Focusing within the dotted box, similar to the phantom results, the letters “A” and “I” are not well resolved, concurring with Bloch simulations. The online adapted GPS-designed 2D selective RF pulse and its corresponding excitation profile are shown on the right. As was the case for the phantom, the online adapted RF pulse has a lower overall amplitude in comparison with the offline design, reflecting the high relative values of the ^^^^1+map it has adapted to. Both letters are now well resolved, also confirmed by and showing good agreement with simulations. The existence of excitation outside the dotted box region is because of the 2D target profile provided as input to GPS being confined to the region within the dotted box, and the center anatomical image is displayed for reference.

[0030] FIG.13 shows profiles of GPS 1D selective RF pulse designed with target profile frequency ranges [-4.096 kHz, 4.096 kHz] (blue), [-8.192 kHz, 8.912 kHz] (orange), [-16.384Atty. Dkt. No.125141.04843.MGH2024-359 kHz, 16.384 kHz] (yellow) and [-32.768 kHz, 32.768 kHz] (purple). Each pulse design shows excellent agreement within their respective target frequency range.

[0031] FIG.14 shows plots of the adiabaticity of the HS1 (left) and GPS-designed B1-insensitive (right) pulse.

[0032] FIG.15 shows that sampling of the RF pulse during the gradient ramp regions can further be exploited to decrease the peak power of the SPSP pulse for a given target flip angle.

[0033] FIG.16 shows GPS-designed 1D selective RF pulse amplitude and phase designed using a rectangular function as target profile (left). Simulation and phantom experiment results are displayed on the right. Comparing the simulation results with SLR of identical specification, the GPS-designed 1D selective pulse exhibits passband ripples 0.1% vs.0.9%, stopband ripples 2% vs.1.2%, and transition width 400 vs.430 Hz. The rectangle function target profile is depicted by the black dashed line in the simulation plot. Detailed Description

[0034] Referring particularly now to FIG.1, an example of a magnetic resonance imaging (MRI) system 100 is illustrated. The MRI system 100 includes an operator workstation 102, which will typically include a display 104, one or more input devices 106, such as a keyboard and mouse, and a processor 108. The processor 108 may include a commercially available programmable machine running a commercially available operating system. The operator workstation 102 provides the operator interface that enables scan prescriptions to be entered into the MRI system 100. In general, the operator workstation 102 may be coupled to four servers: a pulse sequence server 110; a data acquisition server 112; a data processing server 114; and a data store server 116. The operator workstation 102 and each server 110, 112, 114, and 116 are connected to communicate with each other. For example, the servers 110, 112, 114, and 116 may be connected via a communication system 140, which may include any suitable network connection, whether wired, wireless, or a combination of both. As an example, the communication system 140 may include both proprietary or dedicated networks, as well as open networks, such as the internet.

[0035] The pulse sequence server 110 functions in response to instructions downloaded from the operator workstation 102 to operate a gradient system 118 and a radiofrequency (“RF”) system 120. Gradient waveforms necessary to perform the prescribed scan are produced and applied toAtty. Dkt. No.125141.04843.MGH2024-359 the gradient system 118, which excites gradient coils in an assembly 122 to produce the magnetic field gradients Gx, Gy, and Gz used for position encoding magnetic resonance signals. The gradient coil assembly 122 forms part of a magnet assembly 124 that includes a polarizing magnet 126 and a whole-body RF coil 128 and / or local coil, such as a chest or hand coil 129.

[0036] RF waveforms are applied by the RF system 120 to the RF coil 128, or a separate local coil 129, in order to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil 128, or a separate local coil, such as the local coil 129, are received by the RF system 120, where they are amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server 110. The RF system 120 includes an RF transmitter for producing a wide variety of RF pulses used in MRI pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server 110 to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil 128 or to one or more local coils or coil arrays, such as the local coil 129.

[0037] The RF system 120 also includes one or more RF receiver channels. Each RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil 128 / 129 to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at any sampled point by the square root of the sum of the squares of the I and Q components: ^^^^ =�^^^^2 + ^^^^2 (1);and the phase of the received MR signal may also be determined: −1^^^^ ^^^^ = tan^^^^(2).

[0038] The pulse sequence server 110 also optionally receives patient data from a physiological acquisition controller 130. By way of example, the physiological acquisition controller 130 may receive signals from a number of different sensors connected to the patient, such as electrocardiograph (“ECG”) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory monitoring device. Such signals are typically used by the pulse sequence server 110 to synchronize, or “gate,” the performance of the scan with the subject's heart beat or respiration.Atty. Dkt. No.125141.04843.MGH2024-359

[0039] The pulse sequence server 110 also connects to a scan room interface circuit 132 that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit 132 that a patient positioning system 134 receives commands to move the patient to desired positions during the scan.

[0040] The digitized magnetic resonance signal samples produced by the RF system 120 are received by the data acquisition server 112. The data acquisition server 112 operates in response to instructions downloaded from the operator workstation 102 to receive the real-time magnetic resonance data and provide buffer storage, such that no data is lost by data overrun. In some scans, the data acquisition server 112 does little more than pass the acquired magnetic resonance data to the data processing server 114. However, in scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition server 112 is programmed to produce such information and convey it to the pulse sequence server 110. For example, during prescans, magnetic resonance data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server 110. As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system 120 or the gradient system 118, or to control the view order in which k-space is sampled. In still another example, the data acquisition server 112 may also be employed to process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (MRA) scan. By way of example, the data acquisition server 112 acquires magnetic resonance data and processes it in real-time to produce information that is used to control the scan.

[0041] The data processing server 114 receives magnetic resonance data from the data acquisition server 112 and processes it in accordance with instructions downloaded from the operator workstation 102. Such processing may, for example, include one or more of the following: reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data; performing other image reconstruction algorithms, such as iterative or backprojection reconstruction algorithms; applying filters to raw k-space data or to reconstructed images; generating functional magnetic resonance images; calculating motion or flow images; and so on.

[0042] Images reconstructed by the data processing server 114 are conveyed back to the operator workstation 102 where they are stored. Real-time images are stored in a data base memory cacheAtty. Dkt. No.125141.04843.MGH2024-359 (not shown in FIG.1), from which they may be output to operator display 104 or a display 136 that is located near the magnet assembly 124 for use by attending physicians. Batch mode images or selected real time images are stored in a host database on disc storage 138. When such images have been reconstructed and transferred to storage, the data processing server 114 notifies the data store server 116 on the operator workstation 102. The operator workstation 102 may be used by an operator to archive the images, produce films, or send the images via a network to other facilities.

[0043] The MRI system 100 may also include one or more networked workstations 142. By way of example, a networked workstation 142 may include a display 144; one or more input devices 146, such as a keyboard and mouse; and a processor 148. The networked workstation 142 may be located within the same facility as the operator workstation 102, or in a different facility, such as a different healthcare institution or clinic.

[0044] The networked workstation 142, whether within the same facility or in a different facility as the operator workstation 102, may gain remote access to the data processing server 114 or data store server 116 via the communication system 140. Accordingly, multiple networked workstations 142 may have access to the data processing server 114 and the data store server 116. In this manner, magnetic resonance data, reconstructed images, or other data may bexchanged between the data processing server 114 or the data store server 116 and the networked workstations 142, such that the data or images may be remotely processed by a networked workstation 142. This data may be exchanged in any suitable format, such as in accordance with the transmission control protocol (TCP), the internet protocol (IP), or other known or suitable protocols.

[0045] With reference to FIG.2, the RF system 120 of FIG.1 will be further described. The RF system 120 includes a transmission channel 202 that produces a prescribed RF excitation field. The base, or carrier, frequency of this RF excitation field is produced under control of a frequency synthesizer 210 that receives a set of digital signals from the pulse sequence server 110. These digital signals indicate the frequency and phase of the RF carrier signal produced at an output 212. The RF carrier is applied to a modulator and up converter 214 where its amplitude is modulated in response to a signal, R(t), also received from the pulse sequence server 110. The signal, R(t), defines the envelope of the RF excitation pulse to be produced and is produced byAtty. Dkt. No.125141.04843.MGH2024-359 sequentially reading out a series of stored digital values. These stored digital values may be changed to enable any desired RF pulse envelope to be produced.

[0046] The magnitude of the RF excitation pulse produced at output 216 is attenuated by an exciter attenuator circuit 218 that receives a digital command from the pulse sequence server 110. The attenuated RF excitation pulses are then applied to a power amplifier 220 that drives the RF transmission coil 204.

[0047] The MR signal produced by the subject is picked up by the RF receiver coil 208 and applied through a preamplifier 222 to the input of a receiver attenuator 224. The receiver attenuator 224 further amplifies the signal by an amount determined by a digital attenuation signal received from the pulse sequence server 110. The received signal is at or around the Larmor frequency, and this high frequency signal is down converted in a two step process by a down converter 226. The down converter 226 first mixes the MR signal with the carrier signal on line 212 and then mixes the resulting difference signal with a reference signal on line 228 that is produced by a reference frequency generator 230. The down converted MR signal is applied to the input of an analog-to-digital (“ND”) converter 232 that samples and digitizes the analog signal. The sampled and digitized signal is then applied to a digital detector and signal processor 234 that produces 16-bit in-phase (I) values and 16-bit quadrature (Q) values corresponding to the received signal. The resulting stream of digitized I and Q values of the received signal are output to the data acquisition server 112. In addition to generating the reference signal on line 228, the reference frequency generator 230 also generates a sampling signal on line 236 that is applied to the ND converter 232.

[0048] FIG.3 shows a system 300 for RF pulse design used in offline learning. In a non-limiting example, the RF pulse may be one of a one dimensional (1D) selective RF pulse, a ^^^^1-insensitive RF pulse, a spectral-spatial selective (SPSP) RF pulse, or a two dimensional (2D) selective RF pulse. Alternatively, the RF pulse design may include, but is not limited to, parallel transmit (pTx). In a non-limiting example, a target RF excitation profile (^^^^^^^^^^^^^^^^^^^^^^^^) 302 is received as an input by a processor 304. The processor 304 may be a self-supervised AI system. The processor 304 includes a neural network module (^^^^^^^^^^^^(^^^^)) 306, into which the target RF excitation profile 302 is input to generate an RF pulse 308. In a non-limiting example, the neural network module 306 includes a feedforward multi-layer perceptron (MLP).Atty. Dkt. No.125141.04843.MGH2024-359

[0049] The processor 304 further includes a physics module (^^^^(∙)) 310. In a non-limiting example, the physics module 310 utilizes Bloch equations to generate supervisory signals during training of the self-supervised AI system 304. The physics module 310 receives as input the generated RF pulse 308 and generates a Bloch-simulated RF excitation profile (^^^^^∗^^^^^^^) 312 output.

[0050] As will be described in further detail in the Example below, the network parameters (^^^^) of the neural network module 306 are trained by minimizing differences between the target RF excitation profile and the Bloch-simulated RF excitation profile. In a non-limiting example, the network parameters are trained by iterative minimization of the differences between the target and simulated RF excitation profiles.

[0051] In a non-limiting example, the processor 304 minimizes the differences between the target and simulated RF excitation profiles using a mean squared error as a loss function, such as defined by 1^^^^^^^^^^^^^^^^2 ℒ^^^^= ^^^^�^^^^�^^^^^^^^^^^^�^^^^^^^^^^^^�^^^^ − ^^^^^^^^^^^^^^^^^^^^� 2(3)where N represents aloss function may reflect a mean absolute error or mean square logarithmic error.

[0052] Referring now to FIG.3B, the system components described in FIG.3A may be used for online adaptation on an MRI system. For example, the system 300’ may be applied to an MRI system as shown in FIG.1. In the online adaptation, the processor 305 includes the neural network model 306’ with locked network parameters. As will be explained in further detail in the Example, below, the locked neural network model 306’ is trained on an MRI system using the network parameters from the offline embodiment of FIG.3A and a low-rank adaptation method 307 to expedite the learning process. The resulting generated RF pulse 308’ is provided as input into the physics module 310. In a non-limiting example, system imperfections of the MRI system may also be input into the physics module 310 to generate a more accurate Bloch-simulated RF excitation profile 314 with respect to a given MRI system. In a non-limiting example, the MRI system imperfections may include an inhomogeneity of the magnetic resonance (MR) system in either a longitudinal magnetization (^^^^0), a transverse magnetization (^^^^1+), or both. System imperfections may further include, but are not limited to, inaccurate gradient fields.Atty. Dkt. No.125141.04843.MGH2024-359

[0053] As will be described in further detail in the Example below, the processor 305 minimizes the differences between the target RF excitation profile 302 and simulated RF excitation profile 314 using a mean squared error as a loss function, such as defined by 1^^^^^^^2 ℒ^^^^= �^^^^�^^^^ ^^^^^^^^^^^^�^^^^^^^^^^^^^^^^^�^^^^�, ^^^^� − ^^^^^^^^^^^^^^^^^^^^^^^^�2(4)wh N represents athe inhomogeneity of the magnetization, or both.

[0054] In another aspect, the processor 108 FIG.1 may include system 300’ of FIG.3B to create a pulse sequence for MRI. As applied, the system(s) comprise the neural network configured to generate an RF pulse for an MRI pulse sequence based on an input target RF excitation profile. The systems may further include the physics simulation configured to simulate the generated RF pulse to produce a simulated RF excitation profile. Further, in a non-limiting example, the processor 108 may iteratively minimize the difference between the simulated RF excitation profile and the input target RF excitation profile to select a desired RF pulse for the MRI pulse sequence. As described herein, while mathematical operations such as “minimization” or the like may be used to identify an optimal result, such operations may also be used to identify or select a “desired” result. Such, “desired” result may be a reasonable or suitable, or otherwise user- selected, result that is not mathematically “optimal” but still suitable for purposes of commercial or clinical requirements.

[0055] The processor 108 may then cause the MRI system to deliver the desired RF pulse for use by its RF system 120 when performing the MRI pulse sequence.

[0056] Referring now to FIG.4A, a method 400 utilizing the systems of FIGS.3A-3B is shown. At step 402 the processor, such as processors 304 or 305, receive the target RF excitation profile. The target RF excitation profile is input into the neural network module to generate an RF pulse at steps 404-406. The generated RF pulse may then be input into the physics module at step 408 to generate a Bloch-simulated RF excitation profile 410.

[0057] FIG.4B illustrates a method 412 for creating a pulse sequence for MRI. At step 414, a neural network generates an RF pulse for an MRI pulse sequence based on an input target RF excitation profile. At step 416. A physics simulator simulates the generated RF pulse from step 414 to produce a simulated RF excitation profile. Next, at step 418, a processor iterativelyAtty. Dkt. No.125141.04843.MGH2024-359 minimizes a difference between the simulated RF excitation profile and the input target RF excitation profile. As described previously, the physics simulator may simulate the generated RF pulse using an iterative solution to Bloch equations. At steps 420-422, the processor may select a desired RF pulse for the MRI pulse sequence and deliver the RF pulse for use by an RF system of an MRI system.

[0058] The following example provides a non-limiting application and implementation of system and methods described herein.

[0059] Example

[0060] 1. Theory

[0061] 1.1 Supervised learning and self-supervised learning

[0062] Deep learning can facilitate end-to-end mapping of input data to a task-specific domain through learnable parameters. Supervised learning uses a training library consisting of data / ground truth pairs X / Y with the aim of learning a specific task (i.e., image classification, reconstruction, RF pulse design, etc.). A supervised learning network that takes X as input can be trained by minimizing the following optimization formulation: ^^�^^ = argmin�^^^^^^^^∼^^^^(^^^^)�‖^^^^(^^^^|^^^^) − ^^^^‖^^^^ (5)^^^^ where ^^^^(^^^^|^^^^) is a deep learning network with learnable parameters ^^^^ that maps input ^^^^ to ^^^^. ^^^^^^^^∼^^^^(^^^^)[·] is the expectation operator given ^^^^ is sampled from the data distribution ^^^^(^^^^) for loss function ‖ · ‖^^^^.

[0063] Self-supervised learning learns to make its own predictions through pretext tasks put forth for its input data. Instead of relying on ground truth labels or preconstructed references, self-supervised learning generates its own labels or supervisory signals. Training based on these tasks enables the network to learn useful representations of the input data. Its learning process can be formulated as the following: ^�^^^ = argmin�^^^^^^^^∼^^^^(^^^^)�‖^^^^(^^^^(^^^^|^^^^)) − ^^^^‖^^^^ (6)^^^^ where ^^^^ denotes the pretext task

[0064] 1.2 GPS

[0065] The pretext task associated with self-supervised learning can be carried out through the guidance of physics models. The objective function for minimization can be formulated asAtty. Dkt. No.125141.04843.MGH2024-359 ^^�^^ = argmin�^^^^^^^^∼^^^^(^^^^)�‖^^^^(^^^^(^^^^|^^^^)) − ^^^^‖^^^^ (7)^^^^ where ^^^^ is the physics model. In MRI RF pulse design, the governing Bloch equations, which describe the dynamics of spins, can naturally serve this purpose. Moving forward, the Bloch equation simulator will be used as the physics model.

[0066] 1.3 Bloch equations

[0067] In GPS, the Bloch equations are simulated to generate supervisory signals used for training. The Bloch equations in the rotating frame of reference in vector form are given by ^^^^ ^^^^^^^^^�^�^⃗^ = −^^^^ ^�^^⃗^ ext(^^^^) × ^�^�^⃗^ +1 ^^^(^^^^0 − ^^^^z)^̂^^^ −1 �^^^^x^�^^^ + ^^^^y^�^^^� (8)1^ ^^^^2where ^⃗ = ^^^^ ^�^^^^^^^(^^^^) (^^^^1^^^^(^^^^) ^�^^^ + ^^^^1^^^^(^^^^)^�^^^) + (∆^^^^0(^^^^) + ^⃗^^^(^^^^) · ^^^^)^̂^^^ is any externally applied magnetic field,which includes the time-varying RF pulse ^^^^1^^^^(^^^^) ^�^^^ + ^^^^1^^^^(^^^^) ^^�^^ and gradient ^⃗^^^(^^^^) alongwith ^^^^(^^^^) and ∆^^^^0(^^^^), which reflects any transmit and / or static field inhomogeneity present, ^^^^ =^^^^^^�^^ + ^^^^^^�^^ + ^^^^^̂^^^ denotes position, ^^^^0 is the equilibrium magnetization and ^^^^1 and ^^^^2 are the spin–lattice and spin–spin relaxation times, respectively.

[0068] Assuming ^^^^1and ^^^^2is negligible because its value is typically much greater than the length of the RF pulse, the Bloch equations can be iteratively solved using rotation matrices in a finite small time Δ^^^^ as ^�^�^⃗^ (^^^^ + Δ^^^^) = ^^^^(^^^^)^�^�^⃗^ (^^^^) (9)where the 3 × 3 rotation matrix ^^^^(^^^^) is given by ^^^^(^^^^) = ^^^^z(^^^^(^^^^))^^^^y(^^^^(^^^^))^^^^x(^^^^(^^^^))^^^^y(−^^^^(^^^^))^^^^z(−^^^^(^^^^)) (10).Here, ^^^^x,y,zare the rotation matrices with respect to the ^^^^, ^^^^, ^^^^ axes and ^^^^(^^^^), ^^^^(^^^^), ^^^^(^^^^) itsrespective rotation amount. In the case when an RF pulse ^�^^⃗^ 1(^^^^) is applied, ^^^^(^^^^) is the RFphase, ^^^^(^^^^) = 2^^^^^^^^|^�^^⃗^ eff(^^^^) |Δ^^^^ is the incremental flip angle for |^�^^⃗^ eff(^^^^) | =�|^^^^1(^^^^) |2 + |Δ^^^^0(^^^^) |2, where Δ^^^^0(^^^^) is any resonance offset stemming from gradient fieldsor ^^^^ inhomo −1Δ^^^^0(^^^^)0geneity and ^^^^(^^^^) = tan (^^^^).

[0069] 1.4 GPS for

[0070] To apply GPS for RF pulse design, the neural network takes a target profile input and maps it to an RF pulse output. The generated RF pulse is then simulated using the BlochAtty. Dkt. No.125141.04843.MGH2024-359 simulator to generate its corresponding profile. The optimization function for GPS RF pulse design becomes ^^�^^ = argmin�^^^^^^^^∼^^^^(^^^^)^^^^�^^^^RF�^^^^tgt�^^^^ − ^^^^tgt� (11)^^^^PF PF^^^^ where ^^^^tgt is the target profile and ^^^^^^^^∗ = ^^^^ (^^^^tgtP |^^^^)Fis the network-designed RF pulse. Here, the designed RF pulse is simulated using d its output profile is compared with the target profile ^^^^tgsimulator ^^^^ antPFto form supervision. The objective is to minimize the difference between two as a self-supervisedloss.

[0071] 2. Methods

[0072] 2.1 Network architecture and offline learning

[0073] The overall architecture of GPS consists of a neural network module and a physics module. As stated above and referring to FIG.5 Offline Learning, the neural network module takes target profile ^^^^tgt ∗tgtPF as input and generates an RF pulse ^^^^^^^^ = ^^^^RF(^^^^PF|^^^^) as output. The DL network designed RF pulse is subsequently loaded into the physics module, which outputsthe corresponding Bloch simulated profile ^^^^∗PF = ^^^^(^^^^RF(^^^^tgtPF|^^^^)). The network parameters are trained by minimizing the difference between ^^^^its mean squared error as a function1 s ^^^�^^^^ �^^^^tgt^^^^RF PF�^^^^ − ^^^^t2 ℒ = �^gtPF�(12)where ^^^^ is the number of

[0074] A feedforward multi-layer perceptron (MLP) was used as the backbone network for the neural network module of GPS because of MLP's properties of being a universal approximator of any function. The network consists of two individual subnetworks, each tasked with designing the real and imaginary components of the RF pulse. Each subnetwork includes three sequential fully connected (FC) layers activated using a leaky rectified linear unit. The first input layer takes the vectorized target profile ^^^^tgtPFwith dimension d as input and converts it to a hiddenfeature vector with dimension ^^^^second and third FC layers further represent the featurevector into a more abstractive feature vector with dimension ^^^^⁄ 4 followed by the final encodedfeature with dimension ^^^^⁄ 8 (Table 1). The final decoding layer projects the encoded features asreal and imaginary components, resulting in a complex-valued RF pulse. In addition, consideringAtty. Dkt. No.125141.04843.MGH2024-359 that the number of RF pulse elements can vary, the network output dimension was set to a maximum length of 2560 and discarded accordingly during the training process. This provides flexibility with regards to not restricting the number of RF pulse elements (up to 2560) while enabling the design of multidimensional profiles. Furthermore, the equilibrium magnetization (^^^^0) is defined as 1, which limits the profile range to [−1, 1] and, therefore, eliminates the need to preprocess the input data. Table 1. GPS neural network module architecture. Layer Input dimension Output dimension FC d d / 2 Leaky ReLU d / 2 d / 2 FC d / 2 d / 4 Leaky ReLU d / 4 d / 4 FC d / 4 d / 8 FC d / 8 t Abbreviations: FC, fully connected; GPS, generalized RF pulse design using physics -guided self-supervised learning; ReLU, rectified linear unit.

[0075] Notably, instead of using a gigantic database to train a general model for inference, GPS uses a case-specific training strategy where the network needs to be trained independently for each designed RF pulse. This substantially reduces the need for training data, decreases the training time, and increases design accuracy. Although this “overfitted” model trained under ideal system conditions provides a general baseline for the design target, the flexibility and versatility of this RF pulse design method are realized through rapid online adaptation to real system environments during the scan.

[0076] 2.2 Online adaptation

[0077] After offline designing RF pulses for ideal situations, GPS can further adapt the designed RF pulse to compensate for real-time system imperfections during a scan through online adaptation (FIG.5 Online Adaptation). This is implemented by extending the ideal Bloch simulator ^^^^ to consider additional system parameters ^^^^ (e.g., ^^^^0, ^^^^1+inhomogeneity for 2D selective pulse) in the physics module, in which the adaptation loss function can be rewritten as 1tgttgt2 ℒ^^^^= �^^^^�^^^^ �^^^^ ^^^^RF PF�^^^^� , ^^^^� − ^^^^PF�2(13)Atty. Dkt. No.125141.04843.MGH2024-359

[0078] In contrast to offline learning, where the network was randomly initialized, the neural network module in online adaptation was initialized with the learned parameters ^^^^ transferred from offline learning. Low-rank parameters for adaptation (LoRA) were applied to expedite the GPS adaptation process to ensure computational efficiency. LoRA aims to compress a dense network by finding its sparse representation, from where the network can be updated by operating in a small number of network parameters. More specifically, this LoRA implementation fixed the offline learning parameters for MLP to maintain its capability for the specific RF design while fine-tuning a lightweight side network to quickly adapt to a new training condition by only updating a few low-rank network parameters.

[0079] 2.3 GPS RF pulse design

[0080] To show the generalizability of this method, GPS was demonstrated to design 4 types of RF pulses for different applications, including 1D selective, ^^^^1-insensitive, spectral-spatial selective (SPSP), and multidimensional RF pulses.

[0081] 2.3.1 One dimensional selective RF pulse

[0082] A 1D selective target profile was generated from an RF pulse designed using the Shinnar- Le Roux (SLR) algorithm (pulse width, 2.56 ms; time-bandwidth, 6.6; flip angle, 90°; maximum passband / stopband ripples, 1.5%; least-squares design). The frequency range of the target profile used for training was [−32.768 kHz, 32.768 kHz].

[0083] 2.3.2 ^^^^1-insensitive RF pulse

[0084] In designing ^^^^1-insensitive pulses using GPS, the target profile is 2D, whereby the first dimension is the profile, and the second dimension is the peak amplitude (^^^^1max). A 2D target profile was generated from a hyperbolic secant (HS1) pulse (pulse width, 8 ms; bandwidth, 2000 Hz), where ^^^^1maxwas swept from 2.35 to 47 μT in 2.35 μT step increments for a profile frequency range of [−8.192 kHz, 8.192 kHz]. During the design process, the network-generated RF pulse was normalized to [−1, 1]. The normalized pulse was scaled based on the ^^^^1maxvalues used in the target profile and simulated on the physics module.

[0085] 2.3.3 Spectral-spatial selective RF pulse

[0086] Like the ^^^^1-insensitive case, a 2D target profile is used to design spectral-spatial selective RF pulses. However, the second dimension of this design is chemical shift. A 2D target profile for this design was generated from a 23.8 ms SPSP pulse with a flip angle of 45°. The pulse consisted of 201.19 ms spatial sub-pulses with spatial time-bandwidth of 6, whose amplitudesAtty. Dkt. No.125141.04843.MGH2024-359 were modulated by a 20-point spectral envelope with a time-bandwidth of 3. In anticipation of experiments, the corresponding gradients were designed to meet scanner Gmax and slew rate requirements. Two target profiles were generated: one for water excitation at 0 Hz and another for fat excitation at 440 Hz at 3 T. For both profiles, the first-dimension profile frequency range was [−50 kHz, 50 kHz], and the second-dimension chemical shift range was [−750 Hz, 750 Hz].

[0087] 2.3.42D selective RF pulse

[0088] To demonstrate GPS's capability of designing arbitrary profiles, a 2D target profile composed of the letters “AI” was used to design a 2D spatial excitation pulse. The target flip angle was set as 15°, and the pulse was generated using an 11.66 ms, 24-turn variable density spiral-in trajectory designed to meet scanner gradient specifications.

[0089] To assess the performance of the GPS-designed RF pulse, the Euclidean distance measurement (EDM) for 3D vectors, a metric for measuring the similarity between ^^^^tgt ∗PFand ^^^^PF, was used, which is defined as EDM = 1 −^^^^∗tgt2∗tgt2 ∗tgt2 PF,^^^^ − ^^^^PF,^^^^�+�^^^^PF,^^^^ − ^^^^PF,^^^^�+�^^^^PF,^^^^ − ^^^^PF,^^^^�(14)where the subscripts ^^^^, ^^^^, ^^^^ denotes the ^^^^, ^^^^, ^^^^^^^^P∗F . For ^^^^0of 1 used in this study, EDM ranges from [−1,1] where a higher score indicates a closer distance between two magnetic vectors, therefore, better similarity.

[0090] 2.4 Algorithm implementation

[0091] The algorithm was programmed using the Python Language with PyTorch package (v. 2.0.0). The Bloch simulator is converted into a C++ module through just-in-time (JIT) mechanism to ensure accelerated computation of matrix rotation operations for each time step of the RF pulse. The MLP uses Kaiming's method as network initialization for offline learning and AdamW optimizer to update the learnable parameters for both offline learning and online adaptation. The learning rates were set as 1e−3and 1e−2for offline learning and online adaptation, respectively. The maximum training epochs for offline learning varied depending on the RF pulse type, with the training process concluding once the training loss stopped decreasing while the EDM score reached a predetermined threshold. For 1D selective pulse, ^^^^1-insensitive pulse, and SPSP pulse, the threshold for the EDM score was set at 0.999; for 2D selective pulse, it was set at 0.98. As for online adaptation, the maximum fine-tuning epoch was determined when EDM reached 0.98. All experiments were conducted on a Linux operating system (Rocky LinuxAtty. Dkt. No.125141.04843.MGH2024-359 release 8.8) equipped with an Intel Xeon Gold 6338 @ 2.00GHz CPU and an NVIDIA A100 GPU.

[0092] 2.5 Experiments

[0093] 2.5.1 Phantom

[0094] Phantom experiments were conducted to verify the GPS pulses. All phantom scans were performed on a 3 T clinical system equipped with a 20-channel head receiver.

[0095] For the 1D selective and ^^^^1-insensitive pulses, its corresponding profiles were measured and compared with its SLR and HS1 counterpart using a modified 1D gradient-echo sequence on an oil phantom (^^^1^ / ^^^^2 = 200 / 108 ms). For the 1D selective pulse, the frequency encoding readout direction was taken along the slice direction to project its profile. Sequence parameters used are TE = 4 ms, TR = 2 s, averages (avg) = 16, 1D matrix size = 256, yielding 0.5 mm resolution along the profile direction. For the ^^^^1-insensitive pulse, the sequence required further modification to have it applied as a preparatory module before non-selective excitation. Using this modification, two separate measurements were carried out, whereby in just one of the two experiments, the ^^^^1- insensitive pulse was applied before excitation. The difference between the two measurements was taken to extract the profile. Sequence parameters used are TE = 6 ms, TR = 2 s, avg = 16, ^^^^1max = 2.35–28.2 μT in 2.35 μT step increments, 1D matrix size = 256 yielding 0.5 mm resolution along the profile direction.

[0096] The spectral selectivity of the GPS spectral-spatial selective pulses was compared with its conventional counterpart on a homemade phantom consisting of four 20 mL vials filled with mineral oil (^^^^1 / ^^^^2 = 200 / 108 ms) immersed in a 100 μM MnCl2water bath (^^^1^ / ^^^^2 = 1350 / 86 ms) using a 2D gradient-echo sequence. Sequence parameters were: 2D matrix size 160 × 160 yielding 1 × 1 mm resolution along the coronal direction, TE / TR = 15 / 65 ms, and flip angle = 45° using a 5 mm slice thickness. Both target (spectral excitation at 0 and 440 Hz) designed pulses were compared, resulting in four separate measurements.

[0097] The excitation profile of the 2D selective pulse was measured on a cylindrical phantom composed of 3.75 g NiSO4 × 6H2O + 5 g NaCl solution (^^^1^ / ^^^^2 = 107 / 77 ms) using a 3D gradient- echo sequence modified to enable 2D RF excitation. Sequence parameters used are 3D matrix size 128 × 128 × 40 yielding 1.3 × 1.3 × 5 mm resolution along the transversal direction, TE / TR = 15 / 55 ms, and flip angle = 15°. Ramps whose 0thorder moment integrated to 0 were added to the beginning of the gradient table to accommodate for scanner's gradient hardware.Atty. Dkt. No.125141.04843.MGH2024-359

[0098] 2.5.2 In vivo

[0099] In vivo experiments were conducted to verify the GPS-designed RF pulse's applicability in an actual human scan. All in vivo scans were also performed on a 3 T clinical system.

[0100] A knee scan was conducted to evaluate water and fat imaging using the spectral-spatial selective pulse. Images using GPS spectral-spatial selective pulse and its conventional design counterpart were acquired with a 2D gradient echo using a 15-channel knee coil. Sequence parameters were: 2D matrix size 105 × 105 yielding 1 × 1 mm in-plane resolution along the knee sagittal direction, TE / TR = 15 / 60 ms, and flip angle = 45°. Additional anatomical images were acquired using both GPS 1D selective and SLR for comparison and showing anatomical reference. Sequence parameters were: 2D matrix size 105 × 105 yielding 1 × 1 mm in-plane resolution along the sagittal direction, TE / TR = 5 / 50 ms, and flip angle = 90°.

[0101] A brain scan was conducted to evaluate the 2D excitation profile of the 2D selective pulse. Images using GPS 2D selective pulse for exciting letters “AI” were acquired using the same 3D gradient-echo sequence and head coil as the phantom, but with parameters: 3D matrix size 128 × 128 × 40 yielding 1.8 × 1.8 × 5 mm resolution along the brain transversal direction, TE / TR = 15 / 55 ms and flip angle = 15°. An additional image using non-selective excitation with identical sequence parameters was also acquired for anatomical reference.

[0102] 2.5.3 Online adaptation

[0103] To demonstrate GPS online adaptation to compensate for ^^^^0 / ^^^^1+inhomogeneity in 2D selective pulse design for both phantom and brain, the ^^^^0and ^^^^1+maps were independently measured and incorporated into the Bloch simulator of GPS to fine-tune and adapt the RF pulse in LoRA using a rank number of 4. The ^^^^0maps were obtained using two gradient-echo images acquired at different echo times (TE1 / TE2 = 3 / 7 ms) and dividing their phase difference map by the difference in echo time, whereas ^^^^1+maps were obtained using the Bloch-Siegert method.

[0104] 3. Results

[0105] Table 2, presented below, provides detailed information on profile dimensions, training iterations, training time, and GPU usage for designing different RF pulse types with GPS. Table 2. Detailed information on profile dimensions, training iterations, training time, and GPU usage for designing different RF pulse types with GPS in both offline learning and online adaptation.Atty. Dkt. No.125141.04843.MGH2024-359 RF pulse Target No. of RF Iterations Training GPU EDM type profile pulse time memory dimension elements usage (MB) Offline training 1D 2048 256 114 5 min 53 s 1846 0.9996 selective B1-2048 × 20128 302 10 min 333566 0.9995 insensitive s SPSP 192 × 96 2453 111 33 min 1 s 17368 0.9995 2D64 × 641166 606 2 h 8 min 6718 0.9895selective Online adaptation 2D 64 × 64 1166 20 4 min 4 s 5282 0.9856 selective (phantom) 2D 64 × 64 1166 20 4 min 2 s 5282 0.9832 selective (in vivo) Abbreviations: EDM, Euclidean distance measurement; GPS, generalized RF pulse design using physics-guided self-supervised learning; GPU, graphics processing unit; MB, megabyte

[0106] 3.1 GPS RF pulse design (simulation)

[0107] 3.1.1 One dimensional selective RF pulse

[0108] GPS-designed 1D selective RF pulse overlaid with its SLR counterpart is shown in FIG. 6A. Overall, both designed pulses show good agreement, with the GPS design being less smooth, but with a slightly lower peak amplitude (15.15 vs.15.22 μT). The simulated profile generated using both pulses shows excellent agreement.

[0109] Further, an example of the design dynamics for the 1D selective pulse is provided in FIGS.7A-7B. After the first iteration, the neural network module output RF pulse is noise-likeAtty. Dkt. No.125141.04843.MGH2024-359 with low amplitude and a corresponding low amplitude noise-like excitation profile. Zooming in, however, it is evident that the RF pulse already starts to take a single-lobe Gaussian-like shape. As the design process progresses, through the supervision of the physics module, the neural network module learns to design the side lobes, resulting in a profile selectivity that starts to resemble the target (7thiteration). Further down (37thiteration), the overall and relative amplitudes of the 5 lobes are learned, which produces a profile that closely matches the target. In the latter stages of the design process, the pulse is fine-tuned so that its output optimally matches its target (114thiteration), which describes the low rate of decrease in the loss curve.

[0110] 3.1.2 ^^^^1-insensitive RF pulse

[0111] GPS-designed B1-insensitive RF pulse overlaid with its HS1 counterpart is shown in FIG.6B. Similar to the 1D selective case, both designed pulses show relatively good agreement, with the GPS design being less smooth. However, the fluctuation of its phase becomes more pronounced at the beginning and end of the pulse, where the amplitude is relatively low. Despite this, the simulation results of both pulses show excellent agreement in terms of both profiles at various ^^^^1maxvalues and ^^^^1-insensitivity for ^^^^1maxvalues beyond 18.8 μT.

[0112] 3.1.3 SPSP selective RF pulse

[0113] Superimposed GPS-designed and conventional design SPSP pulses are shown in FIGS. 8A-8B for both 0 and 440 Hz spectral excitation. Similar to the above, both pulses show relatively good agreement with the GPS design. However, in the gradient ramp regions where the pulse is 0 in the conventional design, the GPS design shows noise-like characteristics (FIGS.8A- 8B zoom-ins) of similar amplitude throughout the pulse. Nonetheless, the profile simulations of the GPS design and conventional design agree well for both 0 and 440 Hz spectral excitation.

[0114] 3.1.42D selective RF pulse

[0115] The 2D target profile, GPS-designed 2D selective RF pulse, and corresponding 2D simulation profile are shown in FIG.9. Comparing the 2D pulse's simulated profile with the target profile, the simulated profile exhibits some blur, which is because of the limited extent to which excitation k-space is sampled. Nevertheless, both profiles agree well. Considering the variable density spiral trajectory used and good profile agreement indicates that GPS also considers density compensation during the design process.

[0116] 3.2 Experiments

[0117] 3.2.1 PhantomAtty. Dkt. No.125141.04843.MGH2024-359

[0118] The 1D selective profile obtained using GPS design and SLR is presented in FIG. 6A Experiment. In both passband and stopband regions, the phantom experiment results show excellent agreement and further concur with the simulation. ^^^^1-insensitive profiles obtained using GPS design and HS1 are shown in FIG.6B Experiment. The profiles from both pulses agree well over the entire range of applied ^^^^1max, both showing ^^^^1-insensitivity for ^^^^1maxvalues beyond 18.8 μT, in accordance with simulations.

[0119] Phantom images obtained using spectral-spatial selective pulses from GPS design and conventional design is shown in the right column of FIGS.8A-8B for both 0 (water) and 440 Hz (oil) spectral excitation. For 0 Hz spectral excitation, both pulses produce good spectral selectivity that shows good agreement with one another. This can be seen by the bright water bath in the image (FIG.8A), where the mineral oil vials appear dark, indicating that the water bath is excited, whereas the mineral oil vials are not. The same applies to spectral selectivity for 440 Hz. In both GPS design and conventional design, the vials filled with mineral oil appear bright, whereas the water bath appears dark (FIG.8B), indicating this time that the mineral oil vials are excited, but the water bath is not.

[0120] 3.2.2 In vivo

[0121] Anatomical knee images acquired using GPS 1D selective pulse and SLR, SPSP selective pulse for 0 Hz (water) and 440 Hz (fat) using both GPS and conventional designs are presented in FIG.10. For the 1D selective images (FIG.10 left column), both GPS and SLR agree well with no noticeable difference, corroborating with both simulations and phantom experiments. For 0 Hz water selective SPSP (FIG.10 center column), in both GPS and conventional images, the muscle and cartilage appear bright, whereas the bone marrow, infrapatellar fat pad, and other fatty tissue are dark. This demonstrates that both pulse designs achieve good spectral selectivity at 0 Hz, agreeing well with each other with no noticeable difference and further supporting simulation and phantom experiment results. The same can be said for the 440 Hz fat selective case (FIG.10 right column), whereby in both GPS and conventional images, the bone marrow, infrapatellar fat pad, and other fatty tissue appear bright whereas the muscle and cartilage appear dark.

[0122] 3.2.3 Online adaptation

[0123] Phantom ^^^^0 / ^^^^1+inhomogeneity online adaptation results are shown in FIG.11. The left half of this subfigure shows the offline GPS-designed 2D selective RF pulse and itsAtty. Dkt. No.125141.04843.MGH2024-359 corresponding excitation profile in the presence ^^^^0 / ^^^^1+inhomogeneity. The inner triangle region of the letter “A” is not well resolved, appearing bright in the middle instead of dark throughout. There are also two visible line streaks between the letters “A” and “I”. In addition, the bottom right portion of the phantom exhibits an increased streak signature, roughly correlating with the increase in ^^^^0inhomogeneity in this region. The agreement between Bloch simulations obtained with these ^^^^0 / ^^^^1+maps included further confirm this. The online adapted GPS-designed 2D selective RF pulse and its corresponding excitation profile can be seen in the right half of the subfigure. Compared with the offline design, the online adapted RF pulse has a lower overall amplitude, which reflects the high relative values of the ^^^^1+map it has adapted to. Furthermore, both letters are now well resolved, with the previous bright spot of the inner triangle region of the letter “A” and visible line streaks between letters “A” and “I” both removed. This was also confirmed through simulations, which showed good agreement with the experiment.

[0124] In vivo ^^^^0 / ^^^^1+inhomogeneity online adaptation results are shown in FIG.12. The left half of this the offline GPS-designed 2D selective RF pulse and its correspondingexcitation profile in the presence ^^^^0 / ^^^^1+inhomogeneity. Focusing within the dotted box, similar to the phantom results, the inner triangle region of the letter “A” is not well resolved with three dark spots surrounding a bright middle instead of being dark throughout. A visible streak is also exhibited between the letters “A” and “I”. In addition, there is ringing near the top region of A, which corresponds to regions of high ^^^^0inhomogeneity. The existence of excitation outside the dotted box region is because of the 2D target profile provided as input to GPS being confined to the region within the dotted box. The good agreement between Bloch simulations obtained with these ^^^^0 / ^^^^1+maps included further confirms this. The center anatomical image is shown for reference. The online adapted GPS-designed 2D selective RF pulse and its corresponding excitation profile can be seen in the right half of the figure. As was the case for the phantom, the online adapted RF pulse has a lower overall amplitude in comparison with the offline design, reflecting the high relative values of the ^^^^1+map it has adapted to. Both letters are now well resolved, with the previous three dark spots surrounding the bright middle in the inner triangle region of the letter “A” and visible line streaks between letters “A” and “I” both removed. This was also confirmed through simulations, showing good agreement. In all in vivo simulations, the obtained anatomical image with its intensity adjusted for ^^^^1+inhomogeneity was used to accurately simulate.Atty. Dkt. No.125141.04843.MGH2024-359

[0125] 4. Discussion and conclusion

[0126] We have presented GPS, a self-supervised learning framework that integrates a physics model to guide and enforce the learning process for MRI RF pulse design. As a proof-of- concept, the Bloch equations were used as the physics model and demonstrated generalizability for designing a variety of RF pulses, which conventionally require separate dedicated algorithms. In addition, compensation for ^^^^0 / ^^^^1+inhomogeneity was shown using online adaptation in both phantom and in vivo experiments, further demonstrating GPS's flexibility and versatility in adapting to system imperfections in real time. Although 1D selective, ^^^^1-insensitive, SPSP selective, and 2D selective RF pulse designs were demonstrated, GPS is applicable to other types of RF pulse design including but not limited to parallel transmit (pTx). In calculating the loss function, a mean squared error was used but other loss functions including but not limited to mean absolute error and mean squared logarithmic error can be used. Furthermore, compensation for system imperfections other than ^^^^0 / ^^^^1+inhomogeneity including but not limited to inaccurate gradient fields can be applied in this method.

[0127] Despite showing similarities with conventional design, GPS-designed RF pulses exhibit unique features. First, in terms of the design process, GPS designs an RF pulse that adheres to the boundaries of the target profile provided. For the 1D selective RF pulse design, the profiles resulting from GPS-designed pulses using different target profile frequency ranges ([−4.096 kHz, 4.096 kHz] vs. [−8.192 kHz, 8.912 kHz] vs. [−16.384 kHz, 16.384 kHz] vs. [−32.768 kHz, 32.768 kHz]) show excellent agreement within their respective target frequency range. However, in their respective stopband regions outside their target ranges, the profile can differ in its non- periodic randomly fluctuating signature (FIG.13). Second, the adherence to the boundaries of the 2D input target profile for GPS-designed ^^^^1-insensitive RF pulses, which is the profile frequency and ^^^^1maxrange for which it is defined in, equally applies. However, the dynamics in which ^^^^1-insensitivity is accomplished are significantly different from the conventional method. In the conventional method, the time-dependence of the amplitude and frequency modulation ns are designed to meet the adiabatic condition ^^^^(^^^^ ^^^^ ^^^^eff(^^^ maxfunctio max 1 ^1 ,^^^^)1 , ^^^^) =^̇^^^| > 1, whichis the ratio between the effective magnetic field (^^^^eff max1 (^^^^1 , ^^^^))oforientation (^̇^^^),throughout its duration. Comparing the adiabaticity of the HS1 and GPS- designed ^^^^1-insensitive pulse (FIG.14), the HS1 pulse conforms to the adiabatic conditionAtty. Dkt. No.125141.04843.MGH2024-359 throughout its duration for both isochromats. However, for the GPS design, the adiabatic condition is violated for 62% of the duration. This indicates that instead of using the properties of adiabaticity, the physics module of the GPS framework guides the neural network module to invoke other mechanisms to achieve ^^^^1-insensitivity. Finally, as was noted in the Results section, the GPS-designed SPSP pulse was not 0 during the gradient ramp regions as in the conventional design, but instead showed random fluctuations (FIGS.8A-8B zoom-in). Sampling of the RF pulse during the gradient ramp regions can further be exploited to decrease the peak power of the SPSP pulse for a given target flip angle. For example, SPSP pulses can be designed with GPS using regularization of ^^^^1max. This necessitates the pulse to leverage the gradient ramp regions during the design process to lower ^^^^1maxas shown in FIG.15, which decreases ^^^^1maxby 15% compared to the non-regularized design in achieving identical flip angle. Despite these unique differences, in practice, one would use a digitally designed target excitation profile as input to the GPS framework as was done in the 2D selective case. This has also been demonstrated for the 1D selective case where a rectangle function was used for the target excitation profile (FIG.16). Compared to the excitation profile obtained using an SLR pulse of identical pulse width and time-bandwidth, the passband exhibited minimum ripples with a narrower transition width. Overall, this new RF pulse design approach through physics-guided self-supervised learning opens a new avenue to investigate RF pulse mechanisms that might not be observable in conventional RF design, which possess great potential for achieving new design purposes.

[0128] The input–output structure of the GPS framework is different compared to other DL RF pulse design methods whereby the input and output are the same RF excitation profiles. Previous supervised methods rely on a broad input and corresponding output dataset such as diverse 2D excitation profiles with corresponding 2D RF pulses, limiting the type of RF pulse the method is able to design. Although unsupervised methods relieve the requirement of having an output dataset for the corresponding input,17this approach nonetheless requires a broad input dataset, which influences the scope of the type of RF pulse design that is achievable. In GPS, the target learning objective RF pulse is generated at an intermediatory step and input into the Bloch simulator, which is used as a means for self-supervision. Therefore, a case-specific training strategy is used, which forgoes the need of a diverse training dataset and instead trains independently for each excitation profile, allowing for a more general RF pulse design approach.Atty. Dkt. No.125141.04843.MGH2024-359 Whereas overfitting is avoided in dataset-based learning methods because it can lead to a network that does not generalize well, in GPS, overfitting is beneficial because it results in an RF pulse profile that better matches the target input.

[0129] The computational efficiency of this algorithm is ensured through two mechanisms: rapid Bloch simulation through JIT and online adaptation through low-rank network learning. The Bloch simulator used in this study is an iterative solution to Bloch equations, which recursively applies matrix rotation operations for each time step of the RF pulse. This leads to a long chain for backpropagation, which increases computation. Computational efficiency was addressed by converting and running the PyTorch Bloch simulator module in C++ through JIT, which significantly accelerates the computation time for each iteration. Furthermore, to expedite the online adaptation, the pretrained parameters were transferred and fixed from offline learning and only updated the LoRA instead of tuning all network parameters. This is based on the assumption that a change of a smaller subset of low-rank parameters can effectively encapsulate the necessary adjustments for a new task. As shown in Table 2, a 1D pulse design can be completed in minutes, and a more complicated 2D pulse requires tens of minutes to complete during offline learning. With both JIT and LoRA, 2D RF pulse online adaptation can be completed in 4 min to produce dramatic improvement in profile quality by compensating for ^^^^0 / ^^^^1+inhomogeneity. Although this is an encouraging result to show the potential of GPS pulse for imaging applications that are less scan time constrained, more research is needed to further improve the time efficiency for offline training and, more importantly, online adaptation in time-sensitive applications. Some plausible solutions worth deep investigation in this regard are to optimize the implementation of algorithms such as by using adjoint methods (e.g., neural ordinary differential equation) to further accelerate the long chain operation in the Bloch simulation, or to better leverage computational hardware architecture such as distributed GPU computation for parallel computing of gradient backpropagation. Finally, considering this online adaptation of GPS pulse as a system calibration step, management of imaging protocol is also subject to future research where care must be cast to optimize the protocol workflow to avoid unnecessary idle time and improve the overall workflow efficiency.

[0130] As used in this specification and the claims, the singular forms “a,” “an,” and “the” include plural forms unless the context clearly dictates otherwise.Atty. Dkt. No.125141.04843.MGH2024-359

[0131] As used herein, “about”, “approximately,” “substantially,” and “significantly” will be understood by persons of ordinary skill in the art and will vary to some extent on the context in which they are used. If there are uses of the term which are not clear to persons of ordinary skill in the art given the context in which it is used, “about” and “approximately” will mean up to plus or minus 10% of the particular term and “substantially” and “significantly” will mean more than plus or minus 10% of the particular term.

[0132] As used herein, the terms “include” and “including” have the same meaning as the terms “comprise” and “comprising.” The terms “comprise” and “comprising” should be interpreted as being “open” transitional terms that permit the inclusion of additional components further to those components recited in the claims. The terms “consist” and “consisting of” should be interpreted as being “closed” transitional terms that do not permit the inclusion of additional components other than the components recited in the claims. The term “consisting essentially of” should be interpreted to be partially closed and allowing the inclusion only of additional components that do not fundamentally alter the nature of the claimed subject matter.

[0133] The phrase “such as” should be interpreted as “for example, including.” Moreover, the use of any and all exemplary language, including but not limited to “such as”, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed.

[0134] Furthermore, in those instances where a convention analogous to “at least one of A, B and C, etc.” is used, in general such a construction is intended in the sense of one having ordinary skill in the art would understand the convention (e.g., “a system having at least one of A, B and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together.). It will be further understood by those within the art that virtually any disjunctive word and / or phrase presenting two or more alternative terms, whether in the description or figures, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”

[0135] All language such as “up to,” “at least,” “greater than,” “less than,” and the like, include the number recited and refer to ranges which can subsequently be broken down into ranges and subranges. A range includes each individual member. Thus, for example, a group having 1-3Atty. Dkt. No.125141.04843.MGH2024-359 members refers to groups having 1, 2, or 3 members. Similarly, a group having 6 members refers to groups having 1, 2, 3, 4, or 6 members, and so forth.

[0136] The modal verb “may” refers to the preferred use or selection of one or more options or choices among the several described embodiments or features contained within the same. Where no options or choices are disclosed regarding a particular embodiment or feature contained in the same, the modal verb “may” refers to an affirmative act regarding how to make or use an aspect of a described embodiment or feature contained in the same, or a definitive decision to use a specific skill regarding a described embodiment or feature contained in the same. In this latter context, the modal verb “may” has the same meaning and connotation as the auxiliary verb “can.”

Claims

Atty. Dkt. No.125141.04843.MGH2024-359 Claims 1. A radiofrequency (RF) pulse design system, comprising: a processor configured to access a self-supervised artificial intelligence (AI) system including a neural network module (^^^^^^^^^^^^(^^^^)) and a physics module (^^^^(∙)) based on Bloch equations, configured to: (a) receive a target RF excitation profile (^^^^^^^^^^^^^^^^^^^^^^^^); (b) input the ^^^^^^^^^^^^^^^^^^^^^^^^into the neural to generate an RF pulse (^^^^^^^^∗);and (c) input the ^^^^^^^^∗into the ^^^^(∙)to generate a Bloch-simulated RF excitation profile (^^^^^∗^^^^^^^).

2. The system of claim 1, wherein network parameters (^^^^) of the ^^^^^^^^^^^^(^^^^) are trained by minimizing differences between the ^^^^^^^^^^^^^^^^ ∗^^^^^^^^and the ^^^^^^^^^^^^.

3. The system of claim 2, wherein the processor minimizes the differences between the ^^^^^^^^^^^^^^^^^^^^^^^^and the ^^^^^∗^^^^^^^using a mean squared error as a loss function, defined as 1^^^^^^^^^^^^^^^^2 ℒ =�^^^^�^^^^ �^^^^ �^^^^^^^^^^^^ ^^^^^^^^ ^^^ ^^^^ − ^^^^� ^^^^^^^^^ ^^^^^^^^2 where N represents a4. The system of claim 2, wherein the self-supervised AI system is configured to adapt to a magnetic resonance (MR) system.

5. The system of claim 4, wherein the ^^^^^^^^^^^^(^^^^)is further trained on the MR system by using the ^^^^ and a low-rank adaptation method.

6. The system of claim 5, wherein the ^^^^(∙)is further based on one or more system imperfections of the MR system.

7. The system of claim 6, wherein the one or more system imperfections include an inhomogeneity of the magnetic resonance (MR) system in either a longitudinal magnetization (^^^^0), a transverse magnetization (^^^^1+), or both.

8. The system of claim 7, wherein minimizing the differences between the ^^^^^^^^^^^^^^^^ ∗^^^^^^^^and the ^^^^^^^^^^^^for the MR system uses a mean squared error as a loss function, defined as 1^^^^^^^^^^^2 ℒ = �^^^^�^^^^ �^^^^^^^^^^^^^^^^^^ ^^^^^�^^^^�, ^^^^� − ^^^^� ^^^^^^^^^^ ^^^^^^^^ ^^^^^^^^2Atty. Dkt. No.125141.04843.MGH2024-359 where N represents a number of elements of ^^^^^^^^^^^^^^^^^^^^^^^^and I is an additional parameter representing the inhomogeneity of the MR system in either the longitudinal magnetization, the transverse magnetization, or both.

9. The system of claim 1, wherein the ^^^^^^^^^^^^(^^^^) includes a feedforward multi-layer perceptron (MLP).

10. The system of claim 1, wherein the RF pulse is at least one of a one dimensional (1D) selective RF pulse, a ^^^^1-insensitive RF pulse, a spectral-spatial selective (SPSP) RF pulse, or a two dimensional (2D) selective RF pulse.

11. A method of designing a radiofrequency (RF) pulse, comprising: (a) receiving, via a processor including a self-supervised artificial intelligence (AI) system including a neural network module (^^^^^^^^^^^^(^^^^)) and a physics module (^^^^(∙)) based on Bloch equations, a target RF excitation profile (^^^^^^^^^^^^^^^^^^^^^^^^); (b) inputting, via the processor, the ^^^^^^^^^^^^^^^^into( ) ∗^^^^^^^^ the ^^^^^^^^^^^^ ^^^^ to generate a RF pulse (^^^^^^^^ );and(c) inputting, via the processor, into the ^^^^(∙)to generate a Bloch-simulated RF excitation profile (^^^^^∗^^^^^^^).

12. The method of claim 11, wherein network parameters (^^^^) of the ^^^^^^^^^^^^(^^^^) are trained by minimizing differences between the ^^^^^^^^^^^^^^^^ ∗^^^^^^^^and the ^^^^^^^^^^^^.

13. The method of claim 12, wherein minimizing the differences between the ^^^^^^^^^^^^^^^^ ∗^^^^^^^^and the ^^^^^^^^^^^^use a mean squared error as a loss function, defined as 1^^^^^^^^^^^^^^^^^^^^^2 ℒ^^^^= ^^^^�^^^^�^^^^^^^^^^^^�^^^^^^^^^^^^�^^^^ − ^^^^^^^^^^^^^^^� 2 where N represents a14. The method of claim 12, wherein the self-supervised AI system is configured to adapt to a magnetic resonance (MR) system.

15. The method of claim 14, wherein the ^^^^^^^^^^^^(^^^^) is further trained on the MR system by using the ^^^^ and a low-rank adaptation method.

16. The method of claim 15, wherein the ^^^^(∙)is further based on one or more system imperfections of the MR system.

17. The method of claim 16, wherein the one or more system imperfections include an inhomogeneity of the magnetic resonance (MR) system in either a longitudinal magnetization (^^^^0), transverse magnetization (^^^^1+), or both.

18. The method of claim 17, wherein minimizing the differences between the ^^^^^^^^^^^^^^^^ ∗^^^^^^^^and the ^^^^^^^^^^^^for the MR system use a mean squared error as a loss function, defined asAtty. Dkt. No.125141.04843.MGH2024-359 1^^^^^^^^^^^^^^^^^2 ℒ = �^^^^�^^^^ �^^^^�^^^^^^^^^^^^^^ ^^^^^^^^ ^^ ^�, ^^^^� − ^^^^� ^^^^^^^^^^ ^^^^^^^^2 where N represents additional parameter representing themagnetization, the transverse magnetization, or both.

19. The method of claim 11, wherein the ^^^^^^^^^^^^(^^^^)includes a feedforward multi-layer perceptron (MLP).

20. The method of claim 11, wherein the RF pulse is at least one of a one dimensional (1D) selective RF pulse, a ^^^^1-insensitive RF pulse, a spectral-spatial selective (SPSP) RF pulse, or a two dimensional (2D) selective RF pulse.

21. A system for creating a pulse sequence for magnetic resonance imaging (MRI), the system comprising: a neural network configured to generate a radiofrequency (RF) pulse for an MRI pulse sequence based on an input target RF excitation profile; a physics simulator configured to simulate the generated RF pulse to produce a simulated RF excitation profile; and a processor configured to: iteratively minimize a difference between the simulated RF excitation profile and the input target RF excitation profile to select a desired RF pulse for the MRI pulse sequence; and deliver the desired RF pulse for use by an RF system of an MRI system when performing the MRI pulse sequence.

22. The system of claim 21, wherein the physics simulator is configured to simulate the generated RF pulse using an iterative solution to Bloch equations.

23. The system of claim 21, wherein the processor is further configured to adapt the generated RF pulse by incorporating system imperfections into the physics simulator.

24. The system of claim 23, wherein the system imperfections comprise ^^^^0or ^^^^1+inhomogeneities.

25. The system of claim 23, wherein the processor is further configured to use low-rank adaptation to update a subset of parameters of the neural network to adapt the RF pulse.

26. A method for creating a pulse sequence for magnetic resonance imaging (MRI), the method comprising: generating, using a neural network, an RF pulse for an MRI pulse sequence based on an input target RF excitation profile;Atty. Dkt. No.125141.04843.MGH2024-359 simulating, using a physics simulator, the generated RF pulse to produce a simulated RF excitation profile; iteratively minimizing, using a processor, a difference between the simulated RF excitation profile and the input target RF excitation profile to select a desired RF pulse for the MRI pulse sequence; and delivering, using the processor, the desired RF pulse for use by an RF system of an MRI system when performing the MRI pulse sequence.

27. The method of claim 26, wherein the physics simulator is configured to simulate the generated RF pulse using an iterative solution to Bloch equations.

28. The method of claim 26, wherein the processor is further configured to adapt the generated RF pulse by incorporating system imperfections into the physics simulator.

29. The method of claim 28, wherein the system imperfections comprise ^^^^0or ^^^^1+inhomogeneities.

30. The method of claim 28, wherein the processor is further configured to use low-rank adaptation to update a subset of parameters of the neural network to adapt the RF pulse.

Images