Real-time image guidance is crucial for minimally invasive neurosurgical procedures such as biopsies and deep brain stimulation (DBS). Magnetic resonance imaging (MRI) offers excellent soft tissue contrast and anatomical detail, making it an ideal modality for both pre-operative planning and intra-operative guidance. However, the relatively slow acquisition speed of traditional MRI sequences presents a significant challenge for real-time interventional applications. Achieving high spatial resolution while maintaining sufficient temporal resolution to track moving instruments and tissues during the intervention remains a major hurdle. Existing acceleration techniques for MRI, such as balanced steady-state free precession (bSSFP), parallel imaging, generalized series, and keyhole imaging, often struggle to meet the stringent temporal demands of real-time i-MRI. Compressed sensing (CS) methods, leveraging the sparsity of the MR data, have shown promise in accelerating image acquisition. Further improvements have been achieved by incorporating temporal information via k-t methods. Low-rank matrix imaging techniques, decomposing data into low-rank and sparse components, have also become established for fast MRI, including dynamic MRI. However, these methods often involve complex parameter tuning, long computation times, or compromises in spatial resolution, hindering their suitability for real-time applications. Deep learning (DL) offers a potential solution to improve reconstruction quality and accelerate computation speed. Various DL architectures, including convolutional neural networks (CNNs), recurrent neural networks (RNNs), generative adversarial networks (GANs), and transformers, have been explored for fast MRI. Unrolled networks, which unravel iterative algorithms into neural networks, have gained popularity due to their ability to leverage prior knowledge and improve generalizability. However, existing DL-based methods may suffer from limitations such as the need for large-scale training datasets and limited interpretability. Some existing unrolled networks utilize sparse priors but neglect low-rank information. The state-of-the-art methods like SLR-Net and L+S-Net are not suitable for online reconstruction in real-time i-MRI. This research addresses these challenges by proposing LSFP-Net, a deep unrolled neural network specifically designed for real-time i-MRI reconstruction in brain intervention. LSFP-Net leverages both low-rank and sparse priors, optimizing for the slowly changing background and the sparse interventional features. The use of a group-based reconstruction scheme with periodic radial sampling ensures that online reconstruction is feasible for real-time applications. The performance and generalizability of LSFP-Net are evaluated on simulated datasets and validated in phantom and cadaver studies. By integrating the trained model with a custom-designed MR-compatible interventional device, the study demonstrates a complete real-time MRI-guided brain intervention system capable of providing high-quality images with minimal latency.

The field of real-time MRI-guided interventions has seen significant advancements, but challenges remain in balancing speed and image quality. Traditional MRI techniques, while providing high-resolution images, are too slow for real-time guidance. Acceleration methods like bSSFP, parallel imaging, and keyhole imaging have been explored, but they often fall short of the speed required for real-time feedback during procedures. Compressed sensing (CS) techniques, utilizing the inherent sparsity in MR data, have significantly improved acquisition speeds. However, these methods typically require careful parameter tuning and may still struggle with the demands of real-time imaging. The incorporation of temporal information into the reconstruction process has led to the development of k-t methods. These techniques exploit the temporal correlation between successive image frames to further accelerate image acquisition. However, they may still suffer from artifacts and computational complexity, particularly for high-dimensional data. Low-rank matrix decomposition methods, such as low-rank plus sparse (L+S) decomposition and robust principal component analysis (RPCA), have proven effective in separating slowly varying background components from dynamic features in dynamic MRI. These methods have been successfully applied to various applications, but their computational burden can limit their use in real-time scenarios. The application of deep learning (DL) to MRI reconstruction has opened up new possibilities for accelerating image acquisition and improving image quality. CNNs, RNNs, and other architectures have shown promise in learning complex mappings from undersampled k-space data to fully sampled images. Unrolled networks offer an alternative approach, explicitly incorporating prior knowledge into the network architecture by unrolling iterative algorithms. ISTA-Net, ADMM-Net, and variational networks are examples of such unrolled networks, showing impressive results in various applications. However, many existing DL-based methods rely on extensive training datasets and lack the interpretability of traditional methods. Some recent research focuses on combining low-rank and sparse priors with DL to improve reconstruction quality, but adapting these for real-time i-MRI presents unique challenges.

This study introduces LSFP-Net, a deep unrolled neural network designed to address the limitations of existing methods for real-time interventional MRI (i-MRI). The key contributions of the methodology include: **1. Unrolling the LSFP Algorithm:** The core of LSFP-Net is the unrolling of the Low-rank and Sparsity decomposition with Framelet and Primal dual fixed point (LSFP) algorithm. This algorithm is particularly suitable for i-MRI due to its ability to efficiently separate the low-rank background signal from the sparse interventional features. The unrolling process transforms the iterative optimization steps of LSFP into layers of a neural network, allowing for efficient and parallel computation. The hyperparameters within the LSFP algorithm are learned during the training process, eliminating the need for manual tuning. **2. Leveraging Low-Rank and Sparse Priors:** LSFP-Net explicitly incorporates both low-rank and sparse priors into its architecture. The low-rank prior captures the slowly changing background tissue, while the sparse prior models the dynamic changes related to the intervention (e.g., the movement of an interventional needle). This approach effectively reduces redundancy and noise, leading to improved reconstruction quality. Moreover, the network is designed to exploit the spatial sparsity of both low-rank and sparse components, further enhancing its performance. **3. Group-based Reconstruction with Radial Sampling:** To achieve real-time performance, LSFP-Net utilizes a group-based reconstruction scheme with periodic radial sampling. Radial sampling is less sensitive to motion artifacts compared to Cartesian sampling, making it better suited for dynamic interventions. The periodic sampling trajectory is repeated within each group of spokes, leading to highly efficient data acquisition and processing. Multiple frames are reconstructed simultaneously within each group, taking advantage of the temporal correlations among the frames. **4. Network Architecture:** LSFP-Net consists of multiple blocks, each corresponding to an iteration in the original LSFP algorithm. Each block contains convolutional layers to learn the sparse and low-rank transformations, allowing the network to learn optimal representations of the sparse and low-rank components effectively. Rectifier linear units (ReLU) are used as activation functions. The network is trained using simulated data generated from real MR images. **5. Data Acquisition and System Integration:** The study integrated the trained LSFP-Net model with a custom-designed MR-compatible interventional device on a 3T MRI scanner. The device allows for remote controlled intervention and can be precisely positioned and moved within the MRI bore. The system includes a data acquisition pipeline that streams k-space data to the LSFP-Net for real-time reconstruction, displays the reconstructed images on the MRI console, and coordinates the movement of the interventional device based on operator input and real-time feedback. **6. Evaluation:** The performance of LSFP-Net was rigorously evaluated using multiple metrics. The simulated datasets were generated to mimic various interventional scenarios, including different intervention types and movement patterns. The performance of LSFP-Net was compared with several state-of-the-art methods, both iterative (L+S, LSFP) and DL-based (CRNN, ISTA-Net, SLR-Net, L+S-Net), using metrics such as PSNR and SSIM. The accuracy, speed and efficiency of the system were also tested using phantom and cadaver studies. Latency, spatial resolution, and temporal resolution of the reconstructed images are reported.

The key findings of this research demonstrate the effectiveness of LSFP-Net for real-time MRI-guided brain intervention: **1. Superior Performance in Simulated Data:** LSFP-Net consistently outperformed other methods in simulated datasets of brain intervention and DBS electrode placement. It achieved significantly higher PSNR and SSIM values, indicating better image quality and fidelity to the ground truth. Importantly, the reconstruction time was significantly faster, particularly compared to CS-based iterative methods. The improvement in performance is attributed to the combined use of low-rank and sparse priors and the learning of optimal regularization parameters during training. **2. High Acceleration Factors:** The proposed method was tested with different acceleration factors (R=10, 25, and 40). Across all factors, the proposed model showed near optimal performance in terms of PSNR and SSIM scores while having a reconstruction time under one second. **3. Optimal Network Parameters:** The study investigated the optimal number of iterations and convolutional layers in LSFP-Net. A balance between reconstruction quality and computational time was found, leading to the selection of specific network parameters for the phantom and cadaver experiments. **4. Real-Time Performance in Phantom Studies:** In the fruit and porcine brain phantom experiments, the LSFP-Net achieved real-time 2D imaging with a temporal resolution of 80 ms per frame and a latency of 0.4 seconds. The difference between the theoretical intervention depth and the real-time image measurements was less than 1 mm, demonstrating the accuracy of the system. 3D imaging achieved a temporal resolution of 732.8 ms per volume and a latency of 3.66 seconds. The results demonstrated the ability of LSFP-Net to provide reliable real-time feedback during interventions. **5. Successful Cadaver Study:** A cadaver head experiment further validated the feasibility and potential of the system for clinical applications. The system successfully performed real-time 3D MRI-guided intervention on a cadaver brain, with the interventional trajectory tracked precisely using real-time images. This experiment showed the capability of the developed system for clinical neuro-intervention. **6. Comparison with Other Methods:** Quantitative comparison against existing algorithms demonstrated the superior performance of LSFP-Net in terms of image quality (PSNR, SSIM) and speed. LSFP-Net had the fewest artifacts, and its speed was several times faster than comparative methods.

This study presents a significant advance in real-time MRI-guided neurosurgery by introducing LSFP-Net and integrating it into a functional system. The results demonstrate the potential of this technology to improve the accuracy, efficiency, and safety of minimally invasive brain interventions. The superior performance of LSFP-Net compared to existing methods highlights the benefits of combining low-rank and sparse priors with the unrolled network architecture. The ability to learn the optimal regularization parameters during training eliminates tedious manual tuning and improves the generalizability of the method. The use of radial sampling and a group-based reconstruction scheme makes real-time image reconstruction computationally feasible. The successful phantom and cadaver studies validate the real-time performance of the system. The accurate tracking of the interventional needle in both 2D and 3D experiments underscores the potential for improved surgical precision. The combination of high spatial resolution, high temporal resolution, and low latency allows for precise real-time feedback, which is crucial for interventions requiring delicate manipulation in the brain. The study provides compelling evidence that LSFP-Net can be integrated into existing diagnostic MRI systems, enhancing their capabilities for image-guided neurosurgery. The findings contribute to the broader field of image-guided interventions by advancing the state-of-the-art in real-time MRI reconstruction. The proposed framework can be adapted to other interventional settings where real-time image feedback is crucial. Further research could focus on the application of LSFP-Net to other imaging modalities or to different types of interventions.

This research successfully developed and validated LSFP-Net, a deep unrolled neural network for real-time interventional MRI (i-MRI). LSFP-Net, integrated with a custom MR-compatible interventional device, enables real-time MRI-guided brain interventions with high spatiotemporal resolution and low latency. The promising results from phantom and cadaver experiments highlight the potential for this technology to improve the accuracy, safety, and efficiency of neurosurgical procedures. Future work will focus on larger-scale clinical trials and integration with fully fledged robotic systems to ensure safety in live patients.

While this study demonstrates promising results, some limitations should be acknowledged. The training dataset, although large, may not fully capture the diversity of interventional scenarios encountered in clinical practice. Further validation with a larger and more diverse dataset is necessary before widespread clinical implementation. The custom-designed interventional device is currently limited to 4 degrees of freedom; a more flexible system may be required for certain procedures. The current system was evaluated on a specific 3T MRI scanner; further testing on different scanners is necessary to ensure generalizability and compatibility. Finally, the study utilized cadaver tissue, which may not perfectly replicate the characteristics of live tissue, potentially affecting the generalizability of the findings.