⊥-loss: A symmetric loss function for magnetic resonance imaging reconstruction and image registration with deep learning

Convolutional neural networks (CNNs) are increasingly adopted in medical imaging, e.g., to reconstruct high-quality images from undersampled magnetic resonance imaging (MRI) acquisitions or estimate subject motion during an examination. MRI is naturally acquired in the complex domain C, obtaining magnitude and phase information in k-space. However, CNNs in complex regression tasks are almost exclusively trained to minimize the L2 loss or maximizing the magnitude structural similarity (SSIM), which are possibly not optimal as they do not take full advantage of the magnitude and phase information present in the complex domain. This work identifies that minimizing the L2 loss in the complex field has an asymmetry in the magnitude/phase loss landscape and is biased, underestimating the reconstructed magnitude. To resolve this, we propose a new loss function for regression in the complex domain called ⊥-loss, which adds a novel phase term to established magnitude loss functions, e.g., L2 or SSIM. We show ⊥-loss is symmetric in the magnitude/phase domain and has favourable properties when applied to regression in the complex domain. Specifically, we evaluate the ⊥+ℓ 2-loss and ⊥+SSIM-loss for complex undersampled MR image reconstruction tasks and MR image registration tasks. We show that training a model to minimize the ⊥+ℓ 2-loss outperforms models trained to minimize the L2 loss and results in similar performance compared to models trained to maximize the magnitude SSIM while offering high-quality phase reconstruction. Moreover, ⊥-loss is defined in R n, and we apply the loss function to the R 2 domain by learning 2D deformation vector fields for image registration. We show that a model trained to minimize the ⊥+ℓ 2-loss outperforms models trained to minimize the end-point error loss

Real-time 3D motion estimation from undersampled MRI using multi-resolution neural networks

Purpose: To enable real-time adaptive magnetic resonance imaging–guided radiotherapy (MRIgRT) by obtaining time-resolved three-dimensional (3D) deformation vector fields (DVFs) with high spatiotemporal resolution and low latency ((Formula presented.) ms). Theory and Methods: Respiratory-resolved (Formula presented.) -weighted 4D-MRI of 27 patients with lung cancer were acquired using a golden-angle radial stack-of-stars readout. A multiresolution convolutional neural network (CNN) called TEMPEST was trained on up to 32 (Formula presented.) retrospectively undersampled MRI of 17 patients, reconstructed with a nonuniform fast Fourier transform, to learn optical flow DVFs. TEMPEST was validated using 4D respiratory-resolved MRI, a digital phantom, and a physical motion phantom. The time-resolved motion estimation was evaluated in-vivo using two volunteer scans, acquired on a hybrid MR-scanner with integrated linear accelerator. Finally, we evaluated the model robustness on a publicly-available four-dimensional computed tomography (4D-CT) dataset. Results: TEMPEST produced accurate DVFs on respiratory-resolved MRI at 20-fold acceleration, with the average end-point-error (Formula presented.) mm, both on respiratory-sorted MRI and on a digital phantom. TEMPEST estimated accurate time-resolved DVFs on MRI of a motion phantom, with an error (Formula presented.) mm at 28 (Formula presented.) undersampling. On two volunteer scans, TEMPEST accurately estimated motion compared to the self-navigation signal using 50 spokes per dynamic (366 (Formula presented.) undersampling). At this undersampling factor, DVFs were estimated within 200 ms, including MRI acquisition. On fully sampled CT data, we achieved a target registration error of (Formula presented.) mm without retraining the model. Conclusion: A CNN trained on undersampled MRI produced accurate 3D DVFs with high spatiotemporal resolution for MRIgRT

Clinical implementation of MRI-based organs-at-risk auto-segmentation with convolutional networks for prostate radiotherapy.

BACKGROUND: Structure delineation is a necessary, yet time-consuming manual procedure in radiotherapy. Recently, convolutional neural networks have been proposed to speed-up and automatise this procedure, obtaining promising results. With the advent of magnetic resonance imaging (MRI)-guided radiotherapy, MR-based segmentation is becoming increasingly relevant. However, the majority of the studies investigated automatic contouring based on computed tomography (CT). PURPOSE: In this study, we investigate the feasibility of clinical use of deep learning-based automatic OARs delineation on MRI. MATERIALS AND METHODS: We included 150 patients diagnosed with prostate cancer who underwent MR-only radiotherapy. A three-dimensional (3D) T1-weighted dual spoiled gradient-recalled echo sequence was acquired with 3T MRI for the generation of the synthetic-CT. The first 48 patients were included in a feasibility study training two 3D convolutional networks called DeepMedic and dense V-net (dV-net) to segment bladder, rectum and femurs. A research version of an atlas-based software was considered for comparison. Dice similarity coefficient, 95% Hausdorff distances (HD95), and mean distances were calculated against clinical delineations. For eight patients, an expert RTT scored the quality of the contouring for all the three methods. A choice among the three approaches was made, and the chosen approach was retrained on 97 patients and implemented for automatic use in the clinical workflow. For the successive 53 patients, Dice, HD95 and mean distances were calculated against the clinically used delineations. RESULTS: DeepMedic, dV-net and the atlas-based software generated contours in 60 s, 4 s and 10-15 min, respectively. Performances were higher for both the networks compared to the atlas-based software. The qualitative analysis demonstrated that delineation from DeepMedic required fewer adaptations, followed by dV-net and the atlas-based software. DeepMedic was clinically implemented. After retraining DeepMedic and testing on the successive patients, the performances slightly improved. CONCLUSION: High conformality for OARs delineation was achieved with two in-house trained networks, obtaining a significant speed-up of the delineation procedure. Comparison of different approaches has been performed leading to the succesful adoption of one of the neural networks, DeepMedic, in the clinical workflow. DeepMedic maintained in a clinical setting the accuracy obtained in the feasibility study

Deep learning-based image reconstruction and motion estimation from undersampled radial k-space for real-time MRI-guided radiotherapy

To enable magnetic resonance imaging (MRI)-guided radiotherapy with real-time adaptation, motion must be quickly estimated with low latency. The motion estimate is used to adapt the radiation beam to the current anatomy, yielding a more conformal dose distribution. As the MR acquisition is the largest component of latency, deep learning (DL) may reduce the total latency by enabling much higher undersampling factors compared to conventional reconstruction and motion estimation methods. The benefit of DL on image reconstruction and motion estimation was investigated for obtaining accurate deformation vector fields (DVFs) with high temporal resolution and minimal latency. 2D cine MRI acquired at 1.5 T from 135 abdominal cancer patients were retrospectively included in this study. Undersampled radial golden angle acquisitions were retrospectively simulated. DVFs were computed using different combinations of conventional- and DL-based methods for image reconstruction and motion estimation, allowing a comparison of four approaches to achieve real-time motion estimation. The four approaches were evaluated based on the end-point-error and root-mean-square error compared to a ground-truth optical flow estimate on fully-sampled images, the structural similarity (SSIM) after registration and time necessary to acquire k-space, reconstruct an image and estimate motion. The lowest DVF error and highest SSIM were obtained using conventional methods up to. For undersampling factors, the lowest DVF error and highest SSIM were obtained using conventional image reconstruction and DL-based motion estimation. We have found that, with this combination, accurate DVFs can be obtained up to with an average root-mean-square error up to 1 millimeter and an SSIM greater than 0.8 after registration, taking 60 milliseconds. High-quality 2D DVFs from highly undersampled k-space can be obtained with a high temporal resolution with conventional image reconstruction and a deep learning-based motion estimation approach for real-time adaptive MRI-guided radiotherapy

Close binary stars in the solar-age Galactic open cluster M67

We present multi-colour time-series CCD photometry of the solar-age galactic open cluster M67 (NGC 2682). About 3600 frames spread over 28 nights were obtained with the 1.5 m Russian-Turkish and 1.2 m Mercator telescopes. High-precision observations of the close binary stars AH Cnc, EV Cnc, ES Cnc, the $\delta$ Scuti type systems EX Cnc and EW Cnc, and some long-period variables belonging to M67 are presented. Three full multi-colour light curves of the overcontact binary AH Cnc were obtained during three observing seasons. Likewise we gathered three light curves of EV Cnc, an EB-type binary, and two light curves of ES Cnc, a blue straggler binary. Parts of the light change of long-term variables S1024, S1040, S1045, S1063, S1242, and S1264 are obtained. Period variation analysis of AH Cnc, EV Cnc, and ES Cnc were done using all times of mid-eclipse available in the literature and those obtained in this study. In addition, we analyzed multi-colour light curves of the close binaries and also determined new frequencies for the $\delta$ Scuti systems. The physical parameters of the close binary stars were determined with simultaneous solutions of multi-colour light and radial velocity curves. Finally we determined the distance of M67 as 857(33) pc via binary star parameters, which is consistent with an independent method from earlier studies.Comment: 12 pages, 9 Figures, 13 Table

Magnetic Resonance-based Response Assessment and Dose Adaptation in Human Papilloma Virus Positive Tumors of the Oropharynx treated with Radiotherapy (MR-ADAPTOR): An R-IDEAL stage 2a-2b/Bayesian phase II trial.

Background Current standard radiotherapy for oropharynx cancer (OPC) is associated with high rates of severe toxicities, shown to adversely impact patients' quality of life. Given excellent outcomes of human papilloma virus (HPV)-associated OPC and long-term survival of these typically young patients, treatment de-intensification aimed at improving survivorship while maintaining excellent disease control is now a central concern. The recent implementation of magnetic resonance image - guided radiotherapy (MRgRT) systems allows for individual tumor response assessment during treatment and offers possibility of personalized dose-reduction. In this 2-stage Bayesian phase II study, we propose to examine weekly radiotherapy dose-adaptation based on magnetic resonance imaging (MRI) evaluated tumor response. Individual patient's plan will be designed to optimize dose reduction to organs at risk and minimize locoregional failure probability based on serial MRI during RT. Our primary aim is to assess the non-inferiority of MRgRT dose adaptation for patients with low risk HPV-associated OPC compared to historical control, as measured by Bayesian posterior probability of locoregional control (LRC).Methods Patients with T1-2 N0-2b (as per AJCC 7th Edition) HPV-positive OPC, with lymph node <3 cm and <10 pack-year smoking history planned for curative radiotherapy alone to a dose of 70 Gy in 33 fractions will be eligible. All patients will undergo pre-treatment MRI and at least weekly intra-treatment MRI. Patients undergoing MRgRT will have weekly adaptation of high dose planning target volume based on gross tumor volume response. The stage 1 of this study will enroll 15 patients to MRgRT dose adaptation. If LRC at 6 months with MRgRT dose adaptation is found sufficiently safe as per the Bayesian model, stage 2 of the protocol will expand enrollment to an additional 60 patients, randomized to either MRgRT or standard IMRT.Discussion Multiple methods for safe treatment de-escalation in patients with HPV-positive OPC are currently being studied. By leveraging the ability of advanced MRI techniques to visualize tumor and soft tissues through the course of treatment, this protocol proposes a workflow for safe personalized radiation dose-reduction in good responders with radiosensitive tumors, while ensuring tumoricidal dose to more radioresistant tumors. MRgRT dose adaptation could translate in reduced long term radiation toxicities and improved survivorship while maintaining excellent LRC outcomes in favorable OPC.Trial registration ClinicalTrials.gov ID: NCT03224000; Registration date: 07/21/2017

Validating subject-specific RF and thermal simulations in the calf muscle using MR-based temperature measurements

Purpose: Ongoing discussions occur to translate the safety restrictions on MR scanners from specific absorption rate (SAR) to thermal dose. Therefore, this research focuses on the accuracy of thermal simulations in human subjects during an MR exam, which is fundamental information in that debate. Methods: Radiofrequency (RF) heating experiments were performed on the calves of 13 healthy subjects using a dedicated transmit-receive coil while monitoring the temperature with proton resonance frequency shift (PRFS) thermometry. Subject-specific models and one generic model were used for electromagnetic and thermal simulations using Pennes' bioheat equation, with the blood equilibration constant equaling zero. The simulations were subsequently compared with the experimental results. Results: The mean B1+ equaled 15 μT in the center slice of all volunteers, and 95% of the voxels had errors smaller than 2.8 μT between the simulation and measurement. The intersubject variation in RF power to achieve the required B1+ was 11%. The resulting intersubject variation in median temperature rise was 14%. Thermal simulations underestimated the median temperature increase on average, with 34% in subject-specific models and 28% in the generic model. Conclusions: Although thermal measures are directly coupled to tissue damage and therefore suitable for RF safety assessment, insecurities in the applied thermal modeling limit their estimation accuracy

PLANET: An Ellipse Fitting Approach for Simultaneous T1 and T2 Mapping Using Phase-Cycled Balanced Steady-State Free Precession

Purpose: To demonstrate the feasibility of a novel, ellipse fitting approach, named PLANET, for simultaneous estimation of relaxation times T1 and T2 from a single 3D phase-cycled balanced steady-state free precession (bSSFP) sequence. Methods: A method is presented in which the elliptical signal model is used to describe the phase-cycled bSSFP steadystate signal. The fitting of the model to the acquired data is reformulated into a linear convex problem, which is solved directly by a linear least squares method, specific to ellipses. Subsequently, the relaxation times T1 and T2, the banding free magnitude, and the off-resonance are calculated from the fitting results. Results: Maps of T1 and T2, as well as an off-resonance and a banding free magnitude can be simultaneously, quickly, and robustly estimated from a single 3D phase-cycled bSSFP sequence. The feasibility of the method was demonstrated in a phantom and in the brain of healthy volunteers on a clinical MR scanner. The results were in good agreement for the phantom, but a systematic underestimation of T1 was observed in the brain. Conclusion: The presented method allows for accurate mapping of relaxation times and off-resonance, and for the reconstruction of banding free magnitude images at realistic signalto- noise ratios. Magn Reson Med 000:000–000, 2017. VC 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made