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Effects of non-equidistant grids on momentum conservation is studied for simple test cases of an electrostatic 1D PIC code. The aim is to reduce the errors in energy and momentum conservation. Assuming an exact Poisson solver only numerical errors for the particle mover are analysed. For the standard electric field calculation using a central-difference scheme, artificial electric fields at the particle position are generated in the case when the particle is situated next to a cell size change. This is sufficient to destroy momentum conservation. A modified electric field calculation scheme is derived to reduce this error. Independent of the calculation scheme additional fake forces in a two-particle system are found which result in an error in the total kinetic energy of the system. This contribution is shown to be negligible for many particle systems. To test the accuracy of the two electric field calculation schemes numerical tests are done to compare with an equidistant grid set-up. All tests show an improved momentum conservation and total kinetic energy for the modified calculation scheme of the electric field. [ABSTRACT FROM AUTHOR]

This work describes a novel technique for rapid and motion-robust whole-body magnetic resonance imaging (MRI). The method employs highly undersampled radial fast low angle shot (FLASH) sequences to cover large volumes by cross-sectional real-time MRI with automatic slice advancement after each frame. The slice shift typically amounts to a fraction of the slice thickness (e.g., 10% to 50%) in order to generate a successive series of partially overlapping sections. Joint reconstructions of these serial images and their respective coil sensitivity maps rely on nonlinear inversion (NLINV) with regularization to the image and sensitivity maps of a preceding frame. The procedure exploits the spatial similarity of neighboring sections. Whole-body scanning is accomplished by measuring multiple volumes at predefined locations, i.e., at fixed table positions, in combination with intermediate automatic movements of the patient table. Individual volumes may take advantage of different field-of-views, image orientations, spatial and temporal resolutions as well as contrasts. Preliminary proof-of-principle applications to healthy subjects at 3 T without cardiac gating and during free breathing yield high-quality anatomic images with acquisition times of less than 100 ms. Spin-density and T1 contrasts are obtained by spoiled FLASH sequences, while T2-type (i.e., T2/T1) contrast results from refocused FLASH sequences that generate a steady state free precession (SSFP) free induction decay (FID) signal. Total measuring times excluding vendor-controlled adjustment procedures are less than two minutes for a 100 cm scan that, for example, covers the body from head to thigh by three optimized volumes and more than 1,300 images. In conclusion, after demonstrating technical feasibility the proposed method awaits clinical trials., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-23-923/coif). DV and JF report that they are co-inventors of a patent describing the MRI method (Rapid Volume Coverage 2020) used in this study. The other authors have no conflicts of interest to declare., (2023 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

This work is a proof-of-concept realization of a novel technique for rapid volumetric acquisition, reconstruction, and visualization of three-directional (3dir) flow velocities. The technique combines real-time 3dir phase-contrast (PC) flow magnetic resonance imaging (MRI) with real-time cross-sectional volume coverage. It offers a rapid examination without dependence on electrocardiography (ECG) or respiratory gating during a continuous image acquisition at up to 16 fps. Real-time flow MRI utilizes pronounced radial undersampling and a model-based nonlinear inverse reconstruction. Volume coverage is achieved by automatically advancing the slice position of each PC acquisition by a small percentage of the slice thickness. Post-processing involves the calculation of maximum intensity projections along the slice dimension resulting in six direction-selective velocity maps and a maximum speed map. Preliminary applications to healthy subjects at 3 T comprise mapping of the carotid arteries and cranial vessels at 1.0 mm in-plane resolution within 30 s as well as of the aortic arch at 1.6 mm resolution within 20 s. In conclusion, the proposed method for rapid mapping of 3dir flow velocities offers a quick assessment of the vasculature either to provide a first clinical survey or to plan for more detailed studies., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-22-1126/coif). DV and JF report that they are co-inventors of a patent describing the MRI method used here. The other authors have no conflicts of interest to declare., (2023 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

This work describes a dynamic magnetic resonance imaging (MRI) technique for local scanning of the human body with use of a handheld receive coil or coil array. Real-time MRI is based on highly undersampled radial gradient-echo sequences with joint reconstructions of serial images and coil sensitivity maps by regularized nonlinear inversion (NLINV). For this proof-of-concept study, a fixed slice position and field-of-view (FOV) were predefined from the operating console, while a local receive coil (array) is moved across the body-for the sake of simplicity by the subject itself. Experimental realizations with a conventional 3 T magnet comprise dynamic anatomic imaging of the head, thorax and abdomen of healthy volunteers. Typically, the image resolution was 0.75 to 1.5 mm with 3 to 6 mm section thickness and acquisition times of 33 to 100 ms per frame. However, spatiotemporal resolutions and contrasts are highly variable and may be adjusted to clinical needs. In summary, the proposed FLASHlight MRI method provides a robust acquisition and reconstruction basis for future diagnostic strategies that mimic the usage of ultrasound. Necessary extensions for this vision require remote control of all sequence parameters by a person at the scanner as well as the design of more flexible gradients and magnets., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-22-648/coif). DV and JF report that they are co-inventors of a patent describing the MRI method used here. The other authors have no conflicts of interest to declare., (2023 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

Purpose: To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near ± π and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes., Theory and Methods: A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T., Results: Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm 3 spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction., Conclusion: Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application., (© 2021 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine.)

Purpose: The main purpose of this work was to develop an efficient approach for segmentation of structures that are relevant for diagnosis and treatment of obstructive sleep apnea syndrome (OSAS), namely pharynx, tongue, and soft palate, from mid-sagittal magnetic resonance imaging (MR) data. This framework will be applied to big data acquired within an on-going epidemiological study from a general population., Methods: A deep cascaded framework for subsequent segmentation of pharynx, tongue, and soft palate is presented. The pharyngeal structure was segmented first, since the airway was clearly visible in the T1-weighted sequence. Thereafter, it was used as an anatomical landmark for tongue location. Finally, the soft palate region was extracted using segmented tongue and pharynx structures and used as input for a deep network. In each segmentation step, a UNet-like architecture was applied., Results: The result assessment was performed qualitatively by comparing the region boundaries obtained from the expert to the framework results and quantitatively using the standard Dice coefficient metric. Additionally, cross-validation was applied to ensure that the framework performance did not depend on the specific selection of the validation set. The average Dice coefficients on the test set were [Formula: see text], [Formula: see text], and [Formula: see text] for tongue, pharynx, and soft palate tissues, respectively. The results were similar to other approaches and consistent with expert readings., Conclusion: Due to high speed and efficiency, the framework will be applied for big epidemiological data with thousands of participants acquired within the Study of Health in Pomerania as well as other epidemiological studies to provide information on the anatomical structures and aspects that constitute important risk factors to the OSAS development.

This work describes a new method for diffusion-weighted (DW) magnetic resonance imaging (MRI) without susceptibility artifacts. The technique combines a DW spin-echo module and a single-shot stimulated echo acquisition mode (STEAM) MRI readout with undersampled radial trajectories and covers a volume by a gapless series of cross-sectional slices. In a first step, optimal coil sensitivities for all slices are obtained from a series of non-DW acquisitions by nonlinear inverse reconstruction with regularization to the image and coil sensitivities of a directly neighboring slice. In a second step, these coil sensitivities are used to compute all series of non-DW and DW images by linear inverse reconstruction with spatial regularization to a neighboring image. Proof-of-principle applications to the brain (51 sections) and prostate (31 sections) of healthy subjects were realized for a protocol with two b-values and 6 gradient directions at 3 T. Including averaging the measuring times for studies of the brain at 1.0×1.0×3.0 mm 3 resolution (b =1,000 s mm -2 ) and prostate at 1.4×1.4×3.0 mm 3 resolution (b =600 s mm -2 ) were 2.5 min and 4.5 min, respectively. All reconstructions were accomplished online with use of a multi-GPU computer integrated into the MRI system. The resulting non-DW images, mean DW images averaged across directions and maps of the apparent diffusion coefficient confirm the absence of geometric distortions or false signal alterations and demonstrate diagnostic image quality. The novel method for DW STEAM MRI of a volume without susceptibility artifacts warrants extended clinical trials., Competing Interests: Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at http://dx.doi.org/10.21037/qims-20-871). The authors report that they are co-inventors of a pending patent “Diffusion-weighted MRI of a volume without susceptibility artifacts”., (2021 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

Purpose: To develop a rapid and motion-robust technique for volumetric MRI, which is based on cross-sectional real-time MRI acquisitions with automatic advancement of the slice position., Methods: Real-time MRI with a frame-by-frame moving cross-section is performed with use of highly undersampled radial gradient-echo sequences offering spin density, T 1 , or T 2 /T 1 contrast. Joint reconstructions of serial images and coil sensitivity maps from spatially overlapping sections are accomplished by nonlinear inversion with regularization to the preceding section-formally identical to dynamic real-time MRI. Shifting each frame by 20% to 25% of the section thickness ensures 75% to 80% overlap of successive sections. Acquisition times of 40 to 67 ms allow for rates of 15 to 25 sections per second, while volumes are defined by the number of cross-sections times the section shift., Results: Preliminary realizations at 3T comprise studies of the human brain, carotid arteries, liver, and prostate. Typically, coverage of a 90- to 180-mm volume at 0.8- to 1.2-mm in-plane resolution, 4- to 6-mm section thickness, and 0.8- to 1.5-mm section shift is accomplished within total measuring times of 4 to 6 seconds and a section speed of 15 to 37.5 mm per second. However, spatiotemporal resolution, contrast including options such as fat saturation and total measuring time are highly variable and may be adjusted to clinical needs. Promising volumetric applications range from fetal MRI to dynamic contrast-enhanced MRI., Conclusion: The proposed method allows for rapid and motion-robust volume coverage in a variety of imaging scenarios., (© 2019 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.)

The purpose of this work was to develop an acquisition and reconstruction technique for two- and three-directional (2d and 3d) phase-contrast flow MRI in real time. A previous real-time MRI technique for one-directional (1d) through-plane flow was extended to 2d and 3d flow MRI by introducing in-plane flow sensitivity. The method employs highly undersampled radial FLASH sequences with sequential acquisitions of two or three flow-encoding datasets and one flow-compensated dataset. Echo times are minimized by merging the waveforms of flow-encoding and radial imaging gradients. For each velocity direction individually, model-based reconstructions by regularized nonlinear inversion jointly estimate an anatomical image, a set of coil sensitivities and a phase-contrast velocity map directly. The reconstructions take advantage of a dynamic phase reference obtained by interpolating consecutive flow-compensated acquisitions. Validations include pulsatile flow phantoms as well as in vivo studies of the human aorta at 3 T. The proposed method offers cross-sectional 2d and 3d flow MRI of the human aortic arch at 53 and 67 ms resolution, respectively, without ECG synchronization and during free breathing. The in-plane resolution was 1.5 × 1.5 mm 2 and the slice thickness 6 mm. In conclusion, real-time multi-directional flow MRI offers new opportunities to study complex human blood flow without the risk of combining differential phase (i.e., velocity) information from multiple heartbeats as for ECG-gated data. The method would benefit from a further reduction of acquisition time and accelerated computing to allow for extended clinical trials., (© 2019 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.)

Real-time magnetic resonance imaging (MRI) or model-based MRI reconstructions of parametric maps require the solution of an ill-posed nonlinear inverse problem. Respective algorithms, e.g., the iteratively regularized Gauss-Newton method, implicitly combine datasets from multiple receive coils. Because these local coils may exhibit complex sensitivity profiles with rather different phase offsets, the numerical optimization may lead to phase singularities which in turn cause "black holes" in magnitude images. The purpose of this work is to develop a method for inverse reconstructions of multi-coil MRI data which avoids the generation of such spatially selective phase singularities. It is proposed to use volumetric body coil data and start the iterative reconstruction of multi-coil data with a reference image which offers proper phase information. In more detail, inverse reconstructions of multi-coil data are initialized with a complex "seed" image which is obtained by a Fast Fourier Transform (FFT) reconstruction of data from a single body coil element. This is accomplished at no additional cost as only very few body coil scans with identical conditions as the multi-coil acquisitions are needed as part of the regular prep scan period. The method is evaluated for anatomical real-time MRI and model-based phase-contrast flow MRI in real-time at 3 T. The proposed method overcomes phase singularities in all cases for arbitrary sets of receive coils. In conclusion, the automatic use of a single body coil reference image is simple, robust, and further improves the reliability of advanced MRI reconstructions from multi-coil data., Competing Interests: Conflicts of Interest: The authors have no conflicts of interest to declare., (2019 Quantitative Imaging in Medicine and Surgery. All rights reserved.)

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios., (Copyright © 2017 John Wiley & Sons, Ltd.)

Objective: To develop a novel method for rapid myocardial T 1 mapping at high spatial resolution., Methods: The proposed strategy represents a single-shot inversion recovery experiment triggered to early diastole during a brief breath-hold. The measurement combines an adiabatic inversion pulse with a real-time readout by highly undersampled radial FLASH, iterative image reconstruction and T 1 fitting with automatic deletion of systolic frames. The method was implemented on a 3-T MRI system using a graphics processing unit-equipped bypass computer for online application. Validations employed a T 1 reference phantom including analyses at simulated heart rates from 40 to 100 beats per minute. In vivo applications involved myocardial T 1 mapping in short-axis views of healthy young volunteers., Results: At 1-mm in-plane resolution and 6-mm section thickness, the inversion recovery measurement could be shortened to 3 s without compromising T 1 quantitation. Phantom studies demonstrated T 1 accuracy and high precision for values ranging from 300 to 1500 ms and up to a heart rate of 100 beats per minute. Similar results were obtained in vivo yielding septal T 1 values of 1246 ± 24 ms (base), 1256 ± 33 ms (mid-ventricular) and 1288 ± 30 ms (apex), respectively (mean ± standard deviation, n = 6)., Conclusion: Diastolic myocardial T 1 mapping with use of single-shot inversion recovery FLASH offers high spatial resolution, T 1 accuracy and precision, and practical robustness and speed. Advances in knowledge: The proposed method will be beneficial for clinical applications relying on native and post-contrast T 1 quantitation.