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Objective. Dynamic cone-beam CT (CBCT) imaging is highly desired in image-guided radiation therapy to provide volumetric images with high spatial and temporal resolutions to enable applications including tumor motion tracking/prediction and intra-delivery dose calculation/accumulation. However, dynamic CBCT reconstruction is a substantially challenging spatiotemporal inverse problem, due to the extremely limited projection sample available for each CBCT reconstruction (one projection for one CBCT volume). Approach. We developed a simultaneous spatial and temporal implicit neural representation (STINR) method for dynamic CBCT reconstruction. STINR mapped the unknown image and the evolution of its motion into spatial and temporal multi-layer perceptrons (MLPs), and iteratively optimized the neuron weightings of the MLPs via acquired projections to represent the dynamic CBCT series. In addition to the MLPs, we also introduced prior knowledge, in the form of principal component analysis (PCA)-based patient-specific motion models, to reduce the complexity of the temporal mapping to address the ill-conditioned dynamic CBCT reconstruction problem. We used the extended-cardiac-torso (XCAT) phantom and a patient 4D-CBCT dataset to simulate different lung motion scenarios to evaluate STINR. The scenarios contain motion variations including motion baseline shifts, motion amplitude/frequency variations, and motion non-periodicity. The XCAT scenarios also contain inter-scan anatomical variations including tumor shrinkage and tumor position change. Main results. STINR shows consistently higher image reconstruction and motion tracking accuracy than a traditional PCA-based method and a polynomial-fitting-based neural representation method. STINR tracks the lung target to an average center-of-mass error of 1–2 mm, with corresponding relative errors of reconstructed dynamic CBCTs around 10%. Significance. STINR offers a general framework allowing accurate dynamic CBCT reconstruction for image-guided radiotherapy. It is a one-shot learning method that does not rely on pre-training and is not susceptible to generalizability issues. It also allows natural super-resolution. It can be readily applied to other imaging modalities as well.

PURPOSE Recently, two-dimensional-to-three-dimensional (2D-3D) deformable registration has been applied to deform liver tumor contours from prior reference images onto estimated cone-beam computed tomography (CBCT) target images to automate on-board tumor localizations. Biomechanical modeling has also been introduced to fine-tune the intra-liver deformation-vector-fields (DVFs) solved by 2D-3D deformable registration, especially at low-contrast regions, using tissue elasticity information and liver boundary DVFs. However, the caudal liver boundary shows low contrast from surrounding tissues in the cone-beam projections, which degrades the accuracy of the intensity-based 2D-3D deformable registration there and results in less accurate boundary conditions for biomechanical modeling. We developed a deep-learning (DL)-based method to optimize the liver boundary DVFs after 2D-3D deformable registration to further improve the accuracy of subsequent biomechanical modeling and liver tumor localization. METHODS The DL-based network was built based on the U-Net architecture. The network was trained in a supervised fashion to learn motion correlation between cranial and caudal liver boundaries to optimize the liver boundary DVFs. Inputs of the network had three channels, and each channel featured the 3D DVFs estimated by the 2D-3D deformable registration along one Cartesian direction (x, y, z). To incorporate patient-specific liver boundary information into the DVFs, the DVFs were masked by a liver boundary ring structure generated from the liver contour of the prior reference image. The network outputs were the optimized DVFs along the liver boundary with higher accuracy. From these optimized DVFs, boundary conditions were extracted for biomechanical modeling to further optimize the solution of intra-liver tumor motion. We evaluated the method using 34 liver cancer patient cases, with 24 for training and 10 for testing. We evaluated and compared the performance of three methods: 2D-3D deformable registration, 2D-3D-Bio (2D-3D deformable registration with biomechanical modeling), and DL-Bio (DL model prediction with biomechanical modeling). The tumor localization errors were quantified through calculating the center-of-mass-errors (COMEs), DICE coefficients, and Hausdorff distance between deformed liver tumor contours and manually segmented "gold-standard" contours. RESULTS The predicted DVFs by the DL model showed improved accuracy at the liver boundary, which translated into more accurate liver tumor localizations through biomechanical modeling. On a total of 90 evaluated images and tumor contours, the average (± sd) liver tumor COMEs of the 2D-3D, 2D-3D-Bio, and DL-Bio techniques were 4.7 ± 1.9 mm, 2.9 ± 1.0 mm, and 1.7 ± 0.4 mm. The corresponding average (± sd) DICE coefficients were 0.60 ± 0.12, 0.71 ± 0.07, and 0.78 ± 0.03; and the average (± sd) Hausdorff distances were 7.0 ± 2.6 mm, 5.4 ± 1.5 mm, and 4.5 ± 1.3 mm, respectively. CONCLUSION DL-Bio solves a general correlation model to improve the accuracy of the DVFs at the liver boundary. With improved boundary conditions, the accuracy of biomechanical modeling can be further increased for accurate intra-liver low-contrast tumor localization.

We show images produced by an electron beam deflector, a quadrupole lens and a einzel lens fabricated from conducting and non-conducting plastic using a 3D printer. Despite the difficulties associated with the use of plastics in vacuum, such as outgassing, poor conductivity, and print defects, the devices were used successfully in vacuum to steer, stretch and focus electron beams to millimeter diameters. Simulations indicate that much smaller focus spot sizes might be possible for such 3D-printed plastic electron lenses taking into account some possible surface defects. This work was motivated by our need to place electron optical components in difficult-to-access geometries. Our proof-of-principle demonstration opens the door to consider 3D-printed electron microscopes, whose reduced cost would make such microscopes more widely available. Potentially, this may have a significant impact on electron beam science and technology in general and electron microscopy in particular.

Purpose. Real-time three-dimensional (3D) magnetic resonance (MR) imaging is challenging because of slow MR signal acquisition, leading to highly under-sampled k-space data. Here, we proposed a deep learning-based, k-space-driven deformable registration network (KS-RegNet) for real-time 3D MR imaging. By incorporating prior information, KS-RegNet performs a deformable image registration between a fully-sampled prior image and on-board images acquired from highly-under-sampled k-space data, to generate high-quality on-board images for real-time motion tracking. Methods. KS-RegNet is an end-to-end, unsupervised network consisting of an input data generation block, a subsequent U-Net core block, and following operations to compute data fidelity and regularization losses. The input data involved a fully-sampled, complex-valued prior image, and the k-space data of an on-board, real-time MR image (MRI). From the k-space data, under-sampled real-time MRI was reconstructed by the data generation block to input into the U-Net core. In addition, to train the U-Net core to learn the under-sampling artifacts, the k-space data of the prior image was intentionally under-sampled using the same readout trajectory as the real-time MRI, and reconstructed to serve an additional input. The U-Net core predicted a deformation vector field that deforms the prior MRI to on-board real-time MRI. To avoid adverse effects of quantifying image similarity on the artifacts-ridden images, the data fidelity loss of deformation was evaluated directly in k-space. Results. Compared with Elastix and other deep learning network architectures, KS-RegNet demonstrated better and more stable performance. The average (±s.d.) DICE coefficients of KS-RegNet on a cardiac dataset for the 5- , 9- , and 13-spoke k-space acquisitions were 0.884 ± 0.025, 0.889 ± 0.024, and 0.894 ± 0.022, respectively; and the corresponding average (±s.d.) center-of-mass errors (COMEs) were 1.21 ± 1.09, 1.29 ± 1.22, and 1.01 ± 0.86 mm, respectively. KS-RegNet also provided the best performance on an abdominal dataset. Conclusion. KS-RegNet allows real-time MRI generation with sub-second latency. It enables potential real-time MR-guided soft tissue tracking, tumor localization, and radiotherapy plan adaptation.

Objective. Real-time imaging is highly desirable in image-guided radiotherapy, as it provides instantaneous knowledge of patients’ anatomy and motion during treatments and enables online treatment adaptation to achieve the highest tumor targeting accuracy. Due to extremely limited acquisition time, only one or few x-ray projections can be acquired for real-time imaging, which poses a substantial challenge to localize the tumor from the scarce projections. For liver radiotherapy, such a challenge is further exacerbated by the diminished contrast between the tumor and the surrounding normal liver tissues. Here, we propose a framework combining graph neural network-based deep learning and biomechanical modeling to track liver tumor in real-time from a single onboard x-ray projection. Approach. Liver tumor tracking is achieved in two steps. First, a deep learning network is developed to predict the liver surface deformation using image features learned from the x-ray projection. Second, the intra-liver deformation is estimated through biomechanical modeling, using the liver surface deformation as the boundary condition to solve tumor motion by finite element analysis. The accuracy of the proposed framework was evaluated using a dataset of 10 patients with liver cancer. Main results. The results show accurate liver surface registration from the graph neural network-based deep learning model, which translates into accurate, fiducial-less liver tumor localization after biomechanical modeling (Significance. The method demonstrates its potentiality towards intra-treatment and real-time 3D liver tumor monitoring and localization. It could be applied to facilitate 4D dose accumulation, multi-leaf collimator tracking and real-time plan adaptation. The method can be adapted to other anatomical sites as well.

We investigate theoretically how the duration of an isolated attosecond pulse (IAP) can be minimized by carefully selecting frequencies of high-order harmonic generation (HHG) spectra produced by ultrashort driving laser pulses. Based on numerical calculations of HHG by solving the time-dependent Schr\"odinger equation for a single H atom, we provide three strategies for generating shorter IAPs. First, when the high-frequency region of an HHG plateau is selected one should use frequencies below the cutoff. Second, for a wide HHG plateau the low-frequency region can produce shorter IAPs than the high-frequency region. Third, we propose a method of producing IAPs with transform-limited duration by selecting special frequency stripes across the entire HHG plateau. Analytic analyses show that how our strategies work is related to the (Fourier-transform) properties of an Airy function. We also carry out HHG calculations considering macroscopic effects by means of intensity averaging over the focal region. We find that our conclusions for single-atom calculations can still apply for macroscopic HHG spectra as long as they resemble single-atom spectra.

Owing to increasing applications of time-resolved coherent x-ray scattering for the investigation of molecular reaction dynamics, we develop a theoretical model for time-dependent x-ray diffraction from molecular and/or electronic motion in molecules. Our model shows that the violation of centrosymmetry (VOC) is a general phenomenon in time-resolved diffraction patterns. We employ our theoretical model to illustrate the VOC in time-resolved coherent x-ray diffraction from two oriented diatomic molecules undergoing rovibrational motion: lithium hydride (LiD) and hydrogen (HD). Our simulations show asymmetric x-ray diffraction images that reflect the directions of the molecular motions.

Owing to its ability to provide unique information on electron dynamics, time-resolved electron momentum spectroscopy (EMS) is used to study theoretically a laser-driven electronic motion in atoms. Specifically, a chirped laser pulse is used to adiabatically transfer the populations of lithium atoms from the ground state to the first excited state. During this process, impact ionization near the Bethe ridge by time-delayed ultrashort, high-energy electron pulses is used to image the instantaneous momentum density of this electronic population transfer. Simulations with 100 fs and 1 fs pulse durations demonstrate the capability of EMS to image the time-varying momentum density, including its change of symmetry as the population transfer progresses. Moreover, the spectra corresponding to different pulse durations reveal different kinds of electronic motion. We discuss how to properly interpret these time-resolved EMS spectra, which represent a generalization of time-independent EMS.

We investigate theoretically the use of energy-resolved ultrafast electron diffraction to image laser-driven electronic motion in atoms. A chirped laser pulse is used to transfer the valence electron of the lithium atom from the ground state to the first excited state. During this process, the electronic motion is imaged by 100-fs and 1-fs electron pulses in energy-resolved diffraction measurements. Simulations show that the angle-resolved spectra reveal the time evolution of the energy content and symmetry of the electronic state. The time-dependent diffraction patterns are further interpreted in terms of the momentum transfer. For the case of incident 1-fs electron pulses, the rapid $2s\ensuremath{-}2p$ quantum beat motion of the target electron is imaged as a time-dependent asymmetric oscillation of the diffraction pattern.

Recently ultrafast electron diffraction and microscopy have reached unprecedented temporal resolution, and transient structures with atomic precision have been observed in various reactions. It is anticipated that these extraordinary advances will soon allow direct observation of electronic motions during chemical reactions. We therefore performed a series of theoretical investigations and simulations to investigate the imaging of electronic motions in atoms and molecules by ultrafast electron diffraction. Three prototypical electronic motions were considered for hydrogen atoms. For the case of a breathing mode, the electron density expands and contracts periodically, and we show that the time-resolved scattering intensities reflect such changes of the charge radius. For the case of a wiggling mode, the electron oscillates from one side of the nucleus to the other, and we show that the diffraction images exhibit asymmetric angular distributions. The last case is a hybrid mode that involves both breathing and wiggling motions. Owing to the demonstrated ability of ultrafast electrons to image these motions, we have proposed to image a coherent population transfer in lithium atoms using currently available femtosecond electron pulses. A frequency-swept laser pulse adiabatically drives the valence electron of a lithium atom from the 2s to 2p orbitals, and a time-delayed electron pulse maps such motion. Our simulations show that the diffraction images reflect this motion both in the scattering intensities and the angular distributions.

We study the photodetachment of an electron from the hydrogen anion due to short, high-frequency laser pulses by numerically solving the time-dependent Schr\"odinger equation. Simulations are performed to investigate the dependence of the photoelectron spectra on the duration, chirp, and intensity of the pulses. Specifically, we concentrate on the low-energy distributions in the spectra that result from the Raman transitions of the broadband pulses. Contrary to one-photon ionization, the low-energy distribution maintains an almost constant width as the laser bandwidth is expanded by chirping the pulses. In addition, we study the transitions of the ionization dynamics from the perturbative to the strong-field regime. At high intensities, the positions of the net one- and two-photon absorption peaks in the spectrum shift and the peaks split to multiple subpeaks due to multiphoton effects. Moreover, although the one- and two-photon peaks and low-energy distribution exhibit saturation of the ionization yields, the low-energy distribution shows relatively mild saturation.

We investigate theoretically the direct imaging of coherent electronic motion in atoms and molecules using attosecond electron pulses. The theories of time-resolved ultrafast electron diffraction and (e, 2e) momentum spectroscopy as well as the requisite conditions for carrying out time-resolved measurements to obtain timedependent images are discussed. Results of simulations showing images of the motions of coherent superposition states in both the hydrogen atom and the hydrogen molecular ion are shown, thus indicating the capability of ultrafast electron pulses to investigate time-dependent electron dynamics.

The detection of spatial and temporal electronic motion by scattering of subfemtosecond pulses of 10 keV electrons from coherent superpositions of electronic states of both H and ${T}_{2}^{+}$ is investigated. For the H atom, we predict changes in the diffraction images that reflect the time-dependent effective radius of the electronic charge density. For an aligned ${T}_{2}^{+}$ molecule, the diffraction image changes reflect the time-dependent localization or delocalization of the electronic charge density.

A second example of a barrierless reaction between two closed-shell molecules is reported. The reaction F(2)+CH(3)SSCH(3) has been investigated with crossed molecular beam experiments and ab initio calculations. Compared with previous results of the F(2)+CH(3)SCH(3) reaction [J. Chem. Phys. 127, 101101 (2007); J. Chem. Phys. 128, 104317 (2008)], a new product channel leading to CH(3)SF+CH(3)SF is observed to be predominant in the title reaction, whereas the anticipated HF+C(2)H(5)S(2)F channel is not found. In addition, the F+C(2)H(6)S(2)F product channel, the analog to the F+C(2)H(6)SF channel in the F(2)+CH(3)SCH(3) reaction, opens up at collision energies higher than 4.3 kcal/mol. Angular and translational energy distributions of the products are reported and collision energy dependences of the reaction cross section and product branching ratio are shown. The reaction barrier is found to be negligible (1 kcal/mol). Multireference ab initio calculations suggest a reaction mechanism involving a short-lived intermediate which can be formed without activation energy.

The reaction of F(2)+C(2)H(4) has been investigated with crossed molecular beam experiments and high level ab initio calculations. For a wide range of collision energies up to 11 kcal/mol, only one reaction channel could be observed in the gas phase. The primary products of this channel were identified as F+CH(2)CH(2)F. The experimental reaction threshold of collision energy was determined to be 5.5+/-0.5 kcal/mol. The product angular distribution was found to be strongly backward, indicating that the reaction time scale is substantially shorter than rotation. The calculated transition state structure suggests an early barrier; such dynamics is consistent with the small product kinetic energy release measured in the experiment. All experimental results consistently support a rebound reaction mechanism, which is suggested by the calculation of the intrinsic reaction coordinate. This work provides a clear and unambiguous description of the reaction dynamics, which may help to answer the question why the same reaction produces totally different products in the condensed phase.