A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity

We present a systematic study of collisions of homogeneous, plane--fronted, impulsive light--like signals which do not interact after head--on collision. For the head--on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be non--interacting after collision. We then solve the collision problem in general when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.Comment: 14 pages, late

Evaporation and growth of crystals - propagation of step density compression waves at vicinal surfaces

We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in a presence of step-step repulsion and an absence of destabilizing factors (as Schwoebel effect, surface electromigration etc.). The central result is that a critical velocity of the steps in the train exists which separates the stability and instability regimes. When the step velocity exceeds its critical value the plot of these trajectories manifests clear space and time periodicity (step density compression waves propagate on the vicinal surface). This ordered motion of the steps is preceded by a relatively short transition period of disordered step dynamics.Comment: 18 pages, 6 figure

Lattice Effects in Crystal Evaporation

We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of the continuum approximation treated by Frank is checked against numerical calculations and simple, qualitative arguments. The continuum approximation is found to suffer from limitations related, in particular, to the existence of angular points. These limitations are often related to an adatom detachment rate of adatoms which is higher on the lower side of each step than on the upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages, LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119

Shifted-windows transformers for the detection of cerebral aneurysms in microsurgery

Purpose: Microsurgical Aneurysm Clipping Surgery (MACS) carries a high risk for intraoperative aneurysm rupture. Automated recognition of instances when the aneurysm is exposed in the surgical video would be a valuable reference point for neuronavigation, indicating phase transitioning and more importantly designating moments of high risk for rupture. This article introduces the MACS dataset containing 16 surgical videos with frame-level expert annotations and proposes a learning methodology for surgical scene understanding identifying video frames with the aneurysm present in the operating microscope’s field-of-view./ Methods: Despite the dataset imbalance (80% no presence, 20% presence) and developed without explicit annotations, we demonstrate the applicability of Transformer-based deep learning architectures (MACSSwin-T, vidMACSSwin-T) to detect the aneurysm and classify MACS frames accordingly. We evaluate the proposed models in multiple-fold cross-validation experiments with independent sets and in an unseen set of 15 images against 10 human experts (neurosurgeons)./ Results: Average (across folds) accuracy of 80.8% (range 78.5–82.4%) and 87.1% (range 85.1–91.3%) is obtained for the image- and video-level approach, respectively, demonstrating that the models effectively learn the classification task. Qualitative evaluation of the models’ class activation maps shows these to be localized on the aneurysm’s actual location. Depending on the decision threshold, MACSWin-T achieves 66.7–86.7% accuracy in the unseen images, compared to 82% of human raters, with moderate to strong correlation./ Conclusions: Proposed architectures show robust performance and with an adjusted threshold promoting detection of the underrepresented (aneurysm presence) class, comparable to human expert accuracy. Our work represents the first step towards landmark detection in MACS with the aim to inform surgical teams to attend to high-risk moments, taking precautionary measures to avoid rupturing

Global rigid registration of CT to video in laparoscopic liver surgery

PURPOSE: Image-guidance systems have the potential to aid in laparoscopic interventions by providing sub-surface structure information and tumour localisation. The registration of a preoperative 3D image with the intraoperative laparoscopic video feed is an important component of image guidance, which should be fast, robust and cause minimal disruption to the surgical procedure. Most methods for rigid and non-rigid registration require a good initial alignment. However, in most research systems for abdominal surgery, the user has to manually rotate and translate the models, which is usually difficult to perform quickly and intuitively. METHODS: We propose a fast, global method for the initial rigid alignment between a 3D mesh derived from a preoperative CT of the liver and a surface reconstruction of the intraoperative scene. We formulate the shape matching problem as a quadratic assignment problem which minimises the dissimilarity between feature descriptors while enforcing geometrical consistency between all the feature points. We incorporate a novel constraint based on the liver contours which deals specifically with the challenges introduced by laparoscopic data. RESULTS: We validate our proposed method on synthetic data, on a liver phantom and on retrospective clinical data acquired during a laparoscopic liver resection. We show robustness over reduced partial size and increasing levels of deformation. Our results on the phantom and on the real data show good initial alignment, which can successfully converge to the correct position using fine alignment techniques. Furthermore, since we can pre-process the CT scan before surgery, the proposed method runs faster than current algorithms. CONCLUSION: The proposed shape matching method can provide a fast, global initial registration, which can be further refined by fine alignment methods. This approach will lead to a more usable and intuitive image-guidance system for laparoscopic liver surgery

Intelligent viewpoint selection for efficient CT to video registration in laparoscopic liver surgery

PURPOSE: Minimally invasive surgery offers advantages over open surgery due to a shorter recovery time, less pain and trauma for the patient. However, inherent challenges such as lack of tactile feedback and difficulty in controlling bleeding lower the percentage of suitable cases. Augmented reality can show a better visualisation of sub-surface structures and tumour locations by fusing pre-operative CT data with real-time laparoscopic video. Such augmented reality visualisation requires a fast and robust video to CT registration that minimises interruption to the surgical procedure. METHODS: We propose to use view planning for efficient rigid registration. Given the trocar position, a set of camera positions are sampled and scored based on the corresponding liver surface properties. We implement a simulation framework to validate the proof of concept using a segmented CT model from a human patient. Furthermore, we apply the proposed method on clinical data acquired during a human liver resection. RESULTS: The first experiment motivates the viewpoint scoring strategy and investigates reliable liver regions for accurate registrations in an intuitive visualisation. The second experiment shows wider basins of convergence for higher scoring viewpoints. The third experiment shows that a comparable registration performance can be achieved by at least two merged high scoring views and four low scoring views. Hence, the focus could change from the acquisition of a large liver surface to a small number of distinctive patches, thereby giving a more explicit protocol for surface reconstruction. We discuss the application of the proposed method on clinical data and show initial results. CONCLUSION: The proposed simulation framework shows promising results to motivate more research into a comprehensive view planning method for efficient registration in laparoscopic liver surgery