Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

An Optical Survey for Space Debris on Highly Eccentric MEO Orbits

Optical surveys for space debris in high-altitude orbits have been conducted since more than ten years. Originally these efforts concentrated mainly on the geostationary ring (GEO). Corresponding observation strategies, processing techniques and cataloguing approaches have been developed and successfully applied. The ESA GEO surveys, e.g., resulted in the detection of a significant population of small-size debris and later in the discovery of high area-to-mass ratio objects in GEO-like orbits. The observation scenarios were successively adapted to survey the geostationary transfer orbit (GTO) region; and recently surveys to search for debris in the medium Earth orbit (MEO) region of the global navigation satellite constellations were successfully conducted. Comparably less experience (both, in terms of practical observation and strategy definition) is available for eccentric orbits that (at least partly) are in the MEO region, in particular for the Molniya-type orbits. Several breakup events and deliberate fragmentations are known to have taken place in such orbits. Different survey and follow-up strategies for searching space debris objects in highly-eccentric MEO orbits, and to acquire orbits which are sufficiently accurate to catalogue such objects and to maintain their orbits over longer time spans were developed. Simulations were performed to compare the performance of different survey and cataloguing strategies. Eventually, optical observations were conducted in the framework of an ESA study using ESA’s Space Debris Telescope (ESASDT) the 1-m Zeiss telescope located at the Optical Ground Station (OGS) at the Teide Observatory at Tenerife, Spain. A first series of surveys of Molnjya-type orbits was performed between January and April 2013. During these four months survey observations were performed during nine nights. A basic survey consisted of observing a single geocentric field for 10 minutes. If a faint object was found, follow-up observations were performed during the same night to ensure a save rediscovery of the object during the next nights. Additional follow-up observations to maintain the orbits of these newly discovered faint objects were also acquired with AIUB ́s 1m ZIMLAT telescope in Zimmerwald, Switzerland. Eventually 195 basic surveys were performed during these nine nights corresponding to about 32.5 hours of observations. In total 24 uncorrelated faint objects were discovered and all known catalogue objects in the survey fields were detected. On average one uncorrelated object was found every 80 minutes. Some of these objects show a considerable brightness variation and have a high area-to-mass ratio as determined in the orbit estimation process.

The structural architecture of adult mammalian articular cartilage evolves by a synchronized process of tissue resorption and neoformation during postnatal development

OBJECTIVE: During postnatal development, mammalian articular cartilage acts as a surface growth plate for the underlying epiphyseal bone. Concomitantly, it undergoes a fundamental process of structural reorganization from an immature isotropic to a mature (adult) anisotropic architecture. However, the mechanism underlying this structural transformation is unknown. It could involve either an internal remodelling process, or complete resorption followed by tissue neoformation. The aim of this study was to establish which of these two alternative tissue reorganization mechanisms is physiologically operative. We also wished to pinpoint the articular cartilage source of the stem cells for clonal expansion and the zonal location of the chondrocyte pool with high proliferative activity. METHODS: The New Zealand white rabbit served as our animal model. The analysis was confined to the high-weight-bearing (central) areas of the medial and lateral femoral condyles. After birth, the articular cartilage layer was evaluated morphologically at monthly intervals from the first to the eighth postnatal month, when this species attains skeletal maturity. The overall height of the articular cartilage layer at each juncture was measured. The growth performance of the articular cartilage layer was assessed by calcein labelling, which permitted an estimation of the daily growth rate of the epiphyseal bone and its monthly length-gain. The slowly proliferating stem-cell pool was identified immunohistochemically (after labelling with bromodeoxyuridine), and the rapidly proliferating chondrocyte population by autoradiography (after labelling with (3)H-thymidine). RESULTS: The growth activity of the articular cartilage layer was highest 1 month after birth. It declined precipitously between the first and third months, and ceased between the third and fourth months, when the animal enters puberty. The structural maturation of the articular cartilage layer followed a corresponding temporal trend. During the first 3 months, when the articular cartilage layer is undergoing structural reorganization, the net length-gain in the epiphyseal bone exceeded the height of the articular cartilage layer. This finding indicates that the postnatal reorganization of articular cartilage from an immature isotropic to a mature anisotropic structure is not achieved by a process of internal remodelling, but by the resorption and neoformation of all zones except the most superficial (stem-cell) one. The superficial zone was found to consist of slowly dividing stem cells with bidirectional mitotic activity. In the horizontal direction, this zone furnishes new stem cells that replenish the pool and effect a lateral expansion of the articular cartilage layer. In the vertical direction, the superficial zone supplies the rapidly dividing, transit-amplifying daughter-cell pool that feeds the transitional and upper radial zones during the postnatal growth phase of the articular cartilage layer. CONCLUSIONS: During postnatal development, mammalian articular cartilage fulfils a dual function, viz., it acts not only as an articulating layer but also as a surface growth plate. In the lapine model, this growth activity ceases at puberty (3-4 months of age), whereas that of the true (metaphyseal) growth plate continues until the time of skeletal maturity (8 months). Hence, the two structures are regulated independently. The structural maturation of the articular cartilage layer coincides temporally with the cessation of its growth activity - for the radial expansion and remodelling of the epiphyseal bone - and with sexual maturation. That articular cartilage is physiologically reorganized by a process of tissue resorption and neoformation, rather than by one of internal remodelling, has important implications for the functional engineering and repair of articular cartilage tissue.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Estimation of tool pose based on force-density correlation during robotic drilling

The application of image-guided systems with or without support by surgical robots relies on the accuracy of the navigation process, including patient-to-image registration. The surgeon must carry out the procedure based on the information provided by the navigation system, usually without being able to verify its correctness beyond visual inspection. Misleading surrogate parameters such as the fiducial registration error are often used to describe the success of the registration process, while a lack of methods describing the effects of navigation errors, such as those caused by tracking or calibration, may prevent the application of image guidance in certain accuracy-critical interventions. During minimally invasive mastoidectomy for cochlear implantation, a direct tunnel is drilled from the outside of the mastoid to a target on the cochlea based on registration using landmarks solely on the surface of the skull. Using this methodology, it is impossible to detect if the drill is advancing in the correct direction and that injury of the facial nerve will be avoided. To overcome this problem, a tool localization method based on drilling process information is proposed. The algorithm estimates the pose of a robot-guided surgical tool during a drilling task based on the correlation of the observed axial drilling force and the heterogeneous bone density in the mastoid extracted from 3-D image data. We present here one possible implementation of this method tested on ten tunnels drilled into three human cadaver specimens where an average tool localization accuracy of 0.29 mm was observed.

Loss estimation for landslides in mountain areas – An integrated toolbox for vulnerability assessment and damage documentation

Global environmental change includes changes in a wide range of global scale phenomena, which are expected to affect a number of physical processes, as well as the vulnerability of the communities that will experience their impact. Decision-makers are in need of tools that will enable them to assess the loss of such processes under different future scenarios and to design risk reduction strategies. In this paper, a tool is presented that can be used by a range of end-users (e.g. local authorities, decision makers, etc.) for the assessment of the monetary loss from future landslide events, with a particular focus on torrential processes. The toolbox includes three functions: a) enhancement of the post-event damage data collection process, b) assessment of monetary loss of future events and c) continuous updating and improvement of an existing vulnerability curve by adding data of recent events. All functions of the tool are demonstrated through examples of its application.

The impact of common versus separate estimation of orbit parameters on GRACE gravity field solutions

Gravity field parameters are usually determined from observations of the GRACE satellite mission together with arc-specific parameters in a generalized orbit determination process. When separating the estimation of gravity field parameters from the determination of the satellites’ orbits, correlations between orbit parameters and gravity field coefficients are ignored and the latter parameters are biased towards the a priori force model. We are thus confronted with a kind of hidden regularization. To decipher the underlying mechanisms, the Celestial Mechanics Approach is complemented by tools to modify the impact of the pseudo-stochastic arc-specific parameters on the normal equations level and to efficiently generate ensembles of solutions. By introducing a time variable a priori model and solving for hourly pseudo-stochastic accelerations, a significant reduction of noisy striping in the monthly solutions can be achieved. Setting up more frequent pseudo-stochastic parameters results in a further reduction of the noise, but also in a notable damping of the observed geophysical signals. To quantify the effect of the a priori model on the monthly solutions, the process of fixing the orbit parameters is replaced by an equivalent introduction of special pseudo-observations, i.e., by explicit regularization. The contribution of the thereby introduced a priori information is determined by a contribution analysis. The presented mechanism is valid universally. It may be used to separate any subset of parameters by pseudo-observations of a special design and to quantify the damage imposed on the solution.