Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated 3D lumbar intervertebral disc (IVD) segmentation strategy from MRI data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based approach. After that, a three-dimensional (3D) variable-radius soft tube model of the lumbar spine column is built to guide the 3D disc segmentation. The disc segmentation is achieved as a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

3D documentation and visualization of external injury findings by integration of simple photography in CT/MRI data sets (IprojeCT).

This study evaluated the feasibility of documenting patterned injury using three dimensions and true colour photography without complex 3D surface documentation methods. This method is based on a generated 3D surface model using radiologic slice images (CT) while the colour information is derived from photographs taken with commercially available cameras. The external patterned injuries were documented in 16 cases using digital photography as well as highly precise photogrammetry-supported 3D structured light scanning. The internal findings of these deceased were recorded using CT and MRI. For registration of the internal with the external data, two different types of radiographic markers were used and compared. The 3D surface model generated from CT slice images was linked with the photographs, and thereby digital true-colour 3D models of the patterned injuries could be created (Image projection onto CT/IprojeCT). In addition, these external models were merged with the models of the somatic interior. We demonstrated that 3D documentation and visualization of external injury findings by integration of digital photography in CT/MRI data sets is suitable for the 3D documentation of individual patterned injuries to a body. Nevertheless, this documentation method is not a substitution for photogrammetry and surface scanning, especially when the entire bodily surface is to be recorded in three dimensions including all external findings, and when precise data is required for comparing highly detailed injury features with the injury-inflicting tool.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated three-dimensional (3D) lumbar intervertebral disc (IVD) segmentation strategy from Magnetic Resonance Imaging (MRI) data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based template matching approach. Based on the estimated two-dimensional (2D) geometrical parameters, a 3D variable-radius soft tube model of the lumbar spine column is built by model fitting to the 3D data volume. Taking the geometrical information from the 3D lumbar spine column as constraints and segmentation initialization, the disc segmentation is achieved by a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.

Improving Cervical Cancer Nodal Boost Radiation Therapy by Quantifying Uncertainties and Exploring Advanced Radiation Therapy Modalities

Radiation therapy for patients with intact cervical cancer is frequently delivered using primary external beam radiation therapy (EBRT) followed by two fractions of intracavitary brachytherapy (ICBT). Although the tumor is the primary radiation target, controlling microscopic disease in the lymph nodes is just as critical to patient treatment outcome. In patients where gross lymphadenopathy is discovered, an extra EBRT boost course is delivered between the two ICBT fractions. Since the nodal boost is an addendum to primary EBRT and ICBT, the prescription and delivery must be performed considering previously delivered dose. This project aims to address the major issues of this complex process for the purpose of improving treatment accuracy while increasing dose sparing to the surrounding normal tissues. Because external beam boosts to involved lymph nodes are given prior to the completion of ICBT, assumptions must be made about dose to positive lymph nodes from future implants. The first aim of this project was to quantify differences in nodal dose contribution between independent ICBT fractions. We retrospectively evaluated differences in the ICBT dose contribution to positive pelvic nodes for ten patients who had previously received external beam nodal boost. Our results indicate that the mean dose to the pelvic nodes differed by up to 1.9 Gy between independent ICBT fractions. The second aim is to develop and validate a volumetric method for summing dose of the normal tissues during prescription of nodal boost. The traditional method of dose summation uses the maximum point dose from each modality, which often only represents the worst case scenario. However, the worst case is often an exaggeration when highly conformal therapy methods such as intensity modulated radiation therapy (IMRT) are used. We used deformable image registration algorithms to volumetrically sum dose for the bladder and rectum and created a voxel-by-voxel validation method. The mean error in deformable image registration results of all voxels within the bladder and rectum were 5 and 6 mm, respectively. Finally, the third aim explored the potential use of proton therapy to reduce normal tissue dose. A major physical advantage of protons over photons is that protons stop after delivering dose in the tumor. Although theoretically superior to photons, proton beams are more sensitive to uncertainties caused by interfractional anatomical variations, and must be accounted for during treatment planning to ensure complete target coverage. We have demonstrated a systematic approach to determine population-based anatomical margin requirements for proton therapy. The observed optimal treatment angles for common iliac nodes were 90° (left lateral) and 180° (posterior-anterior [PA]) with additional 0.8 cm and 0.9 cm margins, respectively. For external iliac nodes, lateral and PA beams required additional 0.4 cm and 0.9 cm margins, respectively. Through this project, we have provided radiation oncologists with additional information about potential differences in nodal dose between independent ICBT insertions and volumetric total dose distribution in the bladder and rectum. We have also determined the margins needed for safe delivery of proton therapy when delivering nodal boosts to patients with cervical cancer.

Integrated Data Sets of the EU FP5 Research Project ORFOIS: Origin and fate of biogenic particle fluxes in the ocean and their interactions with atmospheric CO2 concentrations as well as the marine sediment

For a reliable simulation of the time and space dependent CO2 redistribution between ocean and atmosphere an appropriate time dependent simulation of particle dynamics processes is essential but has not been carried out so far. The major difficulties were the lack of suitable modules for particle dynamics and early diagenesis (in order to close the carbon and nutrient budget) in ocean general circulation models, and the lack of an understanding of biogeochemical processes, such as the partial dissolution of calcareous particles in oversaturated water. The main target of ORFOIS was to fill in this gap in our knowledge and prediction capability infrastructure. This goal has been achieved step by step. At first comprehensive data bases (already existing data) of observations of relevance for the three major types of biogenic particles, organic carbon (POC), calcium carbonate (CaCO3), and biogenic silica (BSi or opal), as well as for refractory particles of terrestrial origin were collated and made publicly available.