Surface flattening of the human left atrium and proof-of-concept clinical applications

Surface flattening in medical imaging has seen widespread use in neurology and more recently in cardiology to describe the left ventricle using the bull's-eye plot. The method is particularly useful to standardize the display of functional information derived from medical imaging and catheter-based measurements. We hypothesized that a similar approach could be possible for the more complex shape of the left atrium (LA) and that the surface flattening could be useful for the management of patients with atrial fibrillation (AF). We implemented an existing surface mesh parameterization approach to flatten and unfold 3D LA models. Mapping errors going from 2D to 3D and the inverse were investigated both qualitatively and quantitatively using synthetic data of regular shapes and computer tomography scans of an anthropomorphic phantom. Testing of the approach was carried out using data from 14 patients undergoing ablation treatment for AF. 3D LA meshes were obtained from magnetic resonance imaging and electroanatomical mapping systems. These were unfolded using the developed approach and used to demonstrate proof-of-concept applications, such as the display of scar information, electrical information and catheter position. The work carried out shows that the unfolding of complex cardiac structures, such as the LA, is feasible and has several potential clinical uses for the management of patients with AF.</p

Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.National Institute for Biomedical Imaging and Bioengineering (R01 EB001550

DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.Comment: 10 pages, 11 Figure

A New Approach in CAD System for Designing Shoes

The flattening of digitized surfaces is still very important in design of thin walled objects such as the airplane wings, parts of car bodies, textile products, and shoe uppers. Especially in shoe industry, the ability of quick respond to changing market needs is essential for successful competition. To give needed flexibility to a shoe designer, special CAD/CAM systems have been developed. Those systems are based on algorithms for surface reconstruction and surface flattening. In this article a fast algorithm for surface reconstruction and surface flattening is presented. Developable stripes are used to approximate a surface. In this way the surface can be flattened fast and without any distortions

Morphology of the temporomandibular joints regarding the presence of osteoarthritic changes

Osteoarthritis, the most common disease of the temporomandibular joints (TMJs), is diagnosed by clinical and radiographic examination. Cone beam computed tomography (CBCT) is a method of choice for the imaging of osteoarthritic changes. The objective was to compare the morphology of the TMJs in CBCT images regarding the number of the osteoarthritic changes diagnosed in the area of the condyle. (2) A total of 105 patients participated in the study; their 210 TMJs were allocated into one of three groups regarding the number of diagnosed osteoarthritic changes: 1 (none or 1 type), 2 (2 types), 3 (3 or more types). The morphology of the TMJ was examined for each TMJ in the CBCT images. Statistical analysis was performed with STATISTICA version 12.0. The statistical significance level was p = 0.05 for all the measurements included. (3) The articular surface flattening was the most common type of the osteoarthritic changes (90%). The condylar A-P dimension differed significantly among the groups (p = 0.0001). The bigger the number of osteoarthritic changes diagnosed in one joint, the smaller the condylar A-P dimension that was observed. (4) The temporomandibular joints’ osteoarthritic changes occur very often, even among asymptomatic patients. The increased number of osteoarthritic changes seems to have an impact on the condylar anteroposterior dimension