Modularity and robustness of bone networks

Cortical bones, essential for mechanical support and structure in many animals, involve a large number of canals organized in intricate fashion. By using state-of-the art image analysis and computer graphics, the 3D reconstruction of a whole bone (phalange) of a young chicken was obtained and represented in terms of a complex network where each canal was associated to an edge and every confluence of three or more canals yielded a respective node. The representation of the bone canal structure as a complex network has allowed several methods to be applied in order to characterize and analyze the canal system organization and the robustness. First, the distribution of the node degrees (i.e. the number of canals connected to each node) confirmed previous indications that bone canal networks follow a power law, and therefore present some highly connected nodes (hubs). The bone network was also found to be partitioned into communities or modules, i.e. groups of nodes which are more intensely connected to one another than with the rest of the network. We verified that each community exhibited distinct topological properties that are possibly linked with their specific function. In order to better understand the organization of the bone network, its resilience to two types of failures (random attack and cascaded failures) was also quantified comparatively to randomized and regular counterparts. The results indicate that the modular structure improves the robustness of the bone network when compared to a regular network with the same average degree and number of nodes. The effects of disease processes (e. g., osteoporosis) and mutations in genes (e.g., BMP4) that occur at the molecular level can now be investigated at the mesoscopic level by using network based approaches.

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

Inside the `cavernous sinus` or `parasellar region` the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.

Refraction corrected transmission ultrasound computed tomography for application in breast imaging

Purpose: We present an iterative framework for CT reconstruction from transmission ultrasound data which accurately and efficiently models the strong refraction effects that occur in our target application: Imaging the female breast. Methods: Our refractive ray tracing framework has its foundation in the fast marching method (FNMM) and it allows an accurate as well as efficient modeling of curved rays. We also describe a novel regularization scheme that yields further significant reconstruction quality improvements. A final contribution is the development of a realistic anthropomorphic digital breast phantom based on the NIH Visible Female data set. Results: Our system is able to resolve very fine details even in the presence of significant noise, and it reconstructs both sound speed and attenuation data. Excellent correspondence with a traditional, but significantly more computationally expensive wave equation solver is achieved. Conclusions: Apart from the accurate modeling of curved rays, decisive factors have also been our regularization scheme and the high-quality interpolation filter we have used. An added benefit of our framework is that it accelerates well on GPUs where we have shown that clinical 3D reconstruction speeds on the order of minutes are possible.

3D face computational photography using PCA spaces

In this paper, we present a 3D face photography system based on a facial expression training dataset, composed of both facial range images (3D geometry) and facial texture (2D photography). The proposed system allows one to obtain a 3D geometry representation of a given face provided as a 2D photography, which undergoes a series of transformations through the texture and geometry spaces estimated. In the training phase of the system, the facial landmarks are obtained by an active shape model (ASM) extracted from the 2D gray-level photography. Principal components analysis (PCA) is then used to represent the face dataset, thus defining an orthonormal basis of texture and another of geometry. In the reconstruction phase, an input is given by a face image to which the ASM is matched. The extracted facial landmarks and the face image are fed to the PCA basis transform, and a 3D version of the 2D input image is built. Experimental tests using a new dataset of 70 facial expressions belonging to ten subjects as training set show rapid reconstructed 3D faces which maintain spatial coherence similar to the human perception, thus corroborating the efficiency and the applicability of the proposed system.