An Analytical Algorithm for Tensor Tomography From Projections Acquired About Three Axes.

Tensor fields are useful for modeling the structure of biological tissues. The challenge to measure tensor fields involves acquiring sufficient data of scalar measurements that are physically achievable and reconstructing tensors from as few projections as possible for efficient applications in medical imaging. In this paper, we present a filtered back-projection algorithm for the reconstruction of a symmetric second-rank tensor field from directional X-ray projections about three axes. The tensor field is decomposed into a solenoidal and irrotational component, each of three unknowns. Using the Fourier projection theorem, a filtered back-projection algorithm is derived to reconstruct the solenoidal and irrotational components from projections acquired around three axes. A simple illustrative phantom consisting of two spherical shells and a 3D digital cardiac diffusion image obtained from diffusion tensor MRI of an excised human heart are used to simulate directional X-ray projections. The simulations validate the mathematical derivations and demonstrate reasonable noise properties of the algorithm. The decomposition of the tensor field into solenoidal and irrotational components provides insight into the development of algorithms for reconstructing tensor fields with sufficient samples in terms of the type of directional projections and the necessary orbits for the acquisition of the projections of the tensor field.

Reconstruction and visualization of fiber and laminar structure in the normal human heart from ex vivo diffusion tensor magnetic resonance imaging (DTMRI) data.

OBJECTIVE: The human heart is composed of a helical network of muscle fibers organized to form sheets that are separated by cleavage planes responsible for the orthotropic mechanical properties of cardiac muscle. The purpose of this study is the reconstruction and visualization of these structures in 3 dimensions. METHODS: Anisotropic least square filtering followed by fiber and sheet tracking techniques were applied to diffusion tensor magnetic resonance imaging data of the excised human heart. Fibers were reconstructed using the first eigenvectors of the diffusion tensors. The sheets were reconstructed using the second and third eigenvectors and visualized as surfaces. RESULTS: The fibers are shown to lie in sheets that have transmural structure, which correspond to histologic studies published in the literature. Quantitative measurements show that the sheets as appose to the fibers are organized into laminar orientations without dominant populations. CONCLUSIONS: A visualization algorithm was developed to demonstrate the complex 3-dimensional orientation of the fibers and sheets in human myocardium.

My Corporis Fabrica Embryo: An ontology-based 3D spatio-temporal modeling of human embryo development.

BACKGROUND: Embryology is a complex morphologic discipline involving a set of entangled mechanisms, sometime difficult to understand and to visualize. Recent computer based techniques ranging from geometrical to physically based modeling are used to assist the visualization and the simulation of virtual humans for numerous domains such as surgical simulation and learning. On the other side, the ontology-based approach applied to knowledge representation is more and more successfully adopted in the life-science domains to formalize biological entities and phenomena, thanks to a declarative approach for expressing and reasoning over symbolic information. 3D models and ontologies are two complementary ways to describe biological entities that remain largely separated. Indeed, while many ontologies providing a unified formalization of anatomy and embryology exist, they remain only descriptive and make the access to anatomical content of complex 3D embryology models and simulations difficult. RESULTS: In this work, we present a novel ontology describing the development of the human embryology deforming 3D models. Beyond describing how organs and structures are composed, our ontology integrates a procedural description of their 3D representations, temporal deformation and relations with respect to their developments. We also created inferences rules to express complex connections between entities. It results in a unified description of both the knowledge of the organs deformation and their 3D representations enabling to visualize dynamically the embryo deformation during the Carnegie stages. Through a simplified ontology, containing representative entities which are linked to spatial position and temporal process information, we illustrate the added-value of such a declarative approach for interactive simulation and visualization of 3D embryos. CONCLUSIONS: Combining ontologies and 3D models enables a declarative description of different embryological models that capture the complexity of human developmental anatomy. Visualizing embryos with 3D geometric models and their animated deformations perhaps paves the way towards some kind of hypothesis-driven application. These can also be used to assist the learning process of this complex knowledge. AVAILABILITY: http://www.mycorporisfabrica.org/.