Merging of intersecting triangulations for finite element modeling.

Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well.

Vessel surface reconstruction with a tubular deformable model.

Three-dimensional (3-D) angiographic methods are gaining acceptance for evaluation of atherosclerotic disease. However, measurement of vessel stenosis from 3-D angiographic methods can be problematic due to limited image resolution and contrast. We present a method for reconstructing vessel surfaces from 3-D angiographic methods that allows for objective measurement of vessel stenosis. The method is a deformable model that employs a tubular coordinate system. Vertex merging is incorporated into the coordinate system to maintain even vertex spacing and to avoid problems of self-intersection of the surface. The deformable model was evaluated on clinical magnetic resonance (MR) images of the carotid (n = 6) and renal (n = 2) arteries, on an MR image of a physical vascular phantom and on a digital vascular phantom. Only one gross error occurred for all clinical images. All reconstructed surfaces had a realistic, smooth appearance. For all segments of the physical vascular phantom, vessel radii from the surface reconstruction had an error of less than 0.2 of the average voxel dimension. Variability of manual initialization of the deformable model had negligible effect on the measurement of the degree of stenosis of the digital vascular phantom.

Gray-scale skeletonization of small vessels in magnetic resonance angiography.

Interpretation of magnetic resonance angiography (MRA) is problematic due to complexities of vascular shape and to artifacts such as the partial volume effect. We present new methods to assist in the interpretation of MRA. These include methods for detection of vessel paths and for determination of branching patterns of vascular trees. They are based on the ordered region growing (ORG) algorithm that represents the image as an acyclic graph, which can be reduced to a skeleton by specifying vessel endpoints or by a pruning process. Ambiguities in the vessel branching due to vessel overlap are effectively resolved by heuristic methods that incorporate a priori knowledge of bifurcation spacing. Vessel paths are detected at interactive speeds on a 500-MHz processor using vessel endpoints. These methods apply best to smaller vessels where the image intensity peaks at the center of the lumen which, for the abdominal MRA, includes vessels whose diameter is less than 1 cm.

Diastolic shape of the right ventricle of the heart.

BACKGROUND: Knowledge of right ventricular (RV) shape is important to the understanding of RV mechanical function and for the improvement of clinically important RV volume estimation techniques. Refinements to the simplest conceptions of RV shape are presented statistically here, based on a quantitative analysis of three-dimensional magnetic resonance (MR) images of excised lamb hearts. METHODS: The passive shape of the heart in six freshly excised lamb hearts was studied with MR imaging with independent passive pressurization of both ventricles. Global features of shape were assessed, including measurement of short-axis, cross-sectional shape parameters associated with the pinched-arc model. RESULTS: The slice-area x apex-base length was found to be highly correlated with the volume of the RV, with little sensitivity to the degree of filling of the ventricle or to the exact slice chosen (r = 0.987; n = 22 from five hearts). The RV was shown to follow a clockwise helical path around the left ventricle of 47 +/- 17 degrees, below the outflow tract, as seen from the apical view, progressing from the apex to the base. Based on the pinched-arc model, the anterior arc is shallower than the posterior arc, with a larger radius of curvature and a smaller angle between the arc and the septal axis. As the RV is passively filled, opposite changes in shape occur between the anterior and posterior regions tending to equalize their shapes. CONCLUSIONS: A high degree of regularity of shape does exist in the RV and, thus, can be characterized effectively in terms of a representative cross-sectional shape and in terms of the changes in that shape proceeding from the base to the apex.