A 2D Advancing-Front Delaunay Mesh Refinement Algorithm.

I present a generalization of Chew's first algorithm for Delaunay mesh refinement. I split the line segments of an input planar straight line graph (PSLG) such that the lengths of split segments are asymptotically proportional to the local feature size at their endpoints. By employing prior algorithms, I then refine the truly or constrained Delaunay triangulation of the PSLG by inserting off-center Steiner vertices of "skinny" triangles while prioritizing triangles with shortest edges first. This technique inserts Steiner vertices in an advancing front manner such that we obtain a size-optimal, truly or constrained Delaunay mesh if the desired minimum angle is less than 30° (in the absence of small input angles). This is an improvement over prior algorithms that produce size-optimal meshes with minimum angles of about 26.4°and 28.6°for truly and constrained Delaunay meshes, respectively. Even in the presence of small input angles, the upper bound on the maximum angle is an angle strictly greater than 120° (an improvement from about 137°). The lower bound on the minimum angle in the presence of small angles is identical to prior bounds.

A computational method for predicting inferior vena cava filter performance on a patient-specific basis.

A computational methodology for simulating virtual inferior vena cava (IVC) filter placement and IVC hemodynamics was developed and demonstrated in two patient-specific IVC geometries: a left-sided IVC and an IVC with a retroaortic left renal vein. An inverse analysis was performed to obtain the approximate in vivo stress state for each patient vein using nonlinear finite element analysis (FEA). Contact modeling was then used to simulate IVC filter placement. Contact area, contact normal force, and maximum vein displacements were higher in the retroaortic IVC than in the left-sided IVC (144 mm(2), 0.47 N, and 1.49 mm versus 68 mm(2), 0.22 N, and 1.01 mm, respectively). Hemodynamics were simulated using computational fluid dynamics (CFD), with four cases for each patient-specific vein: (1) IVC only, (2) IVC with a placed filter, (3) IVC with a placed filter and model embolus, all at resting flow conditions, and (4) IVC with a placed filter and model embolus at exercise flow conditions. Significant hemodynamic differences were observed between the two patient IVCs, with the development of a right-sided jet, larger flow recirculation regions, and lower maximum flow velocities in the left-sided IVC. These results support further investigation of IVC filter placement and hemodynamics on a patient-specific basis.

Adaptive and Unstructured Mesh Cleaving.

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or "cleave", these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes.