Non-contact techniques for mapping of cardiac electrical activity require the presence of a surface representation onto which electrical activity may be displayed. Localized ultrasound reflections from the wall of a heart chamber form a cloud of points, descriptive of the shape of the interior surface of the heart, from which the surface mesh is to be created. The existence of significant variance in the position of ultrasound reflections obviate the use of conventional meshing techniques. Current strategies suffer from defects such as loss of fidelity reproducing radially oriented structures. A surface reconstruction technique which is robust in the presence of significant variance in the point cloud and sensitive to structures in all orientations is required.
Each point in a 3D set is associated with an approximation of the unit normal vector to the final surface. The existence of an indicator function with value 0 inside the surface and 1 outside is assumed. The gradient of the indicator function is equal to the normal at each point, and a Poisson equation for the Laplacian of the indicator function is obtained. The governing equation is solved on an octree-based grid, and the surface is obtained as a level set of the solution. The final mesh is constructed by standard techniques.
Evaluation of the Poisson-based surface technique is accomplished by consideration of the mesh resulting from in-vitro acquisition of ultrasound from polymer left and right atrium targets. Error between the computed mesh vertices and the target surface was ~1.5 mm average, and the technique is sensitive to surface structures in all orientations.
Construction of an accurate surface mesh from noisy catheter mediated endocardial ultrasound is made possible by application of a robust Poisson-based technique. The resulting surfaces require reduced post-processing and manual intervention relative to currently available methods.