Use of standard meshing approaches to directly model the behavior of biomaterials is not new: techniques in wide use stem directly from work in engineered structures, which employ Delaunay tessellation, i.e. a general triangulation method from scattered points or use pixilated discretization, i.e. a meshing scheme based on digital images. Researchers have also developed a variety of algorithms to achieve automation in such mesh generation.

The persistent obstacles to automation of the complex structures in biosystems are well known, and are generally of two types: 1) trigonometric challenges posed by complex sub-domains comprised of overlapping structures, and 2) achievement of digital meshes which robustly reduce local errors. In this study a high resolution method is developed for mapping the exterior of neuron cell, using successive confocal microscope images of cell boundaries:

Original, grayscale images (single slices which include all features) were first converted into black & white pixels. Edge pixels were used to construct closed-edge polygons. Vertices of polygons obtained at different depths were then connected by 3-D cubic spline curves. A surface mesh constructed by this procedure usually possesses smooth facets, and therefore can be readily converted into a 3D volumetric mesh. However, there are some limitations on object geometries which allow this approach. For example, it is unable to use this technique to reconstruct an object branching along the direction of depth (i.e., an object having multiple peaks in the direction orthogonal to the focal plane of the image).

To overcome this difficulty, gray-scaled image slices were overlaid to form a 3-D matrix, M, in computer memory. By scaling of the three dimensions based on inter-pixel and inter-slice distances, the real-world sampled volume can be reflected. Each interslice distance represented a physical depth; each element of M was thus assigned a specific volume, and denoted a "volume pixel," or "voxel." Generally, the magnitude of a voxel represents the image light intensity at the corresponding spatial location of the object. The boundary of the object can then be determined by a closed end 3-D surface on which the voxel value assumes a certain scale threshold c, i.e. an isosurface of constant c. Thus, the problem of specification of a surface is reduced to finding an isosurface for which all voxels have the same value of c. Matlab contains a complete package of volumetric functions capable of isosurface searching, surface discretization, and surface smoothing. This technique has been broadly used in the areas related to fluid mechanics, and it is similarly suitable for 3D reconstruction of cells.

Reference

Yi, Y. B. and Sastry, A. M., 2005, Three-dimensional Reconstruction of Cell Boundaries and Interior Organelles from Confocal Microscopy, Journal of Computational Physics, submitted.

Matlab Version 6.5 User's Manual, The MathWorks, Inc., 2002.