Resumen de Modeling, analysis and visualization of porous biomaterials
Eduard Vergés Garcia
Many objects of everyday use are composed of porous materials, such as bread, sponges, rocks, concrete or insulating foams. We define a porous materials as being constituted of two differentiated phases, a solid matrix and a void or porous space that can be filled with fluids.
This porous space is, in turn, made up of an aggregation of interconnected and roughly spherical local openings named pores.
The pores are usually dispersed through the full medium and have a particular size and shape and, when connected to the exterior of the object, form a network of pathways where fluids or solutions can flow through. The analysis of the pore shape and pore interconnectivity of this kind of materials is an important element in diverse fields like geology, biology or materials engineering. Apart from the traditional evaluation using laboratory devices for analyzing the pore structure in samples of these materials, the emergence of 3D imaging systems helps the measurement of their porous properties. The internal micro-porosity of a sample can be studied by means of high-resolution 3D scanning devices such as µCT.
The volume images acquired this way can be used to construct a model that represents the material and thus perform queries and simulations on it. This is referred to as in-silice experimentation, made possible thanks to modern computers, which are powerful multi-purpose devices with large memories and high-performance graphics and processing units now available to anyone.
The most common representation model for this volumetric data is the voxel model, which is the natural extension to 3D of 2D bitmaps. In this work two alternative models have also been used, named Extreme Vertices Model (EVM) and Ordered Union of Disjoint Boxes (OUDB). These two models can represent, in a much more compact way, the binary image obtained from a porous sample. The EVM stores only a sorted subset of vertices of the object¿s boundary whereas the OUDB keeps a sorted list of boxes that compose the whole object.
Three different methods are proposed in this work to process the volume images of real porous materials and to construct a pore graph that represents their pores and neighborhood relationships.
The first method, named Pore Tracker, generates a partition of the porous space and its corresponding pore graph by defining pores centered at the voxels that are local maxima of the distance map of the voxel model. This initial model is adjusted by a series of rules and their tunning parameters to provide a better fit.
The second method, named Virtual Porosimetry, mimics the operation of the mercury porosimeter device that intrudes this element into the sample by applying increasing pressures forcing it to traverse smaller narrows or throats. The two versions of this method, implemented using the voxel model and EVM, require a skeleton of the porous space to detect the propagation paths.
A third method, named Pore Granulometry, recognizes pore cavities by inscribing balls of increasing size into them. This is achieved by using morphological openings and Boolean differences. The EVM variant is compared with a reference voxel model implementation.
Moreover, several global structural parameters such as geometric center of gravity or topological connectivity are performed over its EVM representation.
Finally, a voxel model, segmented in individual pores, plus the pore graph constructed with any of the previously mentioned methods, can be visualized using direct volume rendering algorithms. The quality of the presentation can be improved by using illustrative techniques to remark the interesting features from the surrounding context. The proposed methods are tested by studying several real samples of porous materials: sandstones, rabbit¿s femurs, scaffolds and other bone-replacement biomaterials. These large and complex datasets are prepared and then processed to provide useful summarized information regarding their porosity.
