Knowledge discovery using morphologic analysis of complex natural media

Currently, visualization of complex biological and physicochemical systems offers visual, heuristic insights or quantitative, empirical information via statistical summaries. Development of visualization methods to extract quantitative information and knowledge about the various phenomena in such systems is a pressing research need. We report on such a methodology developed based on thermodynamic principles and image analysis. A common characteristic of such systems, comprised of multiple phases separated by distinct boundaries or interfaces, is their complex spatial structure. The interfacial areas between the phases, a
_ij
, (where i and j can be pairs of phases i and j), provide more accurate metrics for morphology, tortuosity, heterogeneity, and anisotropy of such systems. They may be used to improve the analysis and prediction of several phenomena (e.g., flow, reaction coupled with transport, diffusion, heat, mass, and momentum transfer) and behaviors (e.g., self-organization, growth, division, and malignancy), which are strong, direct functions of surface energetics and hence interfacial areas (a
_ij
). Algorithms can be developed, using images or graphics as input, for the calculation of phase interfacial areas, and several quantitative metrics based on the interfacial areas, which represent valuable information about the morphology of the systems. Such metrics are not empirical, but phenomenologically rooted; hence, they can be directly incorporated into the partial differential equations (PDE) based models simulating the various phenomena and behaviors in complex systems, providing effective, quantitative bridges between visualization and computation. Recent work on the use of these metrics for the analysis of several phenomena, such as diffusion, dissolution, bacterial transport, wettability, flow, and transport in porous materials, demonstrates significant improvement in their prediction. Using microbial and geological systems, we demonstrate how the proposed methods can serve as an integral part of experimentation, computation and information (knowledge) discovery.