Three-Dimensional Strain Mapping in Highly Porous Structures, 18-R9676Printer Friendly Version
Inclusive Dates: 01/01/07 01/05/09
Background - Reduction of bone density occurs as a result of aging or disease processes, and the associated increase in risk of skeletal fractures, particularly in trabecular bone structures, is a major clinical problem. The local mechanical environment of the trabecular microstructure plays an important role in maintaining skeletal integrity, both in terms of providing signaling to the bone cells responsible for maintaining a positive balance between bone formation and removal, and the development of damage (i.e., ultrastructural and microstructural cracks) in the bone material and subsequent failure of the microstructure and whole bone. Existing methods for describing three-dimensional microstructural strain distributions are based on sequential captures of microcomputed tomography (microCT) imaging data, with resolutions on the order of 1 to 2 micron and a minimum time step of 10 to 60 minutes imposed by the required scan time. Conversely, two-dimensional strain mapping methods based on high-speed photography have the capability to determine higher resolution displacement and strain distributions with a time scale restricted only by the frequency of image capture, but are of limited value in determining the full 3D strain distribution for complex structures. Within a mathematical and physical framework provided by projective geometry and deformable surface models, SwRI proposes an innovative combination of 2D strain mapping technology and 3D volumetric strain mapping methods to develop a methodology for determining a 3D microstructural strain distribution with the potential for submicron displacement resolution and near real-time mapping frequency.
Approach - The proposed methodology involves (1) capturing 2D images of multiple views of a 3D specimen structure during loading, (2) using projective geometry concepts to determine correspondence between microstructural regions in the 2D images and a 3D microstructure model, (3) determining multiple view 2D deformation maps by applying existing displacement mapping technology to sequential 2D images, and (4) determining the full 3D microstructural strain distribution by transforming the 3D specimen model using finite element methods driven by multiple view 2D strain mapping results. In this initial investigation to demonstrate feasibility, quasi-static stepwise uniaxial deformations of cylindrical specimens with irregular microstructure were considered to validate the methodology.
Accomplishments - To demonstrate the feasibility of this approach, researchers considered quasi-static stepwise uniaxial deformations of cylindrical specimens with irregular microstructure that were machined from bulk aluminum foam, human vertebral trabecular bone, and a single isolated aluminum strut to verify the methodology. A general purpose finite element analysis program was used to determine the 3D strain distribution in both cylindrical porous specimens and a single strut using uniaxial boundary conditions and by imposing boundary conditions based on local surface displacements determined from 2D views. The results show that 2D displacement maps from multiple viewpoints can be automatically related to a 3D microstructural model. Furthermore, applying the resulting surface-based displacement field to the 3D model can be successfully used to generate a full 3D displacement distribution that is similar to that generated during simulation of uniaxial loading of both a cylindrical specimen and an isolated strut. The 3D strain mapping methodology provides a means of inferring the microstructural deformation by using observable 2D displacement patterns in conjunction with prior knowledge of specimen or strut geometry. This methodology will be used in investigations of the effects of global/local mechanical environment on bone cell viability and on damage accumulation at the level of the microstructure and full skeletal structure, specifically in proposals to be submitted to the National Institutes of Health in FY2010.