Three-Dimensional Strain Mapping in Highly Porous Structures, 18-R9676

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Principal Investigators
Todd L. Bredbenner
Daniel P. Nicolella
Ernest A. Franke
Michael P. Rigney
Jian Ling

Inclusive Dates:  01/01/07 – 01/02/09

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 the maintenance of 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 3D microstructural strain distributions are based on sequential captures of microcomputed tomography (microCT) imaging data, with resolutions on the order of 1 to 2 microns 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 3D strain distribution over the entirety of complex structures.

Within a mathematical and physical framework provided by projective geometry and deformable surface models, an innovative combination of 2D strain mapping technology and 3D volumetric strain mapping methods is proposed to develop methodology for determining 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 a cylindrical specimen with irregular microstructure and a single isolated strut with irregular geometry were considered to verify the methodology.

Accomplishments - Several materials were evaluated to identify a suitable specimen material (aluminum foam) possessing porosity on the order of that of human trabecular bone (approximately 85 to 95 percent) and exhibiting negligible amounts of time-dependence in the loading response. Loading protocols and stages were developed to subject cylindrical specimens and isolated struts to stepwise deformations on the order of 10s of microns, while measuring both apparent deformation and specimen reaction force. Local neighborhood thresholding and segmenting methods were developed and applied to generate both 3D microstructural surface models and voxel-based 3D finite element models directly from microCT imaging data of highly porous Al foam specimens. Existing technology has been applied to determine 2D displacement maps for a set of Al foam specimens during stepwise specimen loading. Methods have been developed and applied to correct the associated 2D images based on intrinsic camera parameters, to automatically register 2D images with the 3D microstructural models, and to generate the transformation matrix relating 2D images with the 3D microstructural model. A general purpose finite element analysis program was used to determine the 3D strain distribution in both cylindrical porous specimens and a single strut by imposing boundary conditions based on local displacements determined from 2D views. Results show that multiple 2D displacement maps 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.

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