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Multiscale Modeling of Bone

Musculoskeletal mineralized tissues (MMTs) are natural examples of achieving a unique combination and variability of stiffness and strength. One of the striking features of MMTs is that this diversity of elastic function is achieved by only one common building unit, i.e. the mineralized collagen fibril, but variable structural arrangements at several levels of hierarchical organization. A profound understanding of the structure-function relations in MMTs requires both experimental assessment of heterogeneous elastic and structural parameters and theoretical modeling of the elastic deformation behavior. Multi-scale and multimodal assessment of MMTs will be used to probe not only the microarchitecture, but also anisotropic linear elastic properties from the nanoscale to the macroscale. By combining experimental data obtained from MMTs at various length scales with numerical homogenization approaches in continuum mechanics, we hypothesize to gain new insight into self-assembly mechanisms, construction rules and physiological boundary conditions of MMTs.

This work is funded within the DFG priority program SPP 1420: "Biomimetic Materials Research: Functionality by Hierarchical Structuring of Materials".

Typical impedance alterations in osteonal tissue lamellae (lower part: 1.2 GHz image, image plane perpendicular to the osteonal long axis, upper part: line graphs measured at various frequencies). A representative lamellar unit is highlighted in red.

2. Lamellar bone of a 6-layer lamellar unit. The color indicate fibril layer with parallel alignment and variable thickness, but distinct orientations (0°: parallel to the osteon long axis).

3. From the acoustic image the elastic coefficients c11 and c33 can be directly estimated from the local minima (green line) and maxima (red line). For the fibrils with 30°- and 60° orientations the measured acoustic impedance values correspond to the respective off-axis stiffness values.

4. The dependence of the measured acoustic impedance (SAM) and indentation modulus (NI) can be used to estimate the 5 independent elastic coefficients of the transverse isotropic stiffness tensor of the fibril.