1. Design Automation Lab. – ND Biomechanics Group Cortical Bone Microstructure And Anisotropy Of Mechanical Properties Alejandro A. Espinoza Department of Aerospace & Mechanical Engineering University of Notre Dame

2. Design Automation Lab. – ND Biomechanics Group Hierarchical Structure of Bone Whole bone. Cortical and trabecular bone. Osteonal Architecture. Collagen fibril arrangements. Fibril arrays by themselves. Mineralized collagen. Basic components: collagen, mineral and water. Giraud-Guille (1988), and Weiner-Wagner (1998)

3. Design Automation Lab. – ND Biomechanics Group Bone Mineralization Bone has ~75% of its mineral in the interstitial sites between collagen fibrils. [Hasegawa et al., 1994] Varying degrees of mineralization define bone tissue strength. Mature secondary bone is generally more mineralized than younger primary woven bone. Mineralization and mineral orientation can be quantitatively studied by electron or X-Ray Diffraction patterns. [Sasaki et al.] Ongoing research tries to link mineral orientation to overall elastic anisotropy.

4. Design Automation Lab. – ND Biomechanics Group Research Objectives Structure-property understanding to make possible the development of a biomimetic synthetic bone graft substitute. Increase in the detail and resolution of anisotropy characterization studies. Anisotropy in composites is described by the type of elastic symmetry exhibited by the material and determined by the orientation of bone mineral. Describe and correlate the role of the preferred orientation of bone mineral to anatomical position and microstructural composition of bone tissue.

5. Design Automation Lab. – ND Biomechanics Group Anisotropic Symmetries Orthotropic materials have three orthogonal planes of elastic symmetry (Longitudinal, radial and circumferential). The six main diagonal coefficients of the stiffness matrix C ij are measured experimentally. From these c ij values, E in each direction can be obtained.

6. Design Automation Lab. – ND Biomechanics Group Experimental Techniques Elucidation of structure-function relationship attempted by different routes. Acoustic techniques: Ultrasonic stiffness measurements. Acoustic Scanning Microscopy. Microhardness Experiments: Nano and micro indentation stiffness surveys.

7. Design Automation Lab. – ND Biomechanics Group Sample Preparation Slices are cut in 5% intervals from the cortical bone shaft of a femur.

8. Design Automation Lab. – ND Biomechanics Group Experimental Procedure Final sample shape is 5 mm side cubes whenever possible. Dry and saturated weights recorded according to Archimedes’ principle and used to compute density. Measurement of thickness sample in each orthogonal direction. Ultrasound measurement of longitudinal and shear velocities. Computation of C ij coefficients c ij = v 2 · 

9. Design Automation Lab. – ND Biomechanics Group Experimental Measurements “Time of Flight” ultrasound technique

10. Design Automation Lab. – ND Biomechanics Group Experimental Measurements Calibration with 5 mm thick steel gage block. Time delay  t is used to calculate velocity.

11. Design Automation Lab. – ND Biomechanics Group Stiffness Coefficients

12. Design Automation Lab. – ND Biomechanics Group Anisotropy Ratios

13. Design Automation Lab. – ND Biomechanics Group Anisotropy Ratios

14. Design Automation Lab. – ND Biomechanics Group Results Average density values measured: 1.905 [g/cm 3 ] Test specimen data: Male/78 yrs. old. Coefficients per quadrant (average) [GPa] LAMP c long 27.9227.4527.7825.89 c rad 17.3916.3218.7515.32 c circ 20.3619.2420.7818.57

15. Design Automation Lab. – ND Biomechanics Group Discussion Observed behavior in ratios is: L/R > L/C > R/C. Difference in L/R, L/C and R/C ratios suggests Transverse Isotropy rather than Orthotropy. This fact was noticed also also by Lang (1970), and Yoon and Katz (1976). However, orthotropy is proved in this particular sample by the ANOVA test. 15% to 30% and 75% to 85% sections more anisotropic than the rest of the shaft due to less presence of osteonal bone. Overall, results for stiffness values agree with work by other investigators.

16. Design Automation Lab. – ND Biomechanics Group ANOVA Results Hypothesis: c rad = c circ Significance level  = 0.05 ANOVA by quadrants: Lateral p = 1.082E-2Anterior p = 8.330E-3 Medial p = 3.247E-2Posterior p = 1.892E-3 ANOVA for all data: p = 2.634E-7 Hence, orthotropy is the preferred symmetry.

17. Design Automation Lab. – ND Biomechanics Group Future Work Correlate preferred orientation of bone mineral to anisotropic directions using XRD. Perform stereology studies to characterize morphologic features of cortical bone from 2D samples. Perform these experimental analyses on more human bone specimens.

18. Design Automation Lab. – ND Biomechanics Group Acknowledgements 21 st Century Grant – State of Indiana Faculty Advisors Thank You