MEGN 536 – Computational Biomechanics

1. MEGN 536 – Computational Biomechanics Prof. Anthony J. Petrella Bone Material Properties

2. Bone Macrostructure • Long bone • Epiphysis • Diaphysis • Compact bone (cortical) • Spongy bone (cancellous) 1 2 1www.agen.ufl.edu/~chyn/age2062/lect/lect_19/lect_19.htm 2webschoolsolutions.com/patts/systems/skeleton.htm

3. 1 2 Bone Microstructure • Cortical bone • Note circumferential layers • Structure influences the material properties 1academic.wsc.edu/faculty/jatodd1/351/ch4outline.html 2castlefordschools.com/Kent/Lessons/Advanced%20Biology%20Lessons/chapter%2037/… Advanced%20Biology%20Chapter%2037%20Introduction%20to%20Body%20Structure_files/image026.jpg

4. 2 1 2 Bone Microstructure • Cancellous Bone • Trabeculae – struts • Notice axial alignment • Some plate-like structures 40x 1academic.wsc.edu/faculty/jatodd1/351/ch4outline.html 2www.gla.ac.uk/ibls/fab/public/docs/xbone1x.html

5. Bone Constituents • Red marrow • Red blood cells, platelets, most white blood cells arise in red marrow • Found in flat bones (sternum, pelvis) and epiphyses • Yellow marrow • Some white blood cells arise here • Color comes from much higher fat content • Found in medullary canals of diaphyses in long bones • Both types of marrow contain numerous vessels • Lots of “squishy” stuff here

6. Bone Properties • Like many biological tissues with “squishy” stuff, bone can behave viscoelastically -- Guedes et al., J.Biomech, 2006 • Some studies have shown tensile and compressive behavior similar and linear elastic -- Keaveny et al., J.Biomech, 1994 • Many studies have shown that bone is inhomogeneousand anisotropic • Inhomogeneous – properties vary with location • Anisotropic – properties vary with direction of loading • Modulus for cortical bone usually in the 15-20 GPa range, cancellous bone in the 100-500 MPa range

7. Example: Inhomogeneous Strength

8. Inhomogeneity • The inhomogenous nature of bone suggests that it’s important to model the material properties with correct spatial variation • A recent study shows that patient-specific models are inaccurate without a correct inhomogeneous mapping of material properties -- Taddei et al., J.Biomech,2006 • One of the advantages of Mimics… the software can automate this inhomogeneous mapping

9. Hooke’s Law • Recall Hooke’s law for a linear elastic, isotropic material: s = E e • We also need to know Poisson’s ratio: n • Isotropic elastic requires only two constants: E, n • Many studies have shown that bone is transversely isotropic, which means the axial direction behaves differently than the radial direction • Transverse isotropic materials exhibit properties that are invariant under axial rotation • Recall axial alignment ofbone structure…

10. Constitutive Models for Bone z • A transverse isotropic model requiresfive elastic constants:Ez, Exy, nxz = nyz, nxy, Gxz = Gyz • These constants can be found experimentally, but most basic bone models in the literature still use an isotropic model for simplicity • A transverse isotropic model also cannot be easily parameterized using CT data x y

11. Bone Density • Bone contains many internal structures/spaces and constituents besides calcified tissue • Some density metrics try to account for this • Apparent density (range: 0.05 – 2.0 g/cm3) • Your usual density measure • Mass of sample divided by total volume of sample • Ash density (range: 0.03 – 1.2 g/cm3) • Seeks to eliminate non-calcified tissue • Mass of bone ash divided by volume of bone only • Bone ash created by drying out bone and incinerating

12. Modulus Relationship to Density • Density can be expressed as linear function of Hounsfield units r = a + b * HU (g/cm3) • Modulus and strength have been shown to obey a power-law relationship to density E = c + d * re (GPa) S = f + g * rh (MPa) • Coefficients vary among different studies, but exponents are usually in the 1-3 range -- Keller, J.Biomech, 1994

13. Modulus-Density Relation also Inhomogeneous

14. Mapping Properties with Mimics • For simplicity, we stay with a linear elastic, isotropic constitutive model • Use Mimics automatic mapping to account for inhomogeneity • Necessary number of materials depends on the specific model • How much density variation is there? • How large is the domain? • Typical numbers of distinct materials in validation studies are in the 100-500 range --Taddei, J.Biomech, 2006