MEGN 536 – Computational Biomechanics

Prof. Anthony J. Petrella

Bone Material Properties

Bone Macrostructure

Long bone Epiphysis Diaphysis Compact bone (cortical) Spongy bone (cancellous)

1www.agen.ufl.edu/~chyn/age2062/lect/lect_19/lect_19.htm2webschoolsolutions.com/patts/systems/skeleton.htm

1 2

1academic.wsc.edu/faculty/jatodd1/351/ch4outline.html2castlefordschools.com/Kent/Lessons/Advanced%20Biology%20Lessons/chapter%2037/…Advanced%20Biology%20Chapter%2037%20Introduction%20to%20Body%20Structure_files/image026.jpg

2

Bone Microstructure

Cortical bone Note circumferential layers Structure influences the material properties

1

Bone Microstructure

Cancellous Bone Trabeculae – struts Notice axial alignment Some plate-like structures

40x1academic.wsc.edu/faculty/jatodd1/351/ch4outline.html2www.gla.ac.uk/ibls/fab/public/docs/xbone1x.html

1

2

2

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

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

Example: Inhomogeneous Strength

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

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…

Constitutive Models for Bone

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

zxy

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

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

Modulus-Density Relation also Inhomogeneous

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

We will use 10 materials