Page 245 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

222 BIOMECHANICS OF THE HUMAN BODY

we review the mechanics of cortical bone, trabecular bone, and trabecular tissue material. Rather
than attempt to provide an encyclopedic review of the literature, our intent is to provide a focused
summary that will be most useful as input for biomechanical analyses of whole bone and bone-
implant systems.

9.2 COMPOSITION OF BONE

At the nanometer scale, bone tissue is composed of inorganic and organic phases and water. On a
weight basis, bone is approximately 60 percent inorganic, 30 percent organic, and 10 percent water, 3
whereas on a volume basis, these proportions are about 40 percent, 35 percent, and 25 percent,
respectively. The inorganic phase of bone is a ceramic crystalline-type mineral that is an impure
form of naturally occurring calcium phosphate, most often referred to as hydroxyapatite:
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Ca (PO ) (OH) . Bone hydroxyapatite is not pure hydroxyapatite because the tiny apatite crystals
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10
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(2- to 5-nm-thick × 15-nm-wide × 20- to 50-nm-long plates) contain impurities such as potassium,
magnesium, strontium, and sodium (in place of the calcium ions), carbonate (in place of the phos-
phate ions), and chloride or fluoride (in place of the hydroxyl ions). The organic phase of bone consists
primarily of type I collagen (90 percent by weight), some other minor collagen types (III and VI), and
a variety of noncollagenous proteins such as osteocalcin, osteonectin, osteopontin, and bone sialo-
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protein. The collagen molecules are arranged in parallel with each other head to tail with a gap or
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“hole zone” of approximately 40 nm between each molecule. Mineralization begins in the hole
zones and extends into other intermolecular spaces, resulting in a mineralized fibril. The three-
dimensional arrangement of collagen molecules within a fibril is not well understood. However,
collagen fibrils in bone range from 20 to 40 nm in diameter, suggesting that there are 200 to
800 collagen molecules in the cross section of a fibril.
9.3 BONE AS A HIERARCHICAL COMPOSITE MATERIAL

At the micron scale and above, bone tissue is a hierarchical composite (Fig. 9.1). At the lowest level
(≈0.1-mm scale), it is a composite of mineralized collagen fibrils. At the next level (1- to 10-mm
scale), these fibrils can be arranged in two forms, either as stacked thin sheets called lamellae (about
7 mm thick) that contain unidirectional fibrils in alternating angles between layers or as a block of
randomly oriented woven fibrils. Lamellar bone is most common in adult humans, whereas woven
bone is found in situations of rapid growth, such as in children and large animals, as well as during
the initial stages of fracture healing.
Lamellar bone is found in different types of histological structures at the millimeter scale.
Primary lamellar bone is new tissue that consists of large concentric rings of lamellae that circle the
outer 2 to 3 mm of diaphyses similar to growth rings on a tree. The most common type of cortical
bone in adult humans is osteonal or Haversian bone, where about 10 to 15 lamellae are arranged
in concentric cylinders about a central Haversian canal, a vascular channel about 50 mm in diameter
that contains blood vessel capillaries, nerves, and a variety of bone cells (Fig. 9.2a). The substructures
of concentric lamellae, including the Haversian canal, is termed an osteon, which has a diameter of
about 200 mm and lengths of 1 to 3 mm. Volkmann’s canals are about the same diameter as Haversian
canals but run transverse to the diaphyseal axis, providing a radial path for blood flow within the
bone. Osteons represent the main discretizing unit of human adult cortical bone and are continually
being torn down and replaced by the bone remodeling process. Over time, the osteon can be com-
pletely removed, leaving behind a resorption cavity that is then filled in by a new osteon. Typically,
there are about 13 Haversian canals per square millimeter of adult human cortical bone. Since min-
eralization of a new osteon is a slow process that can take months, at any point in time there is a large
distribution of degree of mineralization of osteons in any whole-bone cross section. A cement line,