Page 254 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BONE MECHANICS 231

found to be the weaker in terms of crack resistance relative to the transverse orientation (ratio of
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1:1.75 for bovine bone ). Fracture toughness decreases with age in the diaphyses of long bones 26,47
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at a rate of 4.1 percent per decade in the femoral shaft. Fracture toughness in mode II loading can
be greater by as much as fivefold than that in mode I. 45,48 The most significant factors that are
correlated with fracture toughness are age and a variety of porosity-related measures (including
apparent density, water content, and osteon density). 47,48
A number of studies have developed micromechanical models for the elastic and strength prop-
erties of cortical bone. This work has been motivated by observations that changes in the mechani-
cal properties with age and disease are accompanied by alterations in the tissue microstructure. 49
While it is generally agreed on that bone behaves mechanically as a composite material, the complex
hierarchy of composite structure has led to disagreements over which scale or scales are most
relevant for a particular aspect of the mechanical behavior. For instance, ultrastructural models have
focused on the role of the mineral phase as reinforcement for the collagen matrix, 50,51 whereas
macrostructural models have treated the Haversian systems as fibers embedded in a matrix of cement
lines and interstitial lamellae. 52–54 On an intermediate scale, the individual mineralized collagen
fibers have been modeled as reinforcement for the noncollagenous mineralized matrix. 55,56 Still
another class of models has used a hierarchical approach to synthesize two or more of these different
length scales. 57–59 These modeling efforts rely extensively on accurate information regarding the
constituent and interface properties. Obtaining this information has proven challenging not only
because of the extremely small scale involved but also because, unlike the case with engineering
composites, isolating the different phases of bone tissue often involves processes that may alter the
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properties being measured. Recent studies using nanoindentation, 61,62 for example, have begun to
address the issue of scale by providing the ability to measure the elastic modulus and microhardness
of various microstructures within cortical tissue. Thus efforts are ongoing to develop micromechanical
constitutive models for cortical bone.
It is also of keen interest to determine the role of mechanical stimuli on bone cells and the inter-
action between cell biology and bone mechanical properties. Biological processes that are active
throughout an individual’s lifetime can alter the bone tissue on many scales. It has often been
suggested that osteocytes act as sensors of mechanical loading and initiators of the bone-adaptation
processes. 63–66 Whether these processes add or remove bone, or whether they are activated at all, is
thought to depend on the level of mechanical loading 67 and on the presence or absence of tissue
damage. 1,2 Many studies have suggested that strain or strain rate is the appropriate measure of
mechanical stimulus, 68–70 although others have used stress or strain energy. 71,72 In addition, other
characteristics of the mechanical loading, such as mode, direction, frequency, duration, and distrib-
ution, have also been identified as important. Using this collective empirical evidence, several
theories of mechanical adaptation have been proposed (see Ref. 73 for a comprehensive treatment of
this topic). When applied to finite-element models of whole bones, some of these theories have been
able to predict the density pattern of the trabecular bone in the proximal femur 74,75 and the loss of
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bone in the regions surrounding a hip implant. This remains an area of active research since exper-
imentally validated mechanobiological constitutive relations of the remodeling process have yet to
be developed.

9.5 MECHANICAL PROPERTIES OF TRABECULAR BONE

Although trabecular bone—also referred to as cancellous or spongy bone—is nonlinearly elastic
even at small strains, 77 it is most often modeled as linearly elastic until yielding. It yields in com-
pression at strains of approximately 1 percent, after which it can sustain large deformations (up to
50 percent strain) while still maintaining its load-carrying capacity. Thus trabecular bone can absorb
substantial energy on mechanical failure. A heterogeneous porous cellular solid, trabecular bone has
anisotropic mechanical properties that depend on the porosity of the specimen as well as the archi-
tectural arrangement of the individual trabeculae. Its apparent (whole-specimen) level properties also
depend on the tissue-level material properties of the individual trabeculae. An overwhelming portion