Biomedical Engineering Reference
In-Depth Information
80 CHAPTER 5. FUTUREDIRECTIONS
Wear is another measure of fatigue and is defined as the removal of material from a contact
surface due to mechanical effects [
648
]. Techniques for quantifying wear include characterizing
released debris, evaluating surface topography, and imaging the bulk tissue. The severity of a dam-
aging abrasion can be determined by measuring the size of released debris as well as the depth of
penetration at the surface [
654
]. Cartilage roughness, as determined using a variety of scanning mi-
croscope techniques, can indicate how well the material will perform under shear or friction. Other
imaging techniques that look at the tissue as a whole can be used to evaluate not only the surface
characteristics but also any breakdown of the tissue below the surface.
5.2.1.6 Mathematical Models of Articular Cartilage
Mathematical models are used to interpret results obtained from carefully designed evaluation tests,
such as those described in the previous section. By fitting a model to experimental data, a quan-
tification of the mechanical properties can be achieved. Numerical representations of mechanical
characteristics are of critical importance for comparison among studies, and researchers typically use
similar testing techniques to facilitate this. Properties such as the Young's modulus, coefficient of
friction, and streaming potential are just a few of the characteristics that can be used to describe the
natural function of articular cartilage.
Some mathematical models are very basic in their description of cartilage while others are
extremely complex. It is important to remember, however, that they are all only representations of
how the tissue might function and do not replicate every possible intricacy. Even simple models can
provide valuable information, though, and can serve a purpose in evaluating a subset of properties.
For example, the elastic components of a material can be described by:
σ
ε
E
=
where
E
is the Young's modulus,
σ
is the stress, and
ε
is the strain. Modeling cartilage just as an
elastic material can provide a measure of its elastic response, but it might not correspond as accurately
with experimental data as more complex models. Combinations of elastic and viscous elements can
help to describe a material with time- or frequency-dependent responses. The viscous components
can be modeled by:
σ
dε
dt
where
η
is the viscosity coefficient and
dε/dt
is the time derivative of strain. By using elastic and
viscous elements, viscoelastic models can be derived.
Biological materials are typically considered to be viscoelastic since their deformation charac-
teristics vary with respect to time and/or frequency. While perhaps also not technically appropriate,
articular cartilage can be modeled as a viscoelastic material. By fitting to either stress relaxation
or creep data, parameters can be extracted that describe the time-dependent response of a mate-
rial. Simple models of viscoelasticity include Maxwell (spring-dashpot in series) and Kelvin-Voigt
(spring-dashpot in parallel). An extension of these models is the Kelvin model, or standard linear solid
η
=
