Biomedical Engineering Reference
In-Depth Information
series of test protocols for calibrating QLV models along with the associated
calibration procedures, using the nonlinear viscoelastic behavior of reconstituted
collagen tissue as an example. The Adaptive QLV model is not only simpler to
calibrate but also more accurate in predicting the mechanical response of the
reconstituted collagen tissue.
1 Nonlinear Viscoelasticity in Biological Systems
Mechanics plays a role in the function of nearly every biologic tissue. Tissues such
as bone and tendons serve roles that are predominantly mechanical. Mechanical
forces play a vital role throughout growth and development [ 1 - 6 ]. Even in tissues
and protein structures whose primary roles are not mechanical, mechanical
responses have important implications for cellular physiology, cellular patholo-
gies, and tissue injury [ 7 - 15 ].
Similarly, mechanics is important in the functionality of engineered, bio-arti-
ficial tissues. In the engineering of replacements and grafts for soft tissues, [ 16 ],
bone [ 17 ], and their attachments [ 18 ], mechanical models are needed to identify
the degree to which the replacement mimics the natural tissue. In the engineering
of tissue microenvironments that serve to guide the differentiation of stem cells,
the dynamic responses of extracellular matrix proteins such as reconstituted col-
lagen determine the mechanical environments of cells (e.g., [ 19 ]). Here,
mechanical models are needed to design microenvironments of appropriate
dynamic stiffness. In engineered tissues that serve as three-dimensional scaffolds
for probing cellular biophysics, mechanical models are required for delineating
cellular responses from those of the engineered tissue as a whole and for esti-
mating cellular forces from motion of markers within an engineered tissue [ 20 -
24 ]. Strain can be measured easily in such systems, but estimation of stresses
requires knowledge of the mechanical responses, or constitutive law, of the
extracellular matrix [ 25 - 27 ].
The constitutive laws of biological and bio-artificial tissues usually depend
upon how quickly the tissues are loaded, and upon how they were loaded previ-
ously. Rapid length increases, over a physiologic range, are usually met with
greater mechanical resistance than are more gradual length increases. If stretched
and then held in the stretched condition, the isometric force needed to retain a
tissue in its stretched configuration usually decreases or ''relaxes'' over time from
the peak value reached immediately following the stretch. From a mechanical
perspective, the materials that exhibit such a behavior are considered viscoelastic.
While many biological and bio-artificial tissues exhibit linear viscoelastic
behavior for sufficiently small loading increments, their viscoelastic force response
to an elongation of Dl 1 ? Dl 2 is often different than the sum of viscoelastic
responses to elongations Dl 1 and Dl 2 , meaning that their viscoelasticiy is nonlinear.
The constitutive relations for such a material, which are mathematical relations
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