Biomedical Engineering Reference
In-Depth Information
Specifically, a change
e
in the solid volume fraction of a porous material with respect
to a reference volume fraction drives the adaptation process:
de
dt
=
a(e)
+
A
ij
(ε
ij
)
(6.68)
Here,
a
and
A
are coefficients that depend on the type of structure, e.g. airway walls,
alveolar walls, etc. Almost all biologic materials are adaptive, i.e.
smart
, and pose
specific characteristics as self-repair, adaptability to various environmental condi-
tions, self-assembly, homeostasis, and the capacity for regeneration.
Recoil pressures at same lung volumes are always less during deflation than in-
flation (hysteresis), hence the mechanical energy (work of breathing) follows the
same property. The area within the pressure-volume loops represents the lost en-
ergy per breathing cycle. During quiet breathing, this area is nearly independent
of frequency. Thus, under constant amplitude cycling, energy dissipation is nearly
independent of frequency. However, the dissipation is proportional to the product
of resistance and frequency, hence, implying that the resistance is inversely propor-
tional to the frequency.
The constant-phase model from [
57
], i.e. (
3.9
), describing the viscoelastic prop-
erties of lung tissues, has been considered superior to the classic spring and dashpot
representation, since it contains a combined element. Although the electrical ana-
logue of viscoelastic processes as well as the phenomenological and mechanical
approaches yield good quantitative correspondence with data, they lack anatomic
and mechanistic specificity.
Later models tried to deal with dynamic tissue behavior on a mechanistic basis.
Some mechanisms have been proposed as contributors to the constant-phase tissue
viscoelasticity, such as the structural disposition of fibers and their instantaneous
configuration during motion, since elastic fibers dissipate energy as they slip with
respect to each other. Additionally, lung tissue might exhibit molecular mechanisms
similar to those proposed for polymer rheology. Maksym [
96
] suggested a role for
the relative stress-bearing contributions of collagen and elastin fibers based on the
differential elastic properties of these two types of fibers, in which collagen fibers
were progressively recruited with strain. Bates [
8
] also proposed that the nonlin-
ear elastic properties and linear elastic behavior of lung tissues arise from different
physical processes, whereas elastic recoil is linked to geometry as fibers rearrange
themselves; stress adaptation would reflect a process of diffusion due to the thermal
motion of the fibers with respect to each other and to the ground substance.
6.6 Summary
Based on the concept laid down in previous chapters, the analogy to mechanical
parametric models has been made. This analogy has been used as a theoretical basis
for analyzing viscoelastic properties in the lung tissue. The relation between the
lumped fractional-order model parameters and viscoelasticity has been developed
and the implications in pathology are discussed.
