Biomedical Engineering Reference
In-Depth Information
28.2.1 3D Model of Individual Alveoli
Since alveoli are the main site of VALI, a detailed knowledge of all involved phe-
nomena on this 'micro-level' is crucial. Therefore, as a first step, we have developed
a comprehensive computational model of individual alveoli. Alveolar tissue can be
characterized as an irregular open foam consisting of mainly polyhedral structures
with average dimensions ranging around 200 µm. Our computational model is based
on both artificial (Wiechert et al., 2008 ) and imaging-based geometries (Rausch et
al., 2011a ).
For modeling of alveolar tissue behavior, a hyperelastic constitutive law intro-
duced originally by Holzapfel et al. ( 2000 ) for arterial tissue has been adapted
(Wiechert et al., 2009 ). The chosen isotropic strain-energy density function is com-
posed of two main parts related to the major stress-bearing elements, i.e. the ma-
trix material including elastin fibers and the collagen fiber network. To satisfy the
quasi-incompressibility constraint typical of all soft biological tissues, the penalty
function proposed by Balzani et al. ( 2006 ) has been implemented. Due to the lack of
experimental data for individual alveolar walls, the material model has been fitted
to available stress-strain curves of lung tissue sheets (Al Jamal et al., 2001 ).
Since alveolar walls are covered with a thin fluid film, the interaction of tissue
and liquid lining mechanics has also been included in the computational model.
However, instead of explicitly discretizing the fluid film, we have proposed a novel
approach based on integrating the interfacial energy in the alveolar wall model
(Wiechert et al., 2009 ). To model the complex behavior of the surface active agents
in the liquid lining, the constitutive law of Otis et al. ( 1994 ) relating the local con-
centration of these substances to the surface stresses has been employed.
The simulation of small alveolar ensembles already becomes computationally
very expensive. Hence, modeling all 500 million alveoli in the human lung is ob-
viously not feasible. To overcome this problem, we have established an advanced
multi-scale model of lung tissue which will be discussed in the following section.
28.2.2 3D Multi-scale Model of Lung Tissue
Although neighboring lung regions influence each other strongly—a phenomenon
known as interdependence (Mead et al., 1970 )—this effect has been completely ne-
glected in previous alveolar models (Kowe et al., 1986 ; Gefen et al., 2001 ; Denny
and Schroter, 2006 ). Due to the lack of physiologically reasonable boundary con-
ditions for alveolar models, clinically relevant predictions of local stresses and
strains during mechanical ventilation were not feasible up to now. Therefore, in-
stead of restricting analyses to isolated alveolar domains, it seems reasonable to
model lung parenchyma—i.e., lung tissue at a global scale—as a whole. In this
case, suitable boundary conditions can be easily derived, e.g., from 4D CT imaging.
Since the alveolar micro-structure cannot be resolved everywhere, we have pro-
posed to employ two complementary approaches. The bulk of lung parenchyma is
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