Biomedical Engineering Reference
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Fig. 8 An example of a multi-scale model of the pulmonary airways that incorporates: a an
anatomically-based organ level model; b an organ-level tissue unit with 90 embedded airway
segments with radii calculated at the tissue level; c a tissue level model where each airway
segment is modeled as a cylinder comprising airway wall, smooth muscle cells, and a
parenchymal layer; and d a cellular/molecular level model which describes the generation of
force in smooth muscle. Reprinted from [
101
], with permission from Elsevier
cycle [
102
] (this is a modified version of the Hai-Murphy model [
103
]). Activation of
molecular level force development is through a cellular-level Ca
2+
model. Active
force development at the cellular level acts against the passive load of the airway
wall, and a constantly oscillating load from the breathing lung parenchyma. The
parenchyma is modeled as in Tawhai et al. [
54
], and the forces that tether the
parenchyma to the airway wall are calculated as spatially- and temporally-varying
elastic recoil pressures plus additional tethering forces that develop locally as the
airway contracts, following the relationship for tethering force proposed by [
104
].
Donovan et al. [
105
] extended the molecular level model to include 'cross-linkers'
that represent the passive properties of the ASM. The critical component of the multi-
scale model is its connection of the spatial scales, which is defined at the individual
airway level. That is, at each airway at each time point the active tension developed
by the cellular and molecular models is explicitly balanced against force develop-
ment in the surrounding tissues.
The basic mechanisms for interaction of VSM with its surrounding force envi-
ronment are the same as for ASM, however the VSM responds differently to agonist
stimulation [
102
]. Reaction to agonist (such as methacholine) is relevant in the study
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