Modeling the Respiratory Tree by Means of Mechanical Analogy - The Human Respiratory System - page 81

Fig. 6.9 A schematic representation of how the mechanical impedance H(s) is calculated from
level 24 by adding levels up to level 16 [ 26 ]

6.3 Stress-Strain Curves

6.3.1 Stepwise Variations of Strain

The elastic modulus is defined as the ratio between stress and strain properties. The
Kelvin-Voigt body is the simplest viscoelastic model that can store and dissipate
energy, consisting of a perfectly elastic element (i.e. spring) arranged in parallel with
a purely viscous element (i.e. dashpot). Connecting the notions introduced in the
previous sections of this chapter, we obtain the link between stress-strain properties
and morphology of the lungs. The corresponding equation is given by

K
A

B
A

dε(t)
dt

σ(t) = ε(t) + (6.13)

with σ the stress, ε the strain, the length, A theareaand K,B the constants of
the spring and dashpot, respectively [ 23 ]. The stress can be defined as pressure,
whereas the latter is given by force distribution over the area. The strain ε is defined
as the ratio of the change in length over the initial length: / . Starting with an