Biomedical Engineering Reference
In-Depth Information
tic arch banding procedure induces severe change in pulse pressure and flow rate
in the common carotid arteries but only modest changes in their mean values. The
adaptation of a mouse left common carotid artery to the perturbation induced by the
aortic banding procedure has been modelled in [8]. The numerical model proves that
the adaptation process in this case is driven mainly by dynamic stimuli (i.e., stress
rates over the cardiac cycle) and that constituents degradation and remodelling as de-
scribed in Sect. 7.2.3 play a fundamental role. The model, in agreement with experi-
mental measurements, predicts a significant increase in arterial caliber and thickness
together with a significant reduction of axial stress and circumferential stiffness.
Concerning thick-wall models, full G&R formulations based on the constrained
mixture theory are under developement [25]. Nevertheless important results can be
obtained by making suitable assumptions on the distribution of the quantities without
modelling the entire G&R process [7]. Using the assumption of constrained mixture,
we can assume a strain energy density of the form
4
c
=
1
φ
e
W
e
F
e
c
W
c
c
m
W
m
m
W
=
φ
(
)+
(
λ
)+
φ
(
λ
)
,
(7.27)
k
are mass fractions for each structurally significant constituent and
W
k
where
φ
are
individual stored energy functions. In Eq. (7.27)
F
e
,
m
represent the elastin
deformation gradient, the collagen fibre stretch, and the smooth muscle stretch, re-
spectively. These quantities are defined with respect to individual stress-free config-
urations (see Fig. 7.2).
It has been shown in [7] that, for basilar arteries, the axial retraction and opening
angle are extremely sensitive to the prestretches of the constituents. In particular the
elastin prestretches play a fundamental role. Elastin is the most stable constituent in
the wall and is deposited early during development in parallel layers starting from
the inner wall and proceeding outward under vessel growth driven by an increased
blood flow rate and luminal pressure; this biological peculiarity suggest that inner
layers deposited earlier during development may experience larger prestretches than
the outer layers. This biologically based assumption leads to a realistic prediction of
the opening angle and axial retraction in a homogeneous wall and leads to a nearly
uniform distribution of stress with the radial position. Moreover the model is able to
reproduce the measured increase in the opening angle with muscle contraction [30]
and the increase in opening angle with age due to a change in transmural distribution
of collagen and elastin [16].
Several other models [1, 2, 35] have been employed to describe the transmu-
ral variation of vascular mechanical properties and its effect on the opening angle
and axial retraction. Nevertheless a microstructurally motivated model, like the one
introduced here, gives further insight in the biological origin of mechanical quanti-
ties and is able to reproduce several different sets of experimental measurements by
simply making reasonable assumptions on the transmural distribution of constituents
and mechanical properties.
c
,and
λ
λ
