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| Physiological
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Following
these works and in parallel to other experimental studies, simulations
of unsteady flows are done alike. Several forms of flows are
studied : oscillating, simply pulsatory and physiologically
pulsatory. These works put into light the importance of of the
unsteady character on the dynamics of the flow, and the reliance
of the post-stenotic characters on the shape of the flow. These
results are interesting as in natural situations, the shape
of the debt and particularly the steep of the systolic acceleration
depends on the anatomic site which is studied. Considering physiologically
pulsed flows, a comparison between numerical and experimental
results shows a good concordance.
Following the numerical and experimental studies on unsteady
velocity fields, a post-stenotic analysis of the distribution
of parietal friction was conducted. According to Ku et al. (1997),
experimental measures of the parietal frictions are only estimated
and can reveal misevaluation of 20 to 50%, which emphasize the
role of numerical simulations. Another point is that the study
of the interactions between intimous hyperlasy and parietal
friction reveals strong correlation between areas of small values
and/or areas of oscillating values of the parietal friction
and the intimous thickening. On the opposite, the areas of high
parietal friction values are generally spared by the thickening.
Still, it is interesting to notice that once the plaques of
atheroms are formed, the high values of the friction can lead
to complications resulting of the cellular wrench (Giddens et
al 1990). Thus, it appears as fundamental to correctly determine
the temporal evolution of the parietal friction downstream from
an arterial stenosis.
With a view to validate the numerical results, a semi-experimental
method was set up. To be preserved from possible mistakes on
measures of velocity in lining, a polynomial method, using experimental
values of the velocity on the symmetry axis, allows to determine
the temporal evolution of the parietal friction in the close
downstream from the stenosis. Various shapes of flow have been
studied, and the case of a pulsatory flow with a negative part
is presented here. On each graph the infinite upstream comportment
is presented so that a comparison with a supposed sane artery
might be done. |

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| Time evolution of the parietal friction ( Rem=203, v=58
) downstream from stenosis. |
It should be noticed that for the close values downstream from
the stenosis, its presence tears the artery in the opposite
way as a sane artery does. This comportment lasts during a long
part of the cycle : from the appearance of swirling structures
(during the acceleration phase) until the phase of flow inversion.
This malfunction of the artery corresponds to a field of small
negative values of the parietal friction. The global evolution
reveals a combination of small negative and oscillating values
of the parietal friction during the cycle, which let us suppose
the formation of a new intimous thickening downstream from an
existing stenosis.
Finally, it is important to observe the evolution of the friction
at the stenosis throat. It is known that at this abscisse the
parietal friction is very high because of the jet effect caused
by the contriction. According to Ku et al. (1997) high values
of the parietal friction may activate platelets and induce thromboses
which can totally block the flow.
The comparison of the numerical results with those obtained
by the semi-experimental method show a good correlation during
most of the cycle duration. Still, at the end of the deceleration
and at the beginning of the acceleration, qualitative and quantitative
differences appear. Considering quality, numerical results show
oscillations of the value of the parietal friction which do
not appear in the experiments. Experimental results are obtained
by taking the average on 40 periods in a volume of measure of
about 2 mm3 and a sampling at 0.01s; the results given by a
such process can therefore only reveal the phenomena of important
scale. On the point of quantity, from z=2.4 cm, the experimental
values are lower than the numerical. The process of turbulence
can partially explain these differences. The numerical model
used is a laminar one which cannot take into account the two
types of turbulence induced by such flows. The pulsatory character
of the flow actually generates turbulence "in time" at the beginning
of deceleration, and turbulence "in space" is generated by the
presence of the stenosis itself. The turbulent process implies
more dissipation, and so a smaller experimental friction. |
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