Biomedical Engineering Reference
In-Depth Information
9.6 Conclusions
In this work a variational foundation for the problem of coupling dimensionally-
heterogeneous models has been explored. It turned out that such an approach can be
understood in the context of kinematical incompatibilities between models, where
the heterogeneities arise as the result of kinematical hypotheses. The consequences
of different considerations regarding the sense in which the models are coupled were
discussed. Further attention was given to the application of these models in the hemo-
dynamics field, which were employed to account for the modelling of either an open-
loop model and a closed-loop model of the CVS with embedded 3D patient-specific
geometries.
Two examples of pathophysiological scenarios were also studied that involved an
abdominal aneurism and a cerebral aneurism, respectively. It is worth remarking that
such an approach made it possible to set up 3D numerical simulations under quite
realistic physiological conditions posed by the surrounding cardiovascular network,
under the assumption that our model of the CVS is correctly calibrated. Particu-
larly, in the case of the abdominal aortic aneurism, it was observed that the solutions
at the coupling interfaces were substantially different from a hypothetical pure 1D
solution, sustaining the need for this kind of heterogeneous modelling to correctly
consider geometrical singularities present in the vasculature.
Therefore this class of formulations is able to deliver realistic cardiovascular sim-
ulations as well as versatility in the setting of different physiological and pathophys-
iological scenarios of interest. For instance, a whole area of research may be readily
accounted for with this model, ranging from the study of the sensitivity of local
blood flow features, and related hemodynamics variables, to alterations in global
cardiovascular parameters and viceversa.
Acknowledgements.
This work was partially supported by the Brazilian agencies CNPq and
FAPERJ. The support of these agencies is gratefully acknowledged.
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