EVENTO
Integrative Computational Modeling and In-vivo Characterization of Residual Deformations in Hemodynamics - TESE DE DOUTORADO
Tipo de evento: Seminário LNCC
This thesis is concerned with two major problems arising in the modeling of the cardiovascular system. The first topic consists in a comprehensive approach for the simulation of arterial blood flow and its effect on the stress state of the arterial wall, and the second topic is concerned with the in-vivo characterization of residual deformations in arterial wall tissues, based on data provided by medical images. Specifically, regarding the first topic, an original modeling framework is proposed for the treatment of hemodynamic problems with increased realism, featuring an unprecedented combination of several modeling techniques in order to account for i) the fact that the initial (image-based) geometry corresponds to a configuration which is at equilibrium with an internal pressure acting over the lumen, and with tethering forces located at the artificial (axial) boundaries delimiting the arterial region of interest; ii) the fluid-structure interaction problem; iii) the complex constitutive behavior of the arterial wall; iv) the influence of surrounding tissues; v) the interaction of the vessel with the rest of the cardiovascular system; and iv) the influence of residual stresses. In order to tackle the issues described above, the preload mechanical problem is solved in a first stage, finding the zero-load material configuration which is employed to define suitable constitutive equations. This is performed by finding the solution for the mechanical equilibrium of the given image configuration considering the vessel at this state to be loaded by an internal baseline pressure and an axial traction (caused by tethering forces) at the artificial boundaries. It is worthwhile to mention that this axial traction is such that a previously defined pre-stretch level is considered on the equilibrium image configuration. Once the reference configuration is obtained, the complete 3D fluid-structure interaction simulation is carried out, coupled with a dimensionally reduced 1D model of the rest of the cardiovascular system. Strong coupling via fixed-point iterations is achieved for the fluid-structure interaction, while the dimensionally heterogeneous coupling is achieved through a Broyden method. Regarding the constitutive modeling, a fiber-reinforced hyperelastic constitutive law is considered. Furthermore, through the analysis of several numerical examples, the sensitivity with respect to the existence of the preload stresses is assessed to quantify the importance of this issue. These results indicate that the stress state of the arterial wall is strongly influenced by the existence of preload. Therefore, the consideration of such preload state is mandatory for the prediction of stresses in arterial tissue. For the second topic, a novel conceptual framework is presented for the in-vivo estimation of residual deformations and stresses. As a given data, a set of known configurations for an arterial segment is considered, which can potentially be obtained from medical imaging techniques. The mechanical equilibrium equations corresponding to such configurations are introduced through a variational approach, highlighting the role of the residual deformations and associated stresses. In this context, a cost functional is proposed to measure the imbalance of the mechanical setting arising from the consideration of inconsistent residual deformations, based on the generalized residuals of the associated variational equations. Then, the characterization of residual deformations becomes an optimization problem, focused on the minimization of this cost functional. For this purpose, a simple gradient descent method and an interior-point algorithm for constrained optimization are explored in this work. The proposed methodology is tested using three numerical examples based on manufactured solutions, a simple clamped bar, a thick-walled cylinder and a three-layered aorta artery. The obtained results are promising and suggest that the present method (or variants based on the present ideas), when coupled with adequate image acquisition techniques, could successfully lead to the in-vivo identification of residual deformations.
Data Início: 11/04/2016 Hora: 07:00 Data Fim: Hora: 07:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Gonzalo Damián Ares - LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA - LNCC - gonzalo@lncc.br