Date of first affiliation: 01/02/2016
Research aim and objectives
Model reduction, uncertainty quantification, data-driven modeling in biomedical applications
Supported by ERC RealTCut, on 1st February 2016 I have joined Prof. Stephane Bordas's team in the Research Unit in Engineering Science at the University of Luxembourg. My research interest focuses on model reduction and domain decomposition method. Within the post-doctoral fellowship, I am investigating the combination of Nitsche-based domain decomposition with reduced element methods to alleviate the computational burden in the on-fly reduced model for large scale biomedical problems.
I am also supporting an interdisciplinary project on numerical simulation of ''Single and double balloon kyphoplasty: uncertainty-quantification based comparative assessment``. In this project in collaboration with the surgeon of CHL and under the supervision of S. Bordas, we are focusing on the comparative assessment of kyphoplasty with single and double balloon treatment, which are used to treat fractured vertebrae.
The preliminary goal reached in this project are:
- development of quasi-automatic pipeline from the medical images to the simulation
- evaluating the criterion for yield fracture in post-augmentation phase
- performing an uncertainty quantification analysis to analyze the propagation of lack of information in material parameters involved (stiffness, anisotropy, Poisson’s ratio, etc.) and in the position of external load in the quantify the Von Mises stress near the balloon surfaces.
The final perspective of this application is to realize a proof-of-concept patient-specific simulation to assess the successful of the kyphoplasty technique and supporting the surgery planning in decision-making.
From 2015, I am a scientific collaborator of Prof.A. Veneziani (Emory University) and Prof. S. Perotto (Politecnico di Milano) concerning the NSF Project DMS 1419060 “Hierarchical Model Reduction Techniques for Incompressible Fluid Dynamics and Fluid-Structure Interaction Problems”.
The "Hierarchical Model Reduction'' (HiMoD) is innovative model reduction technique for application in computational hemodynamics. Noways the computational simulations in hemodynamics frame are incorporated in medical research and clinical practice and it is becoming part of Clinical Trials (CACT-Computer Aided Clinical Trials) and Surgery Planning (SP). The aim of HiMoD is to reduce the computational cost by taking advantage of the specific features of incompressible fluid in pipe-like domain. Finally, the long-term goal of this research project is to develop a proof-of-concept simulation from the medical images to the numerical simulation employed the real-time HiPOD (Hierarchical model reduction with proper orthogonal decomposition) technique. My research contributions in this project are concentrated in:
- scientific computing supporting on the C++ three-dimensional parallel library and
- investigation on combination of the established reduced order methods (reduced basis, proper orthogonal decomposition, generalized proper decomposition) with the underlying Hierarchical Model Reduction.
From 2012, I am a scientific collaborator of nuclear division of Politecnico of Milano concerning application of real-time method for the simulation of nuclear reactor. Between 2012-2015, we have been developed a real-time control-oriented model of nuclear reactor, with reference to a research thermal reactor, TRIGA Mark II, cooled with water circulating in natural convection. Currently we are focusing on the application of the developed real-time approach in the framework of data assimilation and model predictive control for multiphase thermo-hydraulics simulation.
During my PhD in the Mathematic Department of Politecnico of Milano, I was affiliated in MOX team (2012-2015) under the supervision of the director Prof. L. Formaggia. My thesis, founded by MIUR, is concerned with multiscale domain decomposition methods applied to simulate the flow transport in the complex porous media. The methodology reduces significantly the number of iterations for solving a flow problem in high heterogeneous materials, which exhibits high contrast and high oscillation variation at multiple length scales. The original idea of the multiscale domain decomposition concept, originally, has been proposed by Hou, Efendiev and co-workers. My contribution in this framework is:
- new multiscale preconditioner that combines the two-level multiscale additive Schwarz, introduced by Efendiev, with the smoothing technique of geometric multigrid;
- investigation on combination of model reduction and uncertainty quantification to speed-up significantly the multiscale preconditioner developed.
Prior to this, in the master thesis I have investigated the novel model active strain of cardiac mechanics, developed by Ambrosi et al., mathematically described as an incompressible nonlinear elastostatic problem in total Lagrangian deformation-pressure formulation. This formulation is based on the multiplicative decomposition in term of passive and anisotropic active factor, that represents at a macroscopic level, the contraction of the sarcomeres depending on the Calcium release and electrical excitation. To avoid the volumetric locking and to address the exact satisfaction of incompressibility constraint, we have developed a stabilized Discontinuous Galerkin method for solving finite elasticity incompressible materials under the assumption of active strain deformation and we have mathematically proved its optimal convergence and locking free.