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Large-scale topology optimization applied to multiscale craniofacial reconstruction
The future of medical treatments includes intelligent systems for medical intervention. These systems involve interdisciplinary teams, with surgeons interacting with engineers, such that mathematical and computational methods can be actively included in the surgical decision process and underlying medical treatment. Within this scope, I propose to develop patient-tailored topology optimization modeling for craniofacial reconstruction. Patients who would benefit from such development include soldiers with severe damage to their faces in the battlefield, or cancer patients who have lost significant amounts of bone and tissue. The quantitative analysis of such cases requires consideration of biological and mechanical variables such as structural integrity, vascularization, aging, as well as aesthetics, and functionality of the optimal solutions obtained. These variables can be naturally included in a multiscale topology optimization framework, which seeks the optimal layout of the reconstructed craniofacial region. The present computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis of complex three-dimensional realizations. Thus, I propose to develop fast iterative solvers for large three-dimensional topology optimization problems, e.g. with a few million unknowns. The key to overcoming such a challenge consists in reducing the number of iterations and the runtime of the linear solver by recycling selected mathematical spaces (Krylov spaces) from the previous linear systems. The systems are properly preconditioned to ensure faster convergence. A proper rescaling of the linear systems potentially reduces the huge condition numbers that typically occur in standard topology optimization, and leads to physical solutions in space and time. Such an approach should lead to fast and accurate solutions, offering multiple alternatives from which the surgeon could find the best possible shape and reconstruction strategy. I intend to work in such a multidisciplinary environment involving interactions with our collaborator at the MD Anderson Cancer Center, Dr. Michael J. Miller, Director of Microvascular Surgery Unit, Department of Plastic Surgery.
Journal papers:
[1] Talischi C., Paulino G.H. Pereira A., Menezes I.F.M. (2009) Polygonal finite elements for topology optimization: A unifying paradigm. International Journal for Numerical Methods in Engineering. DOI: 10.1002/nme.2763
[2] Talischi C., Paulino G.H., Le C.H. (2009) Honeycomb Wachspress finite elements for structural topology optimization. Journal of Structural and Multidisciplinary Optimization, 37(6): 569-583
Conference presentations and proceedings:
[1] Talischi C., Paulino G. H., Espinha R., Pereira A., Menezes I. F. M., Celes W., Topological embedding using a multilevel mesh representation for topology optimization. 10th US National Congress on Computational Mechanics, 2009.
[2] Paulino G.H., Pereira A., Talischi C., Menezes I.F.M. (2008) Embedding of superelements for three-dimensional topology optimization. Proceedings of Iberian Latin American Congress on Computational Methods in Engineering (CILAMCE) 2008.
[3] Talischi C., Paulino G.H., Le C.H., Wachspress Elements for Topology Optimization, 6th International Conference on Computation of Shell and Spatial Structures IASS-IACM 2008: "Spanning Nano to Mega".
[4] Talischi C., Paulino G.H., Le C.H., Topology Optimization Using Wachspress-Type Interpolation with Hexagonal Elements. Proceedings of the Multiscale and Functionally Graded Materials Conference 2006.
[5] Talischi C. Chasiotis I. Characterization of Mechanical Behavior of Gold Thin Films for Use in Radio Frequency MEMS, Summer Undergraduate Research Opportunity Program, NASA-Illinois Space Grant Consortium. 2005.
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