Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation

Michel Destrade

Chair of Applied Mathematics at NUI Galway

Thursday 18th October 2018

14:00:00

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

Biological soft tissues and soft gels are difficult to study and model mathematically. Bioengineers often see them as engineering materials and try to evaluate their mechanical properties with standard testing protocols, such as tensile testing, simple shear, torsion, etc. These processes are destructive for tissues, as a sample is taken out of the body and placed in a device. The resulting measured parameters and models are expected to be very different from their in vivo counterparts. To test soft tissues properly, non¬-destructively, and non¬-invasively, we can rely on elastic waves. We can study the influence of pre¬stress on their speed and obtain the nonlinear elastic parameter by inverse analysis. This idea forms the basis of the theory of acousto-¬elasticity, which can be dated back to early works of Brillouin, and has been used successfully in the past for "hard" elastic solids such as rocks and metals. With this talk, we will explore the extension of acousto-¬elasticity to "soft" elastic solids, which can be subjected to large deformations in service. We will look at theoretical, numerical, experimental, and even clinical results, generated in particular on gels, brain, breast, and skin. Contact: pasquale.ciarletta@polimi.it

Michel Destrade is Chair of Applied Mathematics at NUI Galway, Adjunct Professor of Solid Mechanics at Zhejiang University, Adjunct Professor of Mechanical Engineering at University College Dublin, and a member of the International Brain Mechanics and Trauma Lab. Previously, he worked successively as a Junior Marie Curie Fellow (FP4) in Mathematical Physics at University College Dublin; as a Visiting Assistant Professor in Mathematics at Texas A&M University, USA; as a Directeur de Recherche with the French National Research Agency CNRS at the Institut d'Alembert, Universite Pierre et Marie Curie, Paris, France (currently on leave), and as a Senior Marie Curie Fellow (FP7) in Mechanical Engineering at University College Dublin. He is Reviews Editor of the Proceedings of the Royal Society A, Contributing Editor of the International Journal of Non-Linear Mechanics, Associate Editor of SIAM Journal on Applied Mathematics, Journal of the Acoustical Society of America, and Editorial Board Member of Quarterly Journal of Mechanics and Applied Mathematics, International Journal of Applied Mechanics. His research interests are in nonlinear elasticity, in stability of elastomers and biological soft tissues, and in linear, linearised, and non-linear waves. In those fields, he has authored more than 110 publications in refereed international journals.