Development of Advanced IsoGeometric Methods with Applications in Active Tissue Modeling

The ability to manufacture biologically active tissues has generated increasing interest over the last years in various fields, ranging from personalized and regenerative medicine to soft robotics. To provide a systematic design framework, many authors have used Finite Element Methods to perform numerical simulations of the electro-mechanical response of contractile tissues. Instead, in this Thesis, I used Isogeometric Analysis to improve the solution of the partial differential equations underlying the tissue models. Specifically, I investigated the extent to which the Isogeometric-Galerkin method enhances the solution of the coupled electro-mechanical problem and proposed innovative approaches based on the Isogeometric-Collocation method. Further, I demonstrated the performance of traditional and novel approaches using classical multi-dimensional geometries (e.g., 1D cables, 2D manifolds) and real-world applications (e.g., tissue-engineered heart ventricles and jellyfish shaped swimmers). Part 1 of this Thesis collects contributions focused on modeling active tissues in various context using traditional isogeometric discretization approaches. Part 2, instead, focuses on the new numerical methodologies based on IgA-Collocation that I developed and validated in this field. Finally, we summarize the potential of Isogeometric Analysis in modeling biologically active tissues in the future. Part of the outcomes of this Thesis are the results of collaborations with other research groups of the University of Pavia, the Polytechnic University of Bari, and the Hamburg University of Technology, as acknowledged in the manuscript.