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Isogeometric Methods for Biomechanics

Final Report Summary - ISOBIO (Isogeometric Methods for Biomechanics)

Computational Mechanics and the numerical analysis of the behavior of structures are becoming a more and more fundamental tool for the engineering design process in many different fields. This is particularly true in Biomechanics, nowadays widely recognized as a fundamental research field, where reliable analyses of structures and fluids (and of their interactions) are often needed on complex geometries described by tools of Computational Geometry.
Isogeometric Analysis (IGA) is a recent (2005) idea proposed to bridge the gap between Computational Mechanics and Computer Aided Design (CAD). The key feature of IGA is to extend the Finite Element Method (FEM) representing geometry by functions, such as Non-Uniform Rational B-Splines (NURBS), which are used by CAD systems, and then invoking the isoparametric concept to define field variables. Thus, the computational domain exactly reproduces the CAD description of the physical domain. Moreover, numerical testing in different situations shows that IGA holds great promises, with a substantial increase in the accuracy-to-computational-effort ratio with respect to standard FEM, also thanks to the high regularity properties of the employed functions.
The fact that IGA is very accurate and with a great potential for better integrating analysis with geometry makes it particularly suitable for the simulation of Biomechanics systems, where the approximation of complicate morphologies is a key issue to go along with the reliability of the numerical results.
Within this context, the main objective of ISOBIO was to exploit the peculiar features of IGA, to perform fast and accurate simulations of complex biomechanical systems (such as arteries, stents, aortic valves, etc.), which can be successfully used for biomedical device design as well as in clinical decision process.
Of course, to realize this ambitious object and tackle such complex problems, many scientific developments were needed along several research directions. As a result, the set of simulation tools and methods that were designed and implemented within the ISOBIO project allow performing analyses of the above-mentioned systems to predict their behavior in a fast and accurate way. Important examples that were successfully studied comprise structural and fluid-structure interaction analyses of heart valves and structural stent placement simulations including stent-artery contact.