Motivation and Practical Relevance

Therapeutic orthoses and bandages are important medical devices in a society that is increasingly health-concious while also ageing. They are used to treat orthopaedic conditions (e.g. joint injuries) or to prevent them (e.g. back problems). The planned improvement of patient-specific therapeutic orthoses and bandages within the collaborative research project is an excellent example of how Mathematical Modelling, Simulation, and Optimization (MMSO) can contribute to advancements in medical technology. The synergies resulting from the combination of analytical and numerical methods for constructing a digital twin accelerate the development of new products and make it possible to take the next step toward patient-specific customization of medical devices, thereby improving comfort and benefits for patients.

Mathematical Focus Areas

The project’s mathematically innovative approaches include, in particular, 

• detailed, exact multiscale modelling,
• analysis using rigorous homogenization and dimension reduction,
• simulation of variational problems on manifolds,
• robust multiscale structural optimization,
• comprehensive software implementation.

Project Goals and Implementation

The aim of the project is to improve patient-specific orthoses and bandages by developing a methodology, and ultimately a digital twin software, that predicts how to print any knitted fabric to achieve targeted local stiffening. To this end, modern methods of modelling, analysis, numerical simulation, and optimization will be combined to enable not only the overall simulation but also the computer-aided realization of the product design in the form of a digital twin. In particular, various approaches to robust two-scale structural optimization and the homogenization of thin, high-contrast composite materials, such as elastic knitted fabrics with stiffening elements, will be investigated. Finally, the simulator for the overall model developed at ITWM will integrate the optimization methods developed in the other subprojects using space mapping. This will enable the optimization of the overall model by combining analytical techniques with data-driven numerical methods.

02.10.2026: On 1 and 2 October 2026, the status meeting “Mathematics for Innovation” took place at the Federal Ministry of Research, Technology and Space (BMFTR) in Bonn. Our collaborative research project MAS-TOB also took part in the meeting. The project team was represented by Julia Orlik, Anna Simon und Carolin Kreisbeck.

04.05.2026: On 1 May 2026, Anna Simon joins the team at the Chair of Analysis. After successfully completing her Master’s degree in Mathematics at the University of Regensburg, she is now beginning her PhD at KU. A warm welcome to Eichstätt, Anna – we very much look forward to working with you!