Conference Agenda

The growing field of in silico medicine is focusing mostly on the two largest classes of medicinal products: medical devices and pharmaceuticals. However, also for advanced therapeutic medicinal products, which essentially combine medical devices with a viable cell or tissue part, the in silico approach has considerable benefits. In this talk an overview will be provided of the budding field of in silico regenerative medicine in general and computational bone tissue engineering (TE) in particular. As basic science advances, one of the major challenges in TE is the translation of the increasing biological knowledge on complex cell and tissue behavior into a predictive and robust engineering process. Mastering this complexity is an essential step towards clinical applications of TE. Computational modeling allows to study the biological complexity in a more integrative and quantitative way. Specifically, computational tools can help in quantifying and optimizing the TE product and process but also in assessing the influence of the in vivo environment on the behavior of the TE product after implantation. Examples will be shown to demonstrate how computational modeling can contribute in all aspects of the TE product development cycle: from providing biological blueprints, over guiding cell culture and scaffold design, to understanding the etiology and optimal treatment strategies for large skeletal defects. Depending on the specific question that needs to be answered the optimal model systems can vary from single scale to multiscale. Furthermore, depending on the available information, model systems can be purely data-driven or more hypothesis-driven in nature. The talk aims to make the case for in silico models receiving proper recognition, besides the in vitro and in vivo work in the TE field.

The interaction between slender fiber- or rod-like components, where one spatial dimension is much larger than the other two, with three-dimensional structures (solids) is an essential mechanism of mechanical systems in numerous fields of science, engineering and bio-mechanics. Examples include reinforced concrete, supported concrete slabs, fiber-reinforced composite materials and the impact of a tennis ball on the string bed of a tennis racket. Applications can also be found in medicine, where stent grafts are a commonly used device for endovascular aneurysm repair, and in many biological systems such as arterial wall tissue with collagen fibers.
The different types of dimensionality of the interacting bodies, i.e., slender, almost one-dimensional fibers and general three-dimensional solids, pose a significant challenge for typical numerical simulation methods. The presented focuses on developing novel computational approaches to simulate the interaction between these fiber-like structures and three-dimensional solids. The key idea is to model the slender components as one-dimensional Cosserat continua based on the geometrically exact beam theory, enabling an accurate and efficient description of the fibers. This results in a mixed-dimensional beam-to-solid interaction problem.
In a first step positional and rotational coupling between the beam centerline and the underlying solid in line-to-volume problems are addressed. Mortar-type methods, inspired by classical mortar methods from domain decomposition or surface-to-surface interface problems, are used to discretize the coupling constraints. A subsequent penalty regularization eliminates the Lagrange multipliers from the global system of equations, resulting in a robust coupling scheme that avoids locking effects. Furthermore, consistent spatial convergence behavior, well within the envisioned application range, is demonstrated.
In a second step, the previously developed algorithms for line-to-volume coupling are extended to to line-to-surface coupling. This introduces the additional complexity of having to account for the surface normal vector in the coupling constraints. Consistent handling of the surface normal vector leads to physically accurate results and guarantees fundamental mechanical properties such as conservation of angular momentum.
Finally, a Gauss point-to-segment beam-to-solid surface contact scheme that allows for the modeling of unilateral contact between one-dimensional beams and two-dimensional solid surfaces is presented.
The previously mentioned building blocks constitute a novel mixed-dimensional beam-to-solid interaction framework, which is verified by theoretical discussions and numerical examples. Already in the present state, the presented framework is an efficient, robust, and accurate tool for beam-to-solid interaction problems and can become a valuable tool in science and engineering.