Trabecular bone is the spongy type of bone found in humans inside vertebrae and in long bones close to joints. In this thesis the biological material trabecular bone is investigated theoretically at two different levels of its structural hierarchy. In the first part, the focus is on the bone material which evolves in time as a result of two processes. During the process of remodeling small bone packets are continuously resorbed from the bone surface and new packets are deposited. In the mineralization process the mineral content in the initially unmineralized new bone packet increases. As a consequence, trabecular looks like a ”patchwork” of bone packets with different mineral content. This heterogeneity of the mineral content can be characterized by a frequency distribution of the mineral content, called the bone mineralization density distribution (BMDD). The BMDD describes the volume of bone with a given mineral content detected in a bone sample. A partial differential equation is developed to describe how remodeling and mineralization influences the amount and the homogeneity of the mineral content. The model is first used to extract information on the mineralization kinetics from the experimentally measured peak-shaped BMDD of healthy humans. The model is then applied to more clinically relevant questions. The time evolution of the BMDD was predicted and compared with experimental data for the two cases of accelerated bone turnover, as typically observed in osteoporosis, and slowed turnover, as caused by standard medications used to treat osteoporosis. Important dynamical effects are discovered, leading to a transient homogenization of the mineral content in the case of turnover reduction, while the opposite is true for increased turnover.

In the second part of the thesis, the connection between trabecular bone architecture and its mechanical performance is investigated. The trabecular architecture is idealized as a cellular solid consisting of a two dimensional network of cylindrical beams (trabeculae). The aim is to find a mechanical description of the structure which allows to identify mechanically weak elements. For this purpose the cellular structure is viewed as consisting of different ”nodes”, where a node is defined by a set of trabeculae joined together at a junction point. The mechanical behavior of a node in two different environments is compared. Either the node is part of a periodic lattice which is constructed with identical copies of itself, or acts as a defect in a regular isotropic lattice. The comparison demonstrates that in addition to the specific geometry of the node, the neighboring nodes also strongly influence its deformation behavior. Only in special cases is the geometrical information of the node enough to predict its mechanical behavior.