In-silico models applied to bone remodeling are widely used to investigate bone mechanics, bone diseases, bone-implant interactions, and also the effect of treatments in bone pathologies. This work proposes a new methodology to solve the bone remodeling problem using one-dimensional (1D) elements to discretize trabecular structures more efficiently. First a concept review on the bone remodelling process and mathematical approaches, such as homogenization for its modelling are revised along with famous previous works on this field, later, in chapter two, the discrete modelling approach is validated by comparing FE simulations with experimental results for a cellular like material created using additive manufacturing and following a tessellation algorithm, and later, applying an optimization scheme based on maximum stiffness for a given porosity. In chapter three, an Euler integration scheme for a bone remodelling problem is coupled with the momentum equations to obtain the evolution of material density at each step. For the simulations, the equations were solved by using the finite element method and a direct formulation, and two benchmark tests were solved varying mesh parameters in two dimensions, an additional three-dimensional benchmark was addressed with the same methodology. Proximal femur and calcaneus bone were selected as study cases given the vast research available on the topology of these bones, and compared with the anatomical features of trabecular bone reported in the literature, the study cases were examined mainly in two dimensions, but the main trabecular groups for the femur were also obtained in three dimensions. The presented methodology has proven to be efficient in optimizing topologies of lattice structures; It can predict the trend in formation patterns of the main trabecular groups from two different cancellous bones (femur and calcaneus) using domains set up by discrete elements as a starting point. Preliminary results confirm that the proposed approach is suitable and useful in bone remodeling problems in 2D and 3D leading to a considerable computational cost reduction. Characteristics similar to those encountered in topological optimization algorithms were identified in the benchmark tests as well, showing the viability of the proposed approach in other applications such as bio-inspired design. Finally, in the last part of this work, the discrete approach developed in chapter two and three is coupled with two classic bone remodelling models, forming a new model that takes into account a variety of biological parameters such as paracrine and autocrine regulators and is able to predict different periodical responses in the bone remodelling process within a 2D domain with mechanical field variables. (Text taken from source)