@article{SchmidtAlbertRitthaleretal.2021, author = {Schmidt, Ina and Albert, Jacob and Ritthaler, Marina and Papastavrou, Areti and Steinmann, Paul}, title = {Bone fracture healing within a continuum bone remodelling framework}, series = {Computer Methods in Biomechanics and Biomedical Engineering}, volume = {25 (2022)}, journal = {Computer Methods in Biomechanics and Biomedical Engineering}, number = {9}, publisher = {Informa UK Limited}, issn = {1476-8259}, doi = {10.1080/10255842.2021.1998465}, pages = {1040 -- 1050}, year = {2021}, abstract = {Bone fracture healing is a complex process which is still under research. Computer-aided patient-specific prediction of bone development, fracture risk, prevention and treatment approaches promises a significant milestone in clinical practice. With this long-term goal in mind, a novel model is presented and examined in this work in the context of continuum bone remodelling. Therein, a clear distinction is made between external mechanical stimulation and the biological healing process of an injured bone tissue. The model is implemented within a finite element framework and investigated for the example of a fractured proximal femur head. The results show promising perspectives for further application. Besides, the model offers the possibility of easily integrating other factors like age-dependency and the availability of nutrition. For the future, further studies with large clinical datasets are essential for validation.}, language = {en} } @article{PapastavrouSchmidtSteinmann2020, author = {Papastavrou, Areti and Schmidt, Ina and Steinmann, Paul}, title = {On biological availability dependent bone remodeling}, series = {Computer Methods in Biomechanics and Biomedical Engineering}, volume = {23 (2020)}, journal = {Computer Methods in Biomechanics and Biomedical Engineering}, publisher = {Informa UK Limited}, issn = {1476-8259}, doi = {10.1080/10255842.2020.1736050}, pages = {13}, year = {2020}, abstract = {Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.}, language = {en} } @article{SchmidtPapastavrouSteinmann2021, author = {Schmidt, Ina and Papastavrou, Areti and Steinmann, Paul}, title = {Concurrent consideration of cortical and cancellous bone within continuum bone remodelling}, series = {Computer Methods in Biomechanics and Biomedical Engineering}, volume = {24 (2021)}, journal = {Computer Methods in Biomechanics and Biomedical Engineering}, number = {11}, publisher = {Informa UK Limited}, address = {London}, issn = {1476-8259}, doi = {10.1080/10255842.2021.1880573}, pages = {1274 -- 1285}, year = {2021}, language = {en} } @article{PapastavrouSchmidtDengetal.2020, author = {Papastavrou, Areti and Schmidt, Ina and Deng, Kefu and Steinmann, Paul}, title = {On age-dependent bone remodeling}, series = {Journal of Biomechanics}, journal = {Journal of Biomechanics}, number = {103}, publisher = {Elsevier BV}, address = {Amsterdam}, issn = {1873-2380}, doi = {10.1016/j.jbiomech.2020.109701}, year = {2020}, abstract = {A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.}, language = {en} } @article{SchallerJaviliSchmidtetal.2022, author = {Schaller, Emely and Javili, Ali and Schmidt, Ina and Papastavrou, Areti and Steinmann, Paul}, title = {A peridynamic formulation for nonlocal bone remodelling}, series = {Computer Methods in Biomechanics and Biomedical Engineering}, volume = {25 (2022)}, journal = {Computer Methods in Biomechanics and Biomedical Engineering}, number = {16}, publisher = {Informa UK Limited}, issn = {1476-8259}, doi = {10.1080/10255842.2022.2039641}, pages = {1835 -- 1851}, year = {2022}, abstract = {Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution.}, language = {en} } @article{PapastavrouSteinmannPivonkaetal.2024, author = {Papastavrou, Areti and Steinmann, Paul and Pivonka, Peter and Schmidt, Ina}, title = {A computational two-scale approach to cancellous bone remodelling}, series = {Advanced Modeling and Simulation in Engineering Sciences}, volume = {11 (2024)}, journal = {Advanced Modeling and Simulation in Engineering Sciences}, doi = {10.1186/s40323-024-00267-1}, pages = {2 -- 21}, year = {2024}, abstract = {We propose a novel two-scale (meso-macro-scale) approach to computationally capture cancellous bone remodelling allowing for efficient and effective numerical implementation. Therein, the macro-scale is governed by the well-established kinematics and kinetics of one-scale continuum bone remodelling. However, the constitutive behaviour is not postulated phenomenologically at the macro-scale, but rather follows from the meso-scale. There, for the sake of computational efficiency, the trabecular architecture is idealised as a truss network with the cross-sectional area of the trabeculae adapting to mechanical loading. Then, the meso- and the macro-scale are coupled through up- and down-scaling. Computational results on benchmark problems from bio-mechanics demonstrate that the proposed two-scale approach is effective from a modelling perspective and efficient from a computational perspective. In particular, it automatically captures anisotropy resulting from the irregular trabecular architecture at the meso-scale, and, most importantly, enables the direct investigation of different trabecular structures at the meso-scale, thereby serving as a virtual "magnifiying glass". As an outlook, the proposed two-scale approach to cancellous bone remodelling provides an excellent launch pad for further extension, e.g., by considering more complex trabecular architectures and/or through inclusion of micro-scale bone cellular activities.}, language = {en} }