Optimal location for fibular osteotomy to provide maximal compression to the tibia in the management of delayed union and hypertrophic non-union of the tibia.

BACKGROUND: Tibial shaft fractures are the commonest long bone fracture, with early weight-bearing improving the rate of bony union. However, an intact fibula can act as a strut that splints the tibial segments and holds them apart. A fibular osteotomy, in which a 2.5 cm length of fibula is removed, has been used to treat delayed and hypertrophic non-union by increasing axial tibial loading. However, there is no consensus on the optimal site for the partial fibulectomy. METHODS: Nine leg specimens were obtained from formalin-embalmed cadavers. Transverse mid-shaft tibial fractures were created using an oscillating saw. A rig was designed to compress the legs with an adjustable axial load and measure the force within the fracture site in order to ascertain load transmission through the tibia over a range of weights. After 2.5cm-long fibulectomies were performed at one of three levels on each specimen, load transmission through the tibia was re-assessed. A beam structure model of the intact leg was designed to explain the findings. RESULTS: With an intact fibula, mean tibial loading at 34 kg was 15.52 ± 3.26 kg, increasing to 17.42 ± 4.13 kg after fibular osteotomy. This increase was only significant where the osteotomy was performed proximal to or at the level of the tibial fracture. Modelling midshaft tibial loading using the Euler-Bernoulli beam theory showed that 80.5% of the original force was transmitted through the tibia with an intact fibula, rising to 81.1% after a distal fibulectomy, and 100% with a proximal fibulectomy. CONCLUSION: This study describes a novel method of measuring axial tibial forces. We demonstrated that a fibular osteotomy increases axial tibial loading regardless of location, with the greatest increase after proximal fibular osteotomy. A contributing factor for this can be explained by a simple beam model. We therefore recommend a proximal fibular osteotomy when it is performed in the treatment of delayed and non-union of tibial midshaft fractures.

Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models.

The increased use of the urban subsurface for competing purposes, such as anthropogenic infrastructures and geothermal energy applications, leads to an urgent need for large-scale sophisticated modelling approaches for coupled mass and heat transfer. However, such models are subject to large uncertainties in model parameters, the physical model itself and in available measured data, which is often rare. Thus, the robustness and reliability of the computer model and its outcomes largely depend on successful parameter estimation and model calibration, which are hampered by the computational burden of large-scale coupled models. To tackle this problem, we develop a novel Bayesian approach for parameter estimation, which allows us to account for different sources of uncertainty, is capable of dealing with sparse field data and makes optimal use of the output data from expensive numerical model runs. This is achieved by combining output data from different models that represent the same physical problem, but at different levels of fidelity, e.g. reflected by different spatial resolution. By applying this new approach to a 1D analytical heat transfer model and a large-scale semi-3D numerical model while using synthetic data, we show that the accuracy and precision of parameter estimation by this multi-fidelity framework by far exceeds the standard single-fidelity results. The consideration of different error terms in the Bayesian framework also allows assessment of the model bias and the discrepancy between the different fidelity levels. These are emulated by Gaussian Process models, which facilitate re-iteration of the parameter estimation without additional model runs.