In silico re-foundation of strain-based healing assessment of fractures treated with an external fixator.

In the last decades, the literature has demonstrated a renewed interest in finding quantitative and non-invasive techniques for the assessment of bone fractures, by replacing X-ray images. Many different approaches have been proposed from ultrasounds to vibrations. This study aims to numerically assess the foundation of a method firstly proposed in 70' years, based on strain gauges measurements on external fixators for fracture healing monitoring. The theoretical basis consists in the load transfer from the fixator to the bone caused by the callus stiffening during healing. The feasibility is questioned since the level of fixator strain and its variation in invivo conditions should be high enough to be detectable by the sensors. A finite element model of a fractured tibia phantom treated with a monolateral external fixator was developed and validated experimentally. Then, this reference model was used to simulate bone healing and to investigate the sensitivity of virtual strain measurements to callus geometry and loading conditions. The analysis of load distribution among fixator components and their strain maps allowed to identify optimum strain gauges locations which resulted on the pins more distant from the callus, regardless of the simulated conditions. Even in the worst case of a very thin (3 mm) transverse callus in constrained compression conditions, the strain level (≈100 με/100 N) and its variation per week (-50 με/100 N/wk) resulted measurable in the first healing phase, before plateau conditions occurring after about 6 weeks from fixation. A thicker callus causes higher strain levels and can significantly improve measurements, whilst the callus orientation and the loading conditions have a minor effect. However, in case of a free compression loading, also the rods could provide useful indications if sensorized. The results support the method applicability in invivo conditions for the considered test case. Further investigations will be addressed to evaluate the effect of the fixator structure and configuration as well as of patient specific healing timing on the method sensitivity.