This study aims to enhance the understanding of the relationship between Ilizarov fixator configuration and its effects on bone fracture healing. Using Taylor spatial frame (TSF) as an example, the roles of critical parameters (ie, TSF ring diameter, wire pre-tension, fracture gap size, and axial load) that govern fracture healing during the early stages were investigated by using computational modelling in conjunction with mechanical testing involving an advanced 3D optical measurement system. The computational model was first validated using the mechanical test results and then used to simulate mesenchymal stem cell (MSC) differentiations within different regions of the fracture site under various combinations of TSF ring diameter, wire pre-tension, fracture gap size, and axial load values. Predicted spatially dependent MSC differentiation patterns and the influence of each parameter on differentiations were compared with in vivo results, and good agreement was seen between the two. Gap size was identified as the most influential parameter in MSC differentiation, and the influence of axial loading and TSF configuration (ie, ring diameter and wire pre-tension) on cell differentiation was seen to be gap size dependent. Most changes in cell differentiation were predicted in the external callus (periosteal), which is the crucial region of the callus in the early stages.However, for small gap sizes (eg, 1 mm), significant changes were predicted in the endosteal callus as well. The study exhibits the potential of computational models in assessing the performance of Ilizarov fixators as well as assisting surgeons in patient-specific clinical treatment planning. KEYWORDS 3D optical measurement system, mechanical test, mechano-regulation, mesenchymal stem cell, Taylor spatial frame

Early weight bearing appears to enhance bone fracture healing under Ilizarov circular fixators (ICFs). However, the role of early weight bearing in the healing process remains unclear. This study aims to provide insights into the effects of early weight bearing on healing of bone fractures stabilized with ICFs, with the aid of mathematical modeling. A computational model of fracture site was developed using poro-elastic formulation to simulate the transport of mesenchymal stem cells (MSCs), fibroblasts, chondrocytes, osteoblasts, osteogenic growth factor (OGF), and chondrogenic growth factor (CGF) and MSC differentiation during the early stage of healing, under various combinations of fracture gap sizes (GS), ICF wire pretension forces, and axial loads. 1 h of physiologically relevant cyclic axial loading followed by 23 h of rest in the post-inflammation phase (i.e., callus with granulation tissue) was simulated. The results show that physiologically relevant dynamic loading could significantly enhance cell and growth factor concentrations in the fracture site in a time and spatially dependent manner. 1 h cyclic loading (axial load with amplitude, PA, of 200 N at 1 Hz) increased the content of chondrocytes up to 37% (in all zones of callus), CGF up to 28% (in endosteal and periosteal callus) and OGF up to 50% (in endosteal and cortical callus) by the end of the 24 h period simulated. This suggests that the synergistic effect of dynamic loading-induced advective transport and mechanical stimuli due to early weight bearing is likely to enhance secondary healing. Furthermore, the study suggests that relatively higher PA values or lower ICF wire pretension forces or smaller GS could result in increased chondrocyte and GF content within the callus.

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Bone fracture treatments using Ilizarov circular fixator (ICF) involve dealing with uncertainties about a range of critical factors that control the mechanical microenvironment of the fracture site such as ICF configuration, fracture gap size, physiological loading etc. To date, the effects of the uncertainties about these critical factors on the mechanical microenvironment of the fracture site have not been fully understood. The purpose of this study is to tackle this challenge by using computational modelling in conjunction with engineering reliability analysis. Particularly, the effects of uncertainties in fracture gap size (GS), level of weight‐bearing (P), ICF wire pretension (T) and wire diameter (WD) on the fracture site mechanical microenvironment at the beginning of the reparative phase of healing was investigated in this study. The results show that the mechanical microenvironment of fracture site stabilised with ICF is very sensitive to the uncertainties in P and GS. For example, an increase in the coefficient of variation of P (COVP) from 0.1 to 0.9 (i.e., an increase in the uncertainty in P) could reduce the probability of achieving a favourable mechanical microenvironment within the fracture site (i.e., Probability of Success, PoS) by more than 50%, while an increase in the coefficient of variation of GS (COVGS) from 0.1 to 0.9 could decrease PoS by around 30%. In contrast, an increase in the uncertainties in T and WD (COV increase from 0.1 to 0.9) has little influence on the fracture site mechanical microenvironment (PoS changes <5%).

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