Abstract
Numerous experimental fracture healing studies are performed on rats, in which different experimental, mechanical parameters are applied, thereby prohibiting direct comparison between each other. Numerical fracture healing simulation models are able to predict courses of fracture healing and offer support for pre-planning animal experiments and for post-hoc comparison between outcomes of different in vivo studies. The aims of this study are to adapt a pre-existing fracture healing simulation algorithm for sheep and humans to the rat, to corroborate it using the data of numerous different rat experiments, and to provide healing predictions for future rat experiments. First, material properties of different tissue types involved were adjusted by comparing experimentally measured callus stiffness to respective simulated values obtained in three finite element (FE) models. This yielded values for Young’s moduli of cortical bone, woven bone, cartilage, and connective tissue of 15,750 MPa, 1,000 MPa, 5 MPa, and 1 MPa, respectively. Next, thresholds in the underlying mechanoregulatory tissue differentiation rules were calibrated by modifying model parameters so that predicted fracture callus stiffness matched experimental data from a study that used rigid and flexible fixators. This resulted in strain thresholds at higher magnitudes than in models for sheep and humans. The resulting numerical model was then used to simulate numerous fracture healing scenarios from literature, showing a considerable mismatch in only 6 of 21 cases. Based on this corroborated model, a fit curve function was derived which predicts the increase of callus stiffness dependent on bodyweight, fixation stiffness, and fracture gap size. By mathematically predicting the time course of the healing process prior to the animal studies, the data presented in this work provides support for planning new fracture healing experiments in rats. Furthermore, it allows one to transfer and compare new in vivo findings to previously performed studies with differing mechanical parameters.
Highlights
The rat is of particular importance for experimental studies in fracture healing
The most important mechanical factor is the interfragmentary movement (IFM) [6]; IFM determines the tissue strains at the fracture site in relation to the fracture gap size and regulates the mechanically induced tissue differentiation [9, 10]
The aims of this study were (a) to adapt an existing numerical algorithm that reasonably simulates fracture healing in sheep [18, 19] and in humans [20, 21] to the conditions found in rats, which includes the determination of callus tissue properties and the calibration of the underlying mechanoregulatory tissue differentiation rules, (b) to simulate in vivo studies from literature and evaluate their agreement and (c) to predict the time course of the callus stiffness under several combinations of fixation stability, bodyweight, and fracture geometry
Summary
The rat is of particular importance for experimental studies in fracture healing. The outcome of the healing process is often evaluated via determination of the callus stiffness by ex vivo mechanical testing at certain healing time points [1, 2, 3, 4, 5]. Mechanical and biological factors influence the manner in which fracture healing progresses [6, 7, 8]. The most important mechanical factor is the interfragmentary movement (IFM) [6]; IFM determines the tissue strains at the fracture site in relation to the fracture gap size and regulates the mechanically induced tissue differentiation [9, 10]. Experimental studies in rats are not directly comparable with each other when different experimental parameters (bodyweight, fixation stiffness, fracture gap size) are used
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