Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli

Abstract

Numerical models of secondary fracture healing are based on mechanoregulatory algorithms that use distortional strain alone or in combination with either dilatational strain or fluid velocity as determining stimuli for tissue differentiation and development. Comparison of these algorithms has previously suggested that healing processes under torsional rotational loading can only be properly simulated by considering fluid velocity and deviatoric strain as the regulatory stimuli. We hypothesize that sufficient calibration on uncertain input parameters will enhance our existing model, which uses distortional and dilatational strains as determining stimuli, to properly simulate fracture healing under various loading conditions including also torsional rotation. Therefore, we minimized the difference between numerically simulated and experimentally measured courses of interfragmentary movements of two axial compressive cases and two shear load cases (torsional and translational) by varying several input parameter values within their predefined bounds. The calibrated model was then qualitatively evaluated on the ability to predict physiological changes of spatial and temporal tissue distributions, based on respective in vivo data. Finally, we corroborated the model on five additional axial compressive and one asymmetrical bending load case. We conclude that our model, using distortional and dilatational strains as determining stimuli, is able to simulate fracture-healing processes not only under axial compression and torsional rotation but also under translational shear and asymmetrical bending loading conditions.

Mechanical microenvironments and protein expression associated with formation of different skeletal tissues during bone healing

“…The finding that lower tensile strains are associated with bone formation over formation of any soft tissue is not consistent with the theory of Carter and colleagues (Carter et al 1998). The present data are also not consistent with studies (Shefelbine et al 2005; Steiner et al 2013) that have implemented the theory of Claes and Heigele (Claes et al 1997; Claes and Heigele 1999) to posit that cartilage formation is favored only in regions of large values of hydrostatic pressure (which may correspond loosely to negative values of dilatation) and is not dependent on the octahedral shear strain. Some of these and other prior studies using numerical simulation of skeletal repair have incorporated physiochemical and/or biological factors such as hypoxia and angiogenesis (Burke et al 2013; Simon et al 2011).…”

“…These features include shear strain and interstitial fluid flow (Lacroix and Prendergast 2002; Prendergast et al 1997), strain and hydrostatic pressure (Claes et al 1997; Claes and Heigele 1999), shear strain only (Gomez-Benito et al 2005), and tensile strain and hydrostatic pressure (Carter et al 1998). Tests of these theories, largely using numerical simulation to estimate the mechanical microenvironment and then to predict the healing outcome, have produced somewhat contradictory results (Isaksson et al 2006; Steiner et al 2013). Experimental evidence obtained by using digital image correlation to measure the strain microenvironment has pointed to the importance of shear strain (as represented by the octahedral shear strain) and, to a lesser extent, tensile strain (as represented by the maximum principal strain) (Morgan et al 2010).…”

Numerical Simulation of Callus Healing for Optimization of Fracture Fixation Stiffness

“…Material properties were obtained in a previous study [26] (cf. Table 1) and were assumed as linear elastic and isotropic.…”

Disadvantages of interfragmentary shear on fracture healing—mechanical insights through numerical simulation

“…This enables a direct comparison between different mechanical conditions. Thus, according to experimental data, we identified more cartilage formation under axial compression than under shear loading conditions …”

“…Tissue composition (a mixture of three tissue types: woven bone, fibrocartilage, and connective tissue), material properties (assumed as linear‐elastic isotropic), and blood supply were assigned to each of the finite elements. For the resulting Young's modulus E j of each element j , a rule of mixtures was used according to Steiner et al: where E conn , E cart , and E bone are the Young's moduli for connective tissue, cartilage, and bone, respectively (cf. Table ); c cart and c bone are the respective tissue fractions for cartilage and bone within one element.…”