Numerical Simulation of Callus Healing for Optimization of Fracture Fixation Stiffness

Abstract

The stiffness of fracture fixation devices together with musculoskeletal loading defines the mechanical environment within a long bone fracture, and can be quantified by the interfragmentary movement. In vivo results suggested that this can have acceleratory or inhibitory influences, depending on direction and magnitude of motion, indicating that some complications in fracture treatment could be avoided by optimizing the fixation stiffness. However, general statements are difficult to make due to the limited number of experimental findings. The aim of this study was therefore to numerically investigate healing outcomes under various combinations of shear and axial fixation stiffness, and to detect the optimal configuration. A calibrated and established numerical model was used to predict fracture healing for numerous combinations of axial and shear fixation stiffness under physiological, superimposed, axial compressive and translational shear loading in sheep. Characteristic maps of healing outcome versus fixation stiffness (axial and shear) were created. The results suggest that delayed healing of 3 mm transversal fracture gaps will occur for highly flexible or very rigid axial fixation, which was corroborated by in vivo findings. The optimal fixation stiffness for ovine long bone fractures was predicted to be 1000–2500 N/mm in the axial and >300 N/mm in the shear direction. In summary, an optimized, moderate axial stiffness together with certain shear stiffness enhances fracture healing processes. The negative influence of one improper stiffness can be compensated by adjustment of the stiffness in the other direction.

Mechanical Regulation of Bone Regeneration: Theories, Models, and Experiments

“…However, while the IFC data are available no quantitative comparison has be made between simulations and the results, instead visually comparing general trends and histological slices has predominated. In Figure 5 , we see simulation results from (A) Burke and Kelly ( 62 ), (B) Lacroix and Prendergast ( 37 ), and (C) Steiner et al ( 65 ) these all consist of a uniform cortical bone and callus geometry, which is made up of non-uniform finite elements, in the case of Burke and Kelly ( 62 ) and Lacroix and Prendergast ( 37 ) they are two dimensional axisymmetric simulations and in Steiner et al ( 65 ) three dimensional. Figure 5 D is a histological section from an in vivo study by Claes and Heigele ( 4 ); we see the callus is non-uniform and asymmetric.…”

“…The model was implemented as a three dimensional linear-elastic simulation. While this model can capture the events of bone regeneration, Steiner et al ( 65 ) conducted a parameter study of fixator stiffness, which encompassed values used several in vivo studies and achieved comparable outcomes, it is a linguistic representation of observed phenomenon. Thus it is entirely phenomenological and does not encompass any underlying mechanism in physical or chemical terms.…”

“…Figure 5 D is a histological section from an in vivo study by Claes and Heigele ( 4 ); we see the callus is non-uniform and asymmetric. This mismatch between the asymmetric callus in the histological images and uniformly simulated calluses complicates direct comparison, additionally axisymmetric boundary conditions implies the simulation should match every quadrant of the histological slice, which is clearly impossible, when using three dimensional models like Steiner et al ( 65 ) one must also find the correct slice of the model to compare to the histology. Vetter et al ( 63 ) compared the use of volumetric strain, deviatoric strain, greatest-shear strain, and principal strain as stimuli for tissue differentiation.…”

Computational characterization of fracture healing under reduced gravity loading conditions

“…It has also been demonstrated that rigid fixation has a deleterious impact on the fracture healing cascade while improved fracture healing occurred when axial micromotion is delivered to the fracture site . While these studies provide valuable insight about the role fracture dynamization and interfragmentary movement of the fracture itself have on the healing process (as compared to static fixation techniques), fewer studies have investigated the direct role of fixation stiffness on in vivo fracture healing in a static environment . Gilbert et al investigated tibial fracture healing over 9 weeks in a canine model and observed no significant differences in failure force, stiffness, or energy to failure as a function of fixator stiffness .…”

“…[13][14][15] While these studies provide valuable insight about the role fracture dynamization and interfragmentary movement of the fracture itself have on the healing process (as compared to static fixation techniques), fewer studies have investigated the direct role of fixation stiffness on in vivo fracture healing in a static environment. 12,[16][17][18] Gilbert et al investigated tibial fracture healing over 9 weeks in a canine model and observed no significant differences in failure force, stiffness, or energy to failure as a function of fixator stiffness. 16 Conversely, Goodship et al reported an inverse relationship between fracture healing time and fixation stiffness in an ovine model.…”