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.

Figure 1. Boundary conditions of the superimposed loading case.

Figure 2. 3 mm osteotomy: characteristic maps of bending stiffness depending on the fracture fixation stiffness in axial (k_fix,axial) and shear (k_fix,shear) direction after A 6 weeks of healing B 9 weeks of healing C 12 weeks of healing.

Bending stiffness (k_Bend) is given as the percentage of the intact (contralateral) bone bending stiffness. Numbered data points refer to experimental data in Table 3, error bars indicate estimated values (20% error) for unknown shear stiffness of the devices. Letters indicate positions of the exemplary simulation results in Figure 5.

Figure 3. 1 mm osteotomy: characteristic maps of bending stiffness depending on the fracture fixation stiffness in axial (k_fix,axial) and shear (k_fix,shear) direction after A 6 weeks of healing B 9 weeks of healing C 12 weeks of healing.

Bending stiffness (k_Bend) is given as the percentage of the intact (contralateral) bone bending stiffness. Letters indicate positions of the exemplary simulation results in Figure 6.

Figure 4. Qualitative characteristic maps of healing outcome depending on the fracture fixation stiffness in axial (k_fix,axial) and shear (k_fix,shear) direction for A 3 mm fracture gap; B 1 mm fracture gap.

Roman numerals refer to areas of different healing outcomes as explained in detail in Table 3. Letters indicate positions of the exemplary simulation results in Figures 5 and 6.

Figure 5. Five different exemplary simulations for a 3 mm gap size.

For each case the initial distortional and dilatational strain field is shown, which determine the tissue differentiation following the hypothetic rules of Claes and Heigele . Respective tissue stimulating strain ranges are indicated at the color bars. Additionally, the tissue distribution, as well as the percentage of extracortical bony callus volume (V_bo), and the callus index (CI) at 3, 6, and 9 weeks of healing are displayed for A optimal fracture fixation; B overly flexible fixation leading to non-union; C overly rigid fixation leading to inhibition of callus development with unstable bending stiffness; D a predominant shear load case; E a predominant axial load case. Letters are according to diagrams in Figures 2 and 4.

Figure 6. Exemplary simulations for a 1 mm gap size.

For each case the initial distortional and dilatational strain field is shown, which determine the tissue differentiation following the hypothetic rules of Claes and Heigele . Respective tissue stimulating strain ranges are indicated at the color bars. Additionally, the tissue distribution at 3, 6, and 9 weeks of healing are displayed for F advantageous fixation; G disadvantageous (overly flexible) fixation. Letters are according to diagrams in Figures 3 and 4.