Influence of the hard callus heterogeneity on the strains

After calculation of the heterogeneous FE models for each of the six stages, hypothetical cases were calculated. In the first set of six hypothetical cases, the hard callus at each stage was modelled as homogeneous by assigning the according mean elastic modulus to each element of the hard callus (Figure II.3). Following the same principle, a homogeneous cortex was assumed in the second set of hypothetical cases according to the mean elastic modulus of the cortical region at each stage.

Afterwards, comparison of the strain distributions was carried out by calculating the differences of the strain distribution in the heterogeneous case and the strain distribution of the homogeneous case. In total, 12 images of strain differences were available for the six healing stages showing the influence of the heterogeneity of hard callus and cortex. All 12 images can be found in Figure 3 of the manuscript (Vetter et al. 2010b), see appendix. Based on these images, the influence of the heterogeneity on the strain distributions at the stages before, during and after bridging of the gap are summarized in Figure II.8. The effect on the heterogeneity changes the mechanical stimuli in the callus and is therefore potentially important for dynamical simulations of bone healing.

Figure II.8: Schematic of the influence of the hard callus heterogeneity on the local strains before bridging, during bridging and after bridging.

The little variation in the stiffness of the cortex, compared to variation in the hard callus, results in a higher influence of the hard callus heterogeneity on the strain distributions, especially in the early healing stages. The influence of the cortex heterogeneity, due to the remodelling of the cortical ends, starts to become important with cartilage bridging and becomes more important with bony bridging.

As one main effect of the decrease of the bone area fraction at the cortical ends, the strains in this region are increased compared to the hypothetical homogeneous case.

This will eventually cause that the strain threshold for resorption of bone will be exceeded in the cortical end region and further resorption will stop.

Some influences of the hard callus heterogeneity on tissue differentiation are given below, based on the interpretation of the strains from a basic mechanobiological point of view (see Chapter 6.5):

1) The initiation of intramembranous ossification is enhanced by the hard callus heterogeneity. This is due to a mechanically “smoother” interface between hard callus and adjacent fibrous tissue, which leads to lower strains in the fibrous tissue enabling intramembranous ossification.

2) The formation of cartilage in the periosteal gap area is strongly influenced by the heterogeneity. The hard callus heterogeneity reduces the strains further outside the periosteal gap. However, compared to the homogeneous case, higher stiffness close to the cortex increases also the strains not only within the gap but also in the osteotomy region close to the cortex. Therefore, the heterogeneity should shift the cartilage formation towards the outside of the callus.

3) In the same way, the endochondral ossification is influenced. Not only do the strains in the cartilage regions at Stage III depend on the hard callus heterogeneity, but also the strains in the cartilage at Stage IV. In the heterogeneous case, higher strains were seen closer to the fracture gap. Neglecting biological influences, the endochondral ossification, occurring between Stage III and Stage V, seems to be driven by the mechanical stimuli which are a result from the heterogeneity of the hard callus (Vetter et al. 2010b).

4) Finally, the mechanical signal for bone resorption is reduced by the hard callus heterogeneity. The outer regions of the hard callus are less loaded due to the mainly vertical transmission of the load, applied on the cortex. Therefore, the strains are very low in that region for a homogeneous hard callus. In the heterogeneous callus, the stiffness is lower at the outer fringes of the hard callus and, therefore, inhibits early resorption of the outer fringes.

6.7. Conclusions

Over the last decade and more Finite Element models have been used to estimate the local strain, stress and fluid flow within the callus. Patterns of these mechanical parameters have been correlated with the patterns of tissue differentiation (Kuiper et al. 1996; Prendergast et al. 1997; Claes and Heigele 1999; Epari et al. 2006b). This section of the thesis was driven by the same idea. Previous studies based their investigations on assumed homogeneous tissue type distributions within the callus

studies. In particular, the mechanical heterogeneity of the hard callus could be quantified. It was found that the overall stiffening of the callus described by its averaged elastic modulus increased exponentially during the healing (Figure II.3).

The dynamical interpretation of the mechanical strain pattern was led by the idea of Perren and Cordey (1980). First, the interfragmentary strain theory (IST) was found to be generally capable to describe the tissue differentiation within the osteotomy gap. However, the threshold value for the formation of fibrous tissue was found to be to low. Therefore, fibrous tissue would not have been formed in the osteotomy gap according to the interfragmentary strain theory which is contradicting to the experimental observation. In a next step, the IST was applied on a local basis as a mechanoregulatory model. The results of these “static simulations” showed the potential of applying only one mechanicals signal (a strain invariant) as mechanical stimulus driving the tissue differentiation. The tissue differentiation could be well explained on the periosteal side of the callus and in the fracture gap. However, the endosteal tissue differentiation can not be explained by this basic mechanoregulatory model. In a mechanobiological model, the biology probably has to inhibit the mechanical signal for tissue maturation within the endosteal region at the initial healing phases. One main advantage of the IST is that only one mechanical signal determines the tissue differentiation. This reduces the complexity which is a demanded property of the mechanobiological computer model which will be used for dynamical simulations of bone healing (see chapter 7).

The heterogeneity of the hard callus is a crucial factor on the strain distribution within the callus (Vetter et al. 2010b). Therefore, it is also an important factor for mechanobiological simulations on bone healing, as the heterogeneity changes the values of the assumed mechanical stimulus. From a mechanobiological viewpoint, the hard callus heterogeneity is an important factor for the shift of the cartilage from the outer periosteal side inwards to the osteotomy gap over time. This shift occurs between Stage III and Stage IV which is approximately between 3.75 weeks and 6 weeks post-op. The comparison with the hypothetical homogeneous calculations showed the importance to incorporate the hard callus development into dynamical simulations of bone healing.

It is not clear whether the bony bridging occurs via endochondral ossification, intramembranous ossification or both and what causes the cartilage to ossify. Some evidences are in favour for endochondral ossification (Epari 2006). Form a mechanobiological viewpoint, one could hypothesise for the healing progression between Stage III and IV: (i) endochondral ossification starting from the outer

periosteal end and processing forward into the intercortical gap and, at the same time, further formation of cartilage towards the intercortical gap; (ii) around the time when cartilage has reached the intercortical region (as seen as cartilage “remnants”

in Stage IV) the stability has considerably increased and reduced strains in the gap so strongly, that bone formation in the gap occurs.

Unfortunately, the animal study did not provide data points between 3 and 6 weeks and detailed insight of the healing process (in particular the bony bridging) between this time is limited. Several questions remain unanswered. Further experimental and computational studies focusing on this healing time could help to clarify some of the following questions. How does bony bridging occur on the endosteal and periosteal side? Is it pure endochondral ossification or does also intramembranous ossification play a role? And how important is the endosteal bridging (seen at Stage IV) for the strain distribution and the shift of the cartilage?