Less than full circumferential fusion of a tibial nonunion is sufficient to achieve mechanically valid fusion--proof of concept using a finite element modeling approach

Abstract

Background: Although minimally invasive approaches are widely used in many areas of orthopedic surgery nonunion therapy remains a domain of open surgery. Some attempts have been made to introduce minimally invasive procedures into nonunion therapy. However, these proof of concept studies showed fusion rates comparable to open approaches never gaining wider acceptance in the clinical community. We hypothesize that knowledge of mechanically relevant regions of a nonunion might reduce the complexity of percutaneous procedures, especially in complex fracture patterns, and further reduce the amount of cancellous bone that needs to be transplanted. The aim of this investigation is to provide a proof of concept concerning the hypothesis that mechanically stable fusion of a nonunion can be achieved with less than full circumferential fusion.

Methods: CT data of an artificial tibia with a complex fracture pattern and anatomical LCP are converted into a finite element mesh. The nonunion area is segmented. The finite element mesh is assigned mechanical properties according to data from the literature. An optimization algorithm is developed that reduces the number of voxels in the non union area until the scaled von Mises stress in the implant reaches 20% of the maximum stress in the implant/bone system that occurs with no fusion in the nonunion area at all.

Results: After six iterations of the optimization algorithm the number of voxels in the nonunion area is reduced by 96.4%, i.e. only 3.6% of voxels in the non union area are relevant for load transfer such that the von Mises stress in the implant/bone system does not exceed 20% of the maximal scaled von Mises stress occurring in the system with no fusion in the non union area at all.

Conclusions: The hypothesis that less than full circumferential fusion is necessary for mechanical stability of a nonunion is confirmed. As the model provides only qualitative information the observed reduction of fusion area may not be taken literally but needs to be calibrated in future experiments. However this proof of concept provides the mechanical foundation for further development of minimally invasive approaches to delayed union and nonunion therapy.

Figure 1

Screw bone interface after repeated runs of the coarsening algorithm. Left panel corresponding to the level 1 finite element mesh, middle panel corresponding to the level 4 finite element mesh, and right panel corresponding to the level 7 finite element mesh.

Figure 2

Finite element mesh generated from the computed tomography data with approximately 7.5 million mesh cells ( = voxels).

Figure 3

Original computed tomography image (left); results of the segmentation process (right).

Figure 4

Finite element mesh of the tibia with titanium implant (blue) and nonunion area (red) after completion of the segmentation process.

Figure 5

Numerical result for axial weight bearing of an 80 kg person with no osseous consolidation in the nonunion area (‘worst case scenario’).

Figure 6

Remaining parts of the nonunion area (red) necessary for load transfer within the boundary criterion after iterative runs of the optimisation algorithm.