Novel approach to estimate distraction forces in distraction osteogenesis and application in the human lower leg.

Purpose: In distraction osteogenesis (DO) of long bones, new bone tissue is distracted to lengthen limbs or reconstruct bone defects. However, mechanical boundary conditions in human application such as arising forces are mainly based on limited empirical data. Our aim was the numerical determination of the callus distraction force (CDF) and the total distraction force (TDF) during DO in the tibia of adults to advance the understanding of callus tissue behavior and optimize DO procedures.

Method: We implemented a mathematical model based on an animal experiment to enable the calculation of forces arising while distracting callus tissue, excluding the influence of surrounding soft tissue (muscles, skin etc.). The CDF progression for the distraction period was calculated using the implemented model and varying distraction parameters (initial gap, area, step size, time interval, length). Further, we estimated the CDF based on reported forces in humans and compared the results to our model predictions. In addition, we calculated the TDF based on our CDF predictions in combination with reported resisting forces due to soft tissue presence in human cadavers. Finally, we compared the progressions to in vivo TDF measurements for validation.

Results: Due to relaxation, a peak and resting CDF is observable for each distraction step. Our biomechanical results show a non-linear degressive increase of the resting and peak CDF at the beginning and a steady non-linear increase thereafter. The calculated resting and peak CDF in the tibial metaphysis ranged from 0.00075 to 0.0089 N and 0.22-2.6 N at the beginning as well as 20-25 N and 70-75 N at the end of distraction. The comparison to in vivo data showed the plausibility of our predictions and resulted in a 10-33% and 10-23% share of resting CDF in the total resting force for bone transport and elongation, respectively. Further, the percentage of peak CDF in total peak force was found to be 29-58% and 27-55% for bone transport and elongation, respectively. Moreover, our TDF predictions were valid based on the comparison to in vivo forces and resulted in a degressive increase from 6 to 125 N for the peak TDF and from 5 to 76 N for the resting TDF.

Conclusion: Our approach enables the estimation of forces arising due to the distraction of callus tissue in humans and results in plausible force progressions as well as absolute force values for the callus distraction force during DO. In combination with measurements of resisting forces due to the presence of soft tissue, the total distraction force in DO may also be evaluated. We thus propose the application of this method to approximate the behavior of mechanical callus properties during DO in humans as an alternative to in vivo measurements.