In a fracture stabilized by external fixation, axial and bending stiffness can be measured by attaching measurement devices to the external fixator pins or longitudinal bars. However, in measurement of axial stiffness, there are three main limitations. First, the measured axial force recorded from the force plate is not necessarily the effective axial vector of the force, and therefore can result in measurement errors. Second, pin osteolysis has a severe influence on the measured value of stiffness, erroneously indicating a higher stiffness [20] and can be difficult to detect. Third, if the fragment ends are in contact, measurement of axial stiffness is impossible, due to dynamic load transfer through the connected bone ends, which leads to erroneous higher fracture stiffness values.
By way of contrast, the assessment of bending stiffness is insensitive to bone contact and has been found clinically to be best suited to the assessment of fracture healing [27, 30]. Available methods to determine bending stiffness use either a straight-leg raise test or a bending test supporting the heel. Due to the indirect application of load, the resulting bending moment at the fracture site often only is an approximation, and can often only be used as a consecutive measurement for each patient.
As opposed to these methods, our custom-made measuring device produces a direct bending moment on the bone fragments, thus simulating a four-point-bending test with a constant bending moment created between both innermost pins. During measurements, the pins are loaded mainly in an axial direction, transferring the load directly to the bone fragments. The bending deformation applied is minimal, with no obvious danger of destroying the newly formed interfragmentary tissue.
To obtain values of bending stiffness in Nm/degree and to get comparable results among individual fracture, calibration of measurement systems on modules with known bending stiffness is required. As in other systems [16, 20]. the calibration curve of our system showed that there is a non-linear relationship between applied load and measured bending stiffness. This finding is not surprising, due to the inherent bending stiffness of the measuring device and the increasing deformation of the pins with higher fracture stiffness. This instrument measures not only the callus stiffness, but also the compound stiffness of the callus+construct. A linear increase in fracture stiffness leads to a non-linear response in the strain/deformation relationship. Since the fracture stiffness is low, a small increase of stiffness results in a large change in the calculated stiffness factor. Therefore, without calibration, measurements represent a predicted increase in stiffness that may not actually exist. Finally, the bending stiffness of the interconnecting bars was reduced to enhance the sensitivity of the device. However, we purposely did not try to minimize the inherent bending stiffness of the instrument because it had to maintain the reduction and the fixation during the measurement.
Testing the validity of the calibration on intact sheep tibiae revealed a rather lower calculated bending stiffness, 5.4% ± 6.2 (mean +/- SD). However, calculation of the error was deliberately done on intact tibiae, representing a high value of bending stiffness. As a result, it can be assumed that the error of measurement below these stiffness values is even smaller, and the accuracy of the system is highly acceptable [31].
In previously described measurement devices, it was found that pin loosening may result in a large measurement error. For example, [25], showed an error of 20% for one pin and 50% for two pins loose. Compared to this, our device showed smaller errors, below 16.5% of the stiffness value for one pin loose, and 51.4% for all four pins loose. In the range of lower actual bending stiffness of up to 10 Nm/degree, a value which can be assumed to be the healing threshold of a sheep tibia, the error of measurement was much smaller, showing errors of 3.4% and 29.3% in case of one or four pins loose, respectively. Other investigations, calculating the errors on probes with equal bending stiffness of 10 Nm/degree, found errors of 22% for intentional errors and additional general errors of 20% [26].
The lower error of our device, in comparison to the conventional method, can be explained on the basis that loading simulates four-point-bending exerts a force mainly along the screw axis, and rather less bending force perpendicular to this axis. If the pins loosen completely, it is obvious that either measurement device will fail.
For the conventional method of measurement, which assesses the amount of stress passing through the external fixator, it might appear that the fracture stiffness had increased. This would be an erroneous interpretation, due to the fact that pin loosening had occurred, with a consequent increased load transfer through the bone and the callus. However, in our measurement device, pin loosening can be detected by an unexpected decrease of bending stiffness. This condition was identified in 7 out of the 12 sheep used in our experiments. In a majority of the sheep this phenomenon was seen from the eighth week on. The ex-vivo four-point bending stiffness test revealed that the in-vivo measurements were valid, because the post mortem stiffness values fell on the expected curve of the healing pattern.
The serious problem of pin loosening was also confirmed, 36 out of 48 pins showed a clear sign of loosening. Pin loosening rates reported in the literature of, 40 % [32] and 42% [33], are considerably less than the 75% in our work. We explain this difference on our careful observation that detected small signs of loosening on the near cortex, which we judged to be due to pin loosening.
However, the question arises of for how long should bending stiffness be measured in order to have sufficient evidence to assess fracture healing? During the first weeks after operation, pin loosening can assumed to be a minor problem. Different investigators were able to show that in tibial fractures a bending stiffness of 15 Nm/degree is sufficient to permit removal of the external fixator [17, 34]. No fracture reaching this value showed a refracture or malalignment. Therefore, 15 Nm/degree is judged to be the value at which the fracture has healed. Assuming an intact human tibia to have a bending stiffness of 60 to 100 Nm/degree ([13] and own unpublished measurements), 15 Nm/degree represents 15 to 25% of the value of the intact tibia. In sheep tibia, the 25% value corresponds to a bending stiffness of 10 Nm/degree, which is reached after six to eight weeks in our experiment. Pin loosening in our experiment obviously started after the eighth week, when most of the sheep showed a bending stiffness of more than 10 Nm/degree. Therefore, up to this value, the measurement error was below 3.4% and 29.3% for one and all four pins loose, respectively. Consequently, measurements in the first seven weeks of the experiment can assumed to be reliable. In the later phase of healing, when pin loosening was obvious, a correction of the apparent stiffness values could be made by the calibration curves. However, the number of slightly loose pins of the individual sheep that may have influenced the measured value is not known. Therefore, a correction of the apparent stiffness value has not been done.
Each sheep showed an individual healing pathway with respect to bending stiffness versus time. In all sheep, bending stiffness was low up to the fourth week, giving the impression that not much healing occurs up to this time. Thus, prediction of good results based on an early increase in fracture stiffness obviously can not be made. However, analysis of the logarithmic increase of actual bending stiffness has been shown to be significant. These data showed a linear increase of actual bending stiffness between the third and seventh weeks (Fig. 8). Interestingly, expected differences in the slopes of the individual logarithmic stiffness data were not found. Instead, there were significant differences found in the third week initial stiffness values (Fig. 8 and Table 3). From our experimental data, no obvious predictive value of future bending stiffness could be made at two weeks, but calculations based on the differences between individual sheep from the third and fourth weeks showed a very strong correlation (r = 0.928, p < 0.001) with regard to the stiffness that was found at the seventh week. Still, there was a strong correlation found, with the changes between the fourth and fifth weeks, predicting stiffness at the tenth week (r = 0.765, p = 0.004). These findings allow us to conclude that the initial biomechanical and biological conditions at the fracture site essentially influence the individual healing path, as has been alluded to in previous investigations [23, 27]. We found that prediction of the healing path can be made between the third and fourth weeks, a phase in which the actual bending stiffness is still low (< 3 Nm/degree).