We explored several methods that defined the relative nucleus position and its cross-sectional area ratio, but there were still several issues with regard to our FEA models [13, 14, 17]. The data from previous studies could not be directly used in our model construction owing to individual differences and the lack of consistent standards [13]. For example, the previously published nucleus position, wherein its centre was located 3.5 mm towards the posterior of the disc, yielded a D2 value of less than 2 mm, which is obviously less than the minimum value measured in our study. Furthermore, the application of this value to the models constructed using imaging data from short volunteers may result in an impossible situation wherein part of the nucleus lies outside the disc’s boundary. The lack of consistent definition methods also leads to repeated attempts at model construction and validation. Finally, we can only define the relative nucleus position as being ‘slightly posterior’ to the centre of the disc, such that the lowest ACC of our model was lower than 70%, which needs to be improved further, even though the model validation process was verified in our previously published studies. Therefore, the calibration of the relative nucleus position and the investigation of a reliable ratio to define the above indicators are vital for improving the ACC of FEA, a widely used research method in the investigation of pathogenesis of DDD and optimization of spine surgical methods [4, 6, 8, 15].
The reduced T2 signal in the MRI data is closely related to disc degeneration and is generally selected to measure such a pathological change [18, 29]. The homogeneity test is important for ensuring the ACC and credibility of the study, as it is based on subjective observer measurements [20, 21]. While the kappa values between observers 1 and 3 are excellent (> 0.75), the rest are only acceptable (> 0.6). Such a phenomenon may be attributed to the small sample size and strict inclusion criteria of this study. These two constraints highlight that the slight interobserver differences can lead to obvious variations in the kappa values. Furthermore, although there is a certain degree of difference between the measured and calibrated relative nucleus positions, the modeled ROMs that are constructed from the measured nucleus position are still quite similar to the values from the in vitro study, with excellent ACC values attained (94.97% under flexion and 96.24% under extension, Fig. 6). The model constructed from the measured values also simulates real biomechanical indicators, such that the model calibration process further improves the ACC values based on the MRI measurements.
Notably, the nucleus itself was supressed during the model calibration process in the current study, even though the measured and calibrated values were closely associated with the nucleus. This is because R1 and R2 have an important impact on both M1 and M2 and their resultant ROMs. The variation in the ROMs is more likely due to the change in the approximately quadrangular annulus areas caused by the change of relative nucleus position and its cross-sectional area rather than the nucleus itself. The nucleus, ligaments and facet joints were therefore suppressed during the model calibration to investigate this factor individually. The FEA study results indicated that the retrodisplacement of the nucleus improved the ACC during the calibration process. Furthermore, the posterior structures overlapped in the model calibration under the extension condition. This phenomenon is not indicated by the computation error; rather, it is caused by the omitted contact types between the bone structures. Therefore, spatial positions are independently calculated when facet cartilages have been suppressed (Fig. 6).
In this study, the nucleus positions before and after calibration clearly changed (Fig. 6). We hypothesized that this change may originate from changes in body positions. The MRI measurement was completed in the supine position, whereas the loading conditions in the biomechanical studies were based on the standing position. Considering that the position of a nucleus cannot be changed once it was determined in the model construction process and that MRI data can be obtained in only the supine position, we believe that this model calibration is an effective method to calibrate this difference caused by body position and improve the computational ACC.
Differences still exist between the ROMs in the current FEA study and the widely cited in vitro study; these differences may be due to the suppressed structures on the ROMs, even though the measurement and calibration of the relative nucleus position and its cross-sectional area ratio increase the ACC. This defect may also affect the ACC because the ligament definition also lacks a standard method. There are no published in vitro ROM values that have been computed from models with the ligaments, facet joints and nucleus removed and with intact bone structures under lateral bending and axial rotation conditions. Although the in vitro study reported by Prof. Heuer et al provided ROM data under bending and axial rotation conditions with ligaments, facet cartilage, and the nucleus removed [30], these data could not be used as references for our model validation because the vertebral arch was also excised and proven to be somewhat related to lumbar instability [30–32]. In other words, ROM from these models will be greater than those of intact posterior structures. Hence, we are unable to calibrate the FEA model under these loading conditions. This defect can provide a good explanation for the lower ACC under lateral bending and axial rotation conditions.
Due to the issue that ROM predictions alone are insufficient to validate models for predicting mechanical contact parameters, as reported by Prof. Woldtvedt et al [33], multi-indicator model validation was necessary to evaluate the credibility of the measured and calibrated factors. In addition, although 10 N m moments were widely used in published finite element studies [6–9, 25], model validations under smaller moments were also necessary for the wider application of these measured and calibrated factors [5, 9, 30]. Hence, IDP and FCF under 7.5 N m moments and DC under 1200N compressive force were computed as validation indicators.
In this process, it is also worth noting that we did not determine the value of FCF from an in vitro study of the L4-L5 segment; hence, FCF from a widely cited in vitro study of the L3-L4 segment was selected as the standard value for the validation of FCF [28]. Computational FCF results indicated that the L4-L5 segment was slightly larger than the in vitro values (Fig. 8), and this result was consistent with the report that the facet contact force gradually increased from the cranial to the caudal side [33]. Despite these defects, we still believe that the difference in the model validation is acceptable because the lowest ACC value computed in the current study (among the ROM, IDP and FCF) is greater than 90% under almost all of loading conditions. Therefore, the measured P2 and calibrated P1 values in our subsequent FEA studies can be used to increase ACC.
The current study still faces some limitations. The ratio measurement of nucleus position is based on cross-sectional areas in a specific two-dimensional plane rather than the three-dimensional volume, such that the models do not capture differences in the lumbar lordotic angle. For example, obvious changes in the disc volume can be observed in the models with the same cross-sectional area ratio and different lordotic angles. Furthermore, the definition of the ligaments was accomplished based on our observer measurements and did not conform to a uniform standard, even though ligaments play a significant role in the maintenance of lumbar stability and are a key index in ROMs [4, 34]. Therefore, the definition of ligaments should be investigated and calibrated in future studies to further develop more accurate FEA models.