## 4 Discussion  
The proposed method aims at identifying a set of possible tone ratios for the trunk muscles based on trunk test data. By matching model-generated trunk stiffness with experimental multidirectional stiffness results, the muscular tone values have been approximated for both the superficial and the deep trunk muscles that are hardly accessible to standard, non-invasive, instrumentation. Figure 6: Solution domain \(D\) in the 3D space: (**a**) section contours, and (**b**) constructed solution domain. Given the complexity of the trunk behavior, the identification is simplified by adopting a number of assumptions and approximations, in addition to those pertaining to the numerical model that was reported previously in [10]. A major assumption is that large families of muscles are assumed to share the same tone ratio. This obviously forces muscles that belong to the same class to artificially take on identical RMTTs. A gross approximation was made in the first, single-class scenario, where the tone ratios were identical for all muscles. In the second, more realistic scenario, three muscle classes were distinguished, each sharing one of three tone ratios. The significance of the identification should improve as the classification is further refined. Nevertheless, as the number of unknowns increases, several issues should arise. The identification procedure should be automated since it cannot be carried out manually. Recalling the tones to be the active forces that achieve a stable equilibrium at the pre-perturbation posture, the redundancy in the muscle recruitment mechanism becomes significant, and requires additional constraints to guard against overestimation of the multidimensional solution domain \(D\). Stability [24] and postural constraints [2], which were not considered in the present study, are relevant additions to the formulation of the tone identification problem. Another limitation lies in the differences in the characteristics of the experiment and the numerical model. For instance, the experimental and the model trunk stiffnesses are assumed to carry the same definition [10; 18]. The model trunk is considered to be clamped at the hip where the sitting subject is only partially restrained [18]. The experimental trunk stiffnesses are averaged over a sample of 15 subjects while the model stiffness relates to a specific skeletal morphology. The primary advantage of the proposed identification method is its ability to safely provide quantitative evaluation of the tones for the deep muscles, without resorting to the existing invasive techniques [12]. The method is safe in that it causes no pain, and raises no risk of infection. In contrast, for the superficial muscles, the tone can be measured easily by existing techniques [7; 12; 13]. While the proposed methodology provides an alternative means for estimating the tone of these muscles, it can also take advantage of the tone data provided by other techniques [12]. The superficial muscle tone data can be used as a reference in the validation of the proposed methodology by comparing the identification results with the direct measurement data. On the other hand, these data can be used as input for the identification of unmeasured tones for a specific subject. As a result, the identification problem is reduced to finding the tones of only a subset of muscles, such as the deep ones, for the subject. The proposed method can then be applied with further gains in accuracy and efficiency in estimating the unmeasured muscle tones [25]. Table 14 shows published reference data [12; 26; 27; 28] in the form of ranges of tone ratios for particular muscles/groups in addition to the gross ranges identified on the basis of three muscle classes. For class C1 and C2 muscles, the minimum ratios of 5% and 6% are significantly large compared to the minimum for class C3. In fact, the latter can numerically be set to zero while maintaining equilibrium because the C3 muscle's role is not to maintain and stabilize vertical posture.