Understanding the form and function in Chinese bound foot from last-generation cases

Purpose: Foot adaptation in the typically developed foot is well explored. In this study, we aimed to explore the form and function of an atypical foot, the Chinese bound foot, which had a history of over a thousand years but is not practised anymore. Methods: We evaluated the foot shape and posture via a statistical shape modelling analysis, gait plantar loading distribution via gait analysis, and bone density adaptation via implementing finite element simulation and bone remodelling prediction. Results: The atypical foot with binding practice led to increased foot arch and vertically oriented calcaneus with larger size at the articulation, apart from smaller metatarsals compared with a typically developed foot. This shape change causes the tibia, which typically acts as a load transfer beam and shock absorber, to extend its function all the way through the talus to the calcaneus. This is evident in the bound foot by i) the reduced center of pressure trajectory in the medial–lateral direction, suggesting a reduced supination–pronation; ii) the increased density and stress in the talus–calcaneus articulation; and iii) the increased bone growth in the bound foot at articulation joints in the tibia, talus, and calcaneus. Conclusion: Knowledge from the last-generation bound foot cases may provide insights into the understanding of bone resorption and adaptation in response to different loading profiles.


Appendix A
Given the strain   , apparent density   and fabric tensor  �  for the current time step  , a mechanical stimulus   is calculated.
where  � , and  ̂ are the Lamé constants of ideal compact bone with null porosity, whose density is represented by  �, and   is a remodelling tensor given by. (2) A weighted sum of stimulus   between the spherical and deviatory part is calculated next Using the scalar weighting factor of  ∈ [0, 1].
Accounting for the weighted sum of stimulus   from the current loading configuration and the number of cycles of loading per day   , the resorption level  t  , and the apposition level  t  ,are calculated Where   * is the reference stimulus level,  is the half-width of the bone equilibrium zone,  is the empirical weighting between the importance of the load intensity and the number of load cycles to bone remodelling, and (  ) and (  ) are constants.
The resorption and apposition levels determine which remodelling criteria is active according to resorption if  t  ≥ 0 and  t  < 0 Following this, the rates for surface remodelling ̇t, density ̇ and remodelling tensor  ̇ are Where   and   are the remodelling velocity for resorption and apposition, respectively,   () is the specific surface (internal surface per unit volume),  is the ratio between the available surface for remodelling and the total internal surface, and  � is the fourth-order rank tensor form of .To avoid unphysiological values of density and numerical problems, the rates were adjusted to ensure that the density remains in the range of 0.01 g cm 3 ⁄ ≤  ≤  � at all the time.
The variables are updated using the forward Euler method, and consequently the constitutive tensor is updated so that its local orthotropy directions coincides with those of the principal axes of the remodelling tensor, and stiffness in the material direction is a function of principal values of the remodelling tensor.This process repeats until the specified simulation period is reached.The parameter values used in the simulation are summarized in the Table A1 below.As expected, the HB and FB feet exhibited shorter lengths due to the foot binding compared to the NF.Moreover, the FB exhibited a high arch in the midfoot forming an extreme dome, compared to the HB and NF.The HB also showed a higher arch compared to the NF.Full details of the bone shapes are presented below.

Fig. B1 .
Fig. B1.Illustration of shape differences in the calcaneus bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B2 .
Fig. B2.Illustration of shape differences in the talus bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B3 .
Fig. B3.Illustration of shape differences in the tibia bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B4 .
Fig. B4.Illustration of shape differences in the fibula bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B5 .
Fig. B5.Illustration of shape differences in the M1 bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B6 .
Fig. B6.Illustration of shape differences in the M2 bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B7 .
Fig. B7.Illustration of shape differences in the M3 bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B8 .
Fig. B8.Illustration of shape differences in the M4 bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.

Fig. B9 .
Fig. B9.Illustration of shape differences in the M5 bone of HB and NF, and FB and NF with quantification of Hausdorff Distance, and Gaussian Distribution.