In estimating the mechanical constants,

*C*_{1} and

*C*_{2}, for fasciae in the above formulae for applied forces, we first determined the constants for the superficial nasal fascia. We used the available experimentally obtained in vitro finite stress-strain data

^{10} for superficial nasal fascia along the longitudinal direction. This longitudinal stress is given by the following:

\[\ {\sigma}={\alpha}E^{{\beta}}\]

In equation (25), σ is the longitudinal Euler's stress, and

*E* is the Green's strain tensor.

^{18} Green's strain tensor is the strain tensor referring to the undeformed coordinates, whereas Euler's strain tensor refers to deformed coordinates. The stress corresponding to Euler's strain is Euler's stress.

^{18} Green's strain tensor can be calculated by the following:

\[\ E=\frac{1}{2}({\lambda}^{2}-1)\]

In equation (26), λ is the stretch ratio. In equation (25), α and β, which were taken from one of the in vitro human superficial nasal fascia specimens (n10js) reported in Zeng et al,

^{10} are: α = 16.85, β = 1.99. We chose this specimen, which was the softest of all four specimens of fascia reported by those researchers,

^{10} to determine if our model equations could predict significant compression and shear in such an extreme case.

We also used the longitudinal stress-strain relation for incompressible material

^{16} in our model. This relation is expressed by the following set of equations:

\[\ {\sigma}=2C_{1}C_{2}({\lambda}^{2}-\frac{1}{{\lambda}})e^{C_{2}(I_{1}-3)},{\ }\mathrm{with}{\ }{\psi}=0,\mathrm{I}_{1}={\lambda}^{2}+\frac{2}{{\lambda}},{\ }\mathrm{using}{\ }{\lambda}_{1}^{2}={\lambda}^{2},{\lambda}_{2}^{2}={\lambda}_{3}^{2}=\frac{1}{{\lambda}}\]

We next used the theoretical stress given by equation (27) and the experimental stress given by equation (25) to calculate the values of

*C*_{1} and

*C*_{2} that would allow the theoretical and experimental curves of stress-stretch ratio to be as close to each other as possible (

Figure 2). Our model minimized the sum of the squares of difference between the theoretical and experimental values of stress by using the least-square method

^{19} directly on equations (25) and (27), in conjunction with a finite-difference method adapted from Newton's method for nonlinear equation systems.

^{20} The computed value of

*C*_{1} was 0.0327 MPa, and that of

*C*_{2} was 8.436 MPa.

Following the above procedure in conjunction with the available in vitro longitudinal stress-strain data from Wright and Rennels,

^{11} we determined the values of the elastic constant,

*C*_{1}, and the dimensionless constant,

*C*_{2}, for fascia lata and plantar fascia (

Table 1). The mechanical constants for superficial nasal fascia were determined based on Zeng et al.

^{10}