The particle velocity maps shown for the
A0 mode in the human cornea (
Fig. 7) are consistent with the characteristic tissue motion associated with anti-symmetric wave propagation. However, particle velocity maps for the
S0 mode do not follow the expected propagation dynamics of the symmetric mode. These results are in agreement with Li and colleagues,
54 where
S0 and
A0 modes were measured simultaneously, and they observed anti-symmetric displacement profiles in the low-frequency range. It is well established from Lamb wave theory that wave propagation dynamics and the displacements profiles for
A0 and
S0 modes vary with frequency.
31,33 At lower frequencies, the sample motion across the thickness for
A0 and
S0 modes linearly varies and converges to the displacement characteristics of conventional axial and flexural plate waves, respectively.
31,33 These displacement characteristics can be clearly observed from
A0 and
S0 corneal particle velocity maps (at 1 kHz) shown in
Figure 7. Furthermore, the corneal particle velocity maps in
Figure 7 also indicate that the wavelength of the mechanical wave for the
A0 mode was shorter than the
S0 mode. This is consistent with Lamb wave theory, which predicts that the
A0 wavelength is always shorter than the
S0 mode.
20,31,33,66 The measured wave speeds for the
A0 and the
S0 modes are also consistent with the product of the mechanical wave wavelength and the frequency at which the mechanical wave was observed. Furthermore, in the low-frequency range, the S
0 mode approximates a conventional axial plate wave, making the Lamb wave speed close to the axial plate wave speed
\({{c}_a} = \sqrt {E/\rho } \) . This speed compares well with the Rayleigh wave speed in the high-frequency range, as illustrated in
Figure 8. Young's moduli calculated from the speeds of the
S0 and
A0 modes in the high-frequency range (0.553 ± 0.1 MPa) show good agreement with the Young's modulus estimated from the axial plate wave speed
ca in the low-frequency range (0.562 ± 0.15 MPa). This further confirms that the
S0 propagation mode is generated in the in vivo human cornea during oblique stimulation.