Corrigendum to “Piezoelectricity in the Intervertebral Disc” [J. Biomech. 102 (2020) 109622] (Journal of Biomechanics (2020) 102, (S0021929020300282), (10.1016/j.jbiomech.2020.109622))

The authors regret the following. In equation 4 from section 2.5 “Data analysis and statistics”, the calculation of the piezoelectric strain constant g₃₃ currently reads as the following: [Formula presented] where [Formula presented] is the piezoelectric voltage constant, [Formula presented] is the piezoelectric strain constant and [Formula presented] is the dielectric constant (calculated as 61.1 F/m at 110 Hz (Gabriel, 1996)), all in the longitudinal direction. This should instead read as the following: [Formula presented] where [Formula presented] is the piezoelectric strain constant, [Formula presented] is the dielectric constant (calculated as 61.1 at 110 Hz (Gabriel, 1996)), all in the longitudinal direction, and [Formula presented] is the permittivity of free space, taken as 8.854 * 10⁻¹² F/m. Following from this correction, the values calculated in section 3.4 “Determining in-vivo voltages generated by longitudinal piezoelectricity” require correction. This section currently reads as the following: “For dehydrated samples, low magnitudes of 1.3 fVm/N and 0.74 fVm/N were generated in the AF and NP, respectively. But PFM measurements of the inverse piezoelectric effect yielded values as high as 22.6 fVm/N in the AF and 9.7 fVm/N in the NP. Hydrated testing suggests a similar piezoelectric voltage in the range of 12.7 fVm/N in the AF and 20 fVm/N in the NP. This agreement indicates that longitudinal piezoelectricity could be responsible for generating voltages in the range of 10–20 fVm/N through the disc.” This section should instead read as: “For dehydrated samples, low magnitudes of 0.15 mVm/N and 0.087 mVm/N were generated in the AF and NP, respectively. But PFM measurements of the inverse piezoelectric effect yielded values as high as 2.65 mVm/N in the AF and 0.18 mVm/N in the NP. Hydrated testing suggests a similar piezoelectric voltage in the range of 1.49 mVm/N in the AF and 2.35 mVm/N in the NP. This agreement indicates that longitudinal piezoelectricity could be responsible for generating voltages in the range of 2 mVm/N through the disc.” In addition, the final sentence of this paragraph currently reads: “Using 0.3 MN/m² as a value for in-vivo loads in the bovine caudal disc (Oshima et al., 1993), measuring the area of discs dissected in this study as 1.25 cm², and taking the height of bovine caudal discs as 5–10 mm thick (Alini et al., 2008), longitudinal piezoelectricity could be expected to generate voltage magnitudes in the range 0.38–1.5 nV locally through the bovine caudal IVD.” This should be amended to the following: “Using 0.3 MPa as a value for in-vivo loads in the bovine caudal disc (Oshima et al., 1993), longitudinal piezoelectricity could be expected to generate charge magnitudes of approximately 0.4 µC/m² locally through the bovine caudal IVD.” From these corrections, the following sentence in the abstract currently reads: “The voltage generated by longitudinal piezoelectricity in-vivo has been calculated to be ∼1 nV locally, indicating that piezoelectric effects may directly affect cell alignment in the AF and may work in conjunction with streaming potentials throughout the IVD.” This should instead read as: “The voltage generated by longitudinal piezoelectricity in-vivo has been calculated to be 2 mVm/N locally, indicating that piezoelectric effects may directly affect cell alignment in the AF and may work in conjunction with streaming potentials throughout the IVD.” Similarly, a sentence in section 4, of the discussion, currently reads as: “However, longitudinal piezoelectricity found here only accounts for ∼1 nV.” This should instead read as: “However, longitudinal piezoelectricity found here only accounts for 2 mVm/N.” Finally, the following reference should be removed as it is no longer applicable: Alini et al., (2008) M. Alini, S.M. Eisenstein, K. Ito, C. Little, A.A. Kettler, K. Masuda, J. Melrose, J. Ralphs, I. Stokes, H. Joachim. Are animal models useful for studying human disc disorders/degeneration? Eur. Spine J., 17 (2008), pp. 2–19. The authors would like to apologise for any inconvenience caused.