Corrigendum: Musculoskeletal modeling of the lumbar spine to explore functional interactions between back muscle loads and intervertebral disk multiphysics

A corrigendum on

Musculoskeletal modeling of the lumbar spine to explore functional interactions between back muscle loads and intervertebral disk multiphysics
by Toumanidou, T. and Noailly, J. (2015). Front. Bioeng. Biotechnol. 3:111. doi: 10.3389/fbioe.2015.00111

In Toumanidou and Noailly (2015), the general forms of the second Piola-Kirchhoff and Cauchy stress tensors on Eqs (12) and (16) in Materials and Methods were not reported correctly. This should read as follows:

$\mathbf{\text{S}}=2\frac{\partial U}{\partial \mathbf{\text{C}}}=\frac{G}{2}\left(2J^{-2∕3}\mathbf{\text{I}}-\frac{2}{3}{\overline{\mathbf{\text{I}}}}_1^C{\mathbf{\text{C}}}^{-1}\right)+K\ln J{\mathbf{\text{C}}}^{-1}+U_F^{\prime }\left[J^{-\frac{2}{3}}{\overline{\mathrm{\lambda }}}_f^{-1}\left(\mathbf{\text{N}}\otimes \mathbf{\text{N}}\right)-\frac{1}{3}{\overline{\mathrm{\lambda }}}_f{\mathbf{\text{C}}}^{-1}\right]$ (12)

The Cauchy stress was related to the second Piola-Kirchhoff stress by:

$\mathrm{\sigma }=\frac{1}{J}\mathit{\text{FS}}{\mathit{\text{F}}}^{-T}=\frac{G}{2J}\left(2\overline{\mathit{\text{B}}}-\frac{2}{3}{\overline{\text{I}}}_1^C\mathbf{\text{I}}\right)+\frac{K\ln J}{J}\mathbf{\text{I}}+\frac{1}{J}\left[U_F^{\prime }\left({\overline{\mathrm{\lambda }}}_f\left(\mathbf{\text{n}}\otimes \mathbf{\text{n}}\right)-\frac{1}{3}{\overline{\mathrm{\lambda }}}_f\mathbf{\text{I}}\right)\right]$ (16)

where n is the direction of the muscle fibers in the deformed fascicle, $\overline{\mathit{\text{B}}}$ the deviatoric part of the left Cauchy-Green tensor B, and I the second-order unit tensor.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.