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Erratum to: Investigating the steady state of multicellular sheroids by revisiting the two-fluid model

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  • In our paper [1], equation (45) has been reported incorrectly. Its actual form is as follows: \begin{align}\label{stresscont3} \frac{2\gamma}{R}=&\frac{1}{\nu(1-\nu)}\frac{\chi R^2}{3K}\left\{\frac{R} {\rho_D^{}} \left[1-\left(\frac{\rho_P^{}}{R}\right)^3\right]-\frac{3}{2}\left[1-\left( \frac{\rho_P^{}}{R}\right)^2\right]\right\} \nonumber\\ +&\frac{4}{3}\eta_C\chi\left(\frac{R}{\rho_D^{}}\right)^3\left[1-\left( \frac{\rho_P^{}}{R}\right)^3\right] \nonumber\\ +&2\sqrt{3}\tau_0\left[\ln\frac{\rho_P^{}}{\rho_D^{}}+\frac{1}{3}\ln \frac{\sqrt{2}(\frac{R}{\rho_P^{}})^3 + \sqrt{1+2(\frac{R}{\rho_P^{}})^6}} {\sqrt{2}+\sqrt{3}}\right]. \end{align} The comments that followed Eq. (45) then change accordingly. It is immediate to realize that the presence of $\tau_0$ has two effects: it increases the minimal value of the surface tension needed for the existence of the steady state, and, given $\gamma$, if (45) has a solution this solution is greater than the solution of (35). However, since it is possible that the surface tension $\gamma$ has a monotone dependence on the yield stress $\tau_0$ (both these quantity have their physical origin in the intercellular adhesion bonds), a partial compensation of the effect of the yield stress on the determination of $R$ can be expected.

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  • [1]

    A. Fasano, M. Gabrielli and A. Gandolfi, Investigating the steady state of multicellular spheroids by revisiting the two-fluid model, Math. Biosci. Eng., 8 (2011), 239-252.doi: 10.3934/mbe.2011.8.239.

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