# American Institute of Mathematical Sciences

2012, 9(3): 697-697. doi: 10.3934/mbe.2012.9.697

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

 1 Università degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, Firenze 2 Dipartimento di Matematica "U. Dini", Universita' di Firenze, Viale Morgagni 67/A, 50134 Firenze 3 Istituto di Analisi dei Sistemi ed Informatica ''A. Ruberti", CNR, Viale Manzoni 30, 00185 Roma

Received  July 2012 Published  July 2012

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.

Citation: Antonio Fasano, Marco Gabrielli, Alberto Gandolfi. Erratum to: Investigating the steady state of multicellular sheroids by revisiting the two-fluid model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 697-697. doi: 10.3934/mbe.2012.9.697
##### References:
 [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.  doi: 10.3934/mbe.2011.8.239.  Google Scholar

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##### References:
 [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.  doi: 10.3934/mbe.2011.8.239.  Google Scholar
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