Commit 45cfacf7 authored by Turnhout, M.C. van's avatar Turnhout, M.C. van
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add 'length', Ld/L is not much smaller than 1

parent e3162f6e
......@@ -753,11 +753,11 @@ Isotropic constructs curl well and the parameter space might have been evaluated
We are fitting a linear model to parameters that may not respond linearly, if only because of the geometrical effects of film curling. Furthermore, the response of the model as function of $\sigma_x$ shows unexpected non-linear effects around $\sigma_x = 0.007$\,MPa for the main read-out $\frac{l}{L}$ (figure \ref{fig:pspaceiso_lL_as}). We hypothesised that some geometrical effect in film curling may predominantly occur around $\sigma_x = 0.007$\,MPa, and a more in-depth analysis of the non-linear (geometrical) effects on film curling in this isotropic parameter space is certainly warranted.\\
\noindent The analysis of film curvature from projected edge does not account for asymmetric boundary conditions and curling edge effects (figure \ref{isospace_dk_fig}), but it is a good estimation for the actual mean local curvature over the length of the constructs (figure \ref{isospace_dR_fig}). Furthermore, constructs hardly change length during curling (figure \ref{isospace_dL_fig}), and these small changes in length only affect the analysis for $l > \frac{2L_d}{\piup}$, by a fraction $\abs{\frac{L_d}{L}} \ll 1$.
\noindent The analysis of film curvature from projected edge does not account for asymmetric boundary conditions and curling edge effects (figure \ref{isospace_dk_fig}), but it is a good estimation for the actual mean local curvature over the length of the constructs (figure \ref{isospace_dR_fig}). Furthermore, constructs hardly change length during curling (figure \ref{isospace_dL_fig}), and these small changes in length only affect the analysis for $l > \frac{2L_d}{\piup}$, by a factor of $\left|\frac{L_d}{L}\right| \simeq 1$.
Grossberg \textsl{et al.} remark that \cite{Grosberg2011}: ``For $x$-projections approaching the length of the film, the radius of curvature increases rapidly; however, that does not negatively impact the accuracy of the stress calculations because the stress at large radius of curvature is very small compared to peak systole.'' We already argued that projected edge $\frac{l}{L}$ is a better metric for $\sigma_x$ than curvature $R$, but we note that $l$ too, is more accurately estimated for constructs that `curl more'.
Grossberg \textsl{et al.} remark that \cite{Grosberg2011}: ``For $x$-projections approaching the length of the film, the radius of curvature increases rapidly; however, that does not negatively impact the accuracy of the stress calculations because the stress at large radius of curvature is very small compared to peak systole.'' We already argued that projected edge length $\frac{l}{L}$ is a better metric for $\sigma_x$ than curvature $R$, but we note that $l$ too, is more accurately estimated for constructs that `curl more'.
Al in all, we can conclude that the analysis of film curvature $R$ from projected edge $\frac{l}{L}$ is valid assessment of cell traction stresses $\sigma_x$ in isotropic constructs. \\
Al in all, we can conclude that the analysis of film curvature $R$ from projected edge length $\frac{l}{L}$ is valid assessment of cell traction stresses $\sigma_x$ in isotropic constructs. \\
\noindent Alford \textsl{et al.} performed an analytical parameter space analysis of free curling constructs with $\nu_\text{film} = \nu_\text{cells} = 0.5$ \cite[figure 5]{Alford2010}. The results of our analysis qualitatively agree with theirs: film thickness and cell layer thickness have an opposite effect, cell layer stiffness has no effect. Alford \textsl{et al.} did not investigate film stiffness $E_\text{film}$. Our analysis suggests that this parameter may be the most important one (based on its coefficient), and that construct length $L$, also not investigated in \cite{Alford2010}, may be as important as cell layer thickness $t_\text{cells}$.
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