@Article{CiCP-21-559,
author = {Xue-Jun Zhang and Zhong-Can Ou-Yang},
title = {Mechanism Behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {2},
pages = {559--569},
abstract = {<p style="text-align: justify;">In the past two decades, a rigorous solution for the shape of human red
blood cell (RBC) with a negative spontaneous curvature $c_0$ has been derived with the
Helfrich model under the condition that both the osmotic pressure ∆$p$ and tensile stress $λ$ are equal to zero. By fitting the experimentally observed shape of RBC, $c_0$$R_0$ has been
predicted to be −1.62, the minus golden ratio, where $R_0$ is the radius of a sphere which
has the same surface area as RBC. In this paper, we verify this prediction by comparing
experimental data with an analytical equation describing the relation between volume
and surface area. Furthermore, it is also found $ρ$<sub>max</sub> /$ρ_B$ ≈ 1.6 with $ρ$<sub>max</sub>&nbsp;the maximal
radius and $ρ_B$ the characteristic radius of RBC, showing an approximate beautiful
golden cross section of RBC. On the basis of a complete numerical calculation, we
propose a mechanism behind the beauty of the minus golden ratio that $c_0$$R_0$ results
from the balance between the minimization of the surface area and the requirement
of adequate deformability of RBC to allow it passing through the spleen, the so called
&quot;physical fitness test&quot;.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0205},
url = {http://global-sci.org/intro/article_detail/cicp/11250.html}
}