Volume 21, Issue 2
Mechanism Behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells

Xue-Jun Zhang & Zhong-Can Ou-Yang

Commun. Comput. Phys., 21 (2017), pp. 559-569.

Published online: 2018-04

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  • Abstract

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$$R_0$ has been predicted to be −1.62, the minus golden ratio, where $R_0$ is the radius of a sphere which has the same surface area as RBC. In this paper, we verify this prediction by comparing experimental data with an analytical equation describing the relation between volume and surface area. Furthermore, it is also found $ρ$max /$ρ_B$ ≈ 1.6 with $ρ$max the maximal radius and $ρ_B$ the characteristic radius of RBC, showing an approximate beautiful golden cross section of RBC. On the basis of a complete numerical calculation, we propose a mechanism behind the beauty of the minus golden ratio that $c_0$$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 "physical fitness test".

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@Article{CiCP-21-559, author = {}, 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 = {

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$$R_0$ has been predicted to be −1.62, the minus golden ratio, where $R_0$ is the radius of a sphere which has the same surface area as RBC. In this paper, we verify this prediction by comparing experimental data with an analytical equation describing the relation between volume and surface area. Furthermore, it is also found $ρ$max /$ρ_B$ ≈ 1.6 with $ρ$max the maximal radius and $ρ_B$ the characteristic radius of RBC, showing an approximate beautiful golden cross section of RBC. On the basis of a complete numerical calculation, we propose a mechanism behind the beauty of the minus golden ratio that $c_0$$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 "physical fitness test".

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0205}, url = {http://global-sci.org/intro/article_detail/cicp/11250.html} }
TY - JOUR T1 - Mechanism Behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells JO - Communications in Computational Physics VL - 2 SP - 559 EP - 569 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0205 UR - https://global-sci.org/intro/article_detail/cicp/11250.html KW - AB -

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$$R_0$ has been predicted to be −1.62, the minus golden ratio, where $R_0$ is the radius of a sphere which has the same surface area as RBC. In this paper, we verify this prediction by comparing experimental data with an analytical equation describing the relation between volume and surface area. Furthermore, it is also found $ρ$max /$ρ_B$ ≈ 1.6 with $ρ$max the maximal radius and $ρ_B$ the characteristic radius of RBC, showing an approximate beautiful golden cross section of RBC. On the basis of a complete numerical calculation, we propose a mechanism behind the beauty of the minus golden ratio that $c_0$$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 "physical fitness test".

Xue-Jun Zhang & Zhong-Can Ou-Yang. (2020). Mechanism Behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells. Communications in Computational Physics. 21 (2). 559-569. doi:10.4208/cicp.OA-2016-0205
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