Biconcave disc

In geometry and mathematical biology, a biconcave disc — also referred to as a discocyte^[1] — is a geometric shape resembling an oblate spheroid with two concavities on the top and on the bottom.

Biconcave discs appear in the study of cell biology, as an approximation to the shape of certain cells, including red blood cells.

Mathematical model

A biconcave disc can be described mathematically by

z(r)=D{\sqrt {1-{\frac {4r^{2}}{D^{2}}}}}\left(a_{0}+{\frac {a_{1}r^{2}}{D^{2}}}+{\frac {a_{2}r^{4}}{D^{4}}}\right)

where $z(r)$ is the height of the surface as a function of radius $r$ , $D$ is the diameter of the disc, and $a 0, a 1, a 2$ are coefficients describing the shape. The above model describes a smooth surface; actual cells can be much more irregular.

Biology

Erythrocytes (also known as Red Blood Cells) are in the shape of a biconcave disc. An erythrocyte is also known as a red blood cell and transports oxygen to and from tissues.^[1]^[2]

References

^ ^a ^b Kuchel, Philip W.; Fackerell, Edward D. (1999). "Parametric-equation representation of biconcave erythrocytes". Bulletin of Mathematical Biology. 61 (2): 209–220. doi:10.1006/bulm.1998.0064. ISSN 1522-9602. PMID 17883208. S2CID 39585695.
^ Muñoz, Sagrario; Sebastián, José L.; Sancho, Miguel F.; Álvarez, Gabriel (2014-03-01). "Elastic energy of the discocyte–stomatocyte transformation". Biochimica et Biophysica Acta (BBA) - Biomembranes. 1838 (3): 950–956. doi:10.1016/j.bbamem.2013.10.020. ISSN 0005-2736. PMID 24192054.

3. Ineza careen shija (2009)https://www.google.com/search?q=biology+careen&oq=biology+careen&gs_lcrp=EgZjaHJvbWUyBggA

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[kuchelfackerell-1] Kuchel, Philip W.; Fackerell, Edward D. (1999). "Parametric-equation representation of biconcave erythrocytes". Bulletin of Mathematical Biology. 61 (2): 209–220. doi:10.1006/bulm.1998.0064. ISSN 1522-9602. PMID 17883208. S2CID 39585695.

[2] Muñoz, Sagrario; Sebastián, José L.; Sancho, Miguel F.; Álvarez, Gabriel (2014-03-01). "Elastic energy of the discocyte–stomatocyte transformation". Biochimica et Biophysica Acta (BBA) - Biomembranes. 1838 (3): 950–956. doi:10.1016/j.bbamem.2013.10.020. ISSN 0005-2736. PMID 24192054.

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