Biconcave disc

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

A biconcave disc

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 a₀, a₁, a₂ are coefficients describing the shape. The above model describes a smooth surface; actual cells can be much more irregular.

Biology

Erythrocytes 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.