The following table shows the possible geometric models which can be applied to the red blood cell.
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Cube |
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Surface Area = 6a2 |
Volume = a3 |
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V/SA = a3/6a2 = a/6 |
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Sphere |
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Surface Area = 4p r2 |
Volume = 4/3 p r3 |
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V/SA = 4p r3/12p r2 = r/3 |
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Cylinder |
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Surface Area = 2p r2+2p rh |
Volume = p r2h |
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V/SA = p r2h/(2p r2+2p rh) |
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Torus |
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Surface Area = 4p 2Rr |
Volume = 2p 2Rr2 |
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V/SA = 2p 2Rr2/4p 2Rr = r/2 |
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| .Images were taken from http://www.geom.umn.edu/docs/reference/CRC-formulas/node60.html and http://www.sisweb.com/math/geometry/index.htm | |||
The following table contains experimental data from Evans and Fung (1972) which demonstrates that the shape and dimensions of the RBC changes depending on the tonicity (ratio of solutes to solvent) of a solution. When the solution is 300 mosmol, the solution is isotonic (net flow of liquid into the RBC equals net flow out). However when the solution is decreased to 217 mosmol and below, the solution is hypotonic (less particles in the solution than in the RBC's), thus fluid flows into the RBC causing it to expand. At 131 mosmol the RBC's become spherical.
| Tonicity (mosmol) | Diameter (micrometer) | Minimum Thickness (micrometer) | Maximum Thickness (micrometer) | Surface Area (square micrometers) | Volume (cubed micrometers) |
| 300 | 7.82 | 0.81 | 2.58 | 135 | 94 |
| 217 | 7.59 | 2.10 | 3.30 | 135 | 116 |
| 131 | 6.78 | *appears spherical* | 145 | 164 | |
The following table contains the average geometric data determined by Tsang (1975) with a sample size of 1581 cells from 14 individuals.
| Tonicity (mosmol) | Diameter (micrometer) | Minimum Thickness (micrometer) | Maximum Thickness (micrometer) | Surface Area (square micrometers) | Volume (cubed micrometers) |
| 300 | 7.65 | 1.44 | 2.84 | 129.95 | 97.91 |
PLEASE
NOTE: The dimensions of a normal red blood cell as shown in the diagram directly
above (from Tsang) should be used for your calculations.
