Parametric-equation representation of biconcave erythrocytes

Bulletin of Mathematical Biology

Volumn 61, Issue 2, 1999, Pages 209-220

  Kuchel, Philip W ^a   Fackerell, Edward D ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CONFOCAL MICROSCOPY; ERYTHROCYTE SHAPE; IMAGE ANALYSIS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NUCLEAR MAGNETIC RESONANCE IMAGING; TARGET CELL; THREE DIMENSIONAL IMAGING;

EID: 0033103468     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1006/bulm.1998.0064     Document Type: Article

References (22)

1. Adams, K. H. (1973). A theory for the shape of the red blood cell. Biophys. J. 13, 1049-1053.
2. Beck, J. S. (1978). Relations between membrane monolayers in some red cell shape transformations. J. Theor. Biol. 75, 487-501.
3. Blachman N. R. and M. J. Mossinghoff (1994). Maple V Quick Reference. Pacific Grove, CA: Brooks/Cole.
4. Bowman, F. (1961). Introduction to elliptic functions. New York, NY: Dover.
5. Dixon, A. C. (1894). The Elementary Properties of the Elliptic Functions with Examples London: Macmillan.
6. Evans, E., and Y.-C. Fung (1972). Improved measurements of the erythrocyte geometry. Microvasc. Res. 4, 335-342.
7. Funaki, H. (1955). Contributions on the shapes of red blood corpuscles. Jpn. J. Physiol. 5, 81-92.
8. Glaser, R. (1979). The shape of red blood cells as a function of membrane potential and temperature. J. Membr. Biol. 51, 217-228.
9. Gulliver, G. (1875). Observations on the sizes and shapes of the red corpuscles of the blood of vertebrates, with drawings of them to a uniform scale, and extended revised tables of measurements. Proc. Zool. Soc. Lond. June 15, 474-495.
10. Hoffman, J. (1987). On the mechanism and measurement of shape transformations of constant volume of human red blood cells. Blood Cells 12, 565-586.
11. Kuchel, P. W., B. T. Bulliman and E. D. Fackerell (1987). Bi-cyclide and flat-ring cyclide coordinate surfaces: Correction of two expressions. Math. Comput. 49, 607-613.
12. Kuchel, P. W. and B. T. Bulliman (1988). Expressions for surfaces in disk-cyclide coordinates: Derivations using symbolic computation. J. Franklin. Inst. 325, 505-508.
13. Kuchel, P. W., and B. T. Bulliman (1989). Perturbation of homogeneous magnetic fields by isolated single and confocal spheroids. Implications for NMR spectroscopy of cells. NMR Biomed. 2, 151-160.
14. Kuchel, P. W., A. Coy, and P. Stilbs (1997). NMR 'diffusion-diffraction' of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics. Magn Reson. Med. 37, 637-643.
15. Lennon, A J., N. Scott, B. E. Chapman and P. W. Kuchel (1995). Haemoglobin affinity for 2,3-bisphosphoglycerate in solutions and intact erythrocytes: Studies using pulsed field gradient NMR and Monte Carlo simulations. Biophys. J. 67, 2096-2109.
16. Moon, P. and D. E. Spencer (1951). Cylindrical and rotational coordinate systems. J. Franklin Inst. 252, 327-344.
17. Moon, P. and D. E. Spencer (1953). Some coordinate systems associated with elliptic functions. J. Franklin Inst. 255, 531-543.
18. Moon, P. and D. E. Spencer (1961). Field Theory for Engineers. Princeton, NJ: Van-Nostrand.
19. Moon, P. and D. E. Spencer (1988). Field Theory Handbook. Including Coordinate Systems Differential Equations and Their Solutions. Berlin: Springer-Verlag.
20. Torres, A. M., R. J. Michniewicz, B. E. Chapman, G. A. R. Young and P. W. Kuchel (1998). Characterisation of erythrocyte shapes and sizes by NMR diffusion-diffraction of water: Correlation with electron micrographs. Magn. Reson. Imag. (In Press).
21. Vayo, H. W. (1983). Some red blood cell geometry. Can. J. Physiol. Pharmacol. 61, 646-649.
22. Wolfram S. (1996). Mathematica: A System for Doing Mathematics by Computer, Version 3. Redwood City, CA: Addison-Wesley.