Mathematical models of naturally "morphed" human erythrocytes: stomatocytes and echinocytes

Bulletin of Mathematical Biology
Timothy J Larkin, Philip W Kuchel

Abstract

We present two mathematical models that describe human red blood cells (RBCs) with morphologies that are attained naturally under certain patho-physiological conditions, namely stomatocytes and echinocytes. Muñoz San Martín et al. (Bioelectromagnetics 27:521-527, 2006) recently presented models of these shapes based on our previous set of parametric equations (Kuchel and Fackerell, Bull. Math. Biol. 61:209-220, 1999) that involve Jacobi elliptic functions and integrals. Thus, both discocytes and stomatocytes are described. Here, we derived the Cartesian forms of these new equations; and, in addition, present a realistic model of a Type III echinocyte, using prolate spheroids 'decorating' a central sphere at the vertices of an internal dodecahedron. The RBC models based on Cartesian equations have been used for representing the shape changes (morphological transformations or "morphing") that occur in RBCs under various experimental conditions; specifically, when the shape changes have been monitored by nuclear magnetic resonance (NMR) micro-imaging.

References

Dec 21, 1978·Journal of Theoretical Biology·J S Beck
Jun 1, 1983·Canadian Journal of Physiology and Pharmacology·H W Vayo
Mar 15, 1980·Experientia·R MartinoA Di Marco
Mar 28, 2002·Biophysical Journal·Ranjan MukhopadhyayMichael Wortis
Dec 10, 2002·Proceedings of the National Academy of Sciences of the United States of America·Gerald Lim H WRanjan Mukhopadhyay
Jun 24, 2003·Physics in Medicine and Biology·Martín S Muñoz SanJ M Miranda
Sep 19, 2003·European Biophysics Journal : EBJ·D KuzmanB Zeks
Oct 30, 2004·Bioelectromagnetics·S MuñozJ M Miranda
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·José Luis SebastiánGabriel Alvarez
Sep 22, 2007·Bulletin of Mathematical Biology·P W Kuchel, E D Fackerell
Nov 26, 2008·Journal of Magnetic Resonance Imaging : JMRI·Guilhem PagesPhilip W Kuchel
Apr 29, 2009·European Biophysics Journal : EBJ·Timothy J Larkin, Philip W Kuchel

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Citations

May 31, 2012·European Biophysics Journal : EBJ·Timothy J LarkinPhilip W Kuchel
Nov 7, 2013·Biochimica Et Biophysica Acta·S MuñozG Alvarez
Apr 10, 2019·Polymers·Marina VoinovaLeonid Gorelik

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