School of Molecular and Microbial Biosciences, Building G08, University of Sydney, Sydney, NSW, 2006, Australia.
Bull Math Biol. 2010 Aug;72(6):1323-33. doi: 10.1007/s11538-009-9493-8. Epub 2010 Feb 2.
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.
我们提出了两个数学模型，描述了在某些病理生理条件下自然获得的具有特定形态的人类红细胞（RBC），即口形红细胞和棘形红细胞。Muñoz San Martín 等人（Bioelectromagnetics 27:521-527, 2006）最近根据我们之前的一组参数方程（Kuchel 和 Fackerell, Bull. Math. Biol. 61:209-220, 1999）提出了这些形状的模型，这些方程涉及雅可比椭圆函数和积分。因此，同时描述了盘状红细胞和口形红细胞。在这里，我们推导出了这些新方程的笛卡尔形式；此外，还使用位于内部十二面体顶点处的中心球体上的拉长球体“装饰”，提出了一个真实的 III 型棘形红细胞模型。基于笛卡尔方程的 RBC 模型已被用于表示在各种实验条件下 RBC 发生的形状变化（形态转变或“变形”）；具体来说，当通过核磁共振（NMR）微成像监测到形状变化时。
