On the different models describing the equilibrium shape of an erythrocyte (original) (raw)

Abstract

As one of the most important types of blood cells in all vertebrate, the study of the equilibrium shape of erythrocytes is of great importance for the understanding of physicochemical and mechanical properties. The present paper is a summary of the existing models and methods to describe the shape of a red blood cell. Starting with the simplest known model – the one based on the Cassini ovals and finishing with the general shape equation for axisymmetric fluid membranes, we compare each model with a set of experimental data. The aim is to classify the models and give suggestions when and for what purpose they can be used, as for example in analytical studies of interactions between the erythrocytes, diagnostics based on shape distribution, experimental study through light scattering etc.

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What models effectively describe the equilibrium shape of erythrocytes?add

The analysis includes Beck's model, Cassinian ovals, Kuchel-Fackerell, Yurkin, Fung-Tong, and Evans-Fung models, each offering varying complexity and accuracy. Notably, Yurkin’s modifications provided significant improvements in shape modeling compared to prior models.

How do Cassinian ovals relate to RBC shape modeling?add

Cassinian ovals serve as a foundational technique for modeling RBC shape, with parameters a and c defining the meridional cross-section. The relationship between these parameters and RBC characteristics varies, leading to multiple potential configurations of the RBC shape.

What are the morphological parameters critical for RBC modeling?add

Key morphological parameters include the maximum thickness (τ max), minimum thickness (τ min), and diameters (D and d). These parameters are essential for calculating the surface area, volume, and sphericity index across various models.

When does the uniqueness in the RBC modeling parameters occur?add

Uniqueness in relationships between modeling parameters and morphological ones is achieved through modified equations that introduce additional degrees of freedom. This was particularly evident when conditions of ε approached infinity, simplifying the model to that of a sphere.

How do RBC models contribute to understanding blood disorders?add

These models provide critical insights into the biophysical properties of RBCs, which are indicators of various blood disorders. For instance, deviations from predicted shapes may signal conditions such as sickle cell anemia or malaria.

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