  Modeling of the red blood cell (RBC) shape is an integral part of the
experimental and computer simulation investigations of light scattering by
these cells for fundamental studies as well as diagnostic applications in
techniques like cytometry and quantitative phase imaging. In the present work,
a comprehensive study of the geometrical characterization of healthy human RBCs
using digital holographic microscopy (DHM) and six frequently employed
parametric shape models is reported. It is shown that the comparison of the
optical phase profiles, and the thickness profiles given by the models with the
DHM results gives a better judgment of the appropriateness of the parametric
shape models. It is also shown that the RBC parametric models offer a simpler
solution to RI-thickness decoupling problem in QPI methods. Results of
geometrical characterization of 500 healthy RBCs in terms of volume, surface
area (SA), and sphericity index (SI) led to the classification of the
parametric models in two categories based on the nature of variation of these
quantities with the cell diameter. In light of the variability of the healthy
RBC shapes, our findings suggest that the parametric models exhibiting a
negative correlation between the SI and the cell diameter would provide more
reliable estimates of the RBC parameters in diagnostic applications.
Statistical distributions and descriptive statistics of the RBC volume, SA and
SI serve as a guide for the assessment of the capability of the studied
parametric models to give a reliable account of the variability of the healthy
RBC shape and size.
