Low frequency behavior of blood

The interfacial polarization of blood is a function of dielectric properties of its constituents: cellular structures and plasma. Dielectric studies of blood considered only plasma and RBC properties, since RBCs constitute more than 99% of cells by volume¹⁹. The Cole–Cole model is used to represent β dispersion of blood. A correlation between the Cole–Cole parameters and physical properties of RBCs could be made using Hanai’s mixture equation (Eq. ⁸) and the single shell model for biological cells assuming the following approximations: the membrane conductivity is negligibly small compared with the conductivity of the cell interior (by a factor of ∼10-5,³⁹); the membrane thickness is negligibly smaller than the cell radius (the cell membrane is in nm range while RBCs are in μm range); the low frequency conductivity of cells is negligibly smaller than that of the external medium as the cell membrane is made mostly of poorly conducting lipids. As a result, the low frequency dielectric behavior of blood is⁴⁰,

where subscripts c, and 0 stand for cell and low frequency limit, respectively, and σDC is the conductivity at DC. In the above equation, εc,0 is the low frequency permittivity of an RBC, and using the above approximations, it takes the following form⁴¹,

where Cmem is the membrane capacitance, r is the equivalent cell radius, and εv is vacuum permittivity.