Passive electrical properties of RBC suspensions: changes due to distribution of relaxation times in dependence on the cell volume fraction and medium conductivity

The intra- and extracellular conductivity, κa and κi as well as the cell membrane capacitance Cm of RBC suspensions are often calculated using the Pauly and Schwan equations which neglected the parameter α of the empirical Cole–Cole function. However, in complex materials such as RBC suspensions with several overlapping relaxation processes the total electrical response is characterized by a broad distribution of relaxation times yielding an α>0. The locus diagram in the conductivity-plane (κ-plane) is a depressed semicircle with the center below the real axis. It is suggested, that α characterizes both the distribution in relaxation times and the interaction between the relaxing units. Here we focus on the influence of interaction on α. Therefore complex conductivity measurements were done on RBC suspensions with the hematocrit p and the conductivity κ of the medium as parameter. The hematocrit was varied from 0.04 to 0.95 while three different media (κ=1.447 S/m, 0.571 S/m, and 0.064 S/m) were chosen. From this we could evaluate the dependence of α on the interactions of the cells. The electrical parameters of the suspension were calculated by the Pauly and Schwan equations and correlated with the hematocrit. The correct value is obtained at low p when α is small (p and α<0.1), because the Pauly and Schwan equations are derived under the presumption of low cell concentration. We compared our values with findings from cell rotation experiments. We propose an algorithm to estimate the correct passive electrical values from measurements carried out at higher p values.