The Search of Cell Positioning in Electrorotation Measurements

Abstract

Electrorotation (ROT) is a wide-used technique to measure the dielectric properties of cells. But the posi- tion of the cell in the measurement brings the error for the non-uniform of the ROT torque. In this paper, The Schwarz-Christoffel mapping (SCM) method was used for obtaining the accurate analytical solution of the ROT torque and the dielectrophoretic (DEP) force distribution in the circular electrode structure. A uniform electric field in the near central region of the circular electrode structure for ROT measurement was defined, which the radius is about 36% of the circular electrode structure's radius. The more, we found that before the ROT measurement, an additional conventional negative dielectrophoretic (nDEP) step can assist the cells well positioning. The analysis of the distribution of the DEP force at nDEP step was described in the paper also using SCM method. measurement, such as robustness and accuracy. So an accurately analysis is needed to correct the error caused by the difference of the cell position. The accurate analytical electric field solutions are generally difficult to obtain, due to the complicated structures of the microelectrodes. In this paper, the electric field generated by the ROT circular electrode structure was calculated by using the Schwarz-Christoffel mapping (SCM) method (11) and an analytical solution for the electric field in the proposed ROT measurements was achieved. The SCM method has been used to solve problems in electrostatics and magnetostatics (12, 13), transmission line and waveguides (12-14), temperature distribution and heat-transfer (15, 16) and fluid flow (17). Latterly, conformal mapping has been used to analyze electromagnetic field problem in micro electro- mechanical system (MEMS) devices (18). The more, Tao Sun et al. used this method to get the accurate analytical solution of DEP force and twDEP force for four-phase periodic potential in the twDEP electrode array (19). Because the SCM method requires no approximations, the results can be expressed exactly and be used straight forward. In this paper, we use the SCM method to solve the electric field and electrorotational torque in the circular electrode structure accurately. In the result, we find that the nearer to the center of the electrodes, the smaller of the variation of the electric field and the magnitude of ROT torque, where called as roughly uniform electric field. This conclusion is quite consistent with our experimental results in previous works (20). In this paper, we discussed the size of the uniform electric field and the relation between its size and the electrode's size. In previous works(21), we found that using nDEP force assisted positioning cells before ROT measurements to avoid the influence of the non-uniformity of electric field is a more efficient method. Using the SCM method, the accurately analysis of the nDEP force was also described below.