Comparison of Computational Methods for the Estimation of the Dielectrophoretic Force Acting on Biological Cells and Aggregates in Silicon Lab-on-chip

Dielectrophoresis (DEP) has been reported as a promising method for cell manipulation without physical contact in miniaturized devices since it exploits the dielectric properties of cells and/or cellular aggregates suspended in a fluid and subjected to a variable gradient electric field E [1]. The mathematical expression of the DEP force is obtained by a multipole expansion of the force itself whose terms involve increasing power of the particle's radius r and subsequent field derivatives. For a single cell, a widely treated situation in literature, the dipole approximation, depending on the third power of r and on the square of the field gradient, is reported to be enough accurate in most cases. However, when the aggregate's radius and/or the field non-uniformity factor become big, more terms in the multipole expansion should be considered [2]. This means that higher order electric field derivatives are introduced and the Weak Form, PDE Mode is added to the AC/DC, Quasi-statics Module, already used in the dipole case to compute E. In this way, the accuracy is improved, but the numerical stability is worsened due to the high order derivatives operator. The aim of this work is to find two numerical indices that permit to decide, given the aggregate radius and the field non-uniformity estimate, which computational method should be used. Indeed, performing several simulations for different radii and field non-uniformity values it is possible to compare the results for the force got using dipole, quadrupole or discrete approximation. In this sense, some functions for the measure of the difference between the various methods' solutions are defined and suitable threshold values are chosen allowing the creation of a graph that, given theaggregate's radius and the field non-uniformity estimate, shows which method should be used (Figure 1). Lastly, the comparison with some experiments is performed both in case of single Saccharomyces cerevisiae yeast cells and of Langerhans islets cellular aggregates and the results agree with the simulations (Figure 2).