A discrete geometric approach to cell membrane and electrode contact impedance modeling

This paper presents a novel discrete model for cell membranes and electrodes contact impedances alternative to the widely used finite elements. The finite element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate the specific electroquasistatic biological problem on the discrete level. Although the finite element technique is explained typically in terms of variational or weighted-residual approaches, another, less familiar way is available to reformulate geometrically the same physical problem. This approach, referred to as discrete geometric approach, allows a direct link between geometry and the degrees of freedom describing the specific biological problem. It is straightforward to implement in any finite element open software and it assures a correct modeling of voltages and currents playing a fundamental role in a biological problem. The validation has been performed, as a first step, against analytical solutions; then, we considered impedance measurements regarding erythrocytes in whole blood flowing in microchannels at high shear rates.