Theoretical Study of Molecular Transport Through a Permeabilized Cell Membrane in a Microchannel Masoumeh Mahboubi 1 • Saeid Movahed 1 • Reza Hosseini Abardeh 1 • Vahid Hoshyargar 2 Received: 28 February 2017 / Accepted: 20 April 2017 Ó Springer Science+Business Media New York 2017 Abstract A two-dimensional model is developed to study the molecular transport into an immersed cell in a microchannel and to investigate the effects of finite boundary (a cell is suspended in a microchannel), ampli- tude of electric pulse, and geometrical parameter (mi- crochannel height and size of electrodes) on cell uptake. Embedded electrodes on the walls of the microchannel generate the required electric pulse to permeabilize the cell membrane, pass the ions through the membrane, and transport them into the cell. The shape of electric pulses is square with the time span of 6 ms; their intensities are in the range of 2.2, 2.4, 2.6, 3 V. Numerical simulations have been performed to comprehensively investigate the molecular uptake into the cell. The obtained results of the current study demonstrate that calcium ions enter the cell from the anodic side (the side near positive electrode); after a while, the cell faces depletion of the calcium ions on a positive electrode-facing side within the microchannel; the duration of depletion depends on the amplitude of electric pulse and geometry that lasts from microseconds to mil- liseconds. By keeping geometrical parameters and time span constant, increment of a pulse intensity enhances molecular uptake and rate of propagation inside the cell. If a ratio of electrode size to cell diameter is larger than 1, the transported amount of Ca 2? into the cell, as well as the rate of propagation, will be significantly increased. By increasing the height of the microchannel, the rate of uptake is decreased. In an infinite domain, the peak con- centration becomes constant after reaching the maximum value; this value depends on the intra–extracellular con- ductivity and diffusion coefficient of interior and exterior domains of the cell. In comparison, the maximum con- centration is changed by geometrical parameters in the microchannel. After reaching the maximum value, the peak concentration reduces due to the depletion of Ca 2? ions within the microchannel. Electrophoretic velocity has a significant effect on the cell uptake. Keywords Electroporation  Electropermeabilization  Cell membrane  Cell uptake  Pore  Electrokinetic Introduction Cell membranes act as containers that enclose the inter- cellular contents of the cell; they also precisely regulate the mass transfer between interior and exterior domains of the cells. Various biological actuators (e.g., mechanical, elec- trical, and chemical) are used to modify the mass transfer through the cell membranes (Clarke and McNEIL 1992; Doherty and McMahon 2009; Dupont et al. 2015; Hapala 1997). Applying a sufficient electric pulse near the cell can induce the perturbation of the membrane structure and generate pores on its membrane which lasts from micro- to milliseconds. This process which is called classical elec- troporation or electropermeabilization can be performed in five steps: In the first step is induction during which the transmembrane potential (TMP) of the cell is induced to reach the critical threshold value by applying high external electric field. This step takes less than one microsecond. In & Saeid Movahed smovahed@aut.ac.ir 1 Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran 15875-4413, Iran 2 Research Lab for Advanced Separation Processes, Department of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran 123 J Membrane Biol DOI 10.1007/s00232-017-9961-2