An apparatus for applying an alternating electric field to a living subject, the apparatus comprising: a flex circuit (25; 145) that includes at least one first conductive pad (20; 140; 310; 410; 500) positioned on a front side of the flex circuit (25; 145), each first conductive pad (20; 140; 310; 410; 500) having a first area, a plurality of second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) positioned on the front side of the flex circuit (25; 145) at locations that are peripheral with respect to the at least one first conductive pad (20; 140; 310; 410; 500), each of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) having a respective area that is at least 10% smaller than the first area, and at least one conductive trace disposed in electrical contact with the at least one first conductive pad (20; 140; 310; 410; 500) and the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500), wherein the at least one conductive trace is arranged so that each first conductive pad (20; 140; 310; 410; 500) and each of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) can be driven by an electrical signal; at least one first flexible polymer region, each first polymer region having a front face and being disposed over and in front of a respective one of each first conductive pad (20; 140; 310; 410; 500) on the front side of the flex circuit (25; 145); and a plurality of second flexible polymer regions, each of the second polymer regions having a front face and being disposed over and in front of a respective one of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) on the front side of the flex circuit (25; 145); wherein, at at least one frequency between 100 kHz and 500 kHz, each of the polymer regions has a dielectric constant of at least 20, and each of the polymer regions has a thickness of less than 20 μm in a direction perpendicular to its front face. a flex circuit (25; 145) that includes at least one first conductive pad (20; 140; 310; 410; 500) positioned on a front side of the flex circuit (25; 145), each first conductive pad (20; 140; 310; 410; 500) having a first area, a plurality of second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) positioned on the front side of the flex circuit (25; 145) at locations that are peripheral with respect to the at least one first conductive pad (20; 140; 310; 410; 500), each of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) having a respective area that is at least 10% smaller than the first area, and at least one conductive trace disposed in electrical contact with the at least one first conductive pad (20; 140; 310; 410; 500) and the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500), wherein the at least one conductive trace is arranged so that each first conductive pad (20; 140; 310; 410; 500) and each of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) can be driven by an electrical signal; at least one first flexible polymer region, each first polymer region having a front face and being disposed over and in front of a respective one of each first conductive pad (20; 140; 310; 410; 500) on the front side of the flex circuit (25; 145); and a plurality of second flexible polymer regions, each of the second polymer regions having a front face and being disposed over and in front of a respective one of the second conductive pads (20; 140; 320, 330, 340; 420, 430; 500) on the front side of the flex circuit (25; 145); wherein, at at least one frequency between 100 kHz and 500 kHz, each of the polymer regions has a dielectric constant of at least 20, and each of the polymer regions has a thickness of less than 20 μm in a direction perpendicular to its front face.