The present invention provides an apparatus and a method to assemble organotypical tissues which can then be perfused and investigated under preferably physiological conditions. This is achieved by a microfluidic system for assembling and subsequently cultivating complex cell arrangements, comprising: a three-dimensional microstructure in which the cell arrangement is assembled and cultivated, at least two microchannel segments running in the microstructure and defining a flow direction, through which microchannel segments the microstructure can be perfused from outside with a medium, whereby the microchannel segments run approximately parallel or equidistant to one another at least in sections, a wall structure which separates the at least two microchannel segments and in which at least one aperture connecting the at least two microchannel segments is provided, and an electrode arrangement provided in or on the microstructure in order to generate an inhomogeneous electric field in the region of the at least one aperture.