Biocompatible porous polymer membranes are prepared by dispersing salt particles in a biocompatible polymer solution. The solvent in which the polymer is dissolved is evaporated to produce a polymer/salt composite membrane. The polymer can then be heated and cooled at a predetermined constant rate to provide the desired amount of crystallinity. Salt particles are leached out of the membrane by immersing the membrane in water or another solvent for the salt but not the polymer. The membrane is dried, resulting in a porous, biocompatible membrane to which dissociated cells can attach and proliferate. A three-dimensional structure can be manufactured using the polymer membranes by preparing a contour drawing of the shape of the structure, determining the dimensions of thin cross-sectional layers of the shape, forming porous polymer membranes corresponding to the dimensions of the layers, and laminating the membranes together to form a three-dimensional matrix having the desired shape.