A cell culture matrix for a perfusion-flow fixed-bed reactor is provided. The cell culture matrix includes a substrate having a porous sheet for adhering cells thereto. The sheet has a first side, a second side opposite the first side, a thickness separating the first side and the second side, and a plurality of openings formed in the substrate, arrayed in a regular pattern, and passing through the thickness of the substrate. The porous sheet is wound into a cylindrical shape having a plurality of wound layers, and the cell culture matrix does not include a spacer material or physical barrier between the plurality of wound layers of the substrate.