A tissue retaining system having a pair of tissue retainers for retaining two end portions of tubular tissue, such as a heart valve, to a bioreactor is disclosed. Each tissue retainer includes a stepped portion that permits custom fitting of the tissue retainer to a particular size of tubular tissue. The stepped portion of each tissue retainer defines a plurality of progressively larger concentric steps in which one of the concentric steps matches the size of a particular tubular tissue being engaged. The tubular tissue is then anchored to the tissue retainer by suture pull downs that anchor the tubular tissue to one of the concentric steps of the tissue retainer in a fluid tight engagement. This engagement process is repeated to secure the other end portion of the tubular tissue to another tissue retainer such that the tissue retaining system may then be engaged to the bioreactor.
