Organ printing is a variant of the biomedical application of additive manufacturing (rapid prototyping) technology or layer-by-layer additive biofabrication of 3D tissue and organ constructs using self-assembled tissue spheroids as building blocks. Bioengineering of perfusable intraorgan branched vascular trees incorporated into 3D tissue constructs is essential for the survival of bioprinted thick 3D tissues and organs. In order to design the optimal 'blueprint' for digital bioprinting of intraorgan branched vascular trees, the coefficients of tissue retraction associated with post-printing vascular tissue spheroid fusion and remodeling must be determined and incorporated into the original CAD. Using living tissue spheroids assembled into ring-like and tube-like vascular tissue constructs, the coefficient of tissue retraction has been experimentally evaluated. It has been shown that the internal diameter of ring-like and the height of tubular-like tissue constructs are significantly reduced during tissue spheroid fusion. During the tissue fusion process, the individual tissue spheroids also change their shape from ball-like to a conus-like form. A simple formula for the calculation of the necessary number of tissue spheroids for biofabrication of ring-like structures of desirable diameter has been deduced. These data provide sufficient information to design optimal CAD for bioprinted branched vascular trees of different human organs desirable final geometry and size.