The study and application of computational design is gaining importance in biomedical engineering as medical devices are becoming more complex, especially with the emergence of 3D printed scaffold structures. Scaffolds are medical devices that act as temporary mechanical support and facilitate biological interactions to regenerate damaged tissues. Past computational design studies have investigated the influence of geometric design in lattice structured scaffolds to investigate mechanical and biological behavior. However, these studies often focus on symmetric cubic structures leaving an opportunity for investigating a larger portion of the design space to find favorable scaffold configurations beyond these constraints. Here, tissue growth behavior is investigated for tetragonal Bravais lattice structured scaffolds by implementing a computational approach that combines a voxel-based design generation method, curvature-based tissue growth modeling, and a design mapping technique for selecting scaffold designs. Results show that tetragonal unit cells achieve higher specific tissue growth than cubic unit cells when investigated for a constant beam width, thus demonstrating the merits in investigating a larger portion of the design space. It is seen that cubic structures achieve around 50% specific growth, while tetragonal structures achieve more than 60% specific growth for the design space investigated. These findings demonstrate the need for continued adaption and use of computational design methodologies for biomedical applications, where the discovery of favorable solutions may significantly improve medical outcomes.