Among the broad palette of surgical techniques employed in the current orthopaedic practice, joint replacement represents one of the most difficult and costliest surgical procedures. While numerous recent advances suggest that computer assistance can dramatically improve the precision and long term outcomes of joint arthroplasty even in the hands of experienced surgeons, many of the joint replacement protocols continue to rely almost exclusively on an empirical basis that often entail a succession of trial and error maneuvers that can only be performed intraoperatively. Although the surgeon is generally unable to accurately and reliably predict a priori what the final malalignment will be or even what implant size should be used for a certain patient, the overarching goal of all arthroplastic procedures is to ensure that an appropriate match exists between the native and prosthetic axes of the articulation.

To address this relative lack of knowledge, the main objective of this thesis was to develop a comprehensive library of numerical techniques capable to:​ 1) accurately reconstruct the outer and inner geometry of the bone to be implanted;​ 2) determine the location of the native articular axis to be replicated by the implant;​ 3) assess the insertability of a certain implant within the endosteal canal of the bone to be implanted;​ 4) propose customized implant geometries capable to ensure minimal malalignments between native and prosthetic axes. The accuracy of the developed algorithms was validated through comparisons performed against conventional methods involving either contact-acquired data or navigated implantation approaches, while various customized implant designs proposed were tested with an original numerical implantation method.

It is anticipated that the proposed computer-based approaches will eliminate or at least diminish the need for undesirable trial and error implantation procedures in a sense that present error-prone intraoperative implant insertion decisions will be at least augmented if not even replaced by optimal computer-based solutions to offer reliable virtual “previews” of the future surgical procedure. While the entire thesis is focused on the elbow as the most challenging joint replacement surgery, many of the developed approaches are equally applicable to other upper or lower limb articulations.