Medical Image Analysis 5 (2001) 317–330 www.elsevier.com / locate / media q A computational model of postoperative knee kinematics * E. Chen, R.E. Ellis , J.T. Bryant, J.F. Rudan Computing and Information Science, Mechanical Engineering, Surgery, Queen’ s University, Kingston, Ontario, Canada K7L 3N6 Received 18 December 2000; received in revised form 28 May 2001; accepted 18 July 2001 Abstract A mathematical model for studying the passive kinematics of total knee prostheses can be useful in computer-aided planning and guidance of total joint replacement. If the insertion location and neutral length of knee ligaments is known, the passive kinematics of the knee can be calculated by minimizing the strain energy stored in the ligaments at any angular configuration of the knee. Insertions may be found intraoperatively, or may come from preoperative 3D medical images. The model considered here takes into consideration the geometry of the prosthesis and patient-specific information. This model can be used to study the kinematics of the knee joint of a patient after total joint replacement. The model may be useful in preoperative planning, computer-aided intraoperative guidance, and the design of new prosthetic joints.  2001 Elsevier Science B.V. All rights reserved. Keywords: Knee; Computer model; Simulation; Total knee arthroplasty; Kinematics 1. Introduction the anterior cruciate ligament (ACL) and, depending on the prosthesis design, may also involve removal of the poste- One of the major goals of total knee replacement is to rior cruciate ligament (PCL). The medial collateral liga- restore the normal function of the knee. The success of ment (MCL) and lateral collateral ligament (LCL) are restoring a patient’s knee function depends, among other critical in holding the joint in place and producing joint factors, on the design and implantation placement of the motion. Fig. 1 shows the knee before and after implanta- prosthesis. The function of the knee after total joint tion of the prosthetic components. replacement is heavily influenced by the design of the In passive knee motion, where no external forces are prosthesis and the surgical placement of the prosthetic present, the femur is kept in contact with the tibia by the devices (Garg and Walker, 1990). This work presents a tensile forces exerted by the surrounding soft tissues. The computational technique for understanding knee motion, geometry of the articular surfaces provides a set of feasible with a primary goal of producing improved computer- contact locations that determine the orientation of the knee. aided implantation of artificial knee joints. The interaction of the surrounding ligaments thus governs A set of knee-prosthesis components consists of: an the contact conditions of the knee. It is supposed here that, anatomically shaped distal femoral element, normally at any given angulation, the contact condition that the knee made of a cobalt-based alloy; a proximal tibial element would naturally assume is the contact condition that would that is normally made of ultra-high-molecular-weight minimize the total strain energy stored in the ligaments of polyethylene (hereafter, simply ‘‘polyethylene’’); and an the knee. optional patellar insert, typically made of polyethylene. The theoretical goal of this work was to understand Implantation of a prosthesis typically requires removal of interactions between the geometry of the articular surfaces and the surrounding ligaments and to study how such q interactions affect the overall kinematics of the knee. The Electronic Annexes available. See www.elsevier.com / locate / media. passive kinematics were analyzed as the instantaneous *Corresponding author. E-mail address: ellis@cs.queensu.ca (R.E. Ellis). quasi-static solution to ligament strain-energy minimiza- 1361-8415 / 01 / $ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII: S1361-8415(01)00049-4