# An Anatomical-Based Subject-Specific Model of In-Vivo Knee Joint 3D Kinematics From Medical Imaging
## 1 Introduction  
Kinematic models of the knee aim at the description of the natural motion of the joint and have many clinically relevant applications, such as articular surface and ligament reconstructions, pre-operative plans [1], gait analysis and soft-tissue artifact compensation through multibody optimization techniques [2]. Many kinematic models of the knee were proposed [2, 3], most of them focusing on the tibo-femoral (TF) joint. Some of these models represent the knee joint as a rigid-link one-degree-of-freedom (1-DoF) mechanism, based on the experimental evidence that, in unloaded conditions, the joint motion exhibits 1-DoF and the joint passive structures show a minimal change in shape or length. Starting from planar models like the hinge and the four-bar linkage [4, 5] these representations evolved into spatial models [6, 7, 8] guided by ligaments and articular surfaces [4, 8, 9, 10, 11, 12]. These spatial models were able also to describe the out-of-plane components of the knee motion, by representing the connection between anatomical structures and joint motion in 3D. Based onthe same principles, three-dimensional kinematic models of the knee joint including also the patello-femoral (PF) joint were proposed [13; 14]. All these models were mainly defined and validated in vitro, using techniques hardly exploitable in vivo in the standard clinical practice, like dissection for anatomical geometry and bone pins for kinematic measurements. However, great attention was devoted recently to develop subject-specific medical procedures and devices customized on the single patient [1; 15; 16]. Therefore, the definition of kinematic models that reproduce the anatomy and the motion of the specific patient in vivo is gathering a growing importance. In this case, personalization and identification of the model geometry are the main problems, since only non-invasive measures can be performed in vivo, and these often present limitations on the quality, type and quantity of the acquired data. A common practice is scaling a generic model to fit specific dimensions of the single subject using corresponding anatomical landmarks [17; 18; 19; 20]. Nevertheless, scaling considers only the gross anthropometry of the subject, disregarding all its distinctive features (ligament attachment positions on the bones, articular surface shapes). Eventually, the final model does not reproduce either the anatomy or the kinematics of the joint and thus it is not actually personalized [21]. An alternative approach is using medical images to personalize the model geometry on the subject anatomy. However, model customization in vivo is not straightforward, particularly for complex spatial models due to the higher number of parameters to be identified and the increased sensitivity to their variations [22; 23]. For these reasons, as a recent review demonstrates [2], simplified representations of the knee joint such as the hinge and the four-bar linkage are often preferred. Whereas these models have the advantage of being based on fewer parameters, they are far from an accurate 3D representation of the behaviour of the knee joint and of its anatomical structures [20; 24]. Several studies investigated the importance of anatomical accuracy of joint models in musculoskeletal modelling [25; 26], concluding that the use of models with a strong anatomical foundation leads to more reliable estimations of motion and forces (i.e., joint reactions, ligament and musculo-tendinous forces) during gait. Nevertheless, only few subject-specific kinematic knee models with such features exist for in vivo applications. A first approach prescribes an experimentally measured joint motion within the musculoskeletal model, like, for instance, in the seminal work of [PERSON] and [PERSON] [27].