From: Leendert Blankevoort , Passive motion characteristics of the human knee joint -- Experiments and computer simulations (ISBN 90-9004358-6). PhD-thesis, 9 October 1991, Catholic University Nijmegen, The Netherlands CHAPTER I Introduction The knee joint is the largest joint in the human body, consisting of a complex arrangement of three bones (tibia, femur and patella), capsular and ligamentous structures, and the menisci interposed between femur and tibia. These passive structures determine the passive motion characteristics of the joint, expressed in terms like flexion range, anterior-posterior laxity, rotatory laxity and coupled varus-valgus rotations. The muscles and tendons crossing the joint interact with the knee structures, and function as active stabilizers during motion and loading in various activities. The actual motion patterns during level walking, for example, are governed by the interplay of the passive and active structures. The axial compressive loads transferred across the knee joint can be as high as 3 to 5 times body weight during level walking and stair climbing (Andriacchi et al., 1980; Cappozzo et al., 1984). The flexion-extension moments, which are the result of the muscle forces and their lever arms relative to the joint rotation axis, value approximately 60 Nm for normal level walking. The corresponding muscle forces are about two times body weight (Biden et al., 1990). When considering a flexion range of about 130 degrees, the knee combines large motions with high loads. Overloading of the knee may lead to injuries of the knee structures. The incidence of knee injuries in western society is estimated at over 2 per 1,000 population per year, as evidenced by the San Diego Kaiser study (Hirshman et al., 1990), in which an incidence of acute knee injuries (not including fractures and dislocations) was observed of 220 per 100,000 population per year. Of the acute knee injuries, 61 percent were caused during sports activities. Forty four percent were ligament injuries, the majority of which (27 percent) caused pathologic motion and laxity. Considering the incidence of acute knee injuries, over 33,000 cases are then presented each year to home physicians, first aid units and clinics, for a population of 15 million such as in the Netherlands. The number of patients with moderate and severe ligament injuries then values 9,000. Although the numbers are not directly comparable due to different classifications, the national hospital registration in the Netherlands confirms these estimates (SIG, 1990). In 1988, over 20,000 patients were admitted to Dutch hospitals with the main diagnosis of knee injury, which included all injuries to the internal structures of the knee, i.e. ligaments, menisci, capsule and articular cartilage. The majority of these patients were treated by orthopaedic surgeons (85 percent). The mean hospitalization period was five days per patient. Over 3,000 surgical restorations and reconstructions were performed of ligament lesions. Diagnosis and treatment of knee injuries are based on knowledge of the anatomy, (patho)physiology and biomechanics of the joint and the joint structures as obtained from experimental evaluation and a qualitative or quantitative analyses of the joint and its structures. Over the past two decades there has been a flood of scientific publications on the biomechanics of the human knee joint. These were both fundamentally and clinically oriented. There were studies on the relation between forces and motions exploring the motion range or laxity in different directions (e.g. Grood et al.,1988) and the effects of sequential cutting of the ligaments (e.g. Markolf et al., 1976; Gollehon et al., 1987; Butler et al., 1980), studies evaluating knee ligament length changes or ligament strain patterns (e.g. van Dijk et al., 1979; van Dijk, 1983; Hefzy and Grood, 1986; Sidles et al., 1988; Arms et al., 1983), and ligament forces (Ahmed et al., 1987; Markolf et al., 1990), and studies on the role of the menisci in the load transfer across the knee (e.g. Fukubayashi and Kurosawa, 1980; Ahmed and Burke, 1983; Jaspers, 1981). Numerous are the studies concerning the structure, function and mechanical properties of the articular cartilage (e.g. Kempson, 1980; Mow et al., 1982; Mak et al., 1986), the menisci (Kelly et al., 1990) and the ligaments (e.g. Butler et al., 1986; Viidik et al., 1990; van Rens et al., 1986). With all of the aforementioned studies and similar publications, more-or-less isolated pieces of information were produced about the mechanical behavior of the knee. However, with all these bits of information, one can not gain a full insight into the knee as a whole system. The 'real' mechanisms governing the behavior of the joint remain hidden in some kind of black box of which only the relation between output and input can be studied. In the first place, more data is needed than those supplied by contemporary experimental studies, as for example data on the total force balance across the knee during specific loadings or motions and, in particular, of the contributions by all joint structures. Secondly, some relation should be introduced, connecting the input and output of the system, which can only be realized by some form of analytical tool. This can be, for example, a mathematical formula, in which a number of parameters describe the aspects of the system. However, the knee is far too complex to be described by a simple formula. It is possible though, to derive mathematical expressions describing the mechanical behavior of the substructures of the knee. The force-length relationship of knee ligaments, the mechanics of the articular cartilage and the geometry of the articular surfaces can each be modeled by more-or-less simple relations, of which the parameters can be determined experimentally. Hence, the mechanical behavior of all the individual substructures of the joint can be described, but the job which remains, is to put all the pieces together. Today, the computer can fulfill this complex task. The mathematical relations describing the individual joint structures are incorporated into a computer program, the knee model, linking all pieces together. Even in the process of designing the knee model for the computer, the joint structures have to be simplified to some level. This simplification is needed in order to make certain aspects of the complex reality comprehensible and manageable. This should then be done in such way, that the resulting description is valid relative to the reality, for those aspect which are aimed at to be studied by the model. A familiar example of a knee model is the so-called four-bar- linkage model (Strasser, 1917; Huson, 1974; Menschik, 1974). In this two-dimensional model, the cruciate ligaments were represented by rigid bars connected to tibia and femur by hinges. The basic assumptions in this model are that the lengths of cruciate ligaments are not changed during knee flexion and that they can be represented by single rigid bars moving in one plane. The correctness of these assumptions is less important than the usefulness of the model. The four-bar-linkage model enhances the understanding of the relation between form and function. It explains the shape of the articular surfaces in the sagittal plane and it describes the roll-back motion of the femur relative to the tibia. The four-bar-linkage model even served as an analytical tool to establish guidelines for surgical reconstruction of the ligaments (Mller, 1982). The developments in the field of knee modeling since the four-bar-linkage model have been very diverse. O'Connor et al. (1990a,b) extended the four-bar-linkage model with either rigid or elastic ligaments, ligament forces, contact forces and muscle forces, and applied it to the 2-D analysis of forces around the knee during normal level walking (Biden et al, 1990). This same approach was used earlier by Morrison (1970) but then for flexion-extension motions around a fixed axis in a 3-D analysis. Crowninshield et al. (1976) and Grood and Hefzy (1982) modeled the 3-D ligament configuration around the knee and used the motions of the joint as input, considering varus-valgus rotation, internal-external rotation and anterior posterior translation, and determined the contribution of the ligaments to the stiffness characteristics of the knee. In addition to this, Hefzy and Grood (1983) proposed analytical models to represent the interaction between ligaments and bone, and the interaction between ligaments. The strategy of combining experimental geometric and kinematic data was also applied by Walker et al. (1988), who employed a computer-graphics model of the knee in which the average geometry of 23 knees was represented and an average knee motion was used as input. The effects of knee bracing (Walker et al., 1988) and different knee prosthesis designs (Garg and Walker, 1990; Walker and Garg, 1991) were studied through parameter adaptations guided by criteria for joint contact and maximum ligament elongations. The most complex knee models are those describing the knee as a three-dimensional system of two rigid bodies which are connected by deformable links representing the ligaments and contacts between the two bones. The knee is then considered as a system in which the external loads on the knee are balanced by the internal forces in the ligaments and the articular contact. Several models were proposed sharing these basic characteristics. Wismans et al. (1980) modeled the knee as two rigid bodies connected by non-linearly elastic springs and rigid contacts. Moeinzadeh and Engin (1988) applied this approach in a dynamic model of the knee. Andriacchi et al. (1983), used a Finite- Element like approach whereby the menisci were interposed between the tibia and femur. Essinger et al. (1989) modeled a simulated standing position with quadriceps loading through a patellar mechanism and used a linearly elastic contact between tibia and femur. Validation of these models was mainly based on a comparison with force-motion relations from experimental literature. Reports on the use of three-dimensional mathematical knee models to study functional or clinical questions are scarce. The knee models discussed are not yet fully operational and not integrated in contemporary biomechanics research. A new impetus to the field of three-dimensional modeling of the knee is indicated. This thesis describes an integrated approach of experiments and mathematical modeling in the analysis of the passive motion characteristics of the human knee. With passive is meant that muscle forces are not considered directly, but are represented as a part of the general external load on the knee. The knee is considered as a system which is externally loaded and then moves to a position where the external loads are balanced by the internal forces, i.e. ligament forces and forces at the articular contact. The approach is to determine the passive motion characteristics of a number of knee-joint specimens in well controlled experiments. The geometry of the articular surfaces and the ligament insertions are measured from the knee specimens and are used as input for the knee model. The knee model can be compared to the experimental data and validated through a parametric analysis on a subject related basis. Hence, of each knee-joint specimen in the experiment a model is made, of which the motion characteristics are evaluated relative to the experimental data. The experimental part of the study consists of an extensive evaluation of the passive motion characteristics of the knee by in-vitro experiments. The results of the experimental studies are described in Chapter II, dealing with the passive motion characteristics of the knee, in Chapter III, evaluating the ligament length changes in terms of ligament recruitment, and in Chapter IV, discussing the motion axes for flexion motions. The three-dimensional mathematical knee-joint model is described in Chapters V and VI. The knee model is similar to the model of Wismans et al. (1980), but the model is extended and the formulation is more general. The extensions include deformable articular contact (Chapter V) and the wrapping of a ligament around bone (Chapter VII). Chapter VIII describes the confrontation of the knee model with the experimental motion data through a parametric validation process. The applications of the knee model in its present form are twofold. 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