The Classic: Joint Laxity as a Criterion for the Design of Condylar Knee Prostheses

Abstract

Introduction Peter S. Walker (Fig 1) studied at the University of Cambridge from which he obtained a Bachelor of Science degree and a Master’s degree in Mechanical Sciences in 1963. After a stint as a research engineer at Dunlop, Ltd in Newcastle upon Tyne, he earned a PhD degree in Mechanical Engineering at the University of Leeds. From 1969 to 1976, he was the Director of Bioengineering at the Hospital for Special Surgery in New York City and an assistant professor at Cornell Medical School. After this, Walker became the Director of Product Development for Howmedica until he moved to Boston. In Boston, he became Director of the Biomechanics Laboratory at Brigham and Women’s Hospital and at the Veterans Administration Hospital, West Roxbury and an associate professor at Harvard Medical School. In 1987, Walker returned to England as the Professor of Biomechanical Engineering at University College, London and Director of the Centre of Biomedical Engineering at the Royal National Orthopaedic Hospital, Stanmore. After 12 years, Walker returned to the United States as Professor and Director of the Center of Biomedical Engineering at the Cooper Union for the Advancement of Science and Art in New York City, the position he now holds.Fig 1.: Dr. Peter S. WalkerWalker has published extensively on the subject of total joint replacement, especially of the knee. He has been the president’s guest lecturer at the Hip Society and the American Academy of Orthopaedic Surgeons. The following paper is considered a seminal work in the design of total knee components. Leonard F. Peltier, MD, PhD The elasticity of the knee was expressed in terms of primary laxity and secondary laxity, and the factors controlling laxity were discussed. Using a laxity rig, the laxity was measured for knee specimens, under cyclic loading conditions. Under a compressive load, the condyle geometry and the menisci were considered to be important. A theoretical analysis showed that if a-p, lateral or rotational movements caused distraction of the joint, large forces were needed to cause these movements. By choosing the maximum forces to be sustained, and the movement allowed, the curvatures of the femoral and tibial condyles of a condylar replacement knee prosthesis were calculated. A prosthesis made on these principles was manufactured and is undergoing clinical trials. The primary movement of the knee joint is in the sagittal plane, but there are other important though smaller movements which occur. The concept of ‘joint sinus’, first described by Fischer (1901), was defined as the boundary of movement of the joint allowed by a ligament preparation. Dempster (1965) applied this to the shoulder joint, and demonstrated that the sinus was increased if a force was applied against the boundary. In normal function, the muscles should move the joint within the ‘sinus’ without allowing excessive forces to be placed on the passive soft tissues such as ligaments. The combination of the muscle control and the limitations to movement provided by the soft tissues, can be regarded as the ‘stability’ of the joint. For the knee joint, there have been numerous studies to determine the role of the different structures in providing stability. Many of the studies have used anatomical observation and palpatation to determine the tightness of ligaments, and in some cases have used selective cutting to determine the specific role of a ligament in restraining a particular motion. The conclusions however are by no means in agreement. Smillie (1970) maintained that the functions of the various structures were closely interrelated, that it was difficult to ascribe a specific function or functions to any particular structure. Brantigan and Voshell (1941) showed the varying tightness of ligaments in different angles of flexion of the joint. Both cruciate ligaments remained taut throughout flexion with more stress in full flexion. A study by Edwards, Lafferty and Lange (1970) used a computation method to determine ligament lengths, and attached gauges to the ligaments to measure the tensions at different angles of flexion. The assumptions made in the calculations probably introduced errors in the results, but their findings were that the anterior cruciate ligaments was in maximum elongation at full extension, the posterior cruciate ligament was in maximum strain at 45°–60° of flexion, and at full flexion, the anterior cruciate ligament had minimum elongation while the posterior cruciate ligament was near maximal elongation. Wang, Walker and Wolf (1974) measured the length patterns of ligaments at flexion of 0°, 30°, 60°, 90° and 120°, in neutral, internal rotation and external rotation at each angle. The anterior cruciate gradually increased in length with flexion, while the posterior cruciate was longer at 0° flexion than at all other angles for which length was constant. Rotation had a significant effect on the cruciate lengths, affecting the anterior more than the posterior cruciate. Rotary stability of the knee joint is provided by several structures. External rotation is checked mainly by the medial collateral ligament and the anterior cruciate and internal rotation by the medial collateral and the posterior cruciate, while the capsule structures, the menisci and various muscles and tendons have also been cited as being involved (Kaplan, 1957; Slocum and Larson 1968; Kennedy and Fowler, 1971; Nicholas, 1973). In a clinical situation, the amount of rotary laxity of the knee is considered to be important because of its relationship to injury of the joint. The ‘Slocum Test’ is commonly used to test laxity on clinical examination. Brantigan and Voshell (1941) measured the angular rotation of knee specimens by applying a torque of 15 Kg. cm. At full extension practically no rotation occurred, but at ninety degrees of flexion, rotation ranged from six degrees to twenty-four degrees in one direction. Anterior-posterior (a-p) movement is also important, controlled by the cruciates, by the medial collateral, and by the menisci. As with rotary laxity, the amount of a-p drawer can vary greatly among different individuals. In actual activity, an infinite variety of movements, forces and moments can occur at the knee. In level walking, a ‘transverse rotation’ at the knee of 9.1° average was measured (Inman, et al., 1948) whilst another study using an externally fitted goniometer obtained an average of 6.1° for rotation. (Kettelkamp, et al, 1970). In other activities, the amounts of rotation will depend upon various factors, which include the angle of flexion, the axial load in the direction of the long axis of the tibia, the rotary torque being applied and the degree of ‘laxity’ inherent in the ligamentous and other restraining structures. In walking, Morrison (1969) has determined maximum forces of about three times body weight to occur, while in ramp or stair climbing, four times body weight. The a-p forces were around one half body weight and the lateral forces about half this amount. In an attempt to more clearly define the laxity in the knee, and the structures and conditions which controlled it, Wang and Walker (1974) defined two types of laxity. In the work reported, the concepts were applied to rotation. Stresses were automatically and cyclically applied to knee joint specimens and graphs of torque against rotation obtained. Primary laxity was defined as the rotation for small applied torque. Secondary laxity was the additional rotation at the extremes of motion, at the maximum torque applied. There was a wide variation in laxity between different knees, with no discernable correlation with age, sex, race or body build. The collateral ligaments were twice as effective as the cruciate ligaments in controlling the rotary laxity while the menisci appeared least important. A compressive load on the knee greatly reduced rotary laxity. This led to the speculation that geometry of the condyles and the menisci might be playing an important role, because with these small angles of rotation, the ligaments would not be stretched sufficiently to provide much restraint. The torque absorbed by friction was calculated to be small compared with the rotational torques which can normally act. In a recent study by Walker and Erkman (1974), the menisci were in fact found to directly carry much of the joint force. It is evident that if an a-p force were applied, the femur could move forwards or backwards on the tibia until the load was shifted to the menisci and they were pushed fully forwards. The femur would then have to ‘ride up’ to produce further movement. A rotation force would produce the same sort of mechanism. The ‘screwing out’ and ‘riding up’ both involve movement against the applied force on the joint, and hence the movement would be restrained. It is apparent from the preceding discussion that the restraining forces to stabilise the knee against externally applied forces and moments are dependent upon several factors. The structures providing the restraint will be: (a) muscle; (b) passive soft tissues (ligaments, capsule and menisci); (c) joint geometry (condyles and menisci). The relative degree to which the above factors will apply depend upon: (a) the position of the joint; (b) the values and directions of the applied forces and moments. In this paper, particular consideration will be given to the joint geometry in conjunction with a compressive load acting on the knee. Experimental For reference purposes axes were considered to be fixed in relation to the tibia. To define and measure the laxity in joints under different conditions, the following experiments were performed: Part 1: measurement of primary and secondary laxity for anterior-posterior movement of intact knee specimens: Part 2: a further study to measure primary and secondary rotary laxity for intact knee specimens; after cutting various structures; and with a compressive load Py applied to intact specimens Part 3: primary and secondary rotary laxity with different prostheses inserted. (i) Method—The apparatus used for part 3 is shown in Fig. 3 (figure not shown). For parts 1 and 2, an earlier version of the apparatus was used. Fresh intact knee specimens were obtained at autopsy. Rods were cemented into the medullary canals and then fixed into the rotary laxity rig. A cyclic force Px (a-p) or torque Qy (rotation) was applied, and graphs of force versus displacement, or torque versus rotation, were plotted automatically. Included in the part 2 tests, were joints where a constant axial load was applied by a pneumatic cylinder. In all the remaining tests, no axial load was applied to the joint, although if the joint distracted when an a-p or rotational force was applied, the elasticity of the apparatus would cause an axial force to occur. The model for this was a spring, for which the stiffness was not determined. Further details of the experimental methods have been described in an earlier paper (Wang and Walker, 1974). (ii) A typical force-displacement graph—The following applied to either force-displacement, as in anterior-posterior movement; or to torque-rotation, as in rotatory movement. A typical shape of the torque-rotation graph shown the following characteristics: (a) a large rotation both in internal and external rotation for only a small applied torque; (b) a ‘stiff’ portion at the extremes of motion where there was relatively little rotation for a large torque; (c) a small hysteresis loop in relation to the magnitude of the rotation and torques. From these torque-rotation graphs, two types of laxity were defined. First primary laxity, was defined as the total angular rotation for a torque of ± 5 Kg. cm. This value was chosen because above that torque, the stiff portion of the graphs generally began. In the case of a-p movement, the force for primary laxity was ± 1 Kg. Primary laxity describes the amount of looseness in the joint before significant soft tissue restraint is exerted. The second type of laxity was the secondary laxity. This was the additional angular rotation occurring between ±5 Kg cm and the maximum torque applied M. Note that for secondary laxity there are values for internal and external rotation. Secondary laxity is a measure of the restraint provided by the soft tissues at the extremes of motion. (iii) Results—Part 1—the displacements for a force applied to the tibia in the anterior and posterior directions are shown in Table 1 (table not shown). The knees were at an angle of 0° flexion. On average, the total anterior-posterior movement for a force of 25 Kg in each direction was 1.57 cm. It was notable that the primary laxity greatly exceeded the secondary laxity. Part 2—the results for rotary laxity are shown in Table 2 (table not shown). The knees were set at a flexion angle of 25°. Again, the 29.7°. Wang and Walker (1974) showed that removal of the menisci caused an increase in primary laxity of 14 per cent, cutting the cruciates in an otherwise intact specimen gave 23 per cent laxity increase, and cutting the collaterals in an otherwise intact specimen gave 40 per cent laxity increase. When a compressive load was applied to the joint however, the rotary laxity decreased considerably. From four knee specimens with compressive loads of 100 Kg applied, the total laxity averaged only 20 per cent of the previous value. Part 3—three types of prostheses were studied: the uni-condylar, which is a condylar replacement of one compartment of the knee; the duo-condylar, which replaces both compartments (Walker and Shoji, 1973; Ranawat and Shine, 1973); and the geometric (Coventry, Finerman, Riley, et al, 1972), which also replaces both compartments, but where the femoral and tibial components are in close conformity. The knees were at an angle of 25° flexion, and measurements were made of rotary laxity at a torque of ±50 Kg cm. The results are shown in Table 3 (table not shown). It can be seen that after insertion of the uni-condylar and the duo-condylar, both primary and secondary laxity did not change to a great extent. This was presumably because the restraint to rotation provided by the curvatures of the prosthetic components were similar to those in the normal joint. For the geometric prosthesis on the other hand, primary laxity was reduced considerably, due to the conformity of the femoral and tibial components requiring significant distraction for rotation of the joint. In the following analysis, it will be postulated that the curvatures of the condyles in either normal or prosthetic knees, in so far as they cause the knee to distract on a-p motion, lateral motion, or rotation, are most important in restraining these motions. Under small joint loads, soft tissues are made to stretch, while under high joint loads the distraction itself provides the stability. Analytical (i) Restraining forces produced by distraction—The joint is represented in lateral view in Fig. 4 (figure not shown). Py is the compressive force acting on the joint. Anterior-posterior movement of the femur on the tibia is in the x-direction. Rotation of the femur is about an axis parallel to the y-axis. Radii of curvature at the contact are given by r for the femoral condyles and by R for the tibial plateaus. R considers the meniscus and upper tibia as an integral unit. In the case of condylar replacement prostheses, r and R are the curvatures of the femoral and tibial components. Assume a relation between the horizontal movement of the femur, and the gain in vertical height of the femur relative to the tibia, as in Fig. 5 (figure not shown). Let the horizontal force producing a small increase in motion δx at a distance x from the central rest position be Fx. The total energy absorbed for moving a distance x with a consequent gain in height y is:EQUATION A similar expression can be derived for rotational movement. If Q is the torque at an angle of rotation θ, then: and EQUATION In the case of the circular geometry assumed in Fig. 4 (figure not shown), the relations between y and x and between θ and x, can be determined. In Fig. 6 (figure not shown): Substituting in equation 1. For a rotation θ (Fig. 7) (figure not shown) EQUATION Hence Substituting in equation (3) By using equations (5) and (8), the horizontal force and the torque which the joint can absorb, can be calculated as a function of the joint force, the joint geometry, and the amount of movement or rotation which occurs. (ii) Application of the theory to the design of condylar prostheses. The two basic types of condylar prostheses are those where the cruciate ligaments are preserved, and those where the cruciates are not preserved. (The patello-femoral surface is not considered here.) In the former type, such as the uni-condylar and the duo-condylar, the object is to reduce the bulk of the prosthesis, reduce the bone resected and obtain some tightness in the joint at surgery so that the cruciate ligaments can play some part in providing stability. In the second type of prosthesis, an example being the Freeman-Swanson, the curvatures of the prosthetic components themselves are intended to provide the stability which were afforded by the cruciates. Considering the importance of the cruciate ligaments themselves, the posterior is regarded as more important and is usually better preserved than the anterior. There are many factors to consider when deciding upon the amount of stability to build into the prosthesis itself. There are of course a variety of instabilities present in the arthritic joint, so that one prosthesis is unlikely to be suitable for all cases. Given the curvatures of the femoral condyles, the plateau can range from being completely flat, to being in exact conformity with the femoral condyles. If the curvatures fall between these extremes, more or less restraint can be provided. The three important degrees of freedom are anterior-posterior (x-axis), lateral (z-axis) and rotation (about the y-axis) (Fig. 2) (figure not shown). Equations (6) and (8) are used to calculate the curvatures to provide the required amount of restraint, for a given axial load Py acting on the joint. Firstly, in normal activity such as walking or standing, a joint force Py of two times body weight (taken to be 75 Kg) is reasonable. Fig. 8 (figure not shown) shows the a-p or lateral forces which are supported by the curvatures of the condyles as a function of x for three different values of R-r. It can be seen that considerable forces are supported. For instance when R-r = 1.5 cm, to move the femur along the x-axis by 0.5 cm requires a force of 50 Kg. Fig. 9 (figure not shown) shows in a similar way the torque absorbed as a function of R-r. The tibial curvature which affects rotation is in the x-direction, seen on a lateral view. In this case, at R-r = 1.5 cm for only 10 degrees of rotation, a torque of nearly 180 Kg cm is required. One difference between the curves for Fx −x and for Q − θ compared with those obtained in the laxity experiments, is the degree of primary laxity. The laxity curves are shown schematically on Figs. 8 and 9 (figures not shown). The laxity curves were not however taken with an axial load on the joint, but rather for an elastic restraint to joint distraction as mentioned earlier. With a constant compressive load, the primary laxity phase may be considerably reduced. To choose suitable curvatures for the prosthesis, maximum a-p (x-direction) and lateral (-direction) forces, and the maximum torque (about the y-axis) will be specified. The maximum desirable movements and rotations comprising both primary and secondary laxity will be specified. The curvatures will then be determined from Figs. 8 and 9 (figures not shown). (iii) The choice of suitable curvatures—The available information on forces and moments in the knee is as follows: Morrison (1969) quoted ligament forces. I assume that the a-p forces are equal to the ligament forces. TABLETableThe mean maximum lateral force (Pz) was 0.26 times body weight = 20 Kg (taking body weight to be 75 Kg). Maximum torque My was 100 Kg cm. Smidt (1973) measured forces at the knee during isometric contractions, and calculated the forces in the x-direction. Maximum values were Px + = 35 Kg, Px − = 151 Kg. Wang and Walker (1973) measured the effect of different rotational torques on laxity. It was found that half the knees tested suffered an irrecoverable increase in laxity at a torque of 125 Kg cm. To summarise, taking into account the limited activity of most arthritic patients, reasonable maximum values required of the prosthesis are:Px = 50 Kg, Pz = 20 Kg, My = 100 Kg cm. Measurements of the deflections were given earlier in this paper. Under the test conditions, average total a-p movement was 1.57 cm at ±25 Kg force. Average total rotation was 29.7° for ±50 Kg cm torque. Lateral laxity was not measured. Under of Kg, these values would be reduced. is that at full extension, the laxity should the be less than in flexion. the following movements at maximum force can be total x = cm cm primary total = cm total y = primary total x = cm cm primary total cm total primary From Figs. 8 and 9 (figures not shown), the curvatures to the above R-r = 1 cm R-r = 1.5 cm R-r = 1.5 cm R-r = 1.5 cm. curvatures are shown in Fig. 10 (figure not shown). A prosthesis which has been to the above principles and curvatures is shown in Fig. (figure not shown). There are several other in relation to the The prosthetic components be to for the laxity movements, without the femoral on to the of the tibial This can be determined the from equations 5 and which the height of distraction y as a function of laxity x, or For the curvatures there is no curvatures are to the prosthesis there is to be some change in due to and of the The design should for this without affecting the It is to be that in a prosthesis where the femoral and tibial components and high forces are supported for small laxity movements, the femoral would to against the of the tibial This is because of the and on the tibial which can stress the It is of to calculate the forces at the joint caused for a horizontal force Px acting between the femur and the tibia. If assume that the friction is then the force at the contact will be along (Fig. (figure not shown). If is the Px = 50 Kg, R-r = 1 cm, x = cm R-r = 1.5 cm, x = cm At full extension, = 50 = Kg. At flexion, = 50 = Kg. Hence the additional force at the joint in a horizontal of force in these is as least as great at the of force acting Py which is Kg. In prostheses where the cruciate ligaments are preserved, are they to carry some of the forces in the a-p This can be for the posterior cruciate on the following Assume that there is a forwards force on the femur, and that the primary laxity phase in both the prosthesis and the ligament has been taken A further 5 forwards movement of the femur would the ligament by about 4 The stiffness of cruciate ligaments has been measured at about 10 and Walker, so that a backwards restraining force of more than Kg is This is a significant of the maximum a-p force which is to occur. Hence the of the cruciate ligaments is that they are of greatly the forces on the prosthesis which could the The various factors controlling joint stability were With a compressive load on the joint, the condyle geometry and the menisci were most important. To the amount of looseness in the knee, the concepts of primary laxity and secondary laxity were (3) Primary and secondary laxity were measured on knee specimens in anterior-posterior movement, and in rotation, by applying cyclic forces and torques in a laxity rig. The average a-p laxity at ± 25 Kg was 1.57 cm. The average rotational laxity for ± 50 Kg cm was 29.7°. axial load on the joint greatly reduced rotation laxity. (5) The laxity after different types of knee prosthesis of and less conformity were (6) A theoretical analysis showed the relationship between the relative curvatures of the femoral and tibial condyles a normal or prosthetic and the a-p, lateral or rotational force which could be In the of a compressive load on the joint, high a-p, lateral or torque forces could be due to the effect of the curvatures of the condyles. (8) The theory was applied to the design of condylar prostheses, by the maximum forces and moments required to be by the prosthesis, and the maximum laxity movements The design of a prosthesis was which could these maximum forces and torques.