Biomechanical analysis of temporomandibular joint dynamics based on real-time magnetic resonance imaging.

AIM: The traditional hinge axis theory of temporomandibular joint (TMJ) dynamics is increasingly being replaced by the theory of instantaneous centers of rotation (ICR). Typically, ICR determinations are based on theoretical calculations or three-dimensional approximations of finite element models. MATERIALS AND METHODS: With the advent of real-time magnetic resonance imaging (MRI), natural physiologic movements of the TMJ may be visualized with 15 frames per second. The present study employs real-time MRI to analyze the TMJ biomechanics of healthy volunteers during mandibular movements, with a special emphasis on horizontal condylar inclination (HCI) and ICR pathways. The Wilcoxon rank sum test was used to comparatively analyze ICR pathways of mandibular opening and closure. RESULTS: Mean HCI was 34.8 degrees (± 11.3 degrees) and mean mandibular rotation was 26.6 degrees (± 7.2 degrees). Within a mandibular motion of 10 to 30 degrees, the resulting x- and y-translation during opening and closure of the mandible differed significantly (10 to 20 degrees, x: P = 0.02 and y: P < 0.01; 20 to 30 degrees, x: P < 0.001 and y: P = 0.01). Rotation of both 0 to 10 degrees and > 30 degrees showed no significant differences in x- and y-translation. Near occlusion movements differed only for y-translation (P < 0.01). CONCLUSION: Real-time MRI facilitates the direct recording of TMJ structures during physiologic mandibular movements. The present findings support the theory of ICR. Statistics confirmed that opening and closure of the mandible follow different ICR pathways, which might be due to muscular activity discrepancies during different movement directions. ICR pathways were similar within maximum interincisal distance (MID) and near occlusion (NO), which might be explained by limited extensibility of tissue fibers (MID) and tooth contact (NO), respectively.

The variability of the curve of Spee : An analysis of multiple setups of the same Angle Class I patient case.

PURPOSE: The aim of this study was to examine possible parameters correlating to the shape of the curve of Spee (COS) by analyzing multiple setups of the same Angle class I patient case. METHODS: In all, 65 setups of the same Angle class I patient case were constructed. We measured the depth of the COS, length and width of the dental arch, steps, rotations, spaces and symmetry of the constructed setups. With a correlation analysis, possible relationships between the depth of the COS and measured parameters were evaluated. RESULTS: The COS in the constructed setups was more exaggerated than in the reference case but none of the measured parameters correlated to the depth of the COS. The largest deviation was found on the mesiobuccal cusp tip of the first molar (-0.5 ± 0.4 mm left side; -0.8 ± 0.5 mm right side). This study found a negative correlation between the length and width of the lower dental arch (r = -0.61). While maintaining Angle class I, a large spread width of the depth of the COS, the dental arch width and length was shown. CONCLUSION: The different manifestations of the COS in this study show the freedom of arrangement of the individual tooth morphology without exhibiting a correlation to parameters of the dental arch.

Elongated styloid process in patients with temporomandibular disorders - Is there a link?

BACKGROUND: Elongated styloid processes may display clinical signs that can easily be confused with symptoms associated with temporomandibular disorders (TMD). Thus, the present study aimed to investigate alterations of the styloid process in patients with TMD. METHODS: Temporomandibular joint (TMJ) X-ray images of 192 patients with RDC/TMD diagnoses were examined retrospectively. On each side, the styloid process and mandibular ramus were evaluated regarding length as well as sagittal angulation. Data were statistically analyzed using two-way ANOVA, Pearson's r and Kruskal-Wallis test. In order to confirm the accuracy of the obtained X-ray measurements, the available cone-beam-computed tomographies (CBCT) of the subjects were also examined as reference standard and compared with the X-ray TMJ data by using Bland-Altman analysis. RESULTS: In a group of TMD patients we assessed a mean styloid length of 40.8mm over both genders. In female subjects the means of length and angulation of the styloid process were 40.4mm and 54.9°, male subjects showed means of 42.1mm and 63.4°. The mean height of the mandibular ramus in males was significantly higher than the same measurement in females (66.8mm vs 59.7mm). Styloid length in relation to ramus height (relative styloid length) was significantly larger in females. No significant correlations between RDC/TMD diagnoses and process length as well as process angle were found. A Bland-Altman analysis revealed conformity of CBCT and digital X-ray results. CONCLUSION: The mean styloid length measured in a group of TMD patients is referred to as elongated, whereas females showed longer styloid in relation to body height. However, it appears that alterations of the styloid are not related to TMD diagnoses.

Kinematics of cervical segments C5/C6 in axial rotation before and after total disc arthroplasty.

PURPOSE: The kinematical properties of C5/C6 segments in axial rotation are evaluated before and after total disc arthroplasty (TDA) with PRESTIGE®-and BRYAN® Cervical Disc (Medtronic) under flexion/extension as parameters and compared with those of C3/C4. METHODS: Eight human segments were stimulated by triangularly varying, axially directed torque (T z(t)) under compressing static axial preloads. Using a 6D-measuring device with high resolution, the response of segmental motion was characterized by the instantaneous helical axis (IHA). The position, direction, and migration path length of the IHA were measured before and after TDA (parameter: position of the axially directed preload). RESULTS: The periodic torque T z(t) generated IHA migrations whereupon the IHA direction was constantly rotated to the dorsal by ≈15.5°. After TDA, the IHA0 (neutral positions) were significantly shifted to the dorsal (PRESTIGE®: 4.3 mm, BRYAN®: 7.0 mm) just as the points of balance of the entire IHA migration paths. CONCLUSIONS: Due to the configuration of the vertebral joints and their interaction with the intervertebral disc, the IHA migrates during the axial rotation within a distinct domain of each C5/C6-segment. Implantation of the PRESTIGE® and BRYAN® prostheses significantly alters these kinematical properties by dorsal displacements of the domains. Statistically TDA of C3/C4 and of C5/C6 are not correlated. Under axial rotation of the cervical spine, additional lateral and/or ventral/dorsal displacements are produced by TDA. Consequently, adjacent level disease (ALD) may be mechanically stimulated.

The upper ankle joint: Curvature morphology of the articulating surfaces and physiological function.

PURPOSE: The curvature morphology of the articulating surfaces determines the physiological movement pattern. We quantitatively examined the curvature morphology of the tibiotalar articulating surfaces and specified their geometric contact patterns. METHODS: Geometrically equivalent cartographic nets were marked on the talar and tibial articulating surfaces of true-to-scale moldings of 20 human ankle joints (intervals of 5 mm) to relate corresponding articulating units of the surfaces. The corresponding contours of the net lines were compared, and the incongruity of articulating surfaces could thus be quantified locally. RESULTS: All tibial sagittal net lines represented circular arcs. Along the sagittal talar net lines, the curvature radii increased medially from anterior to posterior but decreased laterally. Each net line could be approximated by three circular arcs. Examining these three parts of the talar net lines, the anterior sagittal curvature radii increased from medial to lateral, whereas the posterior radii decreased. The tibial and talar transversal net lines were congruent. The articulation surfaces showed a transversal contact line in every dorsal/plantar joint position. The degree of local congruity was solely ascertained by the incongruity of the corresponding sagittal net lines. The maximal degrees of congruity were found laterally for dorsal flexion, laterally/centrally for neutral joint position, and centrally/medially for plantar flexion. CONCLUSIONS: By the transversal line contact, the contact area is broadened over the articulating surfaces from lateral to medial. In dorsal flexion, compressive loads are mainly transferred by lateral/anterior zones and in plantar flexion by medial/posterior zones of the articulating surfaces. Reconstruction of the transversal contact line is essential.

The thumb carpometacarpal joint: curvature morphology of the articulating surfaces, mathematical description and mechanical functioning.

PURPOSE: The purpose is to present a mathematical model of the function of the thumb carpometacarpal joint (TCMCJ) based on measurements of human joints. In the TCMCJ both articulating surfaces are saddle-shaped. The aim was to geometrically survey the shapes of the articulating surfaces using precise replicas of 28 TCMCJs. METHODS: None of these 56 articulating surfaces did mathematically extend the differential geometrical neighbourhood around the main saddle point so that each surface could be characterised by three main parameters: the two extreme radii of curvature in the main saddle point and the angle between the saddles' asymptotics (straight lines). RESULTS: The articulating surfaces, when contacting at the respective main saddle points, are incongruent. Hence, the TCMCJ has functionally five kinematical degrees of freedom (DOF); two DOF belong to flexion/extension, two to ab-/adduction. These four DOF are controlled by the muscular apparatus. The fifth DOF, axial rotation, cannot be adjusted but stabilized by the muscular apparatus so that physiologically under compressive load axial rotation does not exceed an angle of approximately ±3°. CONCLUSIONS: The TCMCJ can be stimulated by the muscular apparatus to circumduct. The mechanisms are traced back to the curvature incongruity of the saddle surfaces. Hence we mathematically proved that none of the individual saddle surfaces can be described by a quadratic saddle surface as is often assumed in literature. We derived an algebraic formula with which the articulating surfaces in the TCMCJ can be quantitatively described. This formula can be used to shape the articulating surfaces in physiologically equivalent TCMCJ-prostheses.

The description of the human knee as four-bar linkage.

PURPOSE: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nägerl which is applicable under form closure. METHODS: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. RESULTS: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. CONCLUSIONS: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee.

The morphology of the articular surfaces of biological knee joints provides essential guidance for the construction of functional knee endoprostheses.

PURPOSE: In comparative examinations of kinematics of the knees of humans and pigs in flexional/extensional motion under compressive loads, the significant differential geometric essentials of articular guidance are elaborated to criticise the shaping of the articular surfaces of conventional knee-endoprostheses and to suggest constructional outlines that allow the endoprosthesis to adopt natural knee kinematics. Implantation is discussed with regard to the remaining ligamentous apparatus. METHODS: Twelve fresh pig knee joints and 19 preserved human knee joints were moved into several flexional/extensional positions. In each joint, the tibia and femur were repeatably caught by metal plates. After removing all ligaments, the tibia and femur were again caught in these positions, and their points of contact were marked on both articular surfaces. Along the marker points, a thin lead wire was glued onto each surface. The positions and shapes of the four contact lines were mapped by teleradiography. RESULTS: All contact lines were found to be plane curves. The medial and lateral planes were parallel, thus defining the joint's sagittal plane. In the human knee, as compared to the lateral, the medial femoral contact line was always shifted anteriorly by several millimetres. The tibial contact curve was laterally convex and medially concave. In the pig knees, the lateral and medial contact lines were asymmetrically placed. Both tibial curves were convex. CONCLUSIONS: Both knees represent cam mechanisms (with one degree of freedom) that produce rolling of the articular surfaces during the stance phase. Implantation requires preservation of the anterior cruciate ligament, and ligamentous balancing is disadvantageous.

Characteristic points and cycles in planar kinematics with application to the human gait.

PURPOSE: We present a novel method to process kinematical data typically coming from measurements of joints. This method will be illustrated through two examples. METHODS: We adopt theoretical kinematics together with the principle of least action. We use motion and inverse motion for describing the whole experimental situation theoretically. RESULTS: By using the principle of least action, the data contain information about inherent reference points, which we call characteristic points. These points are unique for direct and inverse motion. They may be viewed as centers of the fixed and moving reference systems. The respective actions of these characteristic points are analytically calculated. The sum of these actions defines the kinematical action. This sum is by design independent of the choice of reference system. The minimality of the kinematical action can be used again to select numerically one representative cycle in empirically given, approximately periodic motions. Finally, we illustrate the theoretical approach making use of two examples worked out, hinge movement and the sagittal component of the movement of a human leg during gait. CONCLUSIONS: This approach enables automatic cycle choices for evaluating large databases in order to compare and to distinguish empirically given movements. The procedure can be extended to three dimensional movements.

A caveat concerning center of resistance.

The center of resistance is a concept in theoretical orthodontics used to describe tooth movement under loads. It is commonly used to qualitatively predict tooth movement without recourse to complex equations or simulations. We start with a survey of the historical origin of the technical term. After this, the periodontal ligament is idealized as a linear elastic suspension. The mathematical formalism of vector and tensor calculus will clarify our reasoning. We show that a point such as the center of resistance basically only exists in two dimensions or in very special symmetric spatial configurations. In three dimensions, a simple counterexample of a suspension without a center of resistance is given. A second more tooth-like example illustrates the magnitude of the effects in question in dentistry. In conclusion, the center of resistance should be replaced by a newer and wider mathematical concept, the "center of elasticity," together with a limiting parameter, the "radius of resistance."

Does total disc arthroplasty in C3/C4-segments change the kinematic features of axial rotation?

We analyze how kinematic properties of C3/C4-segments are modified after total disc arthroplasty (TDA) with PRESTIGE(®) and BRYAN(®) Cervical Discs. The measurements were focused on small ranges of axial rotation (<0.8°) in order to investigate physiologic rotations, which frequently occur in vivo. Eight human segments were stimulated by triangularly varying, axially directed torque. By using a 6D-measuring device with high resolution the response of segmental motion was characterised by the instantaneous helical axis (IHA). Position, direction, and migration rate of the IHA were measured before and after TDA. External parameters: constant axially directed pre-load, constant flexional/extensional and lateral-flexional pre-torque. The applied axial torque and IHA-direction did not run parallel. The IHA-direction was found to be rotated backwards and largely independent of the rotational angle, amount of axial pre-load, size of pre-torque, and TDA. In the intact segments pre-flexion/extension hardly influenced IHA-positions. After TDA, IHA-position was shifted backwards significantly (BRYAN-TDA: ≈8mm; PRESTIGE-TDA: ≈6mm) and in some segments laterally as well. Furthermore it was significantly shifted ventrally by pre-flexion and dorsally by pre-extension. The rate of lateral IHA-migration increased significantly after BRYAN-TDA during rightward or leftward rotations. In conclusion after the TDA the IHA-positions shifted backwards with significant increase in variability of the IHA-positions after the BRYAN-TDA more than in PRESTIGE-TDA. The TDA-procedure altered the segment kinematics considerably. TDA causes additional translations of the vertebrae, which superimpose the kinematics of the adjacent levels. The occurrence of adjacent level disease (ALD) is not excluded after the TDA for kinematical reasons.

Effect of excessive methionine on the development of the cranial growth plate in newborn rats.

OBJECTIVE: Methionine is an essential amino acid and pivotal for normal growth and development. However, previous animal studies have shown that excessive maternal intake of methionine causes growth restrictions, organ damages, and abnormal growth of the mandible in newborn animals. However, the effect of excessive methionine on the development of the cranial growth plate is unknown. This study investigated histological alterations of the cranial growth plate induced by high methionine administration in newborn rats. DESIGN: Twenty pregnant dams were divided into a control and an experimental group. The controls received a diet for rats and the experimental group was fed from the 18th gestational day with a special manufactured high methionine diet for rats. The high methionine diet was maintained until the end of the lactation phase (day 20). The offspring of both groups were killed at day 10 or 20 postnatally and their spheno-occipital synchondroses were collected for histological analysis. RESULTS: The weight of the high-dose methionine treated experimental group was considerably reduced in comparison to the control group at day 10 and 20 postnatally. The cartilaginous area of the growth plate and the height of the proliferative zone were markedly reduced at postnatal day 10 in the experimental group. CONCLUSIONS: In summary, the diet-induced hypermethioninemia in rat dams resulted in growth retardations and histomorphological changes of the spheno-occipital synchondrosis, an important craniofacial growth centre in newborns. This finding may elucidate facial dysmorphoses reported in patients suffering from hypermethioninemia.

Measurement of the midpalatal suture width.

OBJECTIVE: To conduct a pilot study to investigate the potentiality to determine the midpalatal sutural width radiographically with a flat-panel volume computed tomography (fpVCT) in a porcine model. MATERIALS AND METHODS: Bone samples from the midpalatal suture of five young (16 weeks) and five old (200 weeks) sus scrofa domestica were gathered. The midpalatal suture width was measured via fpVCT and compared to respective histological preparations. Results with P < .05 were considered significant. RESULTS: The data obtained by fpVCT and by histomorphometric analysis reveal a highly significant age dependency of the measured suture width (both P < .0001), with lower suture width values in older subjects compared to the younger group. The averaged suture widths measured in the fpVCT images shows a distinctively higher mean compared to the histomorphometric data with high statistical significance (P < .0001). The evaluated difference between both methods was almost constant. CONCLUSION: fpVCT is a powerful tool for determining midpalatal sutural width.

Total knee replacement with natural rollback.

A novel class of total knee replacement (AEQUOS G1) is introduced which features a unique design of the articular surfaces. Based on the anatomy of the human knee and differing from all other prostheses, the lateral tibial "plateau" is convexly curved and the lateral femoral condyle is posteriorly shifted in relation to the medial femoral condyle. Under compressive forces the configuration of the articular surfaces of human knees constrains the relative motion of femur and tibia in flexion/extension. This constrained motion is equivalent to that of a four-bar linkage, the virtual 4 pivots of which are given by the centres of curvature of the articulating surfaces. The dimensions of the four-bar linkage were optimized to the effect that constrained motion of the total knee replacement (TKR) follows the flexional motion of the human knee in close approximation, particularly during gait. In pilot studies lateral X-ray pictures have demonstrated that AEQUOS G1 can feature the natural rollback in vivo. Rollback relieves the load of the patello-femoral joint and minimizes retropatellar pressure. This mechanism should reduce the prevalence of anterior knee pain. The articulating surfaces roll predominantly in the stance phase. Consequently sliding friction is replaced by the lesser rolling friction under load. Producing rollback should minimize material wear due to friction and maximize the lifetime of the prosthesis. To definitely confirm these theses one has to wait for the long term results.

Construction-conditioned rollback in total knee replacement: fluoroscopic results.

Firstly, the way of implementing approximatively the initial rollback of the natural tibiofemoral joint (TFJ) in a total knee replacement (AEQUOS G1 TKR) is discussed. By configuration of the curvatures of the medial and lateral articulating surfaces a cam gear mechanism with positive drive can be installed, which works under force closure of the femoral and tibial surfaces. Briefly the geometric design features in flexion/extension are described and construction-conditioned kinematical and functional properties that arise are discussed. Due to a positive drive of the cam gear under the force closure during the stance phase of gait the articulating surfaces predominantly roll. As a result of rolling, a sliding friction is avoided, thus the resistance to motion is reduced during the stance phase. Secondly, in vivo fluoroscopic measurements of the patella tendon angle during flexion/extension are presented. The patella tendon angle/ knee flexion angle characteristic and the kinematic profile in trend were similar to those observed in the native knee during gait (0°-60°).

Accuracy of fit of 3-to-3 retainers after adhesive fixation using a neodymium-iron-boron magnet chain.

BACKGROUND AND OBJECTIVE: Six-base retainers are often used to prevent tertiary crowding. To minimize shear stress on the retainer, these should be fitted as precisely as possible. The aim of this study was to compare the accuracy of fit of 6-base retainers after adhesive fixation using a neodymium-iron-boron (NdFeB) magnet chain or a resin positioning aid. MATERIALS AND METHODS: A 6-base retainer was prepared for 40 pseudo-anonymous lower jaw models (2 × 20). Temporary fixation was performed with a resin positioning aid or a NdFeB magnet chain. The adhesive fixation of the retainers was randomized. The area and vertical distance between wire and teeth were determined by histomorphometry. The results were evaluated by ANOVA. The probability of error was specified as 5%. RESULTS: With the magnetic chain method, the area was significantly smaller than with the positioning aid (p = 0.0125). The difference between the two methods was ca. 1.3 mm². Moreover, the measured distance was affected significantly by the method used (p < 0.0002). With the magnet chain, the distance between the tooth and retainer was reduced by a mean of 0.05 mm. Conclusion. The fit of the retainer wire improves somewhat when the NdFeB magnet chain is used even though the wire is not as precisely positioned as it would be with a custom-made positioning aid.

The influence of occlusal forces on force delivery properties of aligners during rotation of an upper central incisor.

OBJECTIVE: To determine the forces and moments delivered to a maxillary central incisor during rotation with aligners when a simulated occlusal force generated during swallowing acts on the appliance. MATERIALS AND METHODS: Five identical appliances were manufactured from four different starting materials (Erkodur 0.8 mm and 1.0 mm; Biolon 0.75 mm and 1.0 mm). An upper central incisor fixed in a measuring device was rotated around its central axis in 0.5-degree steps up to ±10 degrees with the appliance fixed in place. An occlusal force of 30 N generated during swallowing was simulated with a weight positioned on the appliance. For statistical analysis, the moments Tz (rotation) and forces Fz (intrusion) at a deflection of ±0.34 mm to the incisor edge (±5 degrees rotation) were tested. Means and standard deviations for Tz and median and 25% and 75% quartiles for Fz were calculated. An analysis of variance was performed. RESULTS: The simulated occlusal force increased the measured intrusive force Fz (maximum with a weight, -3.7 N [-3.7, -2.4]; minimum without a weight, -1.3 N [-1.4, -1.1]) and the rotary moment Tz (maximum with a weight, -50.8 Nmm [±0.8]; minimum without a weight, 18.2 Nmm [±0.9]) significantly in all cases (P < .01). This was found for all materials measured and for both directions of rotation. CONCLUSION: During rotation with aligners, a simulated occlusal force increases the intrusive force and the rotary moment. The biological adverse side effects of these phenomena remain unclear, especially in patients with periods of bruxism.

Physiologically shaped knee arthroplasty induces natural roll-back.

After total knee replacement the persistence of pain represents a significant problem. In this study, a novel knee arthroplasty (Aequos G1 knee arthroplasty) is investigated that was designed to replicate main features of human knee morphology to reduce the periodically occurring pain after knee replacement. Previous work showed theoretically that this arthroplasty design may reconstruct the four-bar linkage mechanism as it occurs in human knee by contriving a convex lateral tibial compartment and a sagittal offset of the centre of the medial and lateral femur condyles - inducing a roll-back mechanism as it exists in human. The aim of this study was to determine whether this potential roll-back mechanism can be confirmed by in-vivo measurements. This retrospective study showed that the patellar tendon angle decreases during flexion of 0.21° per degree of flexion on average in the 16 knees studied. This amount is similar to physiological knee kinematics and in contrast to existing results in the literature after implantation of conventional total knee replacements which lack physiological knee kinematics. The results suggest that physiological motion after implantation of the Aequos G1 knee arthroplasty occurs during loaded motion up to approximately 45° knee flexion.

Variations in cyclic mandibular movements during treatment of Class II malocclusions with removable functional appliances.

The aim of the study was to establish whether juveniles with a Class II malocclusion change the neuromuscular control of mandibular movements during the course of orthodontic treatment with removable functional appliances (RFAs). Neuromuscular control can be indirectly evaluated by recording cyclic planar mandibular movements which were freely carried out by the patients (28 girls, 14 boys, aged 11.1 ± 1.1 years at the start of treatment) and measured with an ultrasonic device before, during, and after Class II functional appliance therapy, with either an activator or a bite jumping plate. The cyclic movements represented simultaneous rotations of the mandible around a maxillary and mandibular fixed axis (MFHA) and could be characterized by µ(α)-diagrams (µ = swing angle of MFHA, α = mouth opening angle) and path length (L) of the MFHA. The µ(α)-diagrams clearly divided into four parts: movement representing protrusion, mouth opening, and two parts of backward closing as known from Posselt diagrams. Parameters from the Posselt and µ(α)-diagrams were checked by one-factor analysis of variance on a 5 per cent significance level for group dependency. For one-third of the patients investigated, no significant changes were seen in any parameter pre- or post-therapy. However, patients showing an initially large mouth opening capacity or a very short condylar path changed their neuromuscular control to that of Class I subjects. Analysis of µ(α)-diagrams provides the possibility of assessing changes in the neuromuscular control of the mandible during Class II treatment.

Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements.

The mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which--when applying screw theory--represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced.