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.

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°).

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.

Migration of the instantaneous axis of motion during axial rotation in lumbar segments and role of the zygapophysial joints.

The biomechanical role of the zygapophysial joints was investigated for axial rotations of lumbar segments by recording the positions of the instantaneous helical axis (IHA) against the axial rotational angle and by relating these IHA-positions to anatomical landmarks. Cyclically varying pure axial moments were applied to 3 L1/L2, 7 L3/L4 and 3 L4/L5 segments. There were 800 segment positions per cycle taken by a custom-made high precision 3D-position measuring system. In intact segments IHA-migration reached from one zygapophysial joint to the other IHA-paths came up to 10-60 mm within small angular intervals (±1 deg). After removing the right joints, IHA-migration remained comparable with that of intact segments only for segment positions rotated to the right. Rotation to the left, however, approximately yielded stationary IHA-positions as found after resection of both joints. Hence, IHA-migration is determined by the joints already for small rotational angles. Each type of segment showed a typical pattern of IHA-migration.

Quantified contours of curvature in female index, middle, ring, and small metacarpophalangeal joints.

PURPOSE: To study and quantify the morphology of the curvature of the surfaces of metacarpophalangeal metacarpophalangeal joints and to relate joint morphology to joint function. METHODS: Forty metacarpophalangeal joints of the index, middle, ring, and small fingers from 5 right and 5 left hands were taken from female cadavers. The articulating surfaces of the metacarpal head and the base of the proximal phalanx were copied in a true-to-scale fashion. The hard plaster models were sliced in 7 sagittal and 7 transverse planes. The curvatures of the section contours were determined with circular gauges. Statistical analyses were performed by analysis of variance and paired Student t-tests. RESULTS: In the sagittal plane, the cartilaginous surface of the metacarpal head is divided into 2 functional regions and a third dorsal region that does not articulate with the base of the proximal phalanx. The articulating surface of the base of the proximal phalanx approximates a circle in the midsagittal plane. The mean median sagittal radius of curvature of the dorsal articulating aspect of the metacarpal head (6.9 mm) is 33% smaller than that of the base of the proximal phalanx (10.3 mm). The palmar articulating aspect of the metacarpal head (5.8 mm) is 44% smaller than that of the base of the proximal phalanx (10.3 mm). In the median transverse section, the mean radius of curvature of the metacarpal head (7.3 mm) is 18% smaller than that of the base of the proximal phalanx (8.9 mm). CONCLUSIONS: The data demonstrate the highly significant incongruity in the curvature of the articulating pair. This incongruity provides a joint space with its greatest dimension in the sagittal plane. From a mechanical perspective, the metacarpophalangeal joint mechanically represents a joint with 5 kinematic degrees of freedom: 2 for flexion and extension, 2 for abduction and adduction, and 1 for axial rotation.

Non-linearity of flexion-extension characteristics in spinal segments.

Spinal biomechanics is still known just fragmentary since the only description by angle-torque characteristics without simultaneous recording of migration of the instantaneous helical axis (IHA) is not sufficient. Time-dependent flexion/extension following a cyclic laterally directed torque was measured at all six degrees of freedom by a highly precise custom-made 6D apparatus. In order to enhance the localizing resolution of IHA migration as the function of the flexional/extensional angle, small ranges of motion (ROM) were used at several degrees of pre-extension. 4 L3/L4, 3 L4/L5 and 2 T2/T3 human segments were investigated. In extensional motion, wide dorsal IHA-migrations were measured in lumbar segments and correlated with the distinct asymmetric shapes of the characteristics in extensional motion. The respective increase of differential stiffness could mainly be traced back to the enlarging geometrical moment of inertia of the segments by the dorsally migrating IHA. Both thoracic segments showed a predominant IHA-migration in cranial/caudal direction. A simple model makes it evident that the opposite curvature morphology of lumbar and thoracic joint facets conditions the different directions of IHA migration.

Morphology of the interphalangeal joint surface and its functional relevance.

PURPOSE: To study and to clarify the curvature morphology of the articular surfaces of the proximal interphalangeal (PIP) joint and to relate joint morphology and joint kinematics. METHODS: The radii and centers of curvature of 40 PIP joints were determined by sagittal and transverse intersections of highly precise replicas that were prepared by dental methods. RESULTS: The PIP joint is proved to be a nonconforming joint: the articular surface of the proximal end of the middle phalanx has lesser curvatures than the condyles of the proximal phalanx. In intersections through the apex of the radial and ulnar condyles, the measured differences of the radii between the articular surfaces of the PIP joint were sagittally about 30% and transversely about 49% of the respective radii of the condyles. Incongruity of the joint results in 2 morphologically given axes for extension respective to flexion: (1) an axis given by the articular surfaces of both condyles of the proximal phalanx; and (2) a second axis given by the articular surface of the proximal end of the middle phalanx. Both articulating surfaces have 2 contact points in the transverse plane, one each, central to the apex of radial and ulnar condyles, respectively. In the middle of the joint, in the intercondylar groove, a small joint cavity was present in 37 of 40 joints. CONCLUSIONS: The physiological incongruity of the 2 articular surfaces of the PIP joint was defined quantitatively. This allows the derivation of a theoretical model for PIP joint function that explains the kinematics and mechanical stability of the joint as well as the lubrication and nutrition of the cartilaginous structures.

Morphological structures and protrusive cranial border guidance of the temporomandibular joint of Cercopithecus mona.

Morphological parameters of the temporomandibular joint (TMJ) of Cercopithecus mona were analyzed by sagittal medial/lateral slicing of the entire joint. The slice contours of the osseous structures of the joint surfaces were approximated by circles. In this manner, the main parameter of the protrusive cranial border guidance, the protrusive dimeric Link chain (DLC), could be measured. In each joint, all slices yielded protrusive DLCs which were nearly parallel to each other. In medial/lateral direction all parts of the joints participate in force transmission in initial protrusive cranial border function.

Aspects of morphology and guidance of the human temporomandibular joint.

Examinations of the curvature morphology of the temporomandibular joints (TMJs) in macerated human skulls yielded that in initial protrusive cranial border motion, parts of the condylar articulating surfaces are only functional under force transmission. These areas were found on the lateral-central side of the condyle. In contrast to the Cercopithecus mona, a monkey species, the human TMJ apparently possesses a distinctly higher spatial performance range.

The mandibularly fixed hinge axis--investigation of patients with sound and pathological jaws.

In former works, we had proved that test persons with sound temporomandibular joints (TMJs) used a mandibularly fixed hinge axis (MFHA) and were able to pilot the mandible by solely two kinematical degrees of freedom. We wondered if we could evaluate the MFHA the same way for patients who had problems with their TMJs. Actually, the MFHA could be determined likewise. The results could provide information on the reason for the distortion of the movement of the TMJs, which cannot be yielded by X-ray radiographs.