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1

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

Nägerl H., Kubein-Meesenburg D., Fanghänel J., Dathe H., Dumont C., Wachowski M. M.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 3

83--90

EN

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.

2

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

Dathe H., Dumont C., Perplies R., Fanghänel J., Kubein-Meesenburg D., Nagerl H., Wachowski M. M.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 2

103--110

EN

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.

3

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

Nagerl H., Dathe H., Fiedler Ch., Gowers L., Kirsch S., Kubein-Meesenburg D., Dumont C., Wachowski M. M.

Acta of Bioengineering and Biomechanics

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2015

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Vol. 17, no. 2

45--53

EN

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.

4

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

Fiedler Ch., Gezzi R., Frosch K.-H., Wachowski M. M., Kubein-Meesenburg D., Dörner J., Fanghänel J., Nägerl H.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 4

37-49

EN

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.

5

Construction-conditioned rollback in total knee replacement: fluoroscopic results

Wachowski M. M., Fiedler C., Walde T. A., Balcarek P., Schuttrumpf J. P., Frosch S., Frosch K. H., Fanganel J., Gezzi R., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 3

35-42

EN

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°).

6

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

Wachowski M. M., Hawellek T., Hubert J., Lehmann A., Mansour M., Dumont C., Dorner J., Raab B. W., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2010

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Vol. 12, no. 4

39-47

EN

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 (š1 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.

7

Non-linearity of flexion-extension characteristics in spinal segments

Nägerl H., Hawellek T., Lehmann A., Hubert J., Saptschak J., Dörner J., Raab B.W., Fanghänel J., Kubein-Meesenburg D., Wachowski M. M.

Acta of Bioengineering and Biomechanics

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2009

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Vol. 11, nr 4

3-8

EN

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.

8

A novel total knee replacement by rolling articulating surfaces. In vivo functional measurements and tests

Nagerl H., Frosch K. H., Wachowski M. M., Dumont C., Abicht Ch., Adam P., Kubein-Messenburg D.

Acta of Bioengineering and Biomechanics

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2008

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Vol. 10, nr 1

55-60

EN

The purposes of the paper were as follows: to show the fundamental functional differences between the natural knee and common total knee replacements (TKR), to describe the ideas on how main properties of the natural knee can be adopted by a novel TKR and to present some main biomechanical functions of this TKR. By analyzing the morphology of the articulating surfaces and the kinematics of the natural knee the design of the novel TKR was developed. The use was made of the test procedures established in vitro and of lateral X-ray photographs as well as fluoroscopy in vivo. The function of the novel TKR is comparable to that of the natural knee joint in terms of kinematics (roll/slide behaviour), loads of the articulating surfaces (diminished shear loads), stability and leeway under external impacts, reduction of the load in the patellofemoral joint, and ligament balancing.

9

Mechanical properties of cervical motion segments.

Wachowski M. M., Ackenhausen A., Dumont C., Fanghaenel J., Kubein-Meesenburg D., Naegerl H.

Archive of Mechanical Engineering

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2007

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Vol. LIV, nr 1

5-15

EN

Using a highly sensitive and precise apparatus, series of spatial movements of human cervical segments (C3/C4) were measured. They followed cyclic varied pure torques for axial rotation, lateral flexion, and flexion-extension in the presence of axially directed preloads as running parameter, whose force lines were shifted over the segments. By successive resections of the uncovertebral and zygapophysial joints as well as ligamental structures, the reach of these guiding structures for segmental kinematics and stiffness could be evaluated. For the first time, the biomechanical significance of the uncovertebral joints could be substantiated. In axial rotation and in lateral bending, the instantaneous helical axis (IHA) was found to be not stationary. Its position depended on the size of the rotational angle. The ensamble of the skew IHA formed a ruled surface with a waist. Torque and unit vector of the IHA were found to be parallel only for flexion-extension. In this case, all four joints were in guiding function, whereas in axial rotation and lateral flexion the joints alternated with each other. IHA included with torque Tz(t) for axial rotation dsim +30deg, and with torque Tx(t) dsim-30deg: These motions were coupled. Resection of all ligaments did hardly influence the kinematical structure.

PL

Za pomocą czułej i precyzyjnej aparatury zmierzono serię ruchów przestrzennych odcinków szyjnych (C3/C4) kręgosłupa ludzkiego. Obrót osiowy następował pod działaniem czystego, okresowo zmiennego momentu obrotowego, a zgięcie i zgięcie-ekstensja w obecności skierowanych osiowo obciążeń wstępnych, traktowanych jako parametr zmienny, których linie sił przebiegały przez badane odcinki. Wykonując kolejno resekcje stawów międzykręgowych hakowych (Luschki) i stawów wyrostków kręgowych, a także struktur więzadłowych, dokonano oceny wpływu tych elementów na właściwości kinematyczne i sztywność odcinka szyjnego. Po raz pierwszy udało się potwierdzić biomechaniczne znaczenie stawów hakowych (Luschki). Przy rotacji osiowej i przy zgięciu bocznym chwilowa oś spiralna (IHA) okazała się niestacjonarna. Jej położenie zależało od wartości kąta obrotu. Rodzina nachylonych osi IHA utworzyła powierzchnię rozwijaną z przewężeniem. Stwierdzono, że moment obrotowy i wektor jednostkowy osi IHA są wzajemnie równoległe tylko dla ruchu zginania-ekstensji. W tym ruchu brały udział wszystkie cztery stawy, podczas gdy przy ruchu obrotowym i zgięciu bocznym stawy działały naprzemiennie. Oś IHA miała kąt w przybliżeniu równy +30 stopni przy obrocie osiowym dla momentu Tz(t), oraz w przybliżeniu równy -30 stopni dla momentu Tx(t). Ruchy te były sprzężone. Usunięcie wszystkich wiązadeł wpłynęło w niewielkim stopniu na strukturę kinematyczną.