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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 description of the human knee as four-bar linkage

Dathe H., Gezzi R., Fiedler Ch., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2016

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Vol. 18, no. 4

107--115

EN

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.

3

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

Dathe H., Gezzi R., Kubein-Meesenburg D., Nägerl H.

Acta of Bioengineering and Biomechanics

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2015

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Vol. 17, no. 1

75--86

EN

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.

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.