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Research Papers

A Three-Dimensional Ankle Kinetostatic Model to Simulate Loaded and Unloaded Joint Motion

[+] Author and Article Information
Margherita Forlani

DIN-Department of Industrial Engineering,
Health Sciences and Technologies,
Interdepartmental Centre for Industrial
Research (HST-ICIR),
University of Bologna,
Bologna 40136, Italy
e-mail: margherita.forlani2@unibo.it

Nicola Sancisi

DIN-Department of Industrial Engineering,
Health Sciences and Technologies,
Interdepartmental Centre for Industrial
Research (HST-ICIR),
University of Bologna,
Bologna 40136, Italy
e-mail: nicola.sancisi@unibo.it

Vincenzo Parenti-Castelli

DIN-Department of Industrial Engineering,
Health Sciences and Technologies,
Interdepartmental Centre for Industrial
Research (HST-ICIR),
University of Bologna,
Bologna 40136, Italy
e-mail: vincenzo.parenti@unibo.it

Manuscript received March 5, 2014; final manuscript received February 6, 2015; published online March 25, 2015. Assoc. Editor: Tammy L. Haut Donahue.

J Biomech Eng 137(6), 061005 (Jun 01, 2015) (12 pages) Paper No: BIO-14-1105; doi: 10.1115/1.4029978 History: Received March 05, 2014; Revised February 06, 2015; Online March 25, 2015

A kinetostatic model able to replicate both the natural unloaded motion of the tibiotalar (or ankle) joint and the joint behavior under external loads is presented. The model is developed as the second step of a sequential procedure, which allows the definition of a kinetostatic model as a generalization of a kinematic model of the joint defined at the first step. Specifically, this kinematic model taken as the starting point of the definition procedure is a parallel spatial mechanism which replicates the ankle unloaded motion. It features two rigid bodies (representing the tibia–fibula and the talus–calcaneus complexes) interconnected by five rigid binary links, that mimic three articular contacts and two nearly isometric fibers (IFs) of the tibiocalcaneal ligament (TiCaL) and calcaneofibular ligament (CaFiL). In the kinetostatic model, the five links are considered as compliant; moreover, further elastic structures are added to represent all the main ankle passive structures of the joint. Thanks to this definition procedure, the kinetostatic model still replicates the ankle unloaded motion with the same accuracy as the kinematic model. In addition, the model can replicate the behavior of the joint when external loads are applied. Finally, the structures that guide these motions are consistent with the anatomical evidence. The parameters of the model are identified for two specimens from both subject-specific and published data. Loads are then applied to the model in order to simulate two common clinical tests. The model-predicted ankle motion shows good agreement with results from the literature.

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Figures

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Fig. 1

Definition of the kinetostatic model: (a) and (b) represent the definition of the kinematic model (first step of the sequential approach); (c) and (d) show the generalization of this model to obtain the kinetostatic one (second step of the procedure). In particular, the main structures guiding the passive motion are shown in (a): the three bone contacts and the TiCaL and CaFiL. A schematic representation of the kinematic model is reported in (b), where the three articular contacts are modeled as sphere-on-sphere contacts, and the two IFs of TiCaL and CaFiL are modeled by two rigid links. The IFs are considered as compliant (black lines) in (c) and elastic fibers are added (gray lines) to model other ligaments. The 26 fibers identified on the 3D bone surfaces obtained from CT scans of one representative ankle specimen are shown in (d): in particular, the IFs at the TiCaL (IF1) and CaFiL (IF2), and the CFs at the lateral malleolus (C1), at the internal region of the inferior surface of the distal tibia (C2), and at the medial malleolus (C3) are highlighted: these fibers correspond to the five constraints in (b).

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Fig. 2

The joint coordinate system used for description of the ankle motion. The reference frames Sf of the tibia–fibula and Sc of the talus–calcaneus complexes are defined according to the ISB recommendations [21]. The six components of the relative motion between the two bone complexes are described as rotations about and displacements along the axes e1, e2, e3 of the joint coordinate system: axis e1 is coincident to zf, axis e3 is coincident to xc, and e2 is a floating axis perpendicular to e1 and e3.

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Fig. 3

Pose components of the unloaded motion for the specimens A (left) and B (right). Rotations are: D/P = dorsiflexion(+)/plantarflexion(−), Int/Ext = internal(+)/external(−), and Inv/Ev = inversion(+)/eversion(−). Displacements are: L/M = lateral(+)/medial(−), P/D = proximal(+)/distal(−), and A/P = anterior(+)/posterior(−). Crosses are experimental data, while continuous lines represent the model motion.

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Fig. 4

Results of the two kinetostatic models determined for the specimens A (circles) and B (squares) compared with the mean values (crosses) and SDs (lines) of the reference experimental data [29]. The flexion is fixed at the mean value reported in the reference paper, and the other five motion components are rotations and displacements from the neutral pose. In the tables, the absolute and relative (with respect to the corresponding SD) differences between the computed and the mean reference values of the pose components are reported.

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