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Research Papers

Modeling the Human Tibiofemoral Joint Using Ex Vivo Determined Compliance Matrices

[+] Author and Article Information
Giuliano Lamberto

Department of Movement,
Human, and Health Sciences,
Università degli Studi di Roma—Foro Italico,
Piazza Lauro de Bosis 6,
Rome 00194, Italy;
Department of Mechanical Engineering,
INSIGNEO Institute for In Silico Medicine,
University of Sheffield,
Mappin Street,
Sheffield S1 3JD, UK
e-mail: glamberto1@sheffied.ac.uk

Vincent Richard

University of Lyon,
Université Claude Bernard Lyon 1,
IFSTTAR, UMR_T9406, LBMC,
Lyon F69622, France
e-mail: vincent.richard@univ-lyon1.fr

Raphaël Dumas

University of Lyon,
Université Claude Bernard Lyon 1,
IFSTTAR, UMR_T9406, LBMC,
Lyon F69622, France
e-mail: raphael.dumas@ifsttar.fr

Pier Paolo Valentini

Department of Enterprise Engineering
“Mario Lucertini,”
Università degli Studi di Roma—Tor Vergata,
Via del Politecnico 1,
Rome 00133, Italy
e-mail: valentini@ing.uniroma2.it

Ettore Pennestrì

Mem. ASME
Department of Enterprise Engineering
“Mario Lucertini,”
Università degli Studi di Roma—Tor Vergata,
Via del Politecnico 1,
Rome 00133, Italy
e-mail: pennestri@mec.uniroma2.it

Tung-Wu Lu

Institute of Biomedical Engineering
and Department of Orthopaedic Surgery,
National Taiwan University,
No. 1, Section 4, Roosevelt Road,
Taipei 106, Taiwan
e-mail: twlu@ntu.edu.tw

Valentina Camomilla

Department of Movement,
Human, and Health Sciences,
Università degli Studi di Roma—Foro Italico,
Piazza Lauro de Bosis 6,
Rome 00194, Italy
e-mail: valentina.camomilla@uniroma4.it

Aurelio Cappozzo

Department of Movement,
Human, and Health Sciences,
Università degli Studi di Roma—Foro Italico,
Piazza Lauro de Bosis 6,
Rome 00194, Italy
e-mail: aurelio.cappozzo@uniroma4.it

1Corresponding author.

Manuscript received October 8, 2015; final manuscript received April 15, 2016; published online May 11, 2016. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 138(6), 061010 (May 11, 2016) (8 pages) Paper No: BIO-15-1499; doi: 10.1115/1.4033480 History: Received October 08, 2015; Revised April 15, 2016

Several approaches have been used to devise a model of the human tibiofemoral joint for embedment in lower limb musculoskeletal models. However, no study has considered the use of cadaveric 6 × 6 compliance (or stiffness) matrices to model the tibiofemoral joint under normal or pathological conditions. The aim of this paper is to present a method to determine the compliance matrix of an ex vivo tibiofemoral joint for any given equilibrium pose. Experiments were carried out on a single ex vivo knee, first intact and, then, with the anterior cruciate ligament (ACL) transected. Controlled linear and angular displacements were imposed in single degree-of-freedom (DoF) tests to the specimen, and the resulting forces and moments were measured using an instrumented robotic arm. This was done starting from seven equilibrium poses characterized by the following flexion angles: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. A compliance matrix for each of the selected equilibrium poses and for both the intact and ACL-deficient specimen was calculated. The matrix, embedding the experimental load–displacement relationship of the examined DoFs, was calculated using a linear least squares inversion based on a QR decomposition, assuming symmetric and positive-defined matrices. Single compliance matrix terms were in agreement with the literature. Results showed an overall increase of the compliance matrix terms due to the ACL transection (2.6 ratio for rotational terms at full extension) confirming its role in the joint stabilization. Validation experiments were carried out by performing a Lachman test (the tibia is pulled forward) under load control on both the intact and ACL-deficient knee and assessing the difference (error) between measured linear and angular displacements and those estimated using the appropriate compliance matrix. This error increased nonlinearly with respect to the values of the load. In particular, when an incremental posterior–anterior force up to 6 N was applied to the tibia of the intact specimen, the errors on the estimated linear and angular displacements were up to 0.6 mm and 1.5 deg, while for a force up to 18 N, the errors were 1.5 mm and 10.5 deg, respectively. In conclusion, the method used in this study may be a viable alternative to characterize the tibiofemoral load-dependent behavior in several applications.

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Figures

Grahic Jump Location
Fig. 1

(a) A schematic representation of the RJTS and the reference systems used are provided: G is the global coordinate system, Cs is the coordinate system of the load cell, and Cf is the anatomical coordinate system of the femur. (b) Cf was defined as follows: the origin was the midpoint between the MCL and LCL insertions; the z-axis was made to pass through LCL and MCL (transepicondylar axis) and pointed toward the latter point. The y-axis was defined as lying on the plane defined by LCL, MCL, and the centroid of the bone section (frontal plane) and perpendicular to the z-axis pointing toward the proximal part of the bone. Finally, the x-axis was defined to be perpendicular to both the y- and the z-axes and oriented to generate a right-handed frame.

Grahic Jump Location
Fig. 2

The absolute error for the intact knee between displacements (a) and rotations (b) measured and computed with the compliance matrix at 30 deg of F-E is displayed. The values of A-P, P-D, and M-L computed displacements (c) and measured forces (e) of A-A, I-E, and F-E rotations (d) and moments (f) are also illustrated.

Grahic Jump Location
Fig. 3

Compliance matrix validation of the ACL-deficient knee. See Fig. 2 for the explanation.

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