Research Papers

A Multibody Knee Model Corroborates Subject-Specific Experimental Measurements of Low Ligament Forces and Kinematic Coupling During Passive Flexion

[+] Author and Article Information
Mohammad Kia

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: KiaM@hss.edu

Kevin Schafer

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: kevinschafer88@gmail.com

Joseph Lipman

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: LipmanJ@hss.edu

Michael Cross

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: CrossM@hss.edu

David Mayman

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: MaymanD@hss.edu

Andrew Pearle

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: PearleA@hss.edu

Thomas Wickiewicz

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: WickiewiczT@hss.edu

Carl Imhauser

Hospital for Special Surgery,
535 E 70th Street,
New York, NY 10021
e-mail: ImhauserC@hss.edu

1Corresponding author.

Manuscript received May 15, 2015; final manuscript received February 22, 2016; published online March 31, 2016. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 138(5), 051010 (Mar 31, 2016) (12 pages) Paper No: BIO-15-1242; doi: 10.1115/1.4032850 History: Received May 15, 2015; Revised February 22, 2016

A multibody model of the knee was developed and the predicted ligament forces and kinematics during passive flexion corroborated subject-specific measurements obtained from a human cadaveric knee that was tested using a robotic manipulator. The model incorporated a novel strategy to estimate the slack length of ligament fibers based on experimentally measured ligament forces at full extension and included multifiber representations for the cruciates. The model captured experimentally measured ligament forces (≤5.7 N root mean square (RMS) difference), coupled internal rotation (≤1.6 deg RMS difference), and coupled anterior translation (≤0.4 mm RMS difference) through 130 deg of passive flexion. This integrated framework of model and experiment improves our understanding of how passive structures, such as ligaments and articular geometries, interact to generate knee kinematics and ligament forces.

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Fig. 1

Flowchart summarizing the model development procedure (dashed gray box) and subject-specific comparison of model predictions with the physical experiment

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Fig. 2

L-frames were rigidly fixed to the tibia and femur and identified using a 3D digitizer after the knee specimen was mounted to the six degrees-of-freedom robot in full extension

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Fig. 3

Boolean subtraction was used to develop 3D geometries of (a) the tibial and femoral (not shown) articular cartilage and (b) the menisci. The surfaces were subsequently smoothed.

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Fig. 4

Fibers representing the ligaments in the multibody model: (a) ACL (six fibers), (b) PCL (seven fibers), (c) sMCL (three proximal fibers and three distal fibers), POL (three fibers), (d) MPC and LPC (three fibers each), (e) OPL (two fibers), (f) FFL (one fiber), LCL (one fiber), and ALL (one fiber)

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Fig. 5

(a) The anterior and posterior horn attachments of the menisci were each represented by one fiber (total of four fibers). The coronary ligaments were represented by seven fibers (two anterior, three medial, and two posterior) constraining the medial meniscus to the tibial plateau. (b) One fiber represented the coronary ligament constraining the lateral meniscus to the tibia/fibula.

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Fig. 6

Overview of the multibody model including bony geometries, articular cartilage, discretized menisci, and ligament fibers

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Fig. 7

Representative force–elongation response for a ligament fiber consisting of the slack length (l0), the toe region f* (l), linear region (K), and a term (Δt) that identifies the transition between the toe and linear regions

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Fig. 8

The three proximal and three distal fibers of the sMCL were connected in series with 1 mm diameter spheres to simulate wrapping

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Fig. 9

Ligament force predicted by the model (solid line) and measured in the physical experiment (dashed line) during passive flexion from 0 to 130 deg: (a) ACL, (b) PCL, (c) sMCL, (d) LCL, and (e) POL

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Fig. 10

Tibial kinematics with respect to the femur predicted by the model (solid line) and measured in the physical experiment (dashed line) during passive flexion from 0 to 130 deg. A positive direction indicates: (a) internal rotation, (b) anterior translation, (c) distal translation, (d) varus rotation, and (e) lateral translation.

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Fig. 11

(a) Schematic describing the transformations used to register the CT-derived geometries to the anatomical coordinate system of the physical experiment. This included the reference frames for the CT scanner (CT), the digitizer (D), and the L-frames (L) identified both in CT and via the digitizer. The anatomical coordinates systems for the tibia (T) and femur (F) were based on the digitization points (P1–P5). All the symbols are summarized in Appendix A, Table 4. (b) Image of the validation jig used to quantify the accuracy of the method employed to register the CT-derived geometries to the anatomical coordinate system.

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Fig. 12

Predicted force in the individual fibers of the ACL throughout the flexion arc (0–130 deg): (a) AM (two fibers) and AL (one fiber); (b) PL (three fibers)



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