9 Ligaments and tendon mechanics (Bartel Chapter 4)

9.0.1 Summary: tendon and ligament composition and microstructure

  • Tendons and ligaments have similar compositions and microstructures, with subtle differences
    • Tendon forces larger in activities of daily living
    • Ligament forces generally smaller except at the limits of the range of motion
  • Both tendon and ligament contain about 60 percent water.
  • Tendon:
    • By dry weight, about 75-85 percent of mostly type-I collagen, about 1-3 percent elastin, and 1-2 percent proteoglycans.
    • Elastin-the most elastic protein known gives tendon substantial elastic properties.
    • Collagen fibrils are generally aligned with the direction of the tendon, which is along the line of action of the muscle force.
  • Ligament
    • Ligament contains slightly less collagen (70-80 per cent dry weight), much more elastin (1-15 percent dry weight), and a little more proteoglycan (1-3 percent)
    • it also has a more complex orientation of its fibrils than tendon

9.0.2 Length scales in tendon and ligament

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  • Hierarchical structures common to tendon and ligament (Figure 4.1).

  • Collagen triple helix molecule (1.5 nm diameter);

  • Microfibril (3.5 nm diameter), which contains five collagen molecules;

  • Subfibril (10-20 nm diameter);

  • Fibril (50-500 nm diameter).

9.0.3

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In tendon

  • Collagen fibrils are connected by proteoglycans and non-collagenous proteins
    • Arranged in parallel discrete packets called fascicles.
    • Slightly crimped when unloaded
  • The tendon cells (fibroblasts) situated between the fibrils
  • Fascicles held together by a thick layer of connective tissue (endotenon)
    • A variety of nerves, blood vessels, and lymphatics are contained within the endotenon

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  • The fascicles can slide over each other to some extent
  • In regions where tendons slide over bones (pulleys!), slightly cartilaginous morphology
  • Avascular tendons are surrounded by a synovial sheath
    • Promotes low friction but restricts blood supply
    • A thin layer of connective tissue between the tendon and the sheath, the epitenon, secretes lubricating synovial fluid.
  • Vascular tendons have no synovial sheath, surrounded by a thin layer of connective tissue called the paratenon
    • facilitates direct blood supply to the tendon interior

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  • In ligament, the collagen fibrils (150-250 nm diameter) are arranged first into crimped fibers (1-20 mm diameter) and then into subfascicular units (100-250 um diameter).

  • Three to twenty of these subfascicular units form fascicles (250 um to several millimeters in diameter).

    • Fascicles do not have to be aligned with the overall orientation of the ligament
    • Occasional lack of alignment is one of the main differences between tendons and ligaments.

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  • In the anterior cruciate ligament of the knee, for example, the fascicles are spirally wound about each other, whereas in the collateral ligaments they lie parallel to the length of the ligament.
  • The fascicles, or collagen bundles, slide easily over each other
  • The relative independence of the fascicles is important
    • Allows organs to respond to changing loading conditions
    • For example, certain fascicles of the anterior cruciate ligament take most of the load for twisting of the knee; other fascicles are dominant for translation
    • Hence, tendons and ligaments often have heterogeneous substructures, anisotropy

9.0.4 Typical stress-strain in tendon and ligament

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  • Tendon/ligament have similar microstructure
    • Tendon generally stronger/stiffer due to collegen alignment
    • Subtle differences based on function
  • Three regions
    • Non-linear toe (pretensioned away by muscle?)
    • Quasi-linear region
    • Failure/damage region
  • Stress-strain typically described with Lagrangian strain (or “stretch”) due to large strain \[\lambda = \frac{L}{L_{initial}}\]
  • Stress is expressed as:
    • \(\sigma = \frac{F}{A_{initial}} = a \left(e^{b \lambda}-1\right)\)
    • \(a,b\) are curve fit parameters to experiments
  • Note: \(\frac{d \sigma}{d \lambda} = b \sigma + c\) is thus a “tangent modulus”
    • \(c\) is an integration constant (\(c=a b\)) representing the tangent modulus at \(\sigma=0\)

9.0.5 Be careful!

  • A Hookean (linear elastic) description and reported Young’s modulus differs from the above
  • Nevertheless, Young’s modulus often reported
  • Take care in interpretation

Example: Porcine ACL at 2.5% per second strain rate:

  • \(\sigma = \frac{F}{A_{initial}} = a \left(e^{b \lambda}-1\right)\)
  • \(\sigma = \frac{F}{A_{initial}} = 210 \left(e^{0.63 }-1\right)\)
  • \(\frac{d \sigma}{d \lambda} = 0.63 \sigma + 132\)

Compare to midrange elastic behavior ~157MPA

9.0.6 Typical Whole Ligament Structural Properties (mean ± SD)

ACL = Anterior Cruciate Ligament (Knee); PCL = Posterior Cruciate Ligament (Knee); aPC = anterior Posterior Cruciate (bundle of PCL); pPC = posterior Posterior Cruciate (bundle of PCL): AFIL = Anterior FibuloTalar Ligament (Ankle); CALL = cervical Anterior Longitudinal Ligament (Spine): IALL = lumbar Anterior Longitudinal Ligament (Spine).

9.0.7 On the next few slides

  • Tangent modulus changes with strain rate (activity level) and load
  • A single tendon can have sub-structural bundles, properties differ
  • Overall properties change with location in body and age
  • Typical interest is overall strength of the organ (whole ligament)
    • 100N to 2000N depending on site, size

9.0.8 Other simple models

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  • Simple micro-mechanical parallel-spring model of nonlinear elasticity (a) and the resulting stress-strain curve (b).
  • Assumes different fibers recruit at different elongations
  • Discrete steps… though can be continuous in the limit as the number of fibers increases

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Example of the different force-deformation structural characteristics of the different fiber bundles within the human anterior cruciate ligament. Curves have been shifted along the horizontal axis for clarity. (From Woo and Young in Basic Orthopaedic Biomechanics, ed. Mow and Hayes, pp. 199-243. Raven Press New York, 1991.)

9.0.9 Strain rate sensitivity of tendon fascicles

Tensile testing to 20% clamp-to-clamp strain with 3 different rates showing rate sensitivity (engineering stress vs. engineering strain). [@Clemmer2010]

Average tangent modulus of tendon fascicles (n=6), taken from 5% strain. * indicates p<0.05 vs. 0.1%/s. [@Clemmer2010]

9.0.10 Summary of strain rate sensitivity

  • Rate dependence relatively weak for physiologic rates (factor of 2 over 4 orders of magnitude)
  • Also some minor viscoelastic effects

9.0.11 Hypothesized relationship between failure mode vs. age

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  • Don’t forget failure can occur mid-substance or at bony interface (avulsion) – age may be biggest factor?
    • Children/adolescents have different propensity than adults

9.0.12 Remodeling

  • Remodel (to a degree) in response to load
    • Tissues deteriorate faster than they recover

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9.0.13 Time dependence and creep

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Example of load-time response to stretching of the anteromedial bundle of a porcine ACL to 5 percent strain by a ramp load at a strain rate of 2.5 percent per second. The specimen was then held at 5 percent strain for two hours and displayed classical stress relaxation behavior.