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

Length scales in tendon and ligament

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

• 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

• 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.

• 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

Typical stress-strain in tendon and ligament

• 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 \(\sigma=0\)

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

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).

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

Other simple models

• 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

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.)

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]

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

Hypothesized relationship between failure mode vs. age

• 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

Remodeling

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

Time dependence and creep

Intervertebral Disc

• There are 23 intervertebral discs in the spinal column
• Key function is to allow a limited amount of relative motion between the bone 12 transmitting most of the compressive load in the spine
• Heterogeneous organ consisting of three elements:
  • Nucleus pulposus
  • Annulus fibrosus
  • Cartilaginous end plate

Composition

• Nucleus pulposus
  • a fluid-like gel, mostly of water (70 to 90%, decreasing with age)
  • randomly oriented type 2 collagen, proteoglycans (with negative charge)
  • most of the resistance to compression comes from annulus fibrosis (and some build up of pressure)

• Annulus fibrosus
  • alternating sheets of type I collagen similar to lamellar bone but without any mineral
  • increasing collagen the outside surface
  • alternating collagen fiber orientation about 30-35 degrees relative to the end plate

• Cartilaginous end plate
  • Bone and ~0.6 mm thick layer of hyaline cartilage which interfaces between the bone of the vertebral body and each of the annulus fibrosus and nucleus pulposus

Other facts

• Aging degrades the nucleus pulposus, solidifying it, making it more like the annulus fibrosus
• no blood supply to the disc
• no nerves
• nutrition occurs by fluid transport
  • injury affects this process

Mechanics

• Load-bearing mechanisms for a healthy disc loaded by (a) a uniaxial compressive force and (b) anterior bending.
• Poroelastic characteristics typical of cartilage, and nonlinear elastic characteristics like tendon and ligament
• Nucleus pulposus axis a pressurized fluid and it contained by tension in the annulus fibrosus

• Hydrostatic pressure developed in the nucleus pulposus
  • Negative charge brings water in osmotically, the resulting swelling resisted by annulus fibrosus (building pressure)
  • Compression causes a slight bulge in the annulus, creating tension. Some of the water is squeezed out.
  • Compressive loading do to activities of daily living thus brings nutrient

• In healthy tissue, bending create differential tension and compression on opposite sides of the annulus fibrosus. However, it remains in tension overall

Highly viscoelastic due to water content.

May be modeled by a standard spring dashpot model

• With aging, dehydration of the nucleus pulposis, more gelatinous, loss of pressure, loss of support of the end plates

• Typical creep curve for an intervertebral body-disc complex, showing the nonzero deformation that develops after complete unloading.
• This latter feature is not typical of classical viscoelastic materials, but instead is due to water loss from the disc during loading.
• During sleep, this height loss is regained as the disc is rehydrated.

• Comparison of the creep response to the same static load for a healthy vs. severely degenerated disc.
• The healthy disc is more viscoelastic, since it takes a longer time for it to reach its equilibrium configuration.
• It is also stiffer, because its final displacement is smaller

Herniated, or slipped, disc

• Annulus can tear or rupture (called disc prolapse, or “slipped disc”)
  • Excessive load (too much pressure), degeneration (insufficient development of pressure)
• Neuromuscular function can be compromised if there is significant impingement of the herniated disc against the nerve roots that exit laterally from the spinal cord.
• Also, can be severe pain!

• No blood supply, disc damage cannot be repaired biologically, accumulation of micro trauma
• With degeneration, decreased disc height, slack in ligaments, instability!

The creep and stress-relaxation functions for the Maxwell, Kelvin-Voigt, and standard linear solid models, in response to the stress and strain time histories, as shown.

Illustration of the nonlinearity of the monotonic stress-strain response for a constant strain-rate loading experiment of a standard linear solid material. At steady state (large values of strain), the response is approximately linear.

Example of discrete (left) and continuous (right) load histories. Linear superposition theory dictates that the overall response to an arbitrary load history is the sum of the individual responses to each increment in load.

Typical phase lag response seen in a viscoelastic material in response to a sinusoidal loading regimen. In this case, the strain response is out of phase with the input stress history, but has the same frequency.

(Data courtesy of Dr. Jeffrey Lotz, UCSF.)

Examples of typical frequency responses for various spring-dashpot models. Es-loss modulus; E-storage modulus.

Maxwell, Kelvin-Voigt, and standard linear solid spring-dashpot models.

The frequency response of the standard linear solid model (on a semi-log plot) to a sinusoidal loading, showing the storage and loss modulo.

Meniscus

• Crescent shaped
• Anchored to the tibia via anterior/posterior roots, capsule
• Force distribution

[ ( slide credit: @Geeslin2016Cartilage ) ]

Contact mechanics

• Accepted metric for evaluating joint forces
• Pressure = Force/Area
  • Force = Pressure x Area
  • Reciprocally related

Contact pressure “map”

[ ( slide credit: @Geeslin2016Cartilage ) ]

Meniscus

1. Inhomogeneous and (B) anisotropic tensile stiffness

[ @DeLee1994 ] Ch 45

[ ( slide credit: @Geeslin2016Cartilage ) ]

Meniscus repair

• Repair of radial meniscus tear
• PRP augmentation of repair
  • (Platelet rich plasma, mix of growth factors)

[ ( slide credit: @Geeslin2016Cartilage ) ]