8.6 Mechanical properties

• Anisotropic - differ with direction of loading (may be associated with zonal arrangement of collagen)
• Heterogeneous (due to varying collagen, proteoglycan, and water content)
• Poroelastic solid – Biphasic
  • Flow of interstitial fluid through the matrix and resistance of matrix to the flow (and is dominant in dynamic response)
  • Intrinsic: flow-independent behavior of collagen-proteoglycan matrix
    • Intrinsic properties are not representative of in vivo behavior, however, they affect fluid flow

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.1 Material Properties of Articular Cartilage

• “Split lines” - surface collagen fiber pattern; functionally related to tensile strength (and highest modulus aligned with split lines)
• Referred to in @Bartel2006 p133

@Jastifer2010Cartilage

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.2 Uniaxial tensile test

@Bartel2006

Typical stress-strain behavior for articular cartilage subjected to tensile loading at a low constant strain rate.

• Low constant strain rate
  • Values higher than “equilibrium” due to dynamic nature of test
• Some fluid flow occurs (Model does match/accommodate fluid flow present in physiologic loading)
• This dynamic Young’s modulus (from linear region) is ~ 40-400 MPa

[ ( @Bartel2006 Ch 4.2. ) ]

Mechanical Behavior and Material Properties

Cartilage material behavior is anisotropic. This aspect of its behavior is difficult to model mathematically and is therefore generally ignored in most structural analyses, but it is important to be aware of anisotropy when interpreting results from experiments on cartilage material behavior. Cartilage also displays heterogeneity in collagen, proteoglycan, and water content, and the material properties vary accordingly. The material behavior of cartilage can be regarded as that of a poroelastic solid. Its behavior arises from two sources: (1) intrinsic, flow-independent behavior of the collagen-proteoglycan matrix; and (2) flow of the interstitial fluid through the matrix and the resistance of the matrix to this flow. While fluid flow dominates the dynamic, in vivo behavior of cartilage, the intrinsic properties determine in large part many of the parameters that restrict such flow. Therefore, intrinsic behavior is an important aspect of cartilage behavior, even though it does not represent typical in who behavior. The ionic phase also acts to produce swelling in the tissue, which also contributes to the resistance of fluid flow through the matrix. As will be discussed shortly, this swelling depends on the intrinsic properties of the solid matrix. Thus, all three phases are intimately related in how they influence the material behavior.

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.3 Equilibrium stress-strain behavior

• Can be determined from steady-state response of tensile creep loading with no fluid flow
• Linear up to strains of 15%
• Modulus ~ 4-10 MPA depending on specimen location in joint

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.4 Intrinsic compressive properties

Setup for the confined compression test of articular cartilage. (From Mow et al. in Basic Orthopaedic Biomechanics, ed. Mow and Hayes, pp. 143-198. Raven Press, New York. 1991.)

• Confined compression creep test: is a uniaxial strain test.
  • Chamber restrict deformation except along axis of loading
  • an applied constant stress
  • fluid can escape through porous surface of test fixture
  • creep occurs and eventually equilibrium (steady-state is reached when fluid flow stops)
• Experiment is repeated over various stresses and respective strains and aggregate modulus \(H_A\) is obtained (typically 0.3-1.3 MPa)

[ (slide credit: @Jastifer2010Cartilage, @Geeslin2016Cartilage) ]

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8.6.5 Intrinsic compressive properties

• Compressive equilibrium and \(H_A\)
  • Depends on repulsive electrical charges of Proteoglycan, increases with increased Proteoglycan content (next slide)
  • Unrelated to collagen content (structurally) although collagen constrains separation of Proteoglycan, resulting in internal tensile stresses

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8.6.6 Intrinsic compressive properties

• Early load results in fluid efflux
• Late load results in increased charge density due to negative Proteoglycan side-chains

• Note “Permeability” is another factor which can be quantified - Resistance to flow

[ ( adapted from @Jastifer2010Cartilage @Geeslin2016Cartilage ) ]

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8.6.7 “Creep” manifestation in cartilage confined compression tests

• Constant load applied (in the test)
  • Deformation is not instantaneous, as it would be in a single-phase elastic material such as a spring.
• Displacement of the cartilage is a function of time, since the fluid cannot escape from the matrix instantaneously
  • Initially, the displacement is rapid. This corresponds to a relatively large flow of fluid out of the cartilage.
  • As the rate of displacement slows and the displacement approaches a constant value, the flow of fluid likewise slows.
  • Equilibrium takes several thousand seconds

Note this is very different from classical metal creep

[ ( adapted from @Jastifer2010Cartilage ) ]

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8.6.8 Intrinsic compressive properties

@Bartel2006

Dependence of equilibrium compressive aggregate modulus for human patellar cartilage on hyaluronic acid content (a surrogate measure of proteoglycan content).

(From Armstrong and Mow in Clinical Trends in Orthopaedics, ed. Wilson and Straub, pp. 189-197. Thieme-Stratton, New York, 1982.)

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.9 Water content and compressive modulus

@Armstrong1982

• Dependence of equilibrium compressive aggregate modulus for human patellar cartilage on water content. @Armstrong1982
• Less water means less proteoglycan per unit volume? (Also a function of aging.)

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8.6.10 Pure Shear

• Small torsional displacements of cylindrical samples (which produce pure shear), result in no volume change of the cartilage to drive fluid flow.
• The interstitial fluid (water) has low viscosity and does not make an appreciable contribution to resisting shear.
• Therefore, the resistance to shear is due to the solid matrix.
• Tests of cartilage in shear show that the matrix behaves as a viscoelastic solid

@Jastifer2010Cartilage

Reminder: pure shear is equivalent to a combination of tension and compression applied at +/-45 degrees to the plane of shear

[ ( slide credit: @Jastifer2010Cartilage ) ]

8.6.11 Shear

@Bartel2006

• Flow-independent shear rigidity of cartilage likely due to collagen fibers
• Proteoglycan likely interact to support matrix

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.12 Shear: collagen and modulus

@Bartel2006

Positive correlation between the magnitude of the dynamic shear modulus (as measured in dynamic viscoelastic tests) and collagen content for bovine cartilage

, confirming the mechanism proposed in Figure 4.11. (From Mow et al. in Basic Orthopaedic Biomechanics, ed. Mow and Hayes, pp. 143-198 Raven Press, New York, 1991.)

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8.6.13 Shear Stress

• High poison’s ratio, thus normal load leads to large lateral displacement relative to bone, thus high shear stresses at cartilage/bone interface

@Jastifer2010Cartilage

• Not intuitive but joints aren’t normal, and thus see shear stress

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.14 Stress relaxation

@Geeslin2016Cartilage

@Mow1984

• Material subjected to constant deformation
• High initial stress
• Progressive decrease in the stress required to maintain deformation

@Jastifer2010Cartilage

(Mow 1977)

Fig. 12. The top graph shows a controlled ramp displacement for a confined-compression experiment. The middle curve shows a typical stress rise during the compression phase and a typical stress-relaxation response in the relaxation phase. The bottom schematics show that the movement of interstitial fluid predominates the stress-history response. During the compression phase, fluid exudation gives rise to a peak stress a. and during the relaxation phase, fluid redistribution gives rise to the relief of the compacted region at the surface. hence stress relaxation. (For more quantitative details, see Fig. 13.)

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.15 Compression and permeability (of cartilage plug)

@Bartel2006

1. Dependence of permeability of articular cartilage on compressive clamping strain and applied pressure gradient. Modified from Mow et al. (1980) J Biomech Eng 102:73–84. (b) Typical response for a stress relaxation test of articular cartilage, where a uniform displacement is applied and the stress relaxes over time to its steady-state equilibrium value.

As you compress the tissue, you do two things:

• Close the space for water to flow through by compacting tissue
• and Increase charge density thus slowing flow.

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.16 Creep and stress relaxation

Functionally:

• Stress Relaxation
• Nonlinear phenomenon

@Geeslin2016Cartilage

@DeLee1994

[ ( slide credit: @Geeslin2016Cartilage ) ]

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8.6.17 Permeability

• Permeability, κ, is the ease of fluid flow
  • Flow velocity proportional to pressure gradient
  • \(10^{-15}\) to \(10^{-16} m^4/Ns\)

@Jastifer2010Cartilage

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@Jastifer2010SoftTissue

• As cartilage is compressed (and fluid flows from cartilage) the permeability decreases (with increased strain), and stiffness increases which prevents further loss of fluid

A. Experimental configuration used in measuring the permeability of articular cartilage, involving the application of a pressure gradient (P-Ph across a sample of the tissue (h tissue thickness). Because the fluid pressure (P) above the sample is greater than that beneath it (P), fluid will flow through the tissue. The permeability coefficient k in this ex perimeter is given by the expression Q(P.-P.), where is the volumetric discharge per unit time and A is the area of permeation. Adapted from Torzilli, PA, & Mow, VC (1976). On the fundamental fluid transport mechanisms through normal and pathologic cartilage during function. The formulation. J Bio mech, 98541552 B, Experimental curves for articular car. tillage permeability show its strong dependence on compress sieve strain and applied pressure. Measurements were taken at applied pressure differential (P.-P.) and applied strains. The permeability decreased in an exponential manner as a function of both increasing applied compressive strain and increasing applied pressure. Adapted from Lai, WM, & Mow, VC (1980) Drag-induced compression of articular cartilage during a permeation experiment. J Biorheology, 17, 111.

[ ( slide credit: @Jastifer2010Cartilage ) ]

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• If a pressure difference of 210,000 Pa (about the same pressure as in an automobile tire) is applied across a slice of cartilage 1 mm thick, the average fluid velocity will be only \(1\times10^{-8}\) m/s

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8.6.18 Cartilage - putting it together

• As you stand
  • Complex interaction of stress in the cartilage matrix and pressure in the fluid.
  • Cartilage stops itself from “bottoming out” because its permeability decreases with increased strain, and it’s stiffness increases.
  • Cartilage has to be thought of as a dynamic structure (see example 4.2)

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.19 Clinical Correlate

• Arthritic cartilage has a lower modulus and increased permeability (higher water content, lower proteoglycan content).
• This leads to greater and more-rapid deformation than normal.
• Theoretically, these changes may influence the metabolic activity of the chondrocytes, which are known to respond to their mechanical environment (mechanotransduction).

@Jastifer2010Cartilage

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.20 Clinical Correlate

• Hypothesis
  • Cartilage thought to fail in tension/shear at surface that creates a fissure that propagates
• Fact
  • Femoral head arthritis far more likely than talus arthritis (contradiction?)

@Jastifer2010Cartilage

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.21 Clinical Correlate

• Old cartilage fails earlier than young cartilage

@Jastifer2010Cartilage

[ ( slide credit: @Jastifer2010Cartilage ) ]

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8.6.22 Clinical correlates

Return to this figure:

@Armstrong1982

• Disruption of the collagen fibril meshwork allows the Proteoglycan to expand, increases \(H_2O\), decreases Proteoglycan
• Less repulsive electrostatic forces to resist loading
• Decrease in cartilage stiffness, increase in matrix permeability
• In osteoarthritis, decreased Proteoglycan and increased \(H_2O\) - Greater deformation - Altered mechanotransduction?

[ ( slide credit: @Geeslin2016Cartilage ) ]