BME/ME 456 Biomechanics
Cartilage Structure and Function
There are three major types of cartilage in the body: 1) hyaline cartilage, 2) fibrocartilage, and 3) elastic cartilage. Elastic cartilage exists in the epiglottis and the eustachian tube. Fibrocartilage, as we saw in the section on fracture fixation, often exists temporarily at fracture sites. However, fibrocartilage is permanently present in three major locations in the body: 1) the intervertebral disks of the spine, 2) as a covering of the mandibular condyle in the temporomandibular joint, and 3) in the meniscus of the knee. The third type of cartilage, hyaline cartilage, is most prominently found in diarthroidal joints covering long bones. In addition, hyaline cartilage forms the growth plate by which long bones grow during childhood. In this section, we review the structure and mechanical behavior of hyaline cartilage in diathroidal joints, typically called articular cartilage, and the meniscus of the knee. The accompany information in the text is Chapter 4 "Structure and Function of Articular Cartilage and Meniscus" by Van Mow and Anthony Ratcliffe.
II. Diarthroidal Joint Anatomy and Hierarchical Cartilage Structure
Again, although it begins to sound redundant at this point, articular cartilage itself has a hierarhical structure and is also part of a diarthroidal joint which is a composite structure. The nature of the hierarchical structure of both diarthroidal joints and articular cartilage is illustrated in the figure from your text shown below:
The top row of the figure illustrates the composite strcuture of diarthroidal joints which consist of bone, articular cartilage, ligaments, tendons, muscle and the joint capsule. This whole organ level exists at a scale of > .5 cm. The next level in this schematic indicates in more detail the actual bearing surface of the joint, in this case the knee joint as evidenced by the meniscus. The scale is between 100 microns (.1 mm) and 1 cm. At this point the articular cartilage may be viewed as a solid homogeneous material. In the next level of structure, called the microstructure between .0001 mm (.1 microns) and .1 mm (100 microns), we see the existence of the structural features of articular cartilage including the chondrocytes (cells that make cartilage matrix) and the organization of the type II collagen fibrils. The organization at this level can actually be divided into four zones: 1) the superficial tangential zone (10-20% of the cartilage thickness, 2) the middle zone, 60% of the cartilage thickness, 3) the deep zone, 30% of the cartilage thickness, and 4) the calcified cartilage zone where the cartilage interfaces with the bone. The zones contain different collagen organization as well as different amounts of proteoglycans. A schematic of these zones from your text is shown below:
The superficial or tangential zone contains the highest collagen content, about 85% by dry weight. In addition, the collagen fibrils are oriented parallel to the joint surface, indicating that the purpose of this zone may be primarily to resist shear stresses. The amount of collagen decreases in each zone moving closer to the tidemark, dropping to 68% in the middle zone.
At the next level, denoted as the ultrastructural level, between .00001 mm (.01 microns) and .001 mm (1 micron), we see the existence of the major biochemical constituents of articular cartilage including the individual collagen fibrils and the proteoglycan matrix. Finally, at the nanostructural level (.0000001 mm (.1 nanometer) to .000001 mm (1 nanometer) we see the interior structure of the collagen and proteoglycan molecules. As you can see, definition of these structural levels is not cut and dried, but exists as a conceptual tool to help us understand cartilage structure and how that structure influences cartilage function. The other very important point to note is that the micro and ultra structures contain water and electrolytes that are bound to the molecules (mainly proteoglycans and collagen) that constitute the solid matrix of articular cartilage. As we will see later, the fluid-solid interaction is a major determinant of articular cartilage mechanical behavior.
III. Articular Cartilage and Meniscus Composition
Section II outlined the hierarchical structure of articular cartilage. In this section, we outline the chemical composition that is common to articular cartilage and meniscus. There are two major phases of articular cartilage and meniscus: 1) a fluid phase containing water and electrolytes, and 2) a solid phase containing collagen (type I in meniscus and type II in articular cartilage), protoeglycans, glycoproteins and chondrocytes. Chondrocytes are the cells that produce cartilage matrix. The specific percentages of the major constituents for articular cartilage and meniscus are given in table I of the text chapter, reproduced below:
Tissue Water Collagen Proteoglycans
Articular Cartilage 68-85%
Meniscus 60-70% 15-25% (type II) 1-2%
As you can imagine, these three major components act together to determine the mechanical behavior of cartilage. Changes in the relative amounts of these components due to disease will change the time dependent mechanical properties of cartilage.
Of the three major components, the most prevalent is water. About 30% of the total water exists within the intrafibrillar space of collagen. The collagen fibril diameter and the amount of water within the collagen is determined by the swelling pressure due to the fixed charge density (FCD) of the proteogylcans. In other words, the proteogylcans have strong negative electric charges. The proteoglycans are constrained within the collagen matrix. Because the proteogylcans are bound closely, the closeness of the negative charges creates a replusion force that must be neutralized by positive ions in the surrounding fluid. The higher concentration of ions in the tissue compared to outside the tissue leads to swelling pressures. The exclusion of water raises the density of fixed charge, which in turn raises the swelling pressure and charge-charge repulsion. The amount of water present in cartilage depends on 1) the concentration of proteoglycans which determines FCD and swelling pressure, 2) the organization of the collagen network, and 3) the stiffness and strength of the collagen network. The collagen network resists the swelling of the articular cartilage. If the collagen network is degraded, as in the case of OA, the amount of water in the cartilage increases, because more negative ions are exposed to draw in fluid. The increase in fluid can significantly alter the mechanical behavior of the cartilage.
In addition, with a pressure gradient or compression, fluid is squeezed out of the cartilage. When the fluid is being squeezed out, there are drag forces between the fluid and the solid matrix that increase with increasing compression and make it more difficult to exude water. This behavior increases the stiffness of the cartilage as the rate of loading is increased.
Collagen is the component of cartilage that is believed to contribute most to tensile behavior of the tissue. The predominant collagen in articular cartilage is type II while the predominant collagen in meniscus is type I.
The third major component of cartilage are the proteoglycans. Proteoglycans are large biomolecules that consist of a protein core with glycosaminoglycan side chains. These molecules normally occupy must large space when not compacted by a collagen network. The compaction of the proteoglycans affects swelling pressure as well as fluid motion under compression.
IV. Structure-Function Relationships in Articular Cartilage and Meniscus
As perhaps can be gleaned from the previous sections, there are three major factors that contribute to articular cartilage mechanical behavior. First, there is the swelling pressure due to the ionic affects in the tissue. Second, there are the elastic behavior of the solid matrix itself. Third, there is the the fluid-solid interaction in the cartilage under compressive load. We next detail these mechanical behaviors and discuss the how the tissue structure contributes to this behavior.
Solid Matrix Properties
First, let us consider the tensile properties and behavior of the cartilage solid matrix. As with the other soft collagenous tissues that we have studied, the mechanical behavior of the solid matrix is determined by the amount and crimp of collagen in the matrix. Thus, this matrix follows the classic nonlinear stress strain curve for soft tissues as shown below:
where we see a toe region, a linear region, and a failure region. These regions correspond the unfolding of the crimp. A typical dumbell specimen is used to test the matrix tensile properties as shown below:
In terms of structure function relationships, we can see the effect of increasing collagen content on tensile properties by looking at the tensile moduli from the linear portion of the above stress strain curved measured in the different cartilage zones. Some experimental data is shown below in MPa:
Bovine Canine Human
Glenoid Humerus Femoral Groove Femoral Condyle Groove Condyle
Superficial 5.9 13.4 27.4 23.3 13.9 7.8
Middle 0.9 2.7 3.4 4.0
Deep 0.2 1.7 1.0
This result can also be confirmed looking at the plot in your text that relates tensile modulus to the ratio of collagen to proteoglycan in the cartilage matrix:
Osteoarthritis, or OA, a major disease that affects cartilage can have signficant effects on the tensile properties of the solid matrix. In OA, we know histologically that there is a disruption in the collagen fibrils in the solid matrix. This is reflected in decreases in the tensile modulus of the solid matrix, as shown below in the table from your text:
Normal (MPa) Fibrillated (MPa) OA (MPa)
Surface 7.8 7.2 1.4
Subsurface 4.9 7.5 0.85
Middle 4.0 4.9 2.11
Finally, as with other soft tissues that had a nonlinear stress strain curve and could be considered hyperelastic, we can derive a strain energy function that can be used to calculate the dependence of stress on strain. Let us consider the following strain energy function:
where k and B are constants and E is the Green-Lagrange strain. If we differentiate with respect to the strain we obtain the stress as:
which, if we consider the constant A = Bk, is the same result as your text. In addition to articular cartilage, the tensile modulus of the meniscus is significantly dependent on the amount and orientation of collagen fibrils. In the outer meniscus, collagen fibrils are arranged circumferentially in a more organized manner than in the middle of the meniscus. This gives rise to higher tensile moduli in the circumferential zone.
Compressive Fluid-Solid Properties
As was mentioned in the section of cartilage composition, the interaction between the fluid and solid phase of the cartilage plays a significant role in the mechanical behavior of cartilage. The flow of water out of the tissue and the drag this creates on the solid phase are major determinants of the compressive behavior of the tissues. Thus, in this sense, the mechanical behavior of the cartilage is very dependent on how easy it is for the fluid to move in and out of the tissue, a property known as permeability. Flow of fluid through solid, permeable matrices is governed by Darcy's law. Darcy's law states that the rate of volume discharge through a porous solid is related to the pressure gradient applied to the solid and the hydraulic permeability coefficient k. Mathematically, Darcy's law is stated as follows:
where Q is the rate of volume discharge in m^3/sec, k is the permeability coefficient in m^4/Ns, A is the area in m^2, delta P is the pressure gradient in N/m^2 and h is the height of the specimen given in m. Thus, the units work out as:
The permeation speed V is related to Q by dividing Q by the A times the volume fraction of the fluid. The diffusive drag coefficient, how much drag the fluid creates on the solid, determined as:
where K is the drag, k is the permeability and the remaining term is the volume fraction of fluid.
Permeability and load sharing between the solid and fluid components form the basis for the biphasic theory of cartilage behavior. The tenets of biphasic theory are the following:
1. Solid matrix may be linearly elastic or hyperelastic with isotropic or anisotropic behavior.
2. The solid matrix and interstitial fluid are incompressible. This means that cartilage as a whole can only be compressed if fluid is exuded from the cartilage.
3. Energy dissipation is result of fluid flow relative to solid matrix.
4. Frictional drag of the solid vs. the fluid is proportional to relative veloctiry. This is diffusive drag.
The standard stress equilibrium equations are modified for biphasic theory as follows:
where is the solid stress, is the fluid stress, K is the drag coefficient, is the solid velocity and is the fluid velocity.
This theory captures the basic behavior of cartilage under compression. As example of the behavior of cartilage under compression from the text is shown below:
In this case, cartilage is subjected to a fixed displacement at point B. We see a large rise of stress in the graph at the right at point B. Because the fluid cannot immediately leave, it carries a good portion of the load. As the fluid leaves the cartilage, load is shifted to the solid matrix and stress is reduced.
Two key material properties in biphasic theory are equilibrium modulus and permeability. Equilibrium modulus is the stiffness of the cartilage as all the fluid flows out. In progressive OA, permeability increases and the equilibrium modulus decreases. As the permeability increases, this means that less load is shared by the fluid phase, increasing stress on the solid phase.
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