LIGAMENTS AND TENDONS

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1 LIGAMENTS AND TENDONS I. Overview Ligaments and tendons are soft collagenous tissues. Ligaments connect bone to bone Tendons connect muscles to bone. Ligaments and tendons have a hierarchical structure that affects their mechanical behavior. Ligaments and tendons can adapt to changes in their mechanical environment due to injury, disease or exercise. Proprioception: presence of stretch-sensitive mechanoreceptors in joint capsula, ligaments and tendons (called Golgi tendon organs in tendons) that provide feedback control and trigger muscle contractions to protect from extreme motions.

2 LIGAMENTS AND TENDONS I. Overview Ligaments and tendons are soft collagenous tissues. Ligaments connect bone to bone Tendons connect muscles to bone. Ligaments and tendons have a hierarchical structure that affects their mechanical behavior. Ligaments and tendons can adapt to changes in their mechanical environment due to injury, disease or exercise. Proprioception: presence of stretch-sensitive mechanoreceptors in joint capsula, ligaments and tendons (called Golgi tendon organs in tendons) that provide feedback control and trigger muscle contractions to protect from extreme motions. II. Major components (as percent of dry weight) Component Ligament Tendon Skin Collagen (mostly as type I) Elastin < Proteoglycans

3 III. Hierarchical Ligament and Tendon Structure Largest structure: the ligament or the tendon itself. The ligament or tendon is split into smaller entities called fascicles. The fascicle contains the basic fibril of the ligament or tendon, and the fibroblasts, which are the biological cells that produce ligament or tendon. This fibrous structure implies the tissue anisotropy In the absence of load, the collagen fibrils have a waviness (the crimp of the fibril) It contributes significantly to the nonlinear stress strain relationship for ligaments and tendons and, indeed, for basically all soft collagenous tissues.

4 TENDONS Anatomy: 1. Tendons contain collagen fibrils (Type I) 2. Tendons contain a proteoglycan matrix 3. Tendons contain fibroblasts (biological cells) that are arranged in parallel rows Basic Functions: 1. Tendons carry tensile forces from muscle to bone 2. They carry compressive forces when wrapped around bone like a pulley 3. They have an important role of energy storage as elastic energy (in running ~ 50% of the energy stored in Achilles tendon, quadriceps tendon and ligaments of the foot at initial contact and then returned at push-off) Blood Supply: 1. Vessels in perimysium (covering of tendon) 2. Periosteal insertion 3. Surrounding tissues

5 LIGAMENTS Basic Functions: Ligaments bind bones together and support organs. Maintain correct bone and joint geometry: - together with associated joint capsules have the role of passive joint stabilizers, - together with the articular contours they determine a joint s range of motion. Ligamentous damage occurs when the joint is forced beyond its functional range.

6 Anatomy: 1. Similar to tendon in hierarchical structure 2. Collagen fibrils are slightly less in volume fraction and organization than tendon 3. Higher percentage of proteoglycan matrix than tendon 4. Fibroblasts Blood Supply 1. Microvascularity from insertion sites 2. Nutrition for cell population; necessary for matrix synthesis and repair.

7 IV. General overview of ligament and tendon mechanics NONLINEAR ELASTICITY AND DAMAGE Neglecting viscoelastic behaviour, a typical stress strain curve has three major regions: 1) the toe or toe-in region, 2) the linear region and 3) the yield and failure region. In physiologic activity, most ligaments and tendons exist in the toe and early linear region. The toe-in region represents un-crimping of the crimp in the collagen fibrils. It is easier to stretch out the crimp of the fibrils, than to stretch the collagen fibril material. Increase of stiffness as the fibrils become uncrimped, and collagen material is stretched. Decrease of stiffness as individual fibrils within the ligament or tendon begin to fail, and damage accumulates.

8 VISCOELASTICITY % of the wet weight of the ligaments is WATER. A significant amount of water is associated with GROUND SUBSTANCE. On a dry weight basis the ground substance is only ~1% The ground substance provides lubrication and spacing that aid sliding of the fibers. It is a source of viscoelastic behavior. Viscoelasticity means time dependent mechanical behavior. The relationship between stress and strain is not constant but depends on the time of application of displacement or load. Creep is increasing deformation under constant load.

9 Stress relaxation means that the stress reduces or relaxes under a constant deformation.

10 Hysteresis or energy dissipation When a viscoelastic material is loaded and unloaded, the unloading curve will not follow the loading curve. The difference between the two curves represents the amount of energy that is dissipated or lost during loading. Preconditioning The amount of hysteresis under cyclic loading is reduced and eventually the stress-strain curve becomes reproducible. This gives rise to the use of pseudo-elasticity to represent the nonlinearity of ligament/tendon stress-strain behavior.

11 Small rate sensitivity Despite important viscous dissipation effects, most soft biologic tissues are not very sensitive to the rate of application of load for a wide range of load rates. CT: load rate

12 EXERCISE, DISUSE AND RECOVERY Collagen constitutes ~70% of the dry weight of ligament and tendon Collagen has a relatively long turnover rate: its average half-life is 300 to 500 days (slightly longer than bone) Several months may be required for a ligament to alter its structure to meet changes in physical loading or to repair itself after injury.

13 I. Overview BLOOD VESSELS Blood vessels are subject to mechanical stress during the pumping of blood. Blood vessels are soft collagenous tissues (with a good deal of elastin). Stress-strain behavior resembles other soft collagenous tissues like ligaments and tendons. Vessels that deliver oxygenated blood to tissues: arteries, arterioles, and capillaries. Vessels that return blood with carbon dioxide for gas exchange: the veins and venules. Arteries are roughly divided into two types: elastic and muscular. Elastic arteries (like aorta and carotid) are located close to the heart, have relatively large diameters and may be regarded as elastic structures. Muscular arteries (like femoral, celiac and cerebral) are smaller and are located at the periphery, and may be regarded as viscoelastic structures

14 I. Overview BLOOD VESSELS Blood vessels are subject to mechanical stress during the pumping of blood. Blood vessels are soft collagenous tissues (with a good deal of elastin). Stress-strain behavior resembles other soft collagenous tissues like ligaments and tendons. Vessels that deliver oxygenated blood to tissues: arteries, arterioles, and capillaries. Vessels that return blood with carbon dioxide for gas exchange: the veins and venules. Arteries are roughly divided into two types: elastic and muscular. Elastic arteries (like aorta and carotid) are located close to the heart, have relatively large diameters and may be regarded as elastic structures. Muscular arteries (like femoral, celiac and cerebral) are smaller and are located at the periphery, and may be regarded as viscoelastic structures II. Blood Vessel Structure: Basic structure with THREE LAYERS Intima (Innermost layer) Contains endothelial cells Basal lamina (80 nm thick) Subendothelia layer with collagenous bundles, some elastin. Very thin in healthy young individuals: insignificant contribution to solid mech. properties.

15 Media (Middle Layer) Contains mainly smooth muscle cells: responsible for viscoelastic behavior. Collagenous fibrils (type III collagen) Divided from adventia by elastin layer. Close interconnection between elastic and collagen fibrils, elastic laminae and smooth muscle cells together constitute a continuous fibrous helix. The helix has a small pitch: the smooth muscle cells are almost circumferentially oriented. Adventia (Outermost layer) Wavy Collagen fibers (mainly type III, differ in amino acid sequence from I and II) arranged in helical structures that serve to reinforce the wall. Adventitia is less stiff than the media in load-free configuration and at small load pressures. At higher stress, adventitia collagen fibers reach their straightened lengths and adventitia becomes a stiff tube that prevents overstretch and rupture of the artery. Ground substance Fibroblasts

16 Roach and Burton,1957 : Collagen contributed mainly to the linear region of the nonlinear stressstrain curve Elastin contributed mainly to the toe part of the stress-strain curve.

17 Arteries have a larger media layer than veins. Since smooth muscle is generally found in the media layer, this means that arteries have more smooth muscle to contract than do veins. Arteries have a higher amount of elastin than veins. Veins have a higher ratio of collagen to elastin than do arteries. Veins have a thicker adventia layer in proportion to the media layer than do arteries. The ratio of elastin to collagen in the aorta decreases away from the heart

18 Another critical aspect of blood vessel behavior is residual stress. This means that even in the unloaded state, there is still stress in the artery. A mark of the amount of residual stress is how much the blood vessel will open when cut. Since the blood vessel is under stress, when we cut the vessel, the stress holding the vessel together is removed and the blood vessel springs open.

19 III. Identification of Preferred Orientations in Arterial Layers Media: A stained patch reveals the orientation of smooth muscle cells, in particular of the associated nuclei. All connected pixels that make up a nucleus are identified and the principal direction of its inertia tensor relative to the centroid of each nucleus gives its preferred orientation. Statistical analysis provides the 2 preferred orientations of the nuclei in the media relative to the artery circumferential direction ϕ M = ± 8.4º: the smooth muscle cells in the media are almost circumferential.

20 Adventitia: Similar procedure provides the 2 predominant orientations of the collagen fibers, relative to the circumferential direction: ϕ A = ± 41.9º ANISOTROPY

21 ELASTIN AND COLLAGEN Both elastin and collagen fibres are proteins. Protein molecules consist of long chains of aminoacids. Elastin molecules are arranged randomly in terms of orientation and attachment to one another and individual shape. Linear elastic behavior with very small relaxation. When stretched, the molecules themselves do not stretch, but tend to straighten in the direction of stretching. When load is removed, the elastin molecules restore their original orientation and shape. An elastin fibril is made of a number of elastin molecules and an elastin fiber consists of a number of fibrils grouped together. Elastin fibres can be stretched up to 200% Collagen molecules are arranged more regularly: tey tend to be more parallel; they are also attached each other at various points When stretched along the direction of their main orientation collagen molecules quickly straighten (limited extension). Mostly linear elastic too, but it is much more stiff than elastin. A collagen fibril is made of a number of closely aligned parallel collagen molecules and an collagen fiber consists of a number of fibrils grouped together. Collagen fibres can be stretched up to 10%.

22

23 MECHANICAL PROPERTIES OF SOME COMMON MATERIALS Material Young s modulus (MPa) Strength (MPa) Elastin 0.6 Rubber Collagen (along fiber) Wood (oak) Trabecular bone Cortical bone (longitud.) Concrete (compression) 28 Aluminum Mild steel

24 GROUND SUBSTANCE The ground substance forms the nonfibrous part of the matrix. It is a viscous gel consisting mainly of large carborhydrate molecules (molecules consisting of carbon, hydrogen, and oxygen) and carborhydrate-protrein molecular complexes (molecules consisting of a«carbon, hydrogen, oxygen, and nitrogen) suspended in a relatively large volume of water. Many of those substances have an affinity to water and then: they determine the actual volume of water in the ground substance they determine the viscosity of the ground substance The ground substance is responsible for: Facilitating intercellular exchanges. Providing some mechanical support. The glue-like viscosity of the ground substance enables it to bind cells together within the other tissues (muscle, nerve and epithelia); in epithelial tissue the ground substance is the main bonding material between cells; in muscle and nerve tissue the cells are bound together by a combination of ground substance and fibers.

25 Note the strain values: (50%) (12%) (50%) LARGE DEFORMATIONS

26 INCOMPRESSIBILITY Most biological tissues have a water content of more than 70% Therefore they hardly change their volume even if load is applied. That is not the case with articular cartilage, because the tissue is micro-porous, and therefore water can come into and go out from the pores depending upon load.

27 ANISOTROPY

28 FUNG S EXPONENTIAL HYPERELASTICITY A 0 : Cross-section area in reference configuration F: Applied force T = F/A 0 : Nominal stress L 0 : Length in reference configuration L: current length λ = L/L 0 : Stretch ratio dt dλ = BT + C Separating variables: B dt BT + C = B dλ and integrating: ln (BT+ C) = Bλ + D (D is a constant) Imposing no stress T = 0 for no deformation (λ = L/L 0 = 1) D = ln C B T = A {exp [B(λ 1)] 1} A = C/B

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