Introduction to Biomedical Engineering

Transcription

1 Introduction to Biomedical Engineering FW 16/17, AUT Biomechanics of tendons and ligaments G. Rouhi

2 Biomechanics of tendons and ligaments

3 Biomechanics of soft tissues The major soft tissues in musculoskeletal system: tendon, ligament, cartilage, muscle and intervertebral disc

4 Composition and microstructure similar compositions and microstructures Cellular material occupies about 20% of the total tissue volume, the rest is the extracellular matrix 70% of the matrix is water The rest is solid (Collagen I & III + ground substance (proteoglycans, glycoproteins, plasma proteins, ) + elastin)

5 Composition and microstructure By dry weight, tendon contains: % of mostly type I collagen 1-3 % elastin (cartilage does not have elastin) 1-2 % proteoglycans By dry weight, ligament contains: % of mostly type I collagen 1-15 % elastin 1-3 % proteoglycans

6 Composition and microstructure Different arrangement of collagen fibers in Ls & Ts (suited to their functions)

7 Hierarchy of the structure

8 Hierarchy of the structure At the lowest scale is the collagen triple helix molecule (1.5 nm diameter) Collagen triple helix molecule Next is microfibril (3.5 nm diameter), which contains 5 collagen molecules Subfibril (10-20 nm diameter) Fibril ( nm diameter) Arrangement of collagen molecules into tendon

9 Tendons and ligaments The collagen fibrils within fascicles are aligned parallel to each other, but are slightly crimped when unloaded Tendons and ligaments have nonhomogenous substructures

10 Collagen Collagen is the most important building block in the entire animal world- more than one third of the body's proteins are collagens- mechanical function Schematic view of some of the hierarchical features of collagen, ranging from the amino acid sequence level at nanoscale up to the scale of collagen fibers with lengths on the order of 10m

11 Examples of collagen in biological tissues Collagen fibers act like spring; transmit forces; store energy; prevent premature mechanical failure in normal tissues Fibers provide high tensile strength, when they are oriented in the direction of the applied force Collagen fibers Tendon Bone

12 Examples of collagen Bone is a ductile ceramic which is reinforced by collagen fibers D= 1.5 nm

13 Examples of collagen Collagen fibers in cartilage give strength and compressibility to the cartilage matrix, and allow to absorb shocks on joints

14 Collagen fibers orientation

15 Stress-strain curve of collagen The toe region is due to the "uncrimping" of the collagen fibrils When the fibrils start to fail - we have the yield region

16 Summary Collagen is a protein Collagen provides strength and flexibility to many parts of the body Collagen fibers have the ability to transfer forces, store energy, and prevent failure Fibers align in the direction of applied load The stress-strain curve of collagen fiber consists of 3 regions: Toe, linear, and yield region

17 Stress-strain curve: Mechanical behavior 1. The initial nonlinear toe region, large strains produce only small stresses 2. The quasi-linear region, the б- curve is approximately linearly elastic and relatively large stresses develop 3. The failure region, the tangent modulus decreases as collagen fibers become damaged and fracture

18 Mechanical behavior The mechanical behavior of tendons and ligaments are similar, although tendon is stronger and stiffer

19 Stress-strain relation before yielding Stress-strain relation found empirically, for Ts and Ls: b a( e 1) Tangent modulus of elasticity: The instantaneous rate of change of stress as a function of strain Question: Find an expression for the tangent modulus of elasticity!

20 Stress-strain relation before yielding Stress-strain relation found empirically: b a( e 1) Tangent modulus-stress relationship: d b d c where a and b are found experimentally and c=ab

21 Stress-strain relation before yielding The significance of the non-linear б- is that the concept of Young s modulus does not apply, because the tangent modulus depends on the strain until all the collagen fibers have been recruited

22 Material and structural properties Ligaments: Modulus values: MPa, depending on the strain rate Ultimate tensile stress: 4-45 MPa Ultimate tensile strain: percent Tendons: Modulus values: MPa Ultimate tensile stress: MPa Ultimate tensile strain: percent

23 Viscoelastic behavior in tendons and ligaments Tendons and ligaments show VE behavior under loading, and by increasing the strain rate, the linear portion of the stress-strain curve becomes steeper, indicating greater stiffness of the tissue at higher strain rates During cyclic loading, the stress-strain curve is displaced to the right along the deformation axis with each loading cycle, revealing the presence of a plastic component- the amount of permanent deformation is progressively greater with every loading cycle As cyclic loading continues, the specimen shows an increase in E as a result of plastic deformation (molecular displacement)

24 Viscoelastic behavior in tendons and ligaments Strain rate dependence is relatively weak over physiological loading rates (an increase in loading rate by 4 orders of magnitude increases stiffness and strength by a factor of about 2) More complex VE behavior can be seen in the entire bone-ligament-bone complex ACL in knee specimens were tested in tension to failure at slow and fast loading rates- at the slow loading rate, much slower than that of an injury mechanism in vivo, the bony insertion of the ligament was the weakest component of the B-L-B complex- this shows that as the loading rate is increased, bone shows a greater increase in strength than does ligament

25 Vascularization, mobilization and immobilization Living tissues are dynamic and change their mechanical properties in response to mechanical stimuli Tendons and ligaments have a limited vascularization, which affects directly their healing process Some parts of tendons are vascular and some other are avascular- this led researchers to propose a dual pathway for tendon nutrition: a vascular pathway, for the vascular region, and for the avascular regions, a synovial (diffusion) pathway The concept of diffusional nutrition is of primary clinical significance in that it implies that tendon healing and repair can occur in the absence of blood supply

26 Mobilization and immobilization Ligament in comparison with surrounding tissue appears to be hypoavscular (less vascular)- despite the small size and limited blood flow of the vascular system, it s of primary importance in the maintenance of the ligament By providing nutrition for the cellular population, the vascular system maintains the continued process of matrix synthesis and repair- in its absence, damage from normal activities accumulates (fatigue) and the ligament is at risk for rupture Tendons and ligaments remodel in response to the mechanical demands placed on them- they become stronger and stiffer when subjected to increased stress and weaker and less stiff when the stress is reduced Ligaments and tendons have a variety of specialized nerve endings and mechanoreceptors

27 Mobilization and immobilization Physical training can increase the tensile strength of Ts and Ls Immobilization can decrease the tensile strength of ligaments

28 Immobility Animal studies show that ligaments lose mechanical integrity relatively quickly (up to 50% of strength can be lost by immobility in a few weeks), and upon return to mobility, restoration of properties proceeds at a slower rate Effects of immobilization and recovery on biomechanical behavior of ligament

29 Adaptation Ts and Ls have a limited vascularization; providing nutrition for the cells- there are not many cells in tendons and ligaments, that is why it takes a long time to heal if is injured Blue arrow - Collagen bundle Green Arrow - Fibroblast nuclei

30 The insertion site Similar insertion structures into bone in Ts and Ls From more tendinous to more bony material Four zones: Parallel collagen fibers Unmineralized fibrocartilage Mineralized fibrocartilage Cortical bone

31 OA (wear and tear arthritis) Gradual breakdown and loss of joint cartilage; the exact cause of OA is unknown, decreases E substantially Degeneration of AC causes OA

32 Summary The arrangement of the collagen fibers is nearly parallel in tendons, equipping them to withstand high unidirectional loads- the less parallel arrangement of collagen fibers in ligaments allows these structures to carry predominant tensile stresses in one direction and smaller stresses in other directions At the insertion of ligament and tendon into stiffer bone, the gradual change from a more fibrous to a more bony material results in a decreased stress concentration effect Studies suggest that during normal activity, a tendon in vivo is subjected to less than one fourth of its ultimate stress Tendons and ligament show viscoelastic behavior- an additional effect of the rate dependency is the slow deformation, creep The physical properties of collagen are closely associated with the number of crosslinks within and between the collagen molecules- during maturation (up to 20yrs of age), the number and quality of cross-links increases, resulting in increased tensile strength of ligaments and tendons Tendons and ligaments remodel in response to the mechanical demand placed on them

33 Suggested texts D.L. Bartel, D.T. Davy and T.M. Keaveney, Orthopaedic Biomechanics, Mechanics and Design in Musculoskeletal Systems, Prentice Hall, M. Nordin and V.H. Frankel, Basic Biomechanics of the Musculoskeletal System, 3rd edition, Lippincott Williams & Wilkins, S.C. Cowin, Bone Mechanics Handbook, 2nd Edition, CRC Press, R.B. Martin and D.B. Burr, Structure, Function, and Adaptation of Compact Bone, Raven Press, D.R Carter and G.S. Beaupre, Skeletal Function and Form, Mechanobiology of Skeletal Development, Again, and Regeneration, Cambridge University Press, 2001.