# Biomechanical Properties Of Tendon Biology Essay

The main function of tendon is to transmit tensile force. An uniaxal tensile testing was performed to experiment the biomechanical properties of tendon, form the test a stress-strain curve from which the mechanical properties are determined can be obtained (Savio L.Y.Woo, 1991) There are several things which affect the mechanical forces on tendons during normal locomotion.

Different tendons in body are subjected to different forces.

The level of muscle contraction and tendon's C.S.A and its size will affect the mechanical force. The bigger C.S.A of the tendon the greater the force and the larger the stress which tendon undergoes would be.

On the same Different activities induce different level of forces .sp changing the frequency and rate of mechanical forces will give different levels of forces in tendon (H.C.Wang, 2005)

A mechanical force is applied on tendons in vivo. The viscoelastic behaviour and fibre patters of tendon affects on the mechanical property of tendon. (H.C.Wang, 2005) The stress experienced by a tendon depends on the size of the tendon and the contraction of muscle. The bigger C.S.A of the muscle the greater the force and more stress on tendon would be .the larger tendon C.S.A ,it can tolerate a bigger load. (M.Benjamin, 1996)

## During mechanical testing of tendon force and deformation are 2 factors which are important to consider. An external force (N) is applied on tendon which can make a change on its structure, therefore there would be a linear relationship between force and deformation which is explained by Hook's Law in spring :

F =-K .x (equation 1)

where x is displacement from its equilibrium position x=0 and k is spring constant which is a constant positive value ) k measures the stiffness of the spring. . The stiffer the spring the lager the value of k is .the negative value means that the force applied by the spring is always opposite the direction of displacement of the object. (Raymond A.Serway.Chris Vuille, 2008)

## Viscoelastic properties:

Tendons have time dependant viscoelastic properties which results from results from collagen, water, interaction between collagenous and non collagenous proteins (PG). the viscoelasticity of materials has been explained by creep, stress relation and hysteresis. Tendons absorb more energy and this is due to having the viscoelasticity behaviours and they tend to have low strain rates. At high stain rates they become less deformable with a high degree of stiffness and are more effective in moving large loads. (H.C.Wang, 2005) (S.P.Magnusson, 2003) The loading and unloading curve of tendon doesn't follow a same path due to viscoelastic properties which they have and they form a hysteresis loop which shows internal

Figure 7 typical loading and unloading curve from a tensile test adapted from (Margareta Nordin, 2001)energy dissipation (Savio L.Y.Woo, 1991). figure 7 shows a typical loading and unloading curve during a tensile test. The two non linear curves form a hysteresis loop and the shaded area within hysteresis represents the energy loss in tissue .Below 4% strain, a tendon has an elastic behaviour which means it returns to its original position and length .strains more than 4% causes failure (Andrea Hoffmann, 2007). Important viscoelastic behaviour of tendon is creep which is an increase in deformation over time under a constant load and stress relaxation which is an decrease in deformation over time under a constant load. (Savio L.Y.Woo, 1991)

## Structure-function relationship of tendon under Quasi static load

To understand and analyse the tendon mechanical properties the specimens are subjected to a tensile deformation using a constant load. The tendon fascicles are stretched till they ruptured. A resulting load-elongation (stress -strain) curve is plotted which has different regions (Margareta Nordin, 2001). a typical strain-stress curve for a tendon has 3 regions as shown on the figure 8.

## Toe region:

Figure 1Figure 5 typical stress-strain curve for tendon adapted from (H.C.Wang, 2005)the initial region called toe region where tendon is strained up to 2% and tendon deforms readily. This region represents that the crimp pattern is stretched -out .the angles and the crimp pattern of the tendon depends on the type of the tendon. The smaller the crimp angle , the quicker they fail compare to the samples with large crimp angle. (H.C.Wang, 2005) (M.Benjamin, 1996)

## Linear region:

The second region of the stress-strain curve is called linear region where the tendon is stretched less than 4% and collagen fibres lose their crimp pattern (H.C.Wang, 2005).from about 20Mpa upward the curve is linear . (F.Ker, 2007)beyond the toe region the tendon has to apply different mechanics to straighten up the tendons .a microanalysis techniques on rat tail tendon showed that the fascicles strained up to 8%, (Hazel R.C. Screen, 2005) Beyond 8-10% the macroscopic failure occurs and excess extension causes rupture. (H.C.Wang, 2005) the slope of this linear region is young's modulus of the tendon. (H.C.Wang, 2005)

## Total failure:

Following the linear region there is a yield or failure region where at large strains the curve ends or curves downward as a result of failure .the point which the curve levels off towards the strain axis is called the yield point for the tissue (Margareta Nordin, 2001) .in this region tendon deformation is completed by very little increase in stress. Tendon failure occurs as collagen fibres pull apart .the ultimate failure stress of tendon is defined as tendon strength. (Benno Maurus Nigg, 2007) the area under the curve is energy uptake to yield point . (Margareta Nordin, 2001)

When tendon specimens are subjected increasing different loads the linear relationship between stress and strain in the curve becomes steeper and shows greater stiffness at higher strain rates. At higher strain rates, tendons store more energy ,more force needed for failure therefore they have more elongation . (Margareta Nordin, 2001)

During dynamic loading tendon display a non linear viscoelastic respond with an initial toe region. After this region is a non linear viscoelastic region and can be seen during imposed step changes, if the tissue is brought to a new length and maintained for some time, the stress tension will -linear manner decline in a non-linear manner which is called viscoelastic stress relaxation figure9 .if the tendon brought to a new stress it will to a new length it will show a non linearity increase in strain overtime which is called creep figure 10. (S.P.Magnusson, 2003)

There are 2 standard tests which reveal the viscoelasticity of tendons, creep and stress relaxation tests. During stress relaxation test the load is stopped below the linear region of the curve and the strain kept constant over an extended period. The stress decreases quickly at first then more slowly. When this test is repeated cyclically the decrease in stress becomes less noticeable. (Margareta Nordin, 2001)

During the creep test, loading is stopped below the linear region of the curve and stress is kept constant over a period of time .the strain increases relatively quickly at first and then more and more slowly. When this is performed cyclically the increase in strain gradually becomes less pronounced (Margareta Nordin, 2001)

Figure 10 creep: a step change in stress which is maintained and a time dependant non-linear increase in strain adapted from (S.P.Magnusson, 2003)

Figure 9 viscoelastic stress relaxation: a step change in strain which is maintained and a time dependant non-linear decline in stress adapted from (S.P.Magnusson, 2003)

## Stress and strain:

Stress = force per unit area (Equation 3)

Strain= initial length divided by change in length (equation4) (T.Fenner, 1989)

The modulus of elasticity of tendon has been determined by using the stress-strain curve and its based on the linear relationship between stress (load) and strain (elongation) . due to linear relationship the stress in proportional to strain therefore :

(Equation 2)

Where E = modulus of elasticity, σ = stress , ε=strain (Margareta Nordin, 2001)

As we can see from the stress strain curve (figure 6) in the toe region the modulus of elasticity is increasing and in the linear region it stabilizes. (Margareta Nordin, 2001)

Tendons show a nonlinear trend when they are pulled and in the stress-strain curve could be seen that after first toe region there is a linear region. (S.Peter Mangnusson, 2008)another factor which will affect the biomechanics of tendon as well as magnitude of loading is the history which is observed during repeated tensile loading of isolated tendon as the stress-strain curve is moved to the right and the rate of loading

## Effect of different mechanical testing protocols

the shape of the stress-strain curve depends on testing procedure used ,the methods which the tissue samples are gripped, the storage of tendon before testing before testing and the environmental factors during the testing ,the method of measuring data ,the type of tendon used and its biomechanical composition . (Screen, 2003)

the table below shows some of the data for UTS and young's modulus.

Table 1 mechanical characterisation of a selection of tendons

Study by :

UTS (Mpa)

Young's modulus (Mpa)

Strain at failure

Adapted from

Testing parameters (rate)

Johnson et al (1994)

64.7±15.0 (29-50)

53.6±10.0 (64-93)

660±266

504±222

14±6%

15±5%

(H.C.Wang, 2005)

Maganaris and paul (1999)

161

1200

(H.C.Wang, 2005)

(L.Lieber, 1995)

51.6±9.3

74±13.5

540.6±152.6

1020.6±131.9

11.4±1.0

16.6±1.7%

(L.Lieber, 1995)

(Screen, 2003)

80±7

1560±100

(Bennett, 1986)

0.05 mm/s

(Screen, 2003)

69±6

1475±125

(haut,1986)

1mm/s

(Screen, 2003)

932±197

87±13

(Bader et al2000)

1mm/s

Live cells present in tendon can have limited effect on mechanical properties of tendon due to following reasons: -

The proportion by volume is small in mature tendon .it found that proportion of cell in RTT in an adult rat was 2% where as it was 40% in a new born rat.

The cells are arranged in a way which decreases the interaction with the transmission of force through extracellular material.

The elastic modulus of cells is order of magnitude less than that of tendon. (F.Ker, 2007)

## Different testing procedures:

## Qasi tensile test:

A qasi -static tensile test creates an ultimate tensile strength (UTS) of about 100Mpa and failure strain of about 15%.the material properties are dependant on the rate of tensile testing .with values for elastic modulus in range of 1-2 Gpa. (Gerhard A. Holzapfel, 2003)

## Fundamental particles and quantum field theory

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