Tendon Mechanics Lecture

Tendon Mechanics

Biomechanics for Sport III

John McMahon BSc (Hons), ASCC, CSCS

Lecture Aims• To remind you of the mechanical concepts of

strain, stiffness and compliance

• To examine the rheological properties of materials & illustrate mechanical responses to loading

• To discuss the influence of tendon mechanical properties on muscle function

• To introduce the affect of stretching & training on tendon mechanical properties

• To understand in vivo measurement of tendon stiffness during dynamic exercises

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The Muscle-Tendon-Unit (MTU) Vastus Lateralis Gastrocnemius Hill’s Muscle Model

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Strain• The loading of a material will cause a deformation, which is

known as strain

• There are 3 main types of load and therefore strain:

• Tension = pulling force - makes object longer and thinner • Compression = pushing force - makes object shorter and thicker

• Shear = a load comprised of 2 equal, opposite and parallel forces that tend to displace one part of an object with respect to an adjacent part along a plane parallel and between the line of the forces 47

Load Characteristics – Principle Strain

L

∆L

Tensile Compressive Shear

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Loading characteristics

Tension CompressionTension Compression

Combination of tensile and compressive loading forces

Combination of compressive, tensile and shear loading forces

Bending Torsion11

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Calculating Strain

• If the loading is longitudinal i.e. in tension the material will tend to elongate

• The strain can be defined as change in length/original length

• Strain, = Change in length rOriginal length r

• This is unit less i.e. cm/cm and is usually expressed as a percentage - Strain = ∆L/L *100

Stress• When a material undergoes a deformation as a result of

applied forces it reacts to this change

Stress: = the resistance of the intermolecular bonds of an object to the

strain caused by a load = the measure of a material’s ability to resist an applied force

• Can be defined as “the internal force per unit area upon a cross section of that a part of a body”

Stress, = Force F (Pa)Cross-Sectional Area A

• Stress can be longitudinal (normal) or transverse to the cross section

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Rheological Properties of Materials

Rheology - the study of the deformation and flow of matter

• Elasticity – relates to the ability of the material to return to its original dimension after loading – for a purely elastic material the relationship between loading and deformation will be a straight line – i.e. energy is stored

• Viscosity – here the material will deform with loading but will have a lag between developing stress and the resultant strain – the greater the rate of loading, the greater the stress developed – the material will retain its new shape/size – i.e. energy is absorbed

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Rheological Properties of Materials

• Material can possess properties of both viscosity and elasticity and hence be viscoelastic. Here the material will tend to deform and return to its original shape in a non linear fashion

• Plasticity – here when the material is deformed it tends to retain its new shape/size. Deformation tends to be without a lag and energy is absorbed

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Stress – Strain RelationshipStress

Strain

HR = Hookean Range (Linear)

HR

ERER = Elastic Range

PR PR = Plastic Range

A

B

C

A

A

Young’s Modulus E = A

(Elastic Modulus) A14

Stress – Strain Relationship(Stiffness and Compliance)

• It allows the description of the material in terms of the rheological properties previously defined

• It relates to Hooke’s law and allows the determination of the material ‘stiffness’ – Young’s modulus (E = ∆σ/∆ε)

• A very stiff material can tolerate high loads (stress) with only small deformations (strain)

• A higher value for E is indicative of a stiffer material

• Compliance is sometimes used instead of stiffness and is simply the inverse of stiffness i.e. the ratio of strain change to stress change 52

Changes in StiffnessFrom graph – Is line A or line B representative of a stiffer material and why?

Line A represents a stiffer material due to less deformation per unit of force 30

Stress – Strain Relationship• Typical stress – strain curves for different tissues

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Normative Values - Tendon PropertiesPatellar Tendon - O'Brien et al. (2010)

Achilles Tendon - Magnusson et al. (2001)

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Energy and Stress – Strain Curves• Area under the curves represent the energy – Stored

energy is the area under curve A and absorbed energy is the area under curve B

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Hysteresis and Stress - Strain

The amount of energy stored may

not all be given back subsequent to

unloading – this can be illustrated via the stress – strain curve

and can be as a result of damping

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Creep

• With prolonged loading a material may exhibit creep

• Here strain increases under

constant prolonged loading

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Stress Relaxation• When a material experiences a constant strain the

stress will tend to decrease with time

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Material Fatigue• A material can withstand

a finite number of stresses above a given

level after which failure or rupture is likely e.g. stress fracture of bone

• Below endurance limit the material can

withstand an infinite number of stresses

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Tendon InjuryResearch performed using isolated tendons:

For Achilles tendon:• Maximum Modulus: 819 MPa• Failure Load: 5098 N• Failure Stress: 79 MPa (Wren et al., 2001)

Damage may occur at:• 15-30% strain (Haut & Pawlinson, 1990;

Stäubli et al., 1999)43

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Tendon InjuryHowever, in vivo tendon research has shown:

• Tendon strains of 6-14% during MVC and up to 11.4% during SSC without injury occurrence

• Tendon forces to reach in excess of 5000 N

Differences due to:

• Preservatives• Tendon tested• Region of tendon tested

Factors Affecting Mechanical Properties of Tendon

• Age• Gender• Stretching• Training• Fatigue

• Chronic disease• Time of day

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Influence of Tendon Mechanical Properties on Muscle Function

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Why study tendon mechanical properties?

Function of tendons:

• Tensile force transmission

• Storage and release of energy during locomotion(Maganaris and Paul, 2002)

The mechanical properties of tendon significantly affect muscle output and function

Tendon properties can influence the force-velocity relationship of muscle

Tendon acts as a series viscoelastic component in the muscle tendon complex

Tendon stiffness (K) can effect the relationship between force and velocity in muscle

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 0.5 1 1.5 2 2.5 3

Velocity

Force

If a tendon is relatively compliant it can result in a reduced ability to generate force

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Tendon properties can influence the length-tension relationship of muscle

The amount of muscle filament overlap can also be changed with changes in tendon stiffness

Muscle length tension relationship

All things being equal a more compliant tendon will require a greater amount of filament sliding before external force is generated

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Tendon properties can influence changes in pennation angle

Here if we consider a pennate muscle in series with a tendon under isometric loading:

As force is developed and the tendon stretches the muscle fibre can change its angle of Pennation

Rest Contracted59

Tendon properties can influence changes in pennation angle – thus resultant force

This change in angle effects the effective force seen external to the muscle – tendon complex

θ

mf

Ultrasound image of muscle fibres showing pennation angle – effective pull force is cos (penn angle) x muscle force

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Tendon properties can influence rate of force development

In some instances it is required to generate forces rapidly e.g. to correct a trip or in many sporting situations especially where an explosive effort is required

Low K

High K

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RFD - EMDThis also has an effect on electro mechanical delay (the time lag between muscle activation and muscle force production)

This could effect the ability to carry out a number of motor tasks due to the delay between muscle activation and external movement

Compliant tendons would delay action of muscle spindles (stretch reflex)

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Energy storage and release - SSCMovement economy can also be modulated as energy is capable of being stored and released from the tendon

From Kawakami et al. J. Physiol. (2002)

Activation of muscle during lengthening of muscle – increased lengthening of tendon

Energy stored in tendon and released during concentric contraction – up to ~93% of energy is returned (Alexander, 2000)

Stretch-shorten-cycle (SSC)

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Affect of Stretching and Training on Tendon Mechanical Properties

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Passive StretchingAcute:• 10 min calf stretch - ↓ K & Hysteresis (Kubo et al., 2001a)

• 5 min calf stretch - ↓ K & Young’s Modulus (Burgess et al., 2009) - greater decreases in female subjects

• 5 min calf stretch - ↓ K & Hysteresis (Kubo et al., 2002b)

Changes above due to ↓ Viscosity & ↑ Elasticity

Chronic:• 5 x 45s (15s rest) calf stretch 2 x day for 3 weeks: ↔ K & ↓ Hysteresis (Kubo et al., 2002a)

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Isotonic Resistance Training

6 weeks of:• ‘Eccentric’ heel drops (BW): ↔ K (Mahieu et al., 2008)

8 weeks of:• Calf raises (70% 1RM):↑ K & ↔ Hysteresis (Kubo et al., 2002c)

12 weeks of:• Leg extension (70% 1RM): ↑ K (Kongsgaard et al., 2007)

14 weeks of:• Leg extension/leg press (80% 1RM): ↑ K (Reeves et al., 2003a,b)

6 months of:• BW squat: ↔ K (Kubo et al., 2003)

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Isometric Resistance Training

12 weeks of isometric knee extension performed at 70% MVC for 15-20s:

• ↑ K (Kubo et al., 2001c,d; 2006; 2009)• ↑ muscle size and RFD (Kubo et al., 2001d)

↔ K during above exercise when:- Performed for short duration (1s)- Performed at short muscle length (50 deg)- Performed for < 8 weeks

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Isometric Resistance Training

14 weeks of isometric plantar flexion performed at 90% MVC for 3s:

• ↑ K (Arampatzis et al., 2007; 2010)

Authors concluded that the strain magnitude during isometric training should exceed the value experienced during habitual loading for mechanical adaptations in tendon to occur.

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Plyometric Training 14 weeks of plyometric training (SJ, CMJ, DJ

(40+60+80), over barrier)

• ↑ K (Fouré et al., 2010)

Trained with high volume: 36 sessions in total consisting of 200-600 jumps per session

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Combination Training

6 weeks of Plyometric (DJ) vs Isometric (Plantar):• Plyo: ↑ K (29%), ↑ RFD (19%) & ↑ SJ height (59%)• Iso: ↑ K (62%), ↑ RFD (17%) & ↑ SJ height (64%)

(Burgess et al., 2007)

12 weeks of Iso RT (80% 1RM calf raise) vs Plyo (sledge hopping & DJ (20)):• Iso RT: ↑ K, ↑ SJ height• Plyo: ↔ K, ↑ SJ, CMJ & DJ height

(Kubo et al., 2007)

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Endurance Training

• No effect of endurance training on mechanical properties (i.e. K/Young’s Modulus) of the PT or AT

(Rosager et al., 2002; Hansen et al., 2003; Karamanidis and Arampatzis, 2006; Arampatzis et al.,

2007)

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Training Summary

For necessary adaptations of tendon mechanical properties to occur, training should:

• Include high loads • Involve high tendon strains• If isometric, be performed at long muscle lengths• If isometric, be performed for at least 3s/rep• Be performed consistently for at least 6-8 weeks

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Measurement of Tendon Mechanical Properties (in vivo) during Dynamic

Movements

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Measurement of Tendon PropertiesIn order to estimate tendon mechanical properties (stiffness) both elongation and force in the tendon have to be determined

In order to measure the mechanical properties of tendon in vivo we use a combination of:

• Motion Analysis• Ultrasonography• Electromyography• Dynamometry• Force 36

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Motion Analysis – Sagittal Plane

• Can use 2D or 3D motion capture depending on information required for research

• Markers placed on lateral aspects of ankle, knee and hip joints (marker on tendon insertion may also be necessary)

• Sagittal motion of the above joints required to calculate instantaneous MTU length and tendon moment arms using regression equations obtained from cadaver studies (Hawkins and Hull, 1990; Visser et al., 1990)

Example of 3D Motion Analysis

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Ultrasound – Mode of Operation

• B-mode ultrasound is a useful tool for the imaging of soft tissue.

• Its mode of operation is via the transmission and reception of sound waves.

• Ultrasound waves are produced by oscillating crystals at a frequency that is inaudible to the human ear.

• Transducers located in the probe produce sound (for example) at 7.5mhz which is then pulsed at intervals which occur every 20 micro-seconds.

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Ultrasound – Mode of Operation• These sound waves penetrate and encounter the different

tissue interfaces as they travels through the body.

• When sound encounters tissues or tissue planes, part of the wave is reflected back to receivers in this same probe.

• The transducer must be in contact with the medium scanned, in this case skin, so a "transmission jelly" is used to insure a complete "union". The ultrasound produced can not travel through the air and then into the body.

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Ultrasound – Mode of Operation• This mode analyses the intensity of the returning ultrasound

signal as well as the direction and depth from, which it was reflected

• A two-dimensional grey-scale image is constructed with different intensities from the returning signals being assigned different levels of brightness

• Generally, a high-density structure such as tendon/bone will reflect a high-intensity signal back to the probe and be displayed as white on the screen

• We use ultrasonography to measure tendon elongation53

Tendon Elongation – Method 1

Used mainly during isometric assessment of tendon stiffness, but can also be used to measure tendon stiffness during SSC movements if instantaneous tendon insertion can also be tracked (Lichtwark and Wilson, 2005).

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Instantaneous MTU length is determined from sagittal joint angle data (Hawkins and Hull, 1990)

Tendon Elongation – Method 2

θ

Instantaneous muscle length is determined by multiplying muscle fascicle length by cos (penn angle)

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Tendon Elongation – Method 2Finally muscle length is subtracted from MTU length in order to estimate instantaneous SEE length (Fukunaga et al., 2001)

Where Ldt is distal tendon length, Lpt is proximal tendon length, Lmtc is muscle tendon complex length, Lf is muscle fascicle length and cosα is cosine of the pennation angle 13

Electromyography (EMG)The resultant signal from many action potentials is what we measure with the surface EMG (sEMG) signal

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EMG• sEMG allows the determination of when a muscle

is switched on or off

• The root mean square (RMS) value of a sEMG signal has been suggested to be a measure of the strength of muscle activity

• For some muscles it has been shown that there is essentially a linear relationship between sEMG RMS and force output (Lippold, 1952)

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EMG

• Relationship between RMS sEMG and force output of muscles

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EMG How do we measure this electrical activity?

• For simple single differential measurement (to reduce noise) 2 electrodes are placed over the muscle belly of interest

• The signal is then amplified and filtered before being sampled by a computer to be saved

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EMG’s use in determining tendon properties

• To determine levels of co-contraction and hence co-contraction force.

• During agonist muscle contraction antagonists are also active and producing force.

• The agonists must overcome this ‘hidden’ force before external torque is recorded through force readings.

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Dynamometry• Used to determine EMG activity of agonist and antagonist muscles

during MVC – used to calculate antagonist force

Co-contraction effort (CT) defined as: (EMG during extension / Max flexor EMG)*Max flexor torque

Total extensor torque = CT + Extensor torque

• Allows EMG activity attained during dynamic movement to be normalised to EMG activity attained during MVC (when comparing groups)

• Can be assessed over a range of joint angles specific to the range demonstrated during the dynamic task 38

Ground Reaction Force Data

Required to calculate tendon forces

Tendon force is derived by multiplying instantaneous joint moment (as determined using inverse dynamics) by instantaneous tendon moment arm (Visser et al., 1990)

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Calculating Tendon StiffnessTendon stiffness (N·mm-1) is then determined from the slope of the elongation – force relationship

Remember we stated stiffness was ∆force/∆length?

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ResultsDetermination of tendon stiffness and separation of

muscle and tendon components from the whole MTU

Solid line = MTU length, dotted line = tendon length, broken line = muscle length 57

Normalizing Values

• Differences in tendon length and/or cross sectional area can affect the stiffness values

• It is therefore important to normalise the stiffness to account for these dimensional factors when comparing different groups

Young's modulus is such a value: K*(L/CSA) or stress/strain

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Any Questions?