Biomechanics of ligaments & tendons

1. Presented by:
Dharmakant Chaudhary
Manish Lamichhane
Prashant Waiba
Rohit Kyatu Shrestha

2. Objectives of Presentation :
Introduction to Ligaments & Tendons
Hierarchical Structure
Anatomical Positions
Functions
Mechanical Properties
Recent Research & Developments

3. Introduction to Ligaments & Tendons
Tendons: Tendons connect muscles to bone.
 Tendons consists of bundle of collagenous fibers arrange in parallel.They are
arranged this way to form cords which have great tensile strength.
 Origins at muscles, crosses at least one joint and insert in bone.
Ligaments: Ligaments connect bone to bone.
 Ligaments consists mostly of bundles of elastin molecule formed into elastic
fiber with some bundle of collagen.
 Origins and insert in bone.
 More elastic and flexible than tendons.
 Offer less tensile strength.

4. Hierarchical Structure of Ligaments &
Tendons
 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.
 Fibroblasts are the biological cells
that produce ligaments and tendons.
 The fascicle contains fibrils which
are composed of subfibrils and sub
divided into microfibrils .
Figure: Schematic diagram showing hierarchical structure of
Ligaments & Tendons

5. Composition
COMPONENT LIGAMENT TENDON
Cellular Materials:
Fibroblasts 20% 20%
Extracellular:
Water 60-80% 60-80%
Solids 20-40% 20-40%
Collagen 70-80% Slightly higher
Type I 90% 95-99%
Elastin Up to 2x collagen Scarce
Ground substance 20-30% Slightly lesser

6. Anatomical Positions of Tendons
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
Type I Collagen
1. ~86% of tendon dry weight
2. Glycine (~33%)
3. Proline (~15%)
4. Hydroxyproline (~15%, almost unique to collagen, often used to identify)

7. Anatomical Positions of Ligaments
Ligaments
 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.

8. Functions
 Tendons
1. Tendons carry tensile forces from muscle to bone.
2. They carry compressive forces when wrapped around bone like a pulley.
3. They facilitate skeletal muscle movement (movement in joints).
4. Proprioception.
5. Secondary function: Storage of energy.
 Ligaments
1. It maintains correct bone and joint geometry.
2. Ligaments + Associated joint capsules combinely function as passive joint
stabilizers.
3. Secondary function: Proprioception.

9. Mechanical Properties of Ligaments &
Tendons
 The hierarchical structure of ligaments and tendons shows that they exhibit
both nonlinear and viscoelastic behavior even under physiologic loading, which
is more difficult to analyze than the linear behavior of bone.
Non-linear elasticity
If one neglects viscoelastic behaviour, a typical stress strain curve for ligaments
and tendons can be drawn as:
1. Toe region(1.5-3% ε)
a. Collagen crimps removed by elongation, minimal force.
b. More force required as the fibers straighten.
c. The toe region shows no rise in load for significant
change in deformation due to uncoiling of the collagen .

10. Contd…
2. Linear region
a. Molecular cross-links of the collagen stressed.
b. The slope of this region gives the measure of tissue’s modulus of elasticity.
c. Slope=stiffness, [in σ-ε curve ⇒E (1-2GPa)].
3. Yeild & Failure Region
a. Fall in slope represents the yeild point .
b. Onset of cross-link or fiber damage.
c. If loading is continued the tendon or ligament will eventually fail.

11. Contd…
 Viscoelastic Properties:
 Indicates time dependent mechanical
behavior.
 The stress and strain is not constant but
depends upon the time of displacement or
load .
 Major types of behavior of viscoelasticity are:
 Creep:
 Creep is increasing deformation under
constant load.
 This contrasts with an elastic material
which does not exhibit increase
deformation no matter how long the load
is applied.
 Stress Relaxation:
 This means that the stress will be reduced
or will relax under a constant deformation
Figure:Creep
Figure:Stress Relaxation

12. Hysteresis or Energy Dissipation Curve
 This means that if 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.
 The two curves show that 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.

13. Modeling of Ligaments & Tendons As:
1. Non-linear elastic material
To represent the nonlinear elastic behavior of
ligaments, Weiss et al. has developed a
hyperelastic model including a strain energy
function.The strain energy function is given
below:
The 2nd Piola-Kirchoff stress tensor is calculated
from the above strain energy function by the
relationship:
Where,
F1 represents the contribution of the
isotropic ground matrix,
F2 represents the contribution of the
collagen fibers,
F3 represents the interaction between
the collagen fibers and the matrix.

14. Contd…
Another model described by Wiess and Gardiner described
ligament behavior as nonlinear elastic using a transversely isotropic
strain energy function. This was written as:
The general form of the 2nd Piola Kirchoff stress for an
incompressible isotropic hyperelastic material is:
Where,Cij= 2Eij+1

15. Contd…
2. Viscoelastic Materials
 As ligaments and tendons exhibit time dependent behavior, a number of
studies have modeled ligaments and tendons using viscoelastcity, especially
QLV theory.
 From Weiss and Gardiner, QLV implementation as 2nd PK stress tensor is
given:
It is generally assumed that the relaxation function is the same in all directions, which
means that the stress relaxation tensor is actually a scalar and the above is written as:

16. Contd…
With the reduced relaxation function being:
It has been determined that the consant c has the greatest influence on the viscous
behavior and that the time constants t1 and t2 determine fast and slow viscous behavior.
For purposes of finite element analysis, Puso and Weiss approximated the reduced
realxation function as:
Where,
Ge=The equilibrium modulus,
G0=Initial modulus,
Nd=The number of decades on a log
scale, and 10^I0 is the lowest discernible
relaxation time

17. Contd…
 Based on the previously derived
equation, Puso and Weiss showed
that the discrete representation of
the analytical form of the stress
relaxation function as shown below
:
 Application of this model:
 The QLV theory above was applied
to model the mechanical behavior
of normal versus healing ligament;
provided by Abramowitch et
al(2004) using a coefficient fitting
routine developed by Abramowitch
and wu(2004)

18. Age and Mechanical Behavior
 A number of animal studies have
shown that the mechanical
properties of tendons and ligaments
change with age.
 The size of Toe region of the stress-
strain curve decrease and elastic
modulus and ultimate strength
increase during maturation by the
following causes.
a. Increase in collagen content per unit
area, due to steady decline in water
content.
b. Gradual decrease in collagen crimp.
c. Gradual increase in collagen cross-
links which causes molecules to be
stiffer.

19. Contd…
 An experiment was carried out in
New Zealand, in a colony white
rabbits and the following graph
was obtained :
 Note that:
 In the horse, tendon stiffness gradually
increases and then begins to decline
during the aeging.Rats may simply not
live long enough for this to happen to
their tendons.

20. Mechanical Testing:
 The mechanical testing and direct
measurement of tendon and ligament
to study of the behavior is done by
directly gripping the specimen which
can lead to inaccurate measurement
due to slide in grips leading to error in
displacement measurements
 A way around this difficulty is to leave
the ligament attached to the bone and
use optical methods and makers to
measure the strain. A schematic of
such a test setup from the test is shown
below

21. Mechanically Mediated Ligament &
Tendon
 In ligaments and tendons there is less likely to occur changes in
mechanical stiffness because of low vascular supply.
 But the immobilization of a joint for a long time leads to severe changes
in the characteristics of ligaments and tendons.
 For this an experiment on the rabbits knee was carried out to check the
effects.

22. Immobilization experiment:By Woo et
al.
 Experiment was studied under different phases.
1. 9 weeks immobilization:69% decrease in ultimate load
and 82% decrease in energy to failure.
2. 12 weeks immobilization:71% decrease in ultimate
load.
 The effects on stress strain curve from Woo are
shown as:
 The rabbits were left active and there was increase
in stiffness and strength almost back to the
previous after the experiment.

23. Contd…
 The conclusion of this experiment were:
1. Corresponding to reduction in mechanical properties there is a reduction is the
ligament structure, Since the cross-sectional area of ACL of rabbit is also reduced .
2. The above findings emplies that , there is loss of collagen and alteration of
orientation of collagen fibers along with loss of glycosaminoglycans that forms the
ground substance
 Upon remobilization it is found that the mechanical properties were
gained back first, followed by structural properties.

24. Immobilization Vs Exercise:
 Exercise and increased load on tendons &
ligaments is believed to altered their
structural makeup and lead to increased
mechanical properties.
 Various experiments are carried out in
order to elaborate and justify the above
statement.
 Woo puts the findings of immobilization
and exercise together in graph below:

25. Mechanical Affects on Healing
Tendons/Ligament.
 Ligament and repair are a very critical area of orthopaedic
surgery, especially in the sports medicine.
 In case of tendons, which glide within a sheath the
introduction of passive motion for healing and repaired
tendons is believed to be important because it prevents the
adhesion between the sheath and tendons that restrict
motion.
 In case of ligament the relation between the mobilization
and repair is not positive.

26. Contd…
 Many experiment suggest that the
immobilization shows best gain in
strength over time.
 One of the major factor that affect the
wound healing, stiffness and strength
of the healing ligaments is the amount
of Type I Vs Type III collagen present in
the ligaments and tendons
 Type III collagen is a type of collagen
highly associated with relatively fastest
wound healing .
 The graph justifies the above statement
with a curve

27. Injuries in Tendons & Ligaments
 Most common tendon and ligament injuries occur by over use and high
load/stress given to the tendons.
 The tendons which suffers high chances of injuries are:
1. Rotator cuff tendons (shoulder).
2. Achilles tendons (leg).
3. Flexor tendons (hand).
 The ligaments which suffers high chances of injuries are:
1. Anterior cruciate ligament (Knee).
2. Ankle ligaments (Calcaneofibolar, Anterior talofibular, Deltoid).

28. Tissue Engineered Ligaments &
Tendons
 Tissue engineering is a process that affects the structure and
architecture of any viable and non viable tissue with the aim to
increase the effectiveness in biological environment
 Tissue engineering is mainly used in order to recover and strengthen
the injured ligament and tendon.
 Basically tissue engineering could be divided into four major
catagories:
1. Scaffolds :
 Scaffolds in tissue engineering have a major role to provide a suitable environment of
cell attachment , migration , proliferation and matrix remodeling and regeneration.
 It provides the space for the ligament and tendon to regenerate.
 In designing the scaffold for ligament and tendon , one should be carefull about the
cytocompatibity invitro , biocompatibility , biodegradable and healing incorporative.
 The porosity of the scaffold , it’s architecture should also be compatible with the
structure of the ligament and tendon.

29. Contd…
2. Healing Promotive Factor(HPF): HPF is another category of tissue engineering. They
are subdivided into four catagories as:
i. Glycosaminoglycans.
ii. Growth factors.
iii. Proinflammatory mediators.
iv. Healing agents.
 They have specific function during the tissue repair of tendon and ligaments.
3. Gene Therapy: Gene therapy involves the transfer of genetic information to target
cells and may introduce safe and effective tissue healing.
 The two modes of gene delivery is:
i. Viral mode: (adeno virus , retro virus , adeno-accociated virus).
ii. Non viral mode: Liposomes.

30. Contd…
4. Stem cells:
 Large variets of stem cells have been differentiated and tested in both in vitro and in vivo.
 The most well-known stem cells are mesenchymal cells which are differentiated from bone
marrow , adipose tissue and blood.
 The effectiveness of the stem cells is related to their differentiation state; the higher the
differentiation rate , the more effective in the healing.
 This is fet to be confirmed and tested in a high rate as controlled differentiation may lead to
tumors and other complication also