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26
Fig. 2.19 The difference between Newtonian and nonNewtonian uids in a graph of uid strain velocity
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
imposed for travel and speed. Such uids include
liquids made of low-molecular matters such as
water and alcohol in a relatively simple
composition.
Non-Newtonian uids are also called plastic
uids. Such colloidal high-concentration solutions form a strong three-dimensional structure
among the particles, thus requiring certain stress
for their destruction. They will start to ow only
after the stress of a certain size or higher is
applied, which means that there is no proportionate relationship between the sliding speed and the
resistant stress. It is a common trend to see how
well a matter will ow when talking about the
viscosity of a uid by considering only viscosity
as frictional forces between the entire matter and
its external environment regardless of the structure among particles. In case of such highmolecular compounds, however, the components
form a certain structure, which requires force of a
certain size or more to break. The researcher
believes that the structural viscosity of particles
has effects on cohesion, which is the force to
make the particles attract each other and restore
the shape of a material whose structure is broken
by impact. Due to the presence of structural viscosity, there should be a force of a certain size or
more to break the structural viscosity of a ller
after its injection so that the initial travel of matter will start. Once the structural viscosity is bro-
ken, the ller will travel more easily even with a
smaller force.
2.3.1.3 Rheology
As mentioned earlier, elastic materials, which
refer to solids in which the law of elasticity is
applied, have resistance against force imposed
upon them within a certain elastic limit or deformation rate. A deformation means only the current state of a deformed material. When the
applied weight is returned to the original state,
the deformation of the matter will also return to
its original state. In viscous uids to which the
law of viscosity is applied, their resistant stress is
determined by how fast they are being deformed
or ow rather than their certain shapes at a certain
point. In such a case, the yardstick of force lies in
the speed of the deformation rate rather than the
deformation rate itself, which shows how much
deformation is happening as in the elastic material itself.
High-molecular materials, such as leather,
rubber, and plastic, are used in daily life all the
time and have both viscosity and elasticity at the
same time. The same matter will work mainly
under elasticity and have different stress according to the resistance of the degree of deformation,
or it may work mainly under viscosity and have
different stress according to the resistance of the
speed of deformation. Whether elasticity or viscosity, both of which are found in viscoelastic
materials, prevails depends on external conditions, representing an environment imposed on
the matter or the method of deformation. In other
words, the stress of the matter depends on its
deformation history. It is impossible to express
the stress of viscoelastic materials with a common simple functional equation.
These properties of viscoelastic materials are
covered during elementary science classes.
Students blend starch in water to make a sticky
mucous liquid. When it is held with momentary
force, it forms a lump in a solid form. When the
lump is put on the palm with no force applied, it
spreads like a mushy uid right away.
A children’s toy called slime (Silly Putty or
Flubber) is one example of a viscoelastic material
that is commonly found in daily life and offers
2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
Fig. 2.20 Difference in
viscoelastic behaviors
according to the
deformation history of
Slime
27
hints to infer the rheological properties of HA
llers. Slime is a high-molecular compound.
Like clay, one can rub it into any shape that one
wants. Slime made in the shape of a ball will
bounce off the oor when it is thrown like a rubber ball. When it is put on a table with a hole, it
will slowly spread and ow over time.
The former case shows the deformation of
slime at a very high speed, and the latter case
shows its gradual deformation due to its own
weight and gravity. Slime behaves like an elastic
material in cases of a fast deformation and like a
viscous uid in cases of a slow deformation.
Such different reactions of a viscoelastic material
according to its deformation history represent
viscoelastic behavior (Fig.2.20).
Viscoelastic materials have a greater deformation rate (elastic limit) than common elastic
materials and a strong three-dimensional structure among their particles that are not found in
common viscous uids, thus developing structural viscosity rather than simple material
viscosity.
The relationship between the deformation
imposed by the law of physics to show the rheological properties of matter and the stress resisting it is called a constitutive equation. Hooke’s
law of elasticity and Newton’s law of viscosity
are a constitutive equation in a very simple form.
Rheology can be dened as an area of mechanics
of materials whose goal is to develop and assess
constitutive equations to describe the viscoelasticity and ow of matter with a complex constitution that cannot be explained with these two
equations.
2.3.2 Rheological Indicators Used
forEvaluation ofHA Fillers
That Are Viscoelastic
HA llers are basically viscoelastic, which means
that they use common methods to measure the
viscoelastic levels used in rheology, which is the
study of viscoelasticity of materials. These measurements are used to evaluate the viscoelasticity
of HA llers. One can basically gure out the
rheological properties of each ller based on the
numbers representing the llers’ reactions to various kinds of force. There are four types of external forces imposed on an HA ller in a lab: (1)
compression, (2) torsion, (3) stretching, and (4)
lateral shear (Fig.2.21).
Labs use the type of rheometer shown in the
gure below to observe the reactions of llers
after these types of forces are applied. Using a
parallel plate, cone and plate, and concentric cylinder, they apply the four types of force to llers
28
Fig. 2.21 Four external
forces to evaluate the
viscoelastic properties
Fig. 2.22 Rheometer
for the evaluation of
viscoelastic materials
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
and measure the degree of their deformation and
restoration (Fig.2.22).
In rheology, electric vibrations are applied to
an object matter to measure its kinematic viscosity. Such electric vibrations can have impacts on
the structure of molecules that comprise a matter,
representing a sort of shearing force. Electric
vibrations can gradually increase instead of stay-
ing at a certain size. The rate of vibrations
increasing is called the electric shearing rate.
Viscoelastic materials have the internal structure
of their matter rearranged according to shearing
rate, thus adjusting the electric vibrations applied.
Materials show different reactions according to
their differences in viscoelasticity. Matters of
high viscosity close to that of uids have high
2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
Fig. 2.23 Viscous property of the free HA solution
29
stress reacting to stronger stimuli according to
growing shearing force, gradually increasing
their elastic values. On the other hand, shearing
force by such electric vibrations affects an interval between molecules and gradually reduces viscosity based on the gathering of molecules. Free
HA solutions, which are HA molecules simply
blended in water without cross-linking them in
this mechanism, usually have the nature of a uid
and a vulnerable structure to combine molecules,
thus changing their viscoelasticity in reaction to
electric vibrations (Fig.2.23).
When all the conditions are similar except for
electric vibrations in a range of 0.1~10Hz, the
elastic modulus of free HA solutions increases
gradually due to the normal stress of their molecules reacting to the vibrations according to
higher frequency (Fig. 2.24). Conversely, their
viscous modulus drops according to higher frequency as the structural viscosity of their molecules breaks (Fig.2.25).
These phenomena can also be found in daily
life. The process of making the fashionable
Dalgona coffee is an example. Coffee and sugar
are blended in water to turn them into liquid.
After hours of continuous whipping with a hand
or whisk, it will change in its rheological properties and become sticky. In general, people assume
that the whipping causes the change, but the
blending of coffee and sugar in water itself results
in a uid with some viscosity rather than a simple
uid like water. From a rheological perspective,
as shearing force is applied to the uid through
Fig. 2.24 The normal stress growth with increasing shear
rate in the free HA solution
Fig. 2.25 The change of the zero-shear viscosity with
increasing shear rate in the free HA solution
whipping, its molecules will change in the structure and properties. When continuous stimuli are
applied to a viscoelastic material that is mushy
like a uid but not water through whipping, it
will gradually harden with its viscosity dropping
and its elasticity rising. This phenomenon is similar to the reaction of a viscoelastic uid receiving electric vibrations.
HA llers, however, have a higher elastic
modulus when they are stabilized through crosslinking than when they are in a viscoelastic uid
state. They also maintain a certain interval
30
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
between molecules, thus making no changes in
their rheological properties regardless of the
degree of electric vibrations. In rheology that
studies the properties of llers, researchers basically look at the reactions of materials to electric
vibrations to check the stability of HA llers.
Stabilized llers should be able to constantly
maintain their viscoelasticity to some degree
regardless of the degree of electric vibrations
(Fig.2.26).
Oscillatory rotations using parallel plates of a
rheometer are carried out with a gap of 1mm. The
oscillation measurements of HA llers are made
at a room temperature of 25 °C with electric
vibration values in a frequency range of
0.1~10Hz. This is commonly called a linear frequency sweep test as vibrations constantly maintain the amplitude of wavelength and vary only in
numerical value (Fig.2.27).
When llers are injected into the skin, they are
subjected to more diverse forces than simple
external forces of pushing down and twisting
momentarily. Facial muscles around the mouth
make big movements. In parts where the skin and
Fig. 2.26 Stabilized rheological pattern of the crosslinked HA ller with increasing shear rate
its tissues make big movements up and down, it is
important to see how well llers endure slow and
gradual external forces as well as instant forces
when they are consistently pushed down, lifted,
and pulled sideways. This is why more manufacturers are conducting an amplitude sweep test
these days to examine the reactions of materials
to stimuli of electric vibrations and different
amplitudes. An amplitude sweep test examines
how llers adjust to the movements of the face as
its skin is slowly pulled, stretched, and shrunk up,
down, and sideways. This test helps to estimate
the viscoelastic nature of ller particles and the
degree of structural viscosity involved in their
binding or cohesion between the particles
(Fig.2.28).
When external force is applied to HA llers,
they will show both elastic and viscous reactions.
If the material is completely a viscous uid, it
will stay in a deformed state even after the external force is gone. If the material is completely
elastic, it will go back to its original form after
reaching the external force within its elastic limit,
which represents the degree of deformation that it
can endure.
HA llers are viscoelastic materials with both
the properties. When external force is applied to
HA llers, they will show a greater deformation
than the limits of a common solid due to their
nature as a viscous uid. They will restore back
to their original shapes due to their properties as
an elastic material after external force under a
certain level is applied and then removed. If
external force over the elastic limit of a ller is
applied, the ller will break its structure due to its
nature as an elastic material and not restore back
to its original shape even after the external force
is gone. Even in this case, however, the ller will
partially restore back to its original shape due to
Fig. 2.27 Linear
frequency sweep testthe amount of
deformation (strain) is
constant while the
frequency increases
2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
Fig. 2.28 Amplitude
sweep test- the amount
of deformation (strain)
increases
31
its electrical attraction between the particles as a
viscoelastic material, unlike general elastic materials. Nowadays this nature of llers is called
cohesion. The degree of cohesion among the
ller particles can be measured as objectively as
possible by deforming the shape of the ller with
force greater than the elastic limit of its particles,
which determines its elasticity and measures how
much it restores back to its original shape based
on its particles that gather again after the elasticity is broken.
As mentioned earlier, the deformation history
of a viscoelastic material determines which of its
properties will be more prominent. A ller inside
a syringe will pass through the syringe needle or
cannula according to the gradual application of
force, which reveals its nature as a viscous uid.
A high viscous modulus means that the ller will
not break easily in its structure and thus not
deform easily, which means that its matters will
move slowly. Lower viscosity means that the
ller will deform easily in its structure, which
means that its matter will move smoothly and
pass through the syringe easily. When the plunge
is pushed in a rush, the ller matter will not pass
through easily. The abrupt force applied to the
ller changes its deformation history, so at that
moment, the viscoelastic ller will have more of
an elastic nature, thus resisting more strongly to
deformation than the application of soft force.
An examination of parameters measured
with a rheometer to understand the basic rheological properties of a viscoelastic material
identies the representative indicators used
basically such as G′, G″, G
*
, and phase angle
(tangent δ). In addition to these basic indicators,
cohesion is also used as an indicator. Cohesion
represents the degree of cohesiveness among
particles, reecting the properties of a ller to
be injected into the human body, unlike other
matter as was mentioned earlier. For clinicians,
it is more important to gure out the clinical signicance of calculation numbers than to know
how to measure and calculate the moduli values
for the rheological properties of a ller in a lab.
They can choose a ller that meets their procedural goals based on such knowledge and obtain
the best outcomes by using a ller with proper
properties. The researcher will mainly explain
the essential signicance of llers’ rheological
indicators rather than enumerating complex
methods to measure them or numbers of
calculations.
2.3.2.1 G′: Elastic Modulus
Elastic modulus is the measurement of the elasticity of a ller. This index can estimate how
much an elastic material can withstand deformation by external force and keep its original shape.
Here, it is important to consider that different
materials have different deformation rates, which
are deformation limits of common elastic materials rather than hard solids to return to their original shapes after being deformed by an external
force. When the same force is applied, materials
with small elastic modulus, the degree of hardness, and a high deformation rate will show a
greater degree of deformation, whereas materials
with a big elastic modulus and a low deformation
rate will show a lower degree of deformation.
Basically, ller products have differences in the
elastic modulus and deformation rate according
to the manufacturing methods. Hard llers that
are close to an elastic material have a lower
deformation rate than soft llers that are close to
a viscous uid.
32
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
The basic unit of such numbers is Pa at
1Hz-gap 1.0mm/Malvern Kinexus. Pa is Pascal
as a unit of induced pressure in SI (international
system of unit), objectifying the degree of external force.
1 Pascal is the pressure when the force of 1
Newton is applied in an area of 1m2. 1Hz-gap
1.0mm is a unit of electric vibration explained
earlier. It means that an elastic modulus is measured with an increment of 1Hz for 1mm of an
oscillatory rotation gap created by parallel plates.
Malvern Kinexus indicates that rheological properties are measured with a rotary rheometer made
by Malvern.
When an elastic modulus is measured within a
deformation limit, which is the scope of a material being able to restore its original shape by
withstanding external force, greater external
force will be needed to cause the same degree of
deformation to harder materials. G′ will increase
as greater force is needed to deform a ller.
Higher G′ means that the ller is relatively hard.
An elastic material stores the energy created by
external force while it is being deformed by the
force. Once the external force is gone, the material will use the energy stored in it to return to its
original shape. Since it means energy stored, it is
also called storage modulus.
When the same external force is applied to different llers, they will show different degrees of
deformation according to their deformation rates.
However, when force that should be applied to
each force for the same degree of deformation is
measured, llers that require greater external
force will have higher G′. Fillers with higher G′
can withstand the same external force or organizational pressure after an injection than llers
with lower G′, having a remarkable ability to
keep their shapes.
The graph below shows several HA llers that
have been used frequently in the nation in ascending order of elastic modulus measurements under
the same conditions (Fig.2.29).
This graph offers a look at the elastic moduli
of several llers from low to high, showing that
there are highly diverse elastic moduli among different llers. Here one should be reminded that
the elastic modulus numbers are not absolute and
can differ a little bit according to experimental
conditions, rheometers, and companies that measure them. If measurements are made under the
same conditions, llers of better elasticity will
naturally have higher G′ whatever the conditions
might be. Consulting such elastic moduli can be
helpful for choosing a ller with elasticity that
best meets a purpose.
2.3.2.2 G″: Viscous Modulus
This index predicts the degree of viscosity that is
the sticky nature of a ller. A viscous uid keeps
being deformed and moved by external force.
Unlike an elastic material, it does not return to its
Fig. 2.29 Comparison of elastic modulus of various HA llers
2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
33
original shape even after the external force is gone.
External force applied to uids during their deformation is stored in them, but it is gone from uids
unlike elastic materials that store external force
and use it as energy to restore their original shapes.
As it means lost energy, it is called loss modulus.
Materials with high viscosity have their molecules entangled with one another in a stick way
to a high degree, which means that they require
greater force for continuous deformation than
materials that have low viscosity and ow well.
Fillers with high G″ are not deformed easily and
do not move smoothly inside a syringe due to the
high viscosity of their particles, thus requiring
force to get injected. Once injected, however,
they have an advantage of maintaining their original shapes at their original places without being
easily deformed and moved by external force or
movements.
Monophasic HA llers, especially the ones of
extremely high viscosity, have highly viscous and
tough particles that adhere to one another in a
sticky manner, unlike viscous uids. They maintain their original shapes wonderfully with almost
no deformations by external force, thus having a
high elastic modulus to maintain their forms like
biphasic llers.
Biphasic llers are hard and highly elastic
given their manufacturing characteristics, but
they have lower viscosity. One may simply predict that their viscous modulus will be lower, but
actual measurements of viscous modulus in the
lab indicate that biphasic llers of high elastic
modulus will also have high viscous modulus.
However, one should be reminded that this is not
an absolute viscous modulus, but one compared
to elastic modulus. That is, biphasic llers of
high elasticity have high resistance against being
deformed and moved by external force and thus
high measurements of viscous modulus in the
lab. These results do not derive from the sticky
property of such llers but represent absolute values from a lab test with viscoelastic materials that
are hard and barely move for a simple viscous
modulus. One should obtain another modulus
after measuring the elastic and viscous modulus,
and it is the phase angle for the ratio of elastic
and viscous modulus that follows. Biphasic llers have very high elastic modulus for their high
viscous modulus. Compared with monophasic
llers, they have a higher absolute viscous modulus but lower viscous nature.
The graph below shows several HA llers that
are used frequently in the nation in ascending
Fig. 2.30 Comparison of viscous modulus of various HA llers
34
GG
()+()
′′
22
2 Types ofFillers andRheological Considerations forHA (Hyaluronic Acid) Fillers
order of viscous modulus measurements under
the same conditions (Fig.2.30).
Monophasic llers are arranged similarly
between the absolute viscous modulus and the
degree of elasticity, but biphasic llers do not
necessarily have higher viscosity than monophasic llers that are lower than their absolute viscous modulus. Given the manufacturing
characteristics of HA llers, the knowledge of
each ller’s viscous modulus can be helpful for
choosing a ller that meets a procedural purpose,
such as the case of elastic modulus.
2.3.2.3 G*: Complex Modulus
This modulus combines G′, which measures the
degree of resistance to a deformation by external
force in elastic materials that can restore their
original shapes, and G″, which measures how
easily viscous uids with the nature of continuous deformation can be deformed by external
force instead of looking at them separately. It is
calculated in
∗
=
′
G
.
Fillers are viscoelastic, having the elasticity of
an elastic material and the viscosity of a viscous
uid at the same time. By calculating complex
modulus based on elastic and viscous modulus,
one can predict the overall deformation and resistance of a ller against external force in a simpler
way without looking at the elastic and viscous
modulus to gure out how the ller will react to a
deformation.
Monophasic llers basically have high elastic
modulus in proportion to high viscous modulus due
to the characteristics of their manufacturing process, which means that one can infer viscoelasticity
by comparing with complex modulus. Biphasic llers, however, do not necessarily have high elastic
and viscous modulus just because of high absolute
complex modulus as mentioned earlier.
The graph below shows several HA llers that
are frequently used in the nation in ascending
order of complex modulus calculations based on
elastic and viscous modulus (Fig.2.31).
2.3.2.4 Phase Angle (Tangent δ)
G″/G′ is the ratio of viscous modulus for elastic
modulus in a ller measured under the same conditions. This indicator can predict the rheological
properties of a material to see whether a certain
HA ller is closer to an elastic material or a viscous uid (Fig.2.32).
If a ller has a phase angle value close to 1, its
viscous modulus is bigger than its elastic modulus, which means that the ller is a viscoelastic
material with a more prominent nature of a viscous uid than an elastic material. Conversely, if
an HA ller has a phase angle value smaller than
1, its elastic modulus is bigger than its viscous
Fig. 2.31 Comparison of complex modulus of various HA llers
0.8
0.6
0.4
0.2
0.0
ABCDEFGH IJKLMNOPQR STUVWXYZ A’ B’ C’
2.3 Rheological Properties ofHA Fillers asViscoelastic Materials
35
modulus based on measurements, which means
that the ller is a viscoelastic material with the
nature of a harder elastic material than other llers with a higher phase angle value. Viscoelastic
materials whose phase angle value is close to 0
are close to a complete elastic material with little
viscosity for a viscous uid.
The graph below shows several HA llers that
are frequently used in the nation in order from
hard ones close to 0 to soft ones close to 1 according to phase angle (tangent δ) calculations based
on elastic and viscous modulus (Fig.2.33).
Even monophasic llers with similar elastic
modulus can have different phase angle numbers
according to different conditions. Such differences in phase angle values have impacts on the
degree of cohesion, which is one of the properties
of a viscous uid common among monophasic
llers as well. Detailed explanations about this
follow below.
Fig. 2.32 Rheology parameter: Phase angle (tangent δ)
2.3.2.5 Cohesion
There is an electric attraction among molecules
that comprise any type of material. The attraction
works as force for molecules to pull each other.
This force for the molecules of a material to pull
each other is called molecular cohesion. This
type of force is working among the molecules of
a material behind gases binding together and
hardening or liquids coagulating.
When liquids such as water or mercury are
sprayed on the oor, they will form a spherical
shape like a water drop instead of spreading. This
is due to cohesion among the particles made up of
molecules. Viscous uids tend to hold together
due to cohesion that is the force of molecules pulling each other. Similar to cohesion, adhesive force
is the force that works between the molecules of
different materials. Cohesion should be distinguished from adhesive force. While cohesion is
the force of the molecules of the same matter to
pull each other, adhesive force is the force of the
molecules of different matters to pull each other.
Water easily exists in drop form rather than
individual water molecules due to its cohesion.
When water is sprayed on glass, however, it
spreads wide on the glass surface instead of forming a drop and shows adhesive force to some
degree. Water maintains its drop shape on the
waxed glass surface instead of spreading because
only cohesion works with adhesive force between
water and glass shrinking.
Phase angle(tangent δ) at 1Hz-gap 1. 0mm/Malvern Kinexus
1.20
1.00
0
0
0
0.25 0.25 0.25
0.17 0.17 0.17
0
0.09
0.07
0
Fig. 2.33 Comparison of Phase angle (tangent δ) of various HA llers
0.10 0.10
0.11
0.12 0.12
0.13
0.14 0.14
0.15
0.160.16 0.16
0.19
0.31
TM
0.35 0.35
0.37
0.44
0.68
0.95
1. 01