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`- "'::""'II'"
`
`SOCIETY FOR LASER DERMATOLOGY
`1-FICIAL PUBLICATION OF THE EURO~
`ASER AND AESTHET IC SURGERY
`AND THE EUROPEAN SOCIETY F._~
`.. . ..
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`_........__ .,
`MARCIi 2008 · VOIUMI 10 · NUMI\ LR I· l ))N 14 76 - 4172
`+
`•
`•
`•
`w ww. i n form a world . com / c l t
`
`•
`~~~nal of cosmetic and laser therapy
`• G~neral Collection
`Wl J061 2H
`v. iO, no. 1
`Mar. 2008
`
`JOURNAL OF
`COSMETIC AND
`LASER THERAPY
`
`ED ITO RS:
`DAVI D J GOLDBERG, Nrw YORK. USA
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`

`Journal of Cosmetic and Laser Therapy. 2008; 10: 35–42
`
`informa
`
`healthcare
`
`REVIEW ARTICLE
`
`The science of hyaluronic acid dermal fillers
`
`AHMET TEZEL & GLENN H. FREDRICKSON
`
`University of California Santa Barbara, Santa Barbara, California, USA
`
`Abstract
`Background: The use of injectable materials for soft-tissue augmentation has been increasing in the United States, reflecting
`the introduction of new hyaluronic acid (HA)-based dermal fillers. HA dermal fillers vary widely in their physical and
`chemical characteristics and many variables contribute to their overall performance. This article explains the basic science of
`HA and describes how the physical properties of HA dermal fillers may influence clinical outcomes. Hyaluronic acid: The
`chemical composition of disaccharide HA monomers, and how they form polymer chains and are crosslinked into gels for
`dermal fillers are described. Hyaluronic acid dermal fillers: Key concepts and properties relevant to the production and
`performance of HA dermal fillers, such as the degree of crosslinking, gel hardness, gel consistency, viscosity, extrusion force,
`HA concentration, and extent of hydration are explained. New formulations of HA dermal fillers that have recently been
`approved by the US Food and Drug Administration differ from currently available HA fillers and may provide enhanced
`ease of extrusion and persistence over previous fillers. Conclusion: Knowledge of the chemical and physical blueprint of HA
`dermal fillers may help physicians in choosing the appropriate HA dermal filler for facial enhancements. This, together with
`appropriate injector training and injection experience, should lead to results that ultimately will benefit patients.
`
`Key words: Dermal fillers, hyaluronic acid, soft-tissue augmentation
`
`Introduction
`
`As we age, our faces begin to show the effects of
`gravity, sun exposure, and years of facial muscle
`movement, such as smiling, chewing, and squinting.
`The underlying tissues that keep our skin looking
`youthful begin to break down, often leaving laugh
`lines, smile lines, crow’s feet, and facial creases. Soft-
`tissue fillers can help fill in these lines and creases,
`temporarily restoring a smoother, more youthful-
`looking appearance (1). The ideal filler would be
`non-permanent but long-lasting, have minimal side
`effects, not require allergy testing, be easy to use/
`inject, painless upon injection, and cost effective for
`both the physician and the patient (2).
`For more than 20 years, bovine collagens
`(Zyderm, Zyplast; Allergan, Santa Barbara, CA,
`USA) were
`the only US Food and Drug
`Administration (FDA)-approved dermal
`fillers.
`Because these dermal fillers are bovine based, one
`of the main disadvantages has been the need for
`allergy testing. In addition to possible allergic reac-
`tions, cosmetic patients can be impulsive consumers
`and requiring them to wait a month for an allergy
`test before treatment was a significant drawback
`
`(3). In February 2003, human-derived collagens
`received FDA approval (CosmoDerm, CosmoPlast;
`Allergan); they provide the advantage of a signifi-
`cantly reduced risk of allergic reactions and elim-
`inate the requirement of allergy testing.
`Another significant concern with dermal fillers has
`been longevity. The search for fillers that do not
`require allergy testing and potentially last longer
`than collagen-based products brought about the
`development of hyaluronic acid (HA)-based sub-
`stances. In December 2003, the first HA product
`was approved in the United States (Restylane;
`Medicis Aesthetics Holdings Inc., Scottsdale, AZ,
`USA), and was soon followed by other HA fillers
`(Hylaform, Hylaform Plus, Captique,
`Juve´derm
`Ultra,
`and
`Juve´derm Ultra
`Plus;
`Inamed
`Corporation, now Allergan).
`HA has
`features
`that make it an attractive
`substance for dermal filler use, such as its ability to
`bind to large amounts of water, its natural presence
`in the skin, and its low potential
`for adverse
`reactions. Despite these general features, HA dermal
`fillers are not all the same. They differ in character-
`istics such as the type of crosslinker used, degree of
`
`Correspondence: Ahmet Tezel, Allergan, Santa Barbara, California, 5540 Ekwill Street, Santa Barbara, CA 93111, USA. Fax: 1 805 456 2022. E-mail:
`Tezel_Ahmet@allergan.com
`
`(Received 1 June 2007; accepted 29 October 2007)
`
`ISSN 1476-4172 print/ISSN 1476-4180 online # 2008 Informa UK Ltd. (Informa Healthcare, Taylor & Francis AS)
`DOI: 10.1080/14764170701774901
`
`

`

`36
`
`A. Tezel & G. H. Fredrickson
`
`crosslinking, gel hardness, viscosity, extrusion force,
`gel consistency, total HA concentration (amount of
`HA per milliliter of finished product), and lifetime in
`the skin. Key to the performance of an HA dermal
`filler is how all of these characteristics act in concert
`to deliver a product that combines ease of injection
`with long life and efficacy as a filler.
`In order to give practitioners better tools to
`evaluate HA dermal
`fillers,
`this article seeks to
`explain the chemical and physical attributes that
`have been identified as most relevant to product
`performance. A deeper understanding of the science
`underlying HA dermal fillers, and the factors that
`influence final product characteristics, should facil-
`itate making appropriate choices when designing
`therapies for the increasing number of patients
`seeking facial enhancement, restoration, and rejuve-
`nation.
`
`Hyaluronic acid
`
`Chemical composition
`
`Hyaluronic acid (HA, also known as hyaluronan) is a
`polysaccharide (specifically a glycosaminoglycan)
`that consists of repeating D-glucuronic acid and D-
`N-acetylglucosamine disaccharide units. Normally
`the carboxyl group (–COOH) of D-glucuronic acid
`has been converted into its sodium salt, leading to
`the disaccharide structure shown in Figure 1. These
`disaccharide units can be viewed in a broader
`context as ‘monomers’, small molecules that chemi-
`cally bond to other identical or different monomers
`to form a macromolecule, or
`‘polymer’. The
`disaccharide monomers that constitute the HA
`polymer are linked together into a linear chain
`through beta-1,4 glycosidic bonds. Each disacchar-
`ide monomer has a molecular weight of , 400 Da.
`The number of repeating disaccharides, n, in an HA
`polymer chain can reach 25 000 or more, creating a
`polymer with a total molecular weight of , 10 MDa.
`
`about HA is that it differs according to its source:
`animal or bacterial. The basic unit of HA, that is, the
`monomeric unit that composes HA polymer chains,
`is identical regardless of its origin. The principal
`difference between animal-based and bacterial-
`based HA is the length (degree of polymeriza-
`tion n, or molecular weight) of the final polymer
`chain. Polymer chains from bacterial-based HA
`are usually
`shorter,
`comprising
`approximately
`4000–6000 monomeric units per chain that corre-
`spond to an average molecular weight of approxi-
`mately 1.5–2.5 MDa. Animal-based HA chains have
`about 10 000–15 000 monomeric units per chain
`that correspond to an average molecular weight of
`approximately 4–6 MDa (Figure 2).
`
`Water solubility
`
`HA derived from either bacterial or animal sources is
`a highly water soluble polymer that will readily
`dissolve into water to form a viscous clear liquid.
`The water solubility of HA can be traced to a
`number of factors, but especially to the presence of
`four hydroxyl (–OH) groups and one –COO2 Na+
`‘salt’ group per disaccharide repeat unit (Figure 1).
`The hydroxyl groups can participate in hydrogen
`bonding with water, which stabilizes the solvated
`state. Furthermore, the salt group dissociates in
`water with a favorable release of free energy that
`derives from the solvation energy of the resulting
`– COO2 and Na+ ions and the gain in entropy of the
`released sodium ion (Na+). The net effect is that HA
`polymer dissolves readily in water.
`
`Hyaluronic acid dermal fillers
`
`Because the chemical structure of HA is the same
`across all species, the potential for immunologic
`reactions and implant rejection is negligible, making
`HA a very suitable material for use as a dermal filler
`(4).
`
`Chain length and source
`
`Crosslinking of HA polymers
`
`HA, an essential component of the extracellular
`matrix of all adult animal tissues, naturally exists in
`tissues as a biopolymer. A common misconception
`
`0
`
`Figure 1. HA monomeric unit. One disaccharide unit consisting
`the sodium salt of D-glucuronic acid (left) and D-N-
`of
`acetylglucosamine (right) bound together by a beta-1,3 glycosidic
`bond. Note that two disaccharide units are linked by a beta-1,4
`glycosidic bond.
`
`A series of chemical modification and processing
`steps must be applied to HA to develop viable
`formulations for use as dermal fillers. The raw HA
`polymer used to produce dermal fillers is usually
`supplied to the manufacturer in dry powder form.
`Mixing this powder with water creates a viscous
`liquid that has the look and feel of egg white. The
`more HA powder added to a given amount of water,
`the thicker and more viscous the solution will
`become (Figure 3).
`Such a solution is known as free HA, uncros-
`slinked HA, or non-modified HA. If this solution
`was to be used as a dermal filler, the product would
`be rapidly eliminated from the injection site (in less
`than a week). This results from the very limited
`
`

`

`Hyaluronic acid dermal fillers
`
`37
`
`Bacterial-Based HA
`,;,:::;,...,:;::,,..'t'.-,,..,;::::,,.~~ ... ~ \ , ... ~~\,~~
`4000- 6000 monomeric units
`------..---
`Molecular weight: 1.5-2.5 M Da
`monomeric unit
`
`(A)
`
`Animal-Based HA
`~~ ; , . ~~ .. ... ~~ .. . ~~ .. . ~~~ ~~
`10,000-15,000 monomeric units
`Molecular weight: 4-6, M Da
`
`(8)
`
`Figure 2. HA chain lengths. HA polymer chains, made up of several thousand disaccharide monomer units, differ only in their length but
`not in their basic molecular composition. Bacterial-based HA polymer chains (A) are generally shorter than animal-based HA polymer
`chains (B).
`
`chains to each other, creating a polymer ‘network’
`and transforming the viscous liquid into a gel
`(Figure 4). The transformation from solution to gel
`should be familiar to readers who have prepared
`gelatin desserts.
`The resulting HA gel acts as a single unit,
`imposing a physical and chemical barrier to enzy-
`matic and free radical breakdown. Because the gel
`network is multiply connected, enzymes and free
`radicals can break down the chains only in much
`smaller portions at a time. Moreover, due to their
`large size, enzymes can have difficulty penetrating
`the gel network, which will in effect contribute to a
`slower degradation. This
`translates
`into longer
`persistence of the HA gel in the skin when used as
`a dermal
`filler. A useful analogy is to think of
`crosslinkers as mortar between bricks. Just as mortar
`makes a brick wall stronger, the incorporation of
`
`Crosslinkers
`
`+ . '1
`
`I
`
`I
`
`-
`-
`
`1
`
`I
`
`I
`
`I
`I
`
`I
`
`I
`
`residence time of uncrosslinked HA polymers in the
`skin as the body quickly breaks down HA chains that
`are not crosslinked into a gel (see below). Enzymes
`such as hyaluronidase and free radicals that are
`naturally present in the skin can quickly degrade
`uncrosslinked HA polymers, cleaving off
`large
`portions of the polymer chains at a time. As a result,
`its half-life is 1–2 days in tissue, where it undergoes
`aqueous dilution and then, in the liver, enzymatic
`degradation to water and carbon dioxide (5).
`Therefore, uncrosslinked HA solutions do not
`provide the persistence required of a dermal filler
`(6).
`In order to overcome the lack of persistence of
`uncrosslinked HA, dermal filler manufacturers use
`crosslinkers. The crosslinkers bind HA polymer
`
`Water
`
`+
`
`--
`
`(A)
`
`(8)
`
`(C)
`
`(A)
`
`I
`
`I I
`
`(8)
`
`(C)
`
`(D)
`
`(D)
`
`Figure 3. HA solution in water. An HA polymer, represented as
`chains composed of many monomeric units (A), when dissolved in
`water (B), produces a viscous liquid (C), that looks and feels like
`egg white (D).
`
`Figure 4. HA gel. Crosslinking HA polymer chains transform the
`HA solution (A) into a gel (C). Crosslinker molecules (B) bind
`individual HA polymer chains to create a network (C), which
`manifests macroscopically as a gel mass (D).
`
`

`

`38
`
`A. Tezel & G. H. Fredrickson
`
`crosslinkers makes HA a more rigid and durable
`biomaterial.
`Crosslinking is evidently an essential step in
`slowing the breakdown of HA dermal fillers. The
`two crosslinkers used in HA dermal fillers currently
`on the US market are 1,4-butanediol diglycidal ether
`(BDDE), and di-vinyl sulfone (DVS). Both react
`with hydroxyl sites on the HA chains and offer
`similar results in slowing down enzymatic and free
`radical degradation of dermal fillers once injected
`into the skin. Figure 5 shows BDDE used as a
`crosslinker, binding together
`two HA polymer
`chains.
`Crosslinking HA chains can result in the presence
`of unreacted, or residual, crosslinker in the finished
`product. Residual crosslinker molecules are artifacts
`of the manufacturing process and can be toxic at
`high concentrations when unbound to other mole-
`cules. They are highly undesirable, and dermal filler
`manufacturers take special steps to eliminate as
`much of the residual crosslinking agent as possible
`from the finished product.
`To assure the safety of dermal fillers marketed in
`the US,
`the FDA expects
`residual crosslinker
`concentrations in dermal
`fillers to be orders of
`magnitude below a level that might pose health
`concerns to humans.
`
`Degree of crosslinking
`
`When comparing HA dermal fillers, it is important
`to understand the concept of degree of crosslinking.
`The degree of crosslinking indicates the percentage
`of HA disaccharide monomer units that are bound
`to a crosslinker molecule. Thus, to say that a dermal
`filler has a degree of crosslinking of 4% means that,
`on average, there are four crosslinker molecules for
`every 100 disaccharide monomeric units of HA
`(Figure 6). Every other parameter being equal, the
`greater the degree of crosslinking, the harder the gel
`becomes. The significance of gel hardness (or
`softness) will be disuccsed in further sections of the
`manuscript.
`
`•••~~O~o • • ·
`HO~
`NH
`NM
`HO-<
`C=O
`C•O
`"1
`CH.)
`CHi
`
`0
`
`-
`
`BODE
`
`CH1
`C=O
`
`OH
`
`CHs
`C• O
`
`~
`~~OH ~OH
`\,.....--t-\.- \-~o \,---0.- \.i-w .. .
`... o
`
`CH;2'0H O COO- Na,+
`
`O
`
`C~OH O COO- N .i+
`
`monomeric unit
`
`Figure 5. BDDE (1,4-butanediol diglycidal ether) crosslinking
`agent used to bind HA polymer chains to each other, transforming
`liquid HA solutions into gels. Both the primary hydroxyl site
`(–CH2OH) and secondary hydroxyl sites (–CHOH) within the
`HA monomeric unit are possible target sites for reaction with
`BDDE.
`
`When discussing the degree of crosslinking, one
`must recognize that many HA dermal fillers are
`composed of both crosslinked and uncrosslinked
`fractions (in the following sections of the manu-
`script, uncrosslinked HA is defined as the portion of
`the product that includes both uncrosslinked chains
`and lightly crosslinked chains and fragments that will
`aid extrusion/flow; such lightly crosslinked chains
`and fragments will behave similarly to uncrosslinked
`HA – that is, while aiding extrusion and flow,
`providing limited to no contribution to persistent
`wrinkle correction). The degree of crosslinking by
`definition refers only to the fraction of HA that is
`actually crosslinked. The crosslinked HA is relevant
`to maintaining the volume of the filler implanted
`into the skin, as the uncrosslinked HA is cleared
`from the body in a matter of days.
`For HA dermal fillers, when all other factors are
`equal, a higher degree of crosslinking should
`translate into longer persistence of the filler in the
`skin. At the same time, there is an as-yet undefined
`threshold for the highest desirable degree of cross-
`linking, as very high degrees of crosslinking might
`reduce the hydrophilicity (water affinity) of the HA
`polymer chains and, hence, the lifting capacity of the
`gel
`implant
`(see ‘Concentration and extent of
`hydration’ below). Furthermore, exceeding this
`threshold might affect the biocompatibility of the
`product and induce an immune reaction by the body
`to the injected HA gel and, rather than metabolize
`the gel, the body might reject it, initiating undesired
`reactions such as encapsulation of the gel implant
`and formation of a granule or a sterile abscess.
`Therefore, dermal filler manufacturers are pru-
`dent to stay well below that threshold, and achieve a
`balance between crosslinking HA polymer chains
`sufficient
`to achieve extended persistence and
`avoiding any undesired complications,
`such as
`rejections.
`
`Gel hardness
`
`Gel hardness refers to the stiffness of the HA gel
`formulation,
`namely
`its
`resistance
`to
`being
`deformed. Polymer scientists use a variable G9, the
`elastic or storage modulus, to quantify gel hardness
`(7). The concentration of HA, degree of crosslinking
`of HA, amount of uncrosslinked HA, and the
`manufacturing process all contribute to the resulting
`gel hardness, measured by G9.
`Gel hardness can be illustrated as follows: if an
`HA gel is placed between two plates and then the
`upper plate is quickly displaced horizontally a small
`distance while keeping the lower plate stationary, a
`force will be required to hold the (shear) deforma-
`tion in place. G9 is defined as the ratio of the shear
`stress (the force per unit area of plate) to the shear
`strain imposed (the ratio of the horizontal displace-
`ment to the vertical distance between plates). In a gel
`
`

`

`Hyaluronic acid dermal fillers
`
`39
`
`100 monomeric units
`
`2
`
`50
`
`51
`
`97
`
`98
`
`99
`
`100
`
`BODE-+ '
`+-BODE
`+-BODE
`+-BODE
`t..-=-~,:;:'..\,,~,:;:'..\,, t..~~-=- ·~-=-~~ ~"'\'.:'..>.,~,::::..,~,:::.,,,~-=, t,.,:;:.,,,~,::::..,
`1
`2
`50
`51
`97
`98
`99
`100
`
`Figure 6. Degree of crosslinking. If four BDDE crosslinkers are bound to every 100 disaccharide monomeric units, the degree of
`crosslinking is 4%. The specific monomeric units that bind to BDDE are determined statistically by the reaction process. This figure shows
`one of many possibilities.
`
`with a low degree of crosslinking, where the HA
`polymer chains are loosely linked to one another, the
`force required for displacement is low, so the gel
`hardness or G9 increases. As the degree of cross-
`linking is increased, but at the same overall HA
`concentration,
`the network formed by the HA
`polymers becomes more tightly connected, and a
`greater force is required to displace the gel, and the
`gel hardness or G9 increases (Figure 7).
`The above discussion of gel hardness applies to a
`monolithic gel mass produced by crosslinking a
`solution of HA polymer. As will be described in
`more detail below, the manufacturing process used
`to produce HA dermal fillers involves breaking the
`gel mass into small HA gel particles so that they can
`be injected through a needle into the skin. HA
`products containing particles with higher G9 values
`are more difficult to inject, even if the gel particles of
`the finished product are very small in size. In order
`to overcome this difficulty, some manufacturers of
`dermal
`fillers add/use uncrosslinked HA as a
`lubricant to lower the G9 during injection and,
`therefore, the force required for injection. While this
`uncrosslinked HA aids smooth injection of a dermal
`filler, it has a short persistence time and, thus, does
`not contribute to persistent augmentation.
`
`Hyaluronic acid gel consistency
`
`The gel particle size of a finished product is another
`important property that affects the use of HA dermal
`fillers. As discussed above, the crosslinking step in
`
`• Soller gel
`
`(less force
`needed)
`
`the process used to create HA dermal fillers is similar
`to the preparation of gelatin – stirring a powder into
`hot water and letting the solution cool down. After
`this step, the result is a large, connected gel mass.
`This large gel mass must then be ‘sized’ to allow for
`injection into the skin. Sizing can be accomplished
`by passing the gel mass through a series of sieves or
`screens. HA dermal fillers produced through this
`method contain gel particles of a well-defined
`average size. Different products will have distinct
`average gel particle sizes according to the proprietary
`sieving method applied in the manufacturing pro-
`cess. For dermal filler products there is a maximum
`particle size, beyond which gel particles would not
`extrude easily and could clog the needle during
`injection.
`In addition, the relationship between particle size
`and rate of degradation in the body has implications
`for ‘ideal’ particle size. Larger HA particles offer
`limited total surface areas (area per volume of gel)
`for enzymes to break them down, since the enzymes
`are sufficiently large that they cannot easily penetrate
`the HA gel network within a particle. Smaller HA
`particles offer more total surface area for enzymes to
`more readily degrade them. In contrast, the rate of
`degradation of HA gel particles by free radicals is
`expected to be less sensitive to particle size because
`many radicals are small
`in size and can easily
`penetrate to the particle interior. Nonetheless, all
`other relevant variables being the same, including
`the total volume of the implant, the smaller the
`average size of
`the gel particles,
`the faster the
`
`•••
`
`Harder gel
`(more force
`needed)
`
`(A)
`
`(8)
`
`Figure 7. Gel hardness (G9-elastic modulus). G9 is measured by placing the gel between two plates and moving the upper plate horizontally
`relative to the lower one. With two products having the same HA concentration, the lower the degree of crosslinking, the softer the gel will
`be, resulting in a lower G9.
`
`

`

`40
`
`A. Tezel & G. H. Fredrickson
`
`product will degrade in the body and disappear
`(Figure 8). However, given the limited range of gel
`particle sizes in the dermal fillers currently approved
`in the US, the differences in degradation rate may
`not be great enough to exhibit a clinically significant
`difference.
`An alternative way to size a large gel mass is to
`break it down by a homogenization process. The
`result is a gel formulation that displays a smooth
`consistency and looks like thick egg white when
`compared with the more granular consistency gel
`particle formulations mentioned above. Presumably
`the smooth consistency results from a much broader
`distribution of gel particle sizes than in products
`obtained by sieving. The products manufactured
`with this technology are softer gel formulations with
`lower G9 values, and they flow easily so there is no
`need to use screens to limit the maximum particle
`size. Such products have recently been approved by
`the FDA and offer attractive combinations of
`persistence and ease of injection.
`
`Viscosity, elasticity, and extrusion forces
`
`We have discussed the concept of gel hardness G9,
`which is connected to the force required to make a
`small, rapid deformation of a gel. G9 thus provides
`information about the linear elastic properties of the
`gel. Of more clinical relevance is the extrusion force
`that the physician must apply to inject the HA filler
`through a needle and into soft tissue. A schematic of
`such an extrusion force curve is shown in Figure 9,
`where the force F that must be applied to the syringe
`plunger to inject a dermal
`filler is plotted as a
`function of displacement D of the syringe plunger.
`The curve is drawn assuming that the plunger is
`
`l
`
`(A)
`
`(8)
`
`Figure 8. Particle size and rate of degradation. In theory, the
`larger the gel particle (A), the smaller the total surface area
`available for enzymatic degradation in the body. The smaller the
`gel particles (B), the larger the total surface area that is available
`for degradation. All else being equal, if a large particle (A) is sized
`down to a collection of smaller particles (B) that contain the same
`volume, in theory the larger total surface area of the smaller gel
`particles will facilitate more rapid enzymatic attack and, hence,
`more rapid degradation of the filler in the skin. However, due to
`the porous nature of the HA gel particles, the effects of particle
`size become very limited during clinical use as enzymes have
`access to the entire gel particle rather than having only access to
`the particle surface.
`
`18
`
`15
`
`B
`

`z· 12
`!
`.2
`" 0 --;
`i 6
`
`11
`
`IIJ
`
`A
`
`0
`
`05
`
`1,0
`
`1.~
`
`20
`
`2.5
`
`3_0
`
`Dlsplacement, mm, fD)
`
`Figure 9. Force F versus displacement D required to depress a
`syringe plunger of an HA dermal filler injection at a constant rate.
`Region (A) is the linear elastic region with the slope of the curve
`proportional to the gel hardness G9; point (B) is the yield point at
`which the gel begins to flow; and region (C) is the viscous regime
`where F is approximately constant with D and the force level is set
`by the viscosity of the filler.
`
`pushed at a steady rate, simulating a smooth,
`continuous injection. Initially, the force rises linearly
`with displacement D; this is the linearly elastic
`regime. Indeed, the slope of the curve in this regime
`is proportional to the gel hardness G9. A stiff gel will
`cause the force to rise more rapidly with displace-
`ment and the clinician will find it difficult to get the
`plunger moving.
`As the displacement is increased, the F-D curve
`becomes nonlinear and the gel begins to yield and
`plastically deform. After the maximum in the F-D
`curve – the so-called yield point – the gel begins to
`flow into the injection site and the force actually
`drops slightly. Finally, further continuous displace-
`ment of the plunger leads to the viscous regime in
`which F is nearly constant with D and the filler is
`injected smoothly at a steady rate. In this regime a
`second material parameter, the viscosity g, becomes
`important in dictating the level of constant force
`necessary for injection. It is important to note that
`should the clinician stop the injection process at any
`point, he or she will retrace the entire F versus D
`curve as the injection is restarted. Thus, more force
`and effort are required to inject the contents of a
`syringe in starts and st

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