Response of authors: ‘Lift capabilities of hyaluronic acid fillers’

Sirs,

In response to the comments made by Edsman and Helander Kenne (1), the paper ‘Lift capabilities of hyaluronic acid fillers’ (2) was initially prepared and tailored for an audience not familiar or proficient in the area of rheology. Throughout the paper we leveraged terms already used in the field and familiar to physicians (such as linear viscosity and gel hardness) in a conscious effort to define them and adapt them to more accurate scientific terms (such as elastics or storage modulus). Some of the explanations were an oversimplification of complex material properties and interactions; however, all these were conscious decisions in an attempt to connect with the audience and explain complex material physics and properties, based on a strong scientific knowledge, both for fillers and rheology.

By definition, the elastic modulus G′ is a measure of the energy stored by elastic deformation that can be recovered (representative of the elastic behavior of a material, or solid-like contribution), while the viscous (or loss) modulus G″ corresponds to viscous dissipation of the energy of deformation (liquid-like contribution). These quantities were determined with a parallel plate rheometer, imposing an oscillatory shear strain on one plate while measuring an oscillatory shear stress (torque) on a second plate, with the fluid being tested filling the gap between the plates (G′ can be extracted from the measured stress that is in-phase with the applied strain, while G″ is related to the out-of-phase stress component). Not surprisingly, the values of the elastic modulus G′ were significantly higher than the viscous modulus G″ at low stress (representative of the filler behavior ‘at rest’); thus, it was said that these materials (dermal filler gels) display a ‘solid-like’ response, and therefore the relevance of publishing values of G′ (elastic modulus) to characterize the ‘gel strength’ or ‘hardness’ of such materials.

Figure 5 showed typical results for strain sweep measurements of HA dermal fillers. The plateau at which the magnitude of the elastic modulus remains constant is known as the linear viscoelastic region and, as Edsman and Helander Kenne correctly stated, it is generally used to determine an adequate range of strain at which to perform other rheological tests, such as the frequency sweep test, to characterize the rheological properties of viscoelastic materials. Presenting these curves was in fact relevant, although not discussed in detail to avoid misinterpretations or confusion. At small amplitudes of the oscillatory strain the gel will slightly deform; however, if the stress is removed, the gel will recover its original form and the structure of the gel will remain unchanged (this is the characteristic response of a solid elastic material to an external force). On the other hand, as the strain amplitude is increased (i.e. a higher external force is applied), the gel structure will be ultimately broken; in this regime a nonlinear behavior is observed, represented by a rapid drop of the storage modulus G′. At this ‘yield’ point the material goes beyond its elastic limit, and the material starts to ‘plastically’ deform and flow (unlike elastic deformation, plastic deformation is not recoverable, so the gel will retain its ‘new’ configuration or structure). A larger plateau indicates a gel that maintains its configuration over a larger range of strains; that is, the gel wants to maintain its initial shape and form over a larger degree of deformation, quite relevant of dermal filler.

The authors of the article appreciate the concerns highlighted in the letter but would like to once again highlight the fact that the article was tailored for an audience that is not familiar with the field of rheology. The authors were not inclined to demonstrate their expertise in the field by a fairly complex analysis such as the one outlined above. We believe that would have defeated the purpose and objective of the manuscript that is outlined in the first paragraph of this response.

Declaration of interest: Drs Tezel and Borrell and Mr Leslie are employed by Allergan, Inc. The authors alone are responsible for the content and writing of the paper.