Viscoelasticity of biological materials - measurement and practical impact on biomedicine

Mechanical behavior of biological structures under dynamic loading generally depends on elastic as well as viscous properties of biological materials. The significance of "viscous" parameters in real situations remains to be elucidated. Behavior of rheological models consisting of a combination of inertial body and two Voigt's bodies were described mathematically with respect to inverse problem solution, and behavior in impulse and harmonic loadings was analyzed. Samples of walls of porcine and human aorta thoracica in transverse direction and samples of human bone (caput femoris, substantia compacta) were measured. Deformation responses of human skin in vivo were also measured. Values of elastic moduli of porcine aorta walls were in the interval from 10(2)kPa to 10(3) kPa, values of viscous coefficients were in the interval from 10(2) Pa.s to 10(3) Pa.s. The value of shear stress moduli of human caput femoris, substantia compacta range from 52.7 to 161.1 MPa, and viscous coefficients were in the interval from 27.3 to 98.9 kPa.s. The role of viscous coefficients is significant for relatively high loading frequencies - in our materials above 8 Hz in aorta walls and 5 Hz for bones. In bones, the viscosity reduced maximum deformation corresponding to short rectangular stress.     

Fabrication of Hydrogels with Steep Stiffness Gradients for Studying Cell Mechanical Response

Many fundamental cell processes, such as angiogenesis, neurogenesis and cancer metastasis, are thought to be modulated by extracellular matrix stiffness. Thus, the availability of matrix substrates having well-defined stiffness profiles can be of great importance in biophysical studies of cell-substrate interaction. Here, we present a method to fabricate biocompatible hydrogels with a well defined and linear stiffness gradient. This method, involving the photopolymerization of films by progressively uncovering an acrylamide/bis-acrylamide solution initially covered with an opaque mask, can be easily implemented with common lab equipment. It produces linear stiffness gradients of at least 115 kPa/mm, extending from ∼1 kPa to 240 kPa (in units of Young''s modulus). Hydrogels with less steep gradients and narrower stiffness ranges can easily be produced. The hydrogels can be covalently functionalized with uniform coatings of proteins that promote cell adhesion. Cell spreading on these hydrogels linearly correlates with hydrogel stiffness, indicating that this technique effectively modifies the mechanical environment of living cells. This technique provides a simple approach that produces steeper gradients, wider rigidity ranges, and more accurate profiles than current methods.     

Tunable mechanical stability and deformation response of a resilin-based elastomer

Resilin, the highly elastomeric protein found in specialized compartments of most arthropods, possesses superior resilience and excellent high-frequency responsiveness. Enabled by biosynthetic strategies, we have designed and produced a modular, recombinant resilin-like polypeptide bearing both mechanically active and biologically active domains to create novel biomaterial microenvironments for engineering mechanically active tissues such as blood vessels, cardiovascular tissues, and vocal folds. Preliminary studies revealed that these recombinant materials exhibit promising mechanical properties and support the adhesion of NIH 3T3 fibroblasts. In this Article, we detail the characterization of the dynamic mechanical properties of these materials, as assessed via dynamic oscillatory shear rheology at various protein concentrations and cross-linking ratios. Simply by varying the polypeptide concentration and cross-linker ratios, the storage modulus G' can be easily tuned within the range of 500 Pa to 10 kPa. Strain-stress cycles and resilience measurements were probed via standard tensile testing methods and indicated the excellent resilience (>90%) of these materials, even when the mechanically active domains are intercepted by nonmechanically active biological cassettes. Further evaluation, at high frequencies, of the mechanical properties of these materials were assessed by a custom-designed torsional wave apparatus (TWA) at frequencies close to human phonation, indicating elastic modulus values from 200 to 2500 Pa, which is within the range of experimental data collected on excised porcine and human vocal fold tissues. The results validate the outstanding mechanical properties of the engineered materials, which are highly comparable to the mechanical properties of targeted vocal fold tissues. The ease of production of these biologically active materials, coupled to their outstanding mechanical properties over a range of compositions, suggests their potential in tissue regeneration applications.     

Modulation of Huh7.5 Spheroid Formation and Functionality Using Modified PEG-Based Hydrogels of Different Stiffness

Physical cues, such as cell microenvironment stiffness, are known to be important factors in modulating cellular behaviors such as differentiation, viability, and proliferation. Apart from being able to trigger these effects, mechanical stiffness tuning is a very convenient approach that could be implemented readily into smart scaffold designs. In this study, fibrinogen-modified poly(ethylene glycol)-diacrylate (PEG-DA) based hydrogels with tunable mechanical properties were synthesized and applied to control the spheroid formation and liver-like function of encapsulated Huh7.5 cells in an engineered, three-dimensional liver tissue model. By controlling hydrogel stiffness (0.1–6 kPa) as a cue for mechanotransduction representing different stiffness of a normal liver and a diseased cirrhotic liver, spheroids ranging from 50 to 200 μm were formed over a three week time-span. Hydrogels with better compliance (i.e. lower stiffness) promoted formation of larger spheroids. The highest rates of cell proliferation, albumin secretion, and CYP450 expression were all observed for spheroids in less stiff hydrogels like a normal liver in a healthy state. We also identified that the hydrogel modification by incorporation of PEGylated-fibrinogen within the hydrogel matrix enhanced cell survival and functionality possibly owing to more binding of autocrine fibronectin. Taken together, our findings establish guidelines to control the formation of Huh7.5 cell spheroids in modified PEGDA based hydrogels. These spheroids may serve as models for applications such as screening of pharmacological drug candidates.     

A novel experimental procedure based on pure shear testing of dermatome-cut samples applied to porcine skin

This paper communicates a novel and robust method for the mechanical testing of thin layers of soft biological tissues with particular application to porcine skin. The key features include the use of a surgical dermatome and the highly defined deformation kinematics achieved by pure shear testing. Thin specimens of accurate thickness were prepared using a dermatome and were subjected to different quasi-static and dynamic loading protocols. Although simple in its experimental realisation, pure shear testing provides a number of advantages over other classic uni- and biaxial testing procedures. The preparation of thin specimens of porcine dermis, the mechanical tests as well as first representative results are described and discussed in detail. The results indicate a pronounced anisotropy between the directions along and across the cleavage lines and a strain rate-dependent response.     

Skin viscoelasticity studied in vitro by microprobe-based techniques

Time-dependent deformation of porcine skin was studied in vitro using specialized microprobe instruments. The deformation behavior of stratum corneum, dermis, and whole skin is examined in the context of results of creep strain, elastic stiffness, and viscoelastic constants obtained in terms of the hold time, loading/unloading rate, and maximum indentation depth (load). Skin time-dependent deformation is significantly influenced by dermis viscoelasticity up to a critical indentation depth (load) beyond which it is controlled by the outermost hard epidermis, particularly stratum corneum. Skin viscoelastic behavior under constant load (creep) and constant displacement (stress relaxation) is interpreted in the light of phenomenological observations and experimental trends.     

Mechanical and migratory properties of normal,scar, and Dupuytren's fibroblasts

Mechanical properties of myofibroblasts play a key role in Dupuytren's disease. Here, we used atomic force microscopy to measure the viscoelastic properties of 3 different types of human primary fibroblasts derived from a same patient: normal and scar dermal fibroblasts and palmar fascial fibroblasts from Dupuytren's nodules. Different stiffness hydrogels (soft ~1 kPa and stiff ~ 50 kPa) were used as cell culture matrix to mimic the mechanical properties of the natural tissues, and atomic force microscopy step response force curves were used to discriminate between elastic and viscous properties of cells. Since transforming growth factor‐β1 (TGF‐β1) is known to induce expression of α–smooth muscle actin positive stress fibers in myofibroblasts, we investigated the behavior of these fibroblasts before and after applying TGF‐β1. Finally, we performed an in vitro cell motility test, the wound healing or scratch assay, to evaluate the migratory properties of these fibroblasts. We found that (1) Dupuytren's fibroblasts are stiffer than normal and scar fibroblasts, the elastic modulus E ranging from 4.4, 2.1, to 1.8 kPa, for Dupuytren's, normal and scar fibroblasts, respectively; (2) TGF‐β1 enhances the level of α–smooth muscle actin expression and thus cell stiffness in Dupuytren's fibroblasts (E, ~6.2 kPa); (3) matrix stiffness influences cell mechanical properties most prominently in Dupuytren's fibroblasts; and (4) Dupuytren's fibroblasts migrate slower than the other fibroblasts by a factor of 3. Taking together, our results showed that mechanical and migratory properties of fibroblasts might help to discriminate between different pathological conditions, helping to identify and recognize specific cell phenotypes.     

Highly extensible, tough, and elastomeric nanocomposite hydrogels from poly(ethylene glycol) and hydroxyapatite nanoparticles

Unique combinations of hard and soft components found in biological tissues have inspired researchers to design and develop synthetic nanocomposite gels and hydrogels with elastomeric properties. These elastic materials can potentially be used as synthetic mimics for diverse tissue engineering applications. Here we present a set of elastomeric nanocomposite hydrogels made from poly(ethylene glycol) (PEG) and hydroxyapatite nanoparticles (nHAp). The aqueous nanocomposite PEG-nHAp precursor solutions can be injected and then covalently cross-linked via photopolymerization. The resulting PEG-nHAp hydrogels have interconnected pore sizes ranging from 100 to 300 nm. They have higher extensibilities, fracture stresses, compressive strengths, and toughness when compared with conventional PEO hydrogels. The enhanced mechanical properties are a result of polymer nanoparticle interactions that interfere with the permanent cross-linking of PEG during photopolymerization. The effect of nHAp concentration and temperature on hydrogel swelling kinetics was evaluated under physiological conditions. An increase in nHAp concentration decreased the hydrogel saturated swelling degree. The combination of PEG and nHAp nanoparticles significantly improved the physical and chemical hydrogel properties as well as some biological characteristics such as osteoblast cell adhesion. Further development of these elastomeric materials can potentially lead to use as a matrix for drug delivery and tissue repair especially for orthopedic applications.     

New insight into deformation-dependent hydraulic permeability of gels and cartilage,and dynamic behavior of agarose gels in confined compression

Equilibrium, creep, and dynamic behaviors of agarose gels (2.0-14.8%) in confined compression were investigated in this study. The hydraulic permeabilities of gels were determined by curve-fitting creep data to the biphasic model (J. Biomech. Eng. 102 (1980) 73) and found to be similar in value to those published in the literature (AIChE J. 42 (1996) 1220). A new relationship between intrinsic permeability and volume fraction of water was found for agarose gel, capable of predicting deformation-dependent permeabilities of bovine articular cartilage and 2% agarose gel published in literature. This relationship is accurate for gels and cartilage over a wide range of permeabilities (four orders of magnitude variation). The dynamic stiffness of the gels increases with gel concentration and loading frequency (0.01-1.0Hz). The increase in dynamic stiffness with loading frequency is less pronounced for gels with higher concentrations. The results of this study provide a new insight into deformation-dependent permeability behavior of agarose gel and cartilage, and are important for understanding biological responses of cells to interstitial fluid flow in gel or in cartilage under dynamic mechanical loading.     

Influence of tyrosine-derived moieties and drying conditions on the formation of helices in gelatin

The single and triple helical organization of protein chains strongly influences the mechanical properties of gelatin-based materials. A chemical method for obtaining different degrees of helical organization in gelatin is covalent functionalization, while a physical method for achieving the same goal is the variation of the drying conditions of gelatin solutions. Here we explored how the introduction of desaminotyrosine (DAT) and desaminotyrosyl tyrosine (DATT) linked to lysine residues of gelatin influenced the kinetics and thermodynamic equilibrium of the helicalization process of single and triple helices following different drying conditions. Drying at a temperature above the helix-to-coil transition temperature of gelatin (T > T(c), called v(short)) generally resulted in gelatins with relatively lower triple helical content (X(c,t) = 1-2%) than lower temperature drying (T < T(c), called v(long)) (X(c,t) = 8-10%), where the DAT(T) functional groups generally disrupted helix formation. While different helical contents affected the thermal transition temperatures only slightly, the mechanical properties were strongly affected for swollen hydrogels (E = 4-13 kPa for samples treated by v(long) and E = 120-700 kPa for samples treated by v(short)). This study shows that side group functionalization and different drying conditions are viable options to control the helicalization and macroscopic properties of gelatin-based materials.     

Mechanical properties of biomimetic tissue adhesive based on the microbial transglutaminase-catalyzed crosslinking of gelatin

Fibrin sealants are a type of soft tissue adhesive that employs biochemical reactions from the late stages of the blood coagulation cascade. Intrinsic to these adhesives are a structural protein and a transglutaminase crosslinking enzyme. We are investigating an alternative biomimetic adhesive based on gelatin and a calcium-independent microbial transglutaminase (mTG). Rheological measurements show that mTG catalyzes the conversion of gelatin solutions into hydrogels, and gel times are on the order of minutes depending on the gelatin type and concentration. Tensile static and dynamic loading of the adhesive hydrogels in bulk form demonstrated that the Young's modulus ranged from 15 to 120 kPa, and these bulk properties were comparable to those reported for hydrogels obtained from fibrin-based sealants. Lap-shear adhesion tests of porcine tissue were performed using a newly published American Society for Testing and Materials (ASTM) standard for tissue adhesives. The gelatin-mTG adhesive bound the opposing tissues together with ultimate adhesive strengths of 12-23 kPa which were significantly higher than the strength observed for fibrin sealants. Even after failure, strands of the gelatin-mTG adhesive remained attached to both of the opposing tissues. These results suggest that gelatin-mTG adhesives may offer the benefits of fibrin sealants without the need for blood products.     

Combining dynamic stretch and tunable stiffness to probe cell mechanobiology in vitro

Cells have the ability to actively sense their mechanical environment and respond to both substrate stiffness and stretch by altering their adhesion, proliferation, locomotion, morphology, and synthetic profile. In order to elucidate the interrelated effects of different mechanical stimuli on cell phenotype in vitro, we have developed a method for culturing mammalian cells in a two-dimensional environment at a wide range of combined levels of substrate stiffness and dynamic stretch. Polyacrylamide gels were covalently bonded to flexible silicone culture plates and coated with monomeric collagen for cell adhesion. Substrate stiffness was adjusted from relatively soft (G′ = 0.3 kPa) to stiff (G′ = 50 kPa) by altering the ratio of acrylamide to bis-acrylamide, and the silicone membranes were stretched over circular loading posts by applying vacuum pressure to impart near-uniform stretch, as confirmed by strain field analysis. As a demonstration of the system, porcine aortic valve interstitial cells (VIC) and human mesenchymal stem cells (hMSC) were plated on soft and stiff substrates either statically cultured or exposed to 10% equibiaxial or pure uniaxial stretch at 1Hz for 6 hours. In all cases, cell attachment and cell viability were high. On soft substrates, VICs cultured statically exhibit a small rounded morphology, significantly smaller than on stiff substrates (p<0.05). Following equibiaxial cyclic stretch, VICs spread to the extent of cells cultured on stiff substrates, but did not reorient in response to uniaxial stretch to the extent of cells stretched on stiff substrates. hMSCs exhibited a less pronounced response than VICs, likely due to a lower stiffness threshold for spreading on static gels. These preliminary data demonstrate that inhibition of spreading due to a lack of matrix stiffness surrounding a cell may be overcome by externally applied stretch suggesting similar mechanotransduction mechanisms for sensing stiffness and stretch.     

Anomalous rate dependence of the preconditioned response of soft tissue during load controlled deformation

It has been observed in load controlled laboratory tests of myocardium and skin that the tissues can exhibit a decrease in nonlinear stiffness with an increase in loading rate: the faster a test is performed, the more compliant is the preconditioned material behavior. This response seems to conflict with what is generally expected of soft tissues based on stretch or strain controlled tests, in which an increased rate of deformation results in a stiffer material response. It is hypothesized that this anomalous behavior has not been observed previously due to the small number of cyclic load controlled mechanical characterization tests that are geared specifically towards viscoelastic tissue response. The goal of this paper is to examine the preconditioned response of soft tissue to load controlled deformation using nonlinear viscoelastic material models including quasi-linear viscoelasticity, and to determine under what conditions this anomalous behavior becomes apparent. Results from this study suggest that this behavior is a true phenomenon unique to load controlled deformations that results from the interplay of nonlinear effects and creep behavior. These results call for increased attention to experimental parameters when testing and modeling nonlinear viscoelastic material behavior.     

Quantitative Shear-Wave Elastography of the Liver in Preterm Neonates with Intra-Uterine Growth Restriction

The feasibility and reproducibility of liver stiffness measurements using Supersonic Shear-wave Imaging (SSI) in preterm neonate have not been reported. Our aim was to determine if liver stiffness differs between intra-uterine growth restriction (IUGR) and appropriate for gestational age (AGA) preterm infants with/without cholestasis. We measured liver stiffness (in kPa) in 45 AGA and 18 IUGR preterm infants, and assessed reproducibility in 26 preterms using Intraclass Correlation Coefficients (ICC) and Bland-Altman tests. Liver stiffness values were compared between AGA and IUGR with and without cholestasis and correlated with birth weight. Measurements showed high reproducibility (ICC = 0.94–0.98 for intra-operator, 0.86 for inter-operator) with good agreement (95% limits: -1.24 to 1.24 kPa). During the first postnatal week, liver stiffness was higher in IUGR (7.50 ±1.53 kPa) than in AGA infants (5.11 ±0.80 kPa, p<0.001). After day 8, liver stiffness remained unchanged in AGA but increased progressively in IUGR infants (15.57 ±6.49 kPa after day 21). Liver stiffness was higher in IUGR neonates with cholestasis (19.35 ± 9.80 kPa) than without cholestasis (7.72 ± 1.27 kPa, p<0.001). In conclusion, quantitative liver SSI in preterms is feasible and reproducible. IUGR preterms who will develop cholestasis present high liver stiffness even at birth, before biological cholestasis occurs.     

Biodegradable Monocrystalline Silicon Photovoltaic Microcells as Power Supplies for Transient Biomedical Implants

Bioresorbable electronic materials serve as foundations for implantable devices that provide active diagnostic or therapeutic function over a timeframe matched to a biological process, and then disappear within the body to avoid secondary surgical extraction. Approaches to power supply in these physically transient systems are critically important. This paper describes a fully biodegradable, monocrystalline silicon photovoltaic (PV) platform based on microscale cells (microcells) designed to operate at wavelengths with long penetration depths in biological tissues (red and near infrared wavelengths), such that external illumination can provide realistic levels of power. Systematic characterization and theoretical simulations of operation under porcine skin and fat establish a foundational understanding of these systems and their scalability. In vivo studies of a representative platform capable of generating ≈60 µW of electrical power under 4 mm of porcine skin and fat illustrate an ability to operate blue light‐emitting diodes (LEDs) as subdermal implants in rats for 3 d. Here, the PV system fully resorbs after 4 months. Histological analysis reveals that the degradation process introduces no inflammatory responses in the surrounding tissues. The results suggest the potential for using silicon photovoltaic microcells as bioresorbable power supplies for various transient biomedical implants.     

PEGDA hydrogels with patterned elasticity: Novel tools for the study of cell response to substrate rigidity

The ability of cells to migrate in response to mechanical gradients (durotaxis) and differential cell behavior in adhesion, spreading, and proliferation in response to substrate rigidity are key factors both in tissue engineering, in which materials must be selected to provide the appropriate mechanical signals, and in studies of mechanisms of diseases such as cancer and atherosclerosis, in which changes in tissue stiffness may inform cell behavior. Using poly(ethylene glycol) diacrylate hydrogels with varying polymer chain length and photolithographic patterning techniques, we are able to provide substrates with spatially patterned, tunable mechanical properties in both gradients and distinct patterns. The hydrogels can be patterned to produce anisotropic structures and exhibit patterned strain under mechanical loading. These hydrogels may be used to study cell response to substrate rigidity in both two and three dimensions and can also be used as a scaffold in tissue‐engineering applications. Biotechnol. Bioeng. 2010; 105: 636–644. © 2009 Wiley Periodicals, Inc.     

The regulation of osteogenesis by ECM rigidity in MC3T3-E1 cells requires MAPK activation

Once thought to provide only structural support to tissues by acting as a scaffold to which cells bind, it is now widely recognized that the extracellular matrix (ECM) provides instructive signals that dictate cell behavior. Recently we demonstrated that mechanical cues intrinsic to the ECM directly regulate the behavior of pre-osteoblastic MC3T3-E1 cells. We hypothesized that one possible mechanism by which ECM compliance exerts its influence on osteogenesis is by modulating the mitogen-activated protein kinase (MAPK) pathway. To address this hypothesis, the differentiation of MC3T3-E1 cells cultured on poly(ethylene glycol) (PEG)-based model substrates with tunable mechanical properties was assessed. Alkaline phosphatase (ALP) levels at days 7 and 14 were found to be significantly higher in cells grown on stiffer substrates (423.9 kPa hydrogels and rigid tissue culture polystyrene (TCPS) control) than on a soft hydrogel (13.7 kPa). Osteocalcin (OCN) and bone sialoprotein (BSP) gene expression levels followed a similar trend. In parallel, MAPK activity was significantly higher in cells cultured on stiffer substrates at both time points. Inhibiting this activation pharmacologically, using PD98059, resulted in significantly lower ALP levels, OCN, and BSP gene expression levels on the hydrogels. Interestingly, the effectiveness of PD98059 was itself dependent on substrate stiffness, with marked inhibition of MAPK phosphorylation in cells grown on compliant hydrogels but insignificant reduction in cells grown on TCPS. Together, these data confirm a role for MAPK in the regulation of osteogenic differentiation by ECM compliance.     

Elasticity imaging of polymeric media

Viscoelastic properties of soft tissues and hydropolymers depend on the strength of molecular bonding forces connecting the polymer matrix and surrounding fluids. The basis for diagnostic imaging is that disease processes alter molecular-scale bonding in ways that vary the measurable stiffness and viscosity of the tissues. This paper reviews linear viscoelastic theory as applied to gelatin hydrogels for the purpose of formulating approaches to molecular-scale interpretation of elasticity imaging in soft biological tissues. Comparing measurements acquired under different geometries, we investigate the limitations of viscoelastic parameters acquired under various imaging conditions. Quasi-static (step-and-hold and low-frequency harmonic) stimuli applied to gels during creep and stress relaxation experiments in confined and unconfined geometries reveal continuous, bimodal distributions of respondance times. Within the linear range of responses, gelatin will behave more like a solid or fluid depending on the stimulus magnitude. Gelatin can be described statistically from a few parameters of low-order rheological models that form the basis of viscoelastic imaging. Unbiased estimates of imaging parameters are obtained only if creep data are acquired for greater than twice the highest retardance time constant and any steady-state viscous response has been eliminated. Elastic strain and retardance time images are found to provide the best combination of contrast and signal strength in gelatin. Retardance times indicate average behavior of fast (1-10 s) fluid flows and slow (50-400 s) matrix restructuring in response to the mechanical stimulus. Insofar as gelatin mimics other polymers, such as soft biological tissues, elasticity imaging can provide unique insights into complex structural and biochemical features of connectives tissues affected by disease.     

Enhanced tissue adhesiveness of injectable gelatin hydrogels through dual catalytic activity of horseradish peroxidase

Development of bioadhesives with tunable mechanical strength, high adhesiveness, biocompatibility, and injectability is greatly desirable in all surgeries to replace or complement the sutures and staples. Herein, the dual catalytic activity of horseradish peroxidase is exploited to in situ form the hydroxyphenyl propionic acid‐gelatin/thiolated gelatin (GH/GS) adhesive hydrogels including two alternative crosslinks (phenol‐phenol and disulfide bonds) with fast gelation (few seconds – several minutes) and improved physicochemical properties. Their elastic moduli increase from 6.7 to 10.3 kPa by adding GS polymer that leads to the better stability of GH/GS hydrogels than GH ones. GH/GS adhesive strength is respectively 6.5‐fold and 15.8‐fold higher than GH‐only and fibrin glue that is due to additional disulfide linkages between hydrogels and tissues. Moreover, in vitro cell study with human dermal fibroblast showed the cell‐compatibility of GH/GS hydrogels. Taken together, GH/GS hydrogels can be considered as promising potential adhesive materials for various biomedical applications.     

Rheological properties of cross-linked hyaluronan-gelatin hydrogels for tissue engineering

Hydrogels that mimic the natural extracellular matrix (ECM) are used in three-dimensional cell culture, cell therapy, and tissue engineering. A semi-synthetic ECM based on cross-linked hyaluronana offers experimental control of both composition and gel stiffness. The mechanical properties of the ECM in part determine the ultimate cell phenotype. We now describe a rheological study of synthetic ECM hydrogels with storage shear moduli that span three orders of magnitude, from 11 to 3 500 Pa, a range important for engineering of soft tissues. The concentration of the chemically modified HA and the cross-linking density were the main determinants of gel stiffness. Increase in the ratio of thiol-modified gelatin reduced gel stiffness by diluting the effective concentration of the HA component.