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j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 5 3 ( 2 0 1 6 ) 1 1 9 – 1 3 0

http://dx.doi.org/101751-6161/& 2015 El

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Research Paper

Strain-rate and temperature dependent materialproperties of Agar and Gellan Gum usedin biomedical applications

Alessandro Schiavin, Rugiada Cuccaro, Adriano Troia

INRiM – Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy

a r t i c l e i n f o

Article history:

Received 21 January 2015

Received in revised form

28 July 2015

Accepted 4 August 2015

Available online 13 August 2015

Keywords:

Hydrogels

Young's modulus

Relaxation time

Temperature-dependence

Strain-rate-dependence

.1016/j.jmbbm.2015.08.011sevier Ltd. All rights rese

hor. Tel.: þ39 0113919916s: a.schiavi@inrim.it (A.

a b s t r a c t

Agar and Gellan Gum are biocompatible polymers extensively used in several fields of

tissue engineering research (e.g. tissue replacement, tissue support, tissue mimicking), due

to their mechanical behaviour effectively representative of actual biological tissues. Since

mechanical properties of artificial tissues are related to biocompatibility and functionality

of medical implants and significantly influence adhesion, growth and differentiation of

cells in tissue-engineering scaffolds, an accurate characterization of Young's modulus and

relaxation time processes is needed. In this study, the strain-rate and temperature

dependent material properties of Agarose and one among the numerous kind of Gellan

Gum commercially available, known as Phytagels, have been investigated.

Nine hydrogel samples have been realized with different mechanical properties: the

first one Agar-based as a reference material, the further eight samples Gellan Gum based in

which the effect of dispersed solid particles like kieselguhr and SiC, as enhancing

mechanical properties factors, have been investigated as a function of concentration.

Stress–strain has been investigated in compression and relaxation time has been

evaluated by means of the Kohlrausch–Williams–Watts time decay function. Mechanical

properties have been measured as a function of temperature between 20 1C and 35 1C and

at different strain rates, from �10�3 s�1 and �10�2 s�1 (or deformation rate from

�0.01 mm s�1 to �0.1 mm s�1). From experimental data, the combined temperature and

strain-rate dependence of hydrogels Young's modulus is determined on the basis of a

constitutive model.

In addition to a dependence of Young's modulus on temperature, a remarkable

influence of strain-rate has been observed, especially in the sample containing solid

particles; in same ranges of temperature and strain-rate, also relaxation time variations

have been monitored in order to identify a possible dependence of damping properties on

temperature and strain-rate. The result is the impossibility to determine univocally

mechanical properties of studied biomaterials without a proper definition of boundary

conditions at which they have been obtained.

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rved.

; fax: þ39 0113919621.Schiavi), r.cuccaro@inrim.it (R. Cuccaro), a.troia@inrim.it (A. Troia).

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1. Introduction

In the field of tissue engineering and regenerative medicine,tunable mechanical properties for optimizing tissue regen-eration in vivo and tissue formation in vitro are recognized as afundamental requirement for biomaterials. Hydrogels, ingeneral terms, give opportunity to easily develop mimictissues with tunable mechanical properties over a wide rangeof stiffness (Nayar et al., 2011), in particular to simulate softbiological materials (100 kPaoEo1 GPa) (Franke et al., 2008)and ultra-soft biological materials (Eo100 kPa) (Nayar et al.,2011; Ebenstein and Pruitt, 2004). As well as biochemicalproperties, mechanical properties of hydrogels influencemany different biological features such as biocompatibilityand functionality of medical implants and tissue-engineeringscaffolds (Basinger et al., 2009; Colodetti et al., 2007; Frankeet al., 2007), and to degradable biocompatibility of organ-based tissue engineering implants (Verma et al., 2006). More-over, as recently debated, mechanical properties and micro-structure of scaffolds seem to influence cell behaviour andoverall scaffold bioactivity. Recent experiments have revealedthat stem cells respond to biophysical cues as well asnumerous biochemical factors. In the heterogeneous micro-environments referred to as stem cell niches, variousmechanical (united with biomolecular) cues are integratedto maintain pluripotency or to induce differentiation (Daveet al., 2014).

On the other hand, due to their significant similarity toactual human tissues, hydrogels are also extensively used inlaboratory tests. For instance, they are used as versatileplatform in the study of cell–substrate interactions as wellas tissue-mimicking materials (TMMs) in the investigation ofmechanical and thermal effects in tissues due to ultrasounds(Lafon et al., 2005; O'Neill et al., 1994; Arvanitis andMcDannold, 2013). As a consequence, a proper characteriza-tion of the mechanical properties of these materials allows toevaluate with higher accuracy technical performances, biolo-gical behaviours or other related phenomena associatedwith them.

In this work samples of TMMs, Agarose and Phytagels

based, have been opportunely realized with different con-centration of kieselghur and SiC in order to evaluate theeffects on the mechanical behaviour as a function of tem-perature and strain-rate. TMMs here investigated only simu-late soft biological materials in the range between 100 kPaand 1 MPa. Their similarity to soft biological tissues from theattenuation and speed of sound point of view has beenpreviously investigated and some of the results have beenpublished in (Cuccaro et al., 2015).

The mechanical behaviour of hydrogels is evaluated on

the basis of the theories of rubber elasticity and viscoelasti-city (Anseth et al., 1996). Despite during the last decades

mechanical properties of hydrogels have been deeply inves-tigated by means of static, quasi-static and dynamic techni-

ques and the elastic moduli have been determined incompression, extension, torsion, from resonance method

and from micro- and nano-indentation, less known are themechanical properties of hydrogel as a function of tempera-

ture and strain-rate. Temperature fluctuation and different

speed of applied force induce relevant variations in elasticproperties of hydrogels. As a matter of fact, relevant strain-rate dependences in actual human tissues properties havebeen observed (Snedeker et al., 2005; Zioupos et al., 2008;Hansen et al., 2008).

Since environmental conditions, experimental proceduresand measurement methods can affect experimental results,in this work Young's modulus, E, and the relaxation time, τ, ofnine hydrogel samples have been evaluated as a function oftemperature (20 1CoTo35 1C) at different very low strain-rates (0.06 � 10�2 s�1o_εo0.4 � 10�2 s�1) with the aim toachieve an effective characterization of the mechanicalbehaviour of biomaterials under investigation. In the consid-ered ranges of temperature and strain-rate, a constitutivemodel to evaluate the average variability of Young's modulus,i.e. E(T,_ε), is then proposed.

Measurements have been carried out in unconfined com-pression. Yield and tensile strengths have been previouslydetermined for each sample in standard laboratory condi-tions. On twin samples, within the elastic region, the effectsof temperature and strain rate on Young's modulus andrelaxation time have been determined.

2. Materials and experimental methods

2.1. Preparation of tissue mimicking materials

Hydrogel, in particular polysaccharides, as tissue-mimickingmaterials have been widely studied over last ten years.Nevertheless, the natural origin of these molecules, theirpurity, the grade of refining and the catalyst used for poly-merization, when present, lead the researchers to obtain gelwith notable differences in terms of mechanical properties,so that their use as tissue mimicking materials could betuned for a wide class of biological tissues.

In our study we have investigated two types of polysac-charides: Agar and Gellan Gum. Agar is a well-known poly-saccharide formed principally by Agarose (Nayar et al., 2011).It is insoluble in room temperature water, while it dissolvesin boiling water, forming a gel when cooled down to atemperature of about 30–40 1C. This value depends on purity,on Agar concentration and pH. It has been largely studiedfrom a mechanical and thermal point of view (Huang et al.,2004), it is used as phantom material for ultrasound imagingand hyperthermia applications (Culjat et al., 2010), it isrecommended as reference material for flow Doppler test bythe European standard IEC 61685 (IEC 61685, 2002) and, inaddition, it is commonly used as cell culture scaffold (Zohoraand Azim, 2014). Moreover, its stiffness can be altered allow-ing for tuning scaffold mechanical properties. For thesereasons, in this work it has been chosen to investigate, asfirst, a gel made of Agar. The sample has been preparedheating on a hot plate an aqueous solution of Agar (3% inweight) at 100 1C. Maintaining the solution under stirring,Benzalkonium chloride (0.9% in weight) as anti-fungal agenthas been added. Successively, while the sample cooled, it hasbeen cast carefully into a cylindrical mould to avoid bubblesformation and obtain very smooth and flat surfaces,

Table 1 – Summary of investigated TMMs composition. All reported values refer to in weight% concentration. Anti-fungalfor TMM1 is the anti-fungal agent represented by Benzalkonium chloride (0.9% in weight), while for all other TMMs is givenby Potassium Sorbate (0.1% in weight).

Agar Phytagels Ca2SO4 Kieselghur SiC Anti-fungal

TMM 1 3 – – – – xTMM 2 – 2 0.5 – – xTMM 3 – 2 0.5 0.75 – xTMM 4 – 2 0.5 1.5 – xTMM 5 – 2 0.5 – 0.5 xTMM 6 – 2 0.5 – 1 xTMM 7 – 2 0.5 0.75 0.5 xTMM 8 – 2 0.5 1.5 1 xTMM 9 – 2 0.5 3 2 x

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fundamental to exercise an homogeneous force distribution,important aspect for Young's modulus measurements.

Gellan Gum is a more complex polysaccharide. During lastfive years, this product have received more attention becauseof its higher temperature stability, higher mechanicalstrength and better clarity than Agar, besides a substantiallylower cost, which makes it an attractive polymer for therealization of TMM matrix. Furthermore, modifying its che-mical structure, its properties can be tuned to be suitable fortissue engineering purposes (Gong et al., 2009). Structurally itcomprises a repeated tetrasaccharide unit of two β-D glucose,one of β-D glucuronate and one α-L rhamnose and, commer-cially, it is available with different trade name like Gelrites,Kelcogels or Phytagels, whose different name corresponds tothe different grade of deacylation. The native state has high“acyl” grade, while low “acyl” is prepared via alkali treatment.High “acyl” Gellan Gum forms a gel upon cooling from 65 1Ccreating a soft flexible hydrogel, while low “acyl” Gellan Gumforms a gel upon cooling below 45 1C creating a rigid andbrittle hydrogel. Gellan Gum, like Agar or other polysacchar-ides, forms a physical gel by undergoing from random coil todouble helix transition upon heating and cooling treatment.Stiffer gel are formed if cations are present during the sol–geltransition. Particularly, monovalent cations, like Na or K,form an intermediate strength hydrogel through electrostaticinteraction with carboxylate group (Morris et al., 2012), whiledivalent cations, like Mg or Ca, form stronger gels by theaggregation of multiple helix. In our preparations, we haveused Phytagels (by Sigma-Aldrich company) which has lowdeacylation grade, so that an hard and brittle gel has beenexpected to be obtained (CP Kelco, 2007).

We have developed a new synthesis procedure to obtainan hard and strong TMM using calcium sulphate as catalystand Potassium Sorbate as antifungal. In detail, we haveprepared a solution of Ca2SO4 dihydrate (0.5% in weight)and of Potassium Sorbate (0.1% in weight); the solution hasbeen gradually heated up to 90 1C while kept under stirring.During this step, Phytagels powder (conc. of 2% in weight)has been added to the solution. The presence of salt preventsthe formation of lumps, allowing to keep homogenous thesolution during the heating step. Hence the solution is heatedup to boiling for 2 min (temperature about 95–100 1C) and leftcooling down to 80 1C. At this step, the solution is rapidlypoured into a cylindrical mould in order to minimize theinclusion of bubbles on the two surfaces, which should be

very flat in order to exercise an homogeneous forces on thesample during the measurements. As it is reported inKirchmajer et al. (2014), the presence of calcium could affectthe jellification temperature of Gellan Gum. To this end, wehave observed a slight increase of the jellification tempera-ture respect to temperatures (30–40 1C) reported inKirchmajer et al. (2014). Investigated samples solidify veryrapidly when in contact with mould cold surfaces, althoughthe temperature of the solution is more than 60 1C. Thischaracteristic has been exploited to minimize the settling ofsolid particles dispersed in TMM samples with the aim ofenhancing their mechanical properties. Thus, we prepareddifferent samples in which a specific amount of kieselguhr, anatural siliceous sedimentary powder with a particles dimen-sion in range of 10–200 μm, and/or Silicon Carbide (SiC)particles, with a mean dimension of 47 μm, have beendispersed on Phytagels matrix. Both this particles are con-sidered biocompatible (Saddow, 2012; Gnanamoorthy et al.,2014; López-Alvarez et al., 2009). We added the particlesduring the heating step, when the solution reach 70 1C. Theamount added to the solution varied from 0.5% up to 2% andfrom 0.75% up to 3% in weight respectively for SiC andkieselguhr. The whole preparation set with respective ingre-dients is summarized in Table 1 and, hereafter, the name ofeach sample will correspond to the name given in the firstcolumn of the table.

The choice of samples to study has been triggered byprevious investigations of speed of sound and attenuationcoefficient conducted on these materials (Cuccaro et al.,2015). Recently, several alternative TMMs have been proposedbeyond the recipe reported in the European standard IEC61685, since one of the key point is to obtain an homogeneousTMM with higher attenuation coefficient and enhancedmechanical properties.

2.2. Mechanical quantities measured

As many biological materials, TMMs investigated in this workshow a viscoelastic behaviour. Performances of viscoelasticmaterials are affected by strain amplitude and strain-rate, byvibration frequency, static load and temperature.

At low strain rates, that means in standard compressivetests, heat generated by compression work is mainly dis-persed in the environment, making the experiments to beconsidered about isothermal. On the contrary, at high strain-

Fig. 1 – Stress–strain (grey) and stress relaxation (red) curve,with σ0 and ε0 respectively starting stress and strain values,E Young's modulus, σ(t) stress relaxation time, and τ0relaxation time at which Φ(t) decays to the value 1/e. (Forinterpretation of the references to colour in this figurelegend, the reader is referred to the web version of thisarticle.)

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rates, the energy cannot be dispersed prior to material failure.The result is a localized increase in temperature in thedamaged region and an adiabatic strain response to appliedstress. Since traumatic failures and lacerations in vivo(Snedeker et al., 2005; Zioupos et al., 2008) have been relatedto the effects of strain-rate also for actual human tissues, anadequate characterization of TMMs mechanical behaviour asa function of the strain-rate could provide useful informationfor trauma mathematical models implementation or for theinvestigation of organ injury mechanisms.

The occurring variability of TMMs mechanical propertiesin a limited temperature range included between laboratory(20 1C) and human body (37 1C) temperature has been alsoquantified. Experimentally, Young's modulus values aredetermined from the ratio between the incremental stressand the incremental strain applying the classical Hooke's lawat a constant strain rate, as shown below

E¼ ΔσΔε

¼ FA

Ul0Δl

; ð1Þ

where E is Young's modulus (Pa), Δσ is the incremental stress(Pa), Δε is the incremental strain (dimensionless), F is thecompression force (N), A is the surface area of the sample(m2) on which the force acts, l0 is the initial thickness of thesample (m) and Δl is the deformation in thickness (m)resulting from the application of F within the region in whichthe sample under investigation shows an elastic behaviour.Plotting the incremental stress as a function of the strain, it ispossible to determine the value of the sample elastic mod-ulus by means of a linear fit.

Moreover, hydrogels viscoelastic behaviour can be evalu-ated from relaxation time processes after deformation, e.g. bymeans of the relation σ tð Þ ¼ EUε0 1�ΦðtÞð Þ, where ε0 is thestarting strain value and Φ tð Þis the empirical Kohlrausch–Williams–Watts (KWW) time decay function. This functionallows to obtain a more accurate interpolation of typicalviscoelastic time decay than simple exponential Debye func-tion. The KWW function is widely used to model severaltime-decaying behaviour of relaxation processes of viscoe-lastic materials and it is also used in polymers dynamics andin bone and muscle rheology (Anderssen et al., 2004). KWWfunction is given by the following expression:

Φ tð Þ ¼ exp � tτ0

� �γ

; ð2Þ

where t is the time, τ0 is the relaxation time at which Φ(t)decays to the value 1/e and the exponent γ describes thebreadth of the distribution in the limits of 0rγr1. Thedistribution of relaxation times changes from a broad, sym-metric distribution to a sharp, asymmetric one increasing γ

from 0 to 1. The relaxation time is directly related to thematerial damping properties. In general terms, as τ0decreases, the internal damping tends to increase, and viceversa. As a result, a greater aptitude to dissipate or absorbingenergy of mechanical stress occurs.

In the following, τ0 and γ experimental data are analyzedin order to highlight any possible influence of temperatureand strain-rate over them.

In Fig. 1, an example of a stress–strain and stress relaxa-tion curve is shown. Red curve qualitatively represents theadopted measurement procedure from experimental data.

2.3. Experimental apparatus and procedure

To measure the mechanical properties of TMMs, an uniaxialunconfined compression has been performed using a properdevice specifically designed and realized at INRiM. Measure-ments have been carried out in displacement control and theresulting force has been measured downstream. The lineardisplacement has been performed by a stepping motor(Orientalmotor α-GRADE AR Series – AR HM 40093E 24DC)connected to a screw by means of a reduction gear. Thedisplacement rates can be opportunely tuned from about1 mm/s to 0.1 μm/s. The linear displacement has been mea-sured by means of a linear encoder Solartron LE25/S with anaccuracy of 1 μm (resolution 0.1 μm). The resulting forceshave been measured by means of a load cell HBM typeZ3H3R, with a resolution of 5 mN. The evaluated uncertaintyof the force, in the range between 10 N and 1000 N, can beconsidered lesser thanr1%. Calibration of the linear encoderand of the load cell has been performed at INRiM on the basisof the international standard calibration (ISO 376, 2011; ISO5893, 2002) fulfilling proper metrological requirements. Fig. 2shows the experimental apparatus.

Compressive testing requires that TMMs have flat andparallel surfaces, characteristics that are guaranteed by theshape of the mould used for the gel casting. The mouldconsists of a Plexiglas cylinder furnished of two smooth capsin Teflon. Moreover, the presence of a lateral hole on thecylinder surface lets the air to come out, preventing itsentanglement inside the phantom during the samplejellification.

Once cooled, TMM samples thickness is measured bymeans of a height gauge joined to a feeler pin, whoseresolution is70.01 mm and the accuracy is70.03 mm, while

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gels diameter is measured using a digital calliper with aresolution of70.01 mm. Sample dimensions are measured atthe laboratory temperature of about T¼ (23.070.5) 1C andambient pressure.

During the experiment, both the experimental apparatusand samples have been placed in a temperature chamber toguarantee the temperature stability during the measurementand to have the possibility to change T value during the test.The temperature of the sample under test has been mon-itored by means of a platinum resistance thermometer (PRT)placed inside a twin gel of that one investigated and posi-tioned in the same chamber.

Since hydrogels can be subject to relevant degradation ifnot preserved in a controlled environment, during the experi-ment TMMs have been stored in a sealed and isolatingmembrane to avoid water evaporation and to maintainconstant their humidity. Indeed, with the increase of thetemperature during the experiment, changes in the hydrogelstructure can occur because of water loss. As a consequence,variations in elastic modulus values associated to the resultof the water loss rather than to the properties of the sampleof interest (Anseth et al., 1996) could be observed.

Fig. 2 – (a) Experimental apparatus designed and realised at INRthe experimental apparatus during a sample compression.

Table 2 – Thickness, l0, radius, r, and density, ρ, of investigated

l0 (mm) u(l0) (mm) r (mm)

TMM 1 29.99 0.05 25.08TMM 2 30.16 0.05 25.08TMM 3 30.23 0.05 25.08TMM 4 29.79 0.05 25.08TMM 5 30.12 0.05 25.08TMM 6 30.16 0.05 25.08TMM 7 30.18 0.05 25.08TMM 8 30.17 0.05 25.08TMM 9 30.03 0.05 25.08

3. Results and discussion

3.1. Fundamental mechanical behaviour

The mechanical behaviour of TMMs have been firstly inves-tigated in compression until failure on the basis of stress–strain measurement in order to define their elastic regionbelow the value of the yield strength, σy, and to define thetensile strength, σT, to which yield strain, εy and tensile strain,εT, values correspond.

Samples have been placed between two aluminium par-allels plates and have been compressed by a linear displace-ment acting perpendicularly on the upper surface of gels.Parallel plates have been lubricated with a thin layer ofglycerine in order to prevent any friction between samplesand plates and also to guarantee a homogeneous uniaxialdeformation. The effect of lateral expansion during compres-sion, in terms of surface area variation dA (at boundary, dA/dt¼0), has been taken into account in order to draw directlythe stress–strain curve, as a function of the actual surfacearea expansion, AþdA, due to the lateral poissonian defor-

iM to perform uniaxial unconfined compression. (b) Detail of

tissue mimicking materials with respective uncertainties.

u(r) (mm) ρ (kg m�3) u(ρ) (kg m�3)

0.26 1026 210.26 984 210.26 1045 220.26 1034 220.26 1030 220.26 1043 220.26 1027 210.26 1049 220.26 1076 23

Fig. 3 – Stress–strain curves in compression test until failure with the indication of εy, σy, εT and σT values of the nine testedhydrogels. (a) TMM 1, ▬ TMM 2; (b) ▬ TMM 2, TMM 4, TMM 3; (c) ▬ TMM 2, TMM 6, TMM 5; (d) ▬ TMM 2, ▬ TMM 9,

TMM 8, TMM 7.

Table 3 – Tissue-mimicking mechanical properties whereσy and σT are respectively the yield and tensile strengths,while εy and εT are respectively the yield and tensilestrains.

σy (kPa) εy (%) σT (kPa) εT (%)

TMM 1 45.69 14.32 55.13 17.57TMM 2 66.43 14.08 74.39 16.91TMM 3 73.31 10.35 76.78 11.72TMM 4 47.74 14.95 57.66 18.85TMM 5 42.52 6.71 74.20 13.87TMM 6 31.33 6.68 62.54 15.28TMM 7 44.91 6.67 66.89 11.67TMM 8 84.75 14.08 102.28 18.24TMM 9 50.89 11.07 77.54 20.79

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mation. Surface area variation dA has been determinedevaluating the difference between the surface area at 0 andat 0.10 of strain values. The dA measurement uncertaintyranges between 0.7% and 1%.

Measurements have been carried out at the constanttemperature of 20 1C and at a constant strain rate of 0.1 � 10�2

s�1. Initially, all investigated samples have a cylindricalshape with thickness, l0, radius, r, and density, ρ, values asreported in Table 2.

TMM sample stress–strain curves obtained from the com-pressive tests are shown in Fig. 3. To compare samples proper-ties, stress–strain curves have been divided in four differentgroups. In Fig. 3a, TMM 1 and TMM 2, both samples withoutscattering agents, are represented to show differences between asimple Agar based tissue-mimicking material, largely studiedfrom a mechanical and thermal point of view, and a Gellan Gumbased TMM. On the contrary in panel b, c and d of the samefigure, TMM 2 has been compared to TMMs with scatteringagents, respectively only kieselghur (panel b), only SiC (panel c)and both kieselghur and SiC in different concentrations (panel d).For each sample, values of σy, εy, σT and εT are reported in Table 3.

The yield strength point, σy, represents the limit ofthe sample elastic region, that means that, within thecorrespondent strain range, the sample shows an elasticbehaviour. Maintaining ε opportunely below εy, it is possibleto prevent any permanent deformation in the samples duringexperimental tests. For each sample, the yield strength point

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has been determined calculating the polynomial curve thatbetter approximates the experimental points of the stress–strain curve and studying the second derivative behaviour.The yield strain represents the ε value for which the secondderivative nullifies.

Fig. 4 – Young's modulus, E, and corresponding uncertaintyas a function of the temperature, T, for TMM 1. ●ε¼0.06 .10�2 s�1; ○ ε¼0.1 .10�2 s�1; ■ ε¼0.23 .10�2 s�1; □ε¼0.4 .10�2 s�1.

Fig. 5 – Young's modulus, E, and corresponding uncertaintyas a function of the strain-rate, ε, for TMM 1. ● T¼20 1C; ○T¼25 1C; ■ T¼30 1C; □ T¼35 1C.

Table 4 – Uncertainty budget for Young's modulusmeasurement

Quantity Relative uncertainty (%)

Force, F 0.2Area, A 2.1Lateral expansion, dA 1.0Thickness, l0 0.2Thickness displacement, Δl0 0.2Fit parameter 3.4Selection of measurement region 6.1Overall Young's modulus uncertainty 7.4

3.2. Temperature and strain-rate effects

Within the elastic region, Young's modulus of twin TMMssamples has been determined both as a function of tempera-ture (T varying between 20 1C and 35 1C) and as a functionof strain-rate (_ε varying between 0.06 � 10�2 s�1 and0.4 � 10�2 s�1).

Measurements have been performed in a temperaturechamber whose temperature stability is 70.5 1C. The wholemeasuring device has been placed inside the chamber inorder to keep both materials under test and instrumentationin thermal equilibrium. In the considered range of tempera-ture, the thermal effects do not affect the effectiveness of thelinear encoder and the load cell. Moreover, consequences dueto the thermal dilatation of the measuring system can beconsidered as irrelevant respect to displacements underinvestigation. Measurements have been carried out at stepsof 5 1C and samples have been compressed at four differentconstant strain-rate values included between 0.06 � 10�2 s�1

and 0.4 � 10�2 s�1, approximately doubling the speed of therate at each step.

Before starting measurements, TMMs, sealed by means ofan isolating membrane, have been conditioned for six hoursin the temperature chamber at the T value chosen forthe test.

Considering Eq. (1), the quantity E has been determinedapplying a linear fit to the measured stress–strain curve inthe previously defined elastic region. The line angular coeffi-cient supplies Young's modulus value.

Figs. 4 and 5 show values of elastic moduli resulting fromcompression measurements carried out at different tempera-tures and strain-rate for TMM 1, taken as an example since itswell-known properties.

The uncertainty bars associated to E values have beenobtained combining contributions listed in Table 4 andapplying the uncertainty propagation to Eq. (1).

As it is possible to notice from Table 4, the main part of theuncertainty balance is given by the choice of the measure-ment region considered for the linear fit. Within the elasticregion, varying the ε range in which the curve is fitted, arelative uncertainty of about 6% is introduced on the Equantity. Repeatability has been evaluated by measuring bothYoung's modulus and yield strength on 3 different samples ofAgarose (TMM 1) and 3 different samples of Phytagel (TMM 2).Obtained values are consistent within the overall Young'smodulus uncertainty. Repeatability strongly depends onTMMs realization and conservation. Inaccurate preparationinvolves, as an example, differences in shape and/or presenceof bubbles in the bulk; inaccurate conservation involvesdegradation due to water loss.

As observed from experimental data, stiffness varies, with alinear behaviour, as a function of the temperature, T, and witha logarithmic behaviour, as a function of the strain-rate, _ε.

In order to gather the temperature and strain-rate depen-dence of Young's modulus, a 3D-graph from experimental datahas been generated, as shown in Fig. 6. The following repre-sentation allows to clearly identify the whole Young's modulusaverage variability in the considered ranges of temperature and

Fig. 6 – 3D-graph of Young's modulus, E, and correspondinguncertainty as a function of temperature, T, and strain-rate,ε, for TMM 1.

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strain-rate. The grey surface area, i.e. E(T,_ε), is obtained fromthe best fit of experimental data, on the basis of a constitutivemodel, as explained in the following section.

3.3. Young's modulus constitutive model

Hydrogels properties are dependent on both temperature andstrain-rate and it is useful to curve-fit the whole range of testresults to a single equation, that is temperature and strain-ratedependent. So using experimental data, a statistical methodincorporating multiple linear regression has been employed toidentify the temperature and strain-rate dependent mechanicalproperties of tested hydrogel samples. The combined effects oftemperature and strain-rate on E can be determined on thebasis of the following constitutive model (Shi et al., 1999):

EðT; _εÞ ¼ ða0 þ a1TÞ þ ða2 þ a3TÞU lnð_εÞ; ð3Þ

where _ε is the strain-rate, T is the temperature, a0, a1, a2, and a3are constants depending on thematerial properties. Introducingtwo temperature dependent parameters α(T)¼ (a0þa1T) and β

(T)¼ (a2þa3T), Eq. (3) can be simplified as

EðT; _εÞ ¼ α Tð Þ þ β Tð ÞU lnð_εÞ: ð4Þ

Relations (3) and (4) allow to evaluate the combined variation ofYoung's modulus as a function of temperature and strain-rate,as depicted in the following graphs. Young's modulus depen-dence is represented as a surface in the area defined byexperimental data, as shown in the Fig. 7.

As the strain-rate increases and temperature decreases,viscoelastic materials tend to become more brittle, being themost apparent result an increase in yield stress. As anexample, the stress–strain curves of alginate hydrogels (Druryet al., 2004) are highly dependent on the strain-rate and exhibita nonlinear behaviour, which is also observed in tensile tests oftendons and ligaments (Woo and Young, 1991; Park and Lakes,2001). Even for very low strain-rate values, a relevant increasein hydrogel TMMs Young's modulus is observed, as in othertypology of polymers (Zhou and Mallick, 2002) occurs.

In Table 5, fitting parameters and related uncertaintiesare shown.

Using the proposed constitutive model, it is possible toquantify the magnitude of the average variation of the testedTMMs mechanical behaviour as a function of temperatureand strain-rate.

Moreover, it is possible to extend the surface valuesbeyond the experimental data, in order to estimate themechanical behaviour of tested TMMs, for lower or highervalues of temperature and strain-rate. Nevertheless, theestimated values must be considered within probabilisticuncertainties increasing with arithmetical progression for Tand geometrical progression for _ε.

3.4. Relaxation time

Relaxation time, joined to stress, strain and elastic moduli,allows to implement several classic models from whichviscoelastic properties of materials can be gather from. Theslope of the stress relaxation curve (see Fig. 8) is fitted byusing the Kohlrausch–Williams–Watts (KWW) (Matsuoka,1986; Fancey, 2005) time decay function (Eq. 2).

This function establishes a relation between the relaxationtime and the molecular behaviour of a material. Indeed, the γ-term in the KWW stretched-exponential characterizes thedegree of non-exponentiality of the relaxation function and,physically, it describes the extent of the molecular couplingwithin a polymer (Ngai and Roland, 1993; Jancar et al., 2013).The γ-term can be associated with a coupling parameter,n¼1�γ, describing the degree of intermolecular cooperativity(Ngai and Roland, 1993). For TMMs studied in this work, τ0and γ values resulting from the KWW non-linear fittinganalysis are reported in Table 6 as a function of strain-rateand temperature.

As it is possible to notice from experimental data analysis,in Phytagel samples the presence of different quantity andkind of solid particles allows to modify the stress relaxationtime τ0, therefore the whole viscoelastic behaviour of sam-ples. Stress relaxation time greatly decreases as temperatureincreases, while it seems to be less sensitive with respect tostrain-rate effects. In general terms, the observed resultssuggest that samples tend to become more dampenedincreasing T toward human body typical temperature (37 1C).

On the other hand, since values of exponent γ variesbetween �0.7 and �0.4, a non-linear viscoelastic behaviourcan be recognized (where for classical linear viscoelasticbehaviour is intended Maxwell or Voigt models), as actuallyexcepted in polymers (Roylance, 2001).

3.5. Microscopy and microanalysis characterization

The results obtained from mechanical tests have highlightedthe need of further investigations in order to explain theremarkable difference of σy and σT observed for samples con-taining SiC and/or kieselguhr. Thus, a microscopic analysis hasbeen performed on a sample containing both particles, speci-fically on sample classified as TMM 8. Microanalysis andsecondary electrons SEM imaging have been performed with aFEI Inspect-F SEM-FEG equipped with EDAX, while low-vacuum

Fig. 7 – 3D-graph of Young's modulus, E, and corresponding uncertainty as a function of temperature, T, and strain-rate, ε, for(a) TMM 2, (b) TMM 3, (c) TMM 4, (d) TMM 5, (e) TMM 6, (f) TMM 7, (g) TMM 8, (h) TMM 9.

j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 5 3 ( 2 0 1 6 ) 1 1 9 – 1 3 0 127

Table 5 – Parameters values and respective uncertainties obtained from fitting procedure of experimental data with Eq. (3).

Samples a0 (kPa) u(a0) (kPa) a1 (kPa 1C�1) u(a1) (kPa 1C�1) a2 (kPa) u(a2) (kPa) a3 (kPa 1C�1) u(a3) (kPa 1C�1)

TMM 1 470 39 �6 1 42 12 �1.1 0.4TMM 2 1033 196 �7 7 102 57 0.3 1.9TMM 3 1747 207 �7 7 129 62 0.9 2.1TMM 4 495 51 �6 2 43 16 �0.8 0.5TMM 5 1512 348 �15 12 208 101 �2.7 3.5TMM 6 1465 210 �17 7 171 60 �1.4 2.0TMM 7 1522 149 �19 5 209 43 �3.2 1.5TMM 8 569 58 �8 2 71 17 �1.4 0.6TMM 9 652 71 �7 3 64 21 �1.0 0.7

Fig. 8 – Relaxation experimental curve (grey) and fitting KWW time decay function (dotted line) at T¼30 1C andε¼0.06∙10�2 s�1 for (a) TMM 1 and (b) TMM 2.

Table 6 – Values of relaxation time, τ0, and γ term as a function of the strain-rate, ε, and the temperature, T, for all samplesinvestigated.

τ0 (s) γ7σ(γ)

_ε (s�1) 0.06 � 10�2 0.23 � 10�2

T (1C) 20 25 30 35 20 25 30 35

TMM 1 1600 1250 1020 (1400) 1080 930 800 740 0.6170.05TMM 2 470 360 280 230 490 420 300 250 0.5070.08TMM 3 310 260 180 150 350 290 180 140 0.4270.02TMM 4 880 880 820 770 900 840 730 720 0.6370.06TMM 5 430 380 300 260 480 440 350 300 0.5370.04TMM 6 780 650 540 460 (500) 620 540 520 0.5470.04TMM 7 440 380 350 320 520 430 360 340 0.5370.03TMM 8 1000 1100 1000 800 1150 1200 1100 800 0.7370.05TMM 9 580 540 460 400 620 500 470 440 0.5170.01

j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 5 3 ( 2 0 1 6 ) 1 1 9 – 1 3 0128

SEM imaging has been performed with the dual-beam FEIQuanta 3D –FEG.

As it is possible to observe in Fig. 9, which shows a SEMimage of a slice of TMM 8, the solid particles are well evidenton the polymer matrix surface. It is worth to note that thekieselguhr particles (round drilled cylinders) appear stillembedded under the surface and, owing to their shape,surrounded and filled by the polymer matrix. On the contrary,SiC particles do not have a uniform and characteristic shape

and appear more as solid small bits dispersed on polymericmatrix surface. Although this image shows only a smallfraction of the sample, a speculation about these particleseffects on σy and σT values can be assumed. Comparing σyvalues between TMM 3 and TMM 4 and between TMM 5 andTMM 6, it appears evident the presence of a “saturation”effect on the increase of gel strength associated to solidparticles presence. This phenomenon, also observed in poly-mers filled with nanocomposites (Zhou and Mallick, 2002),

Fig. 9 – SEM image of TMM 8. Kieselghur cylindrical particlesare well visible. On the top (white square) a kieselghurparticle surrounded by the polymer matrix is evidenced.

j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 5 3 ( 2 0 1 6 ) 1 1 9 – 1 3 0 129

might be due to the presence of micro-defects and/or theformation of low-tensile cracking edges inside the sample. Asthe concentration of solid particle increases beyond a thresh-old, a reduction of gel strength is observed. Moreover,comparing TMM 5 to TMM 3, it is evident that the presenceof kieselguhr enhances σy value. In this case, the effect couldbe ascribed to the different shape of these filling particles.Cylindrical hollow shape of kieselguhr lets it to be easilysurrounded and filled by the polymer, while its drilled shapecreates a sort of micro-grids which give to the sample agreater resistance to mechanical stress respect to when onlySiC particles are present. This softening effect is also evidentby comparing different relaxation times (see Table 5), whichappear longer for samples TMM 4 and TMM 6 than forsamples TMM 3 and TMM 5 respectively. The temperaturedependence of relaxation time is greater for samples with alower value of γ (see for example γ value for samples TMM 4and TMM 6), that should mean a greater intermolecularcooperativity of the polymer (Park and Lakes, 2001; Zhouand Mallick, 2002). The γ value of TMM 4 lets to suppose thatmicro-grids given by kieselguhr mostly reduce the elasticresponse of the polymer matrix. However, results obtainedfor TMM 7, 8, 9 reveal that the behaviour of samples filledwith both particles is less predictable. In this case, a “satura-tion” effect on the yield strengths is evident (see Table 3), butthe relaxation time data show that a sort of “competitive”effect between the two filling particles occurs. Indeed, yieldstrengths of TMM 7 and TMM 9 samples result similar to thatone of TMM 4 or TMM 5, as if the effects caused by thepresence of SiC were predominant; on the contrary, sampleTMM 8 shows the greater value of σy but also the longerrelaxation time and the greater value of γ. Our hypothesis isthat, for this particular concentration value, the kieselguhreffects are predominant, while for lower and greater concen-tration the defects formation, given by the presence of SiC,hides the hardening effect of kieselghur. Of course thishypothesis should be confirmed by further investigations,

varying each particles concentration respect to the others,while in this case we chose to maintain constant the ratio ofthe two filling particles, evidencing their role on modifyingand tuning mechanical properties of tissue mimicking poly-saccharide for scaffold and biomedical applications.

4. Conclusions

Since hydrogels mechanical properties are strictly linked toseveral biological features, such as biocompatibility andfunctionality of biomaterials, and, as recently observed,Young's modulus significantly influences adhesion, growthand differentiation of cells in scaffolds, an accurate charac-terization of their elastic and viscoelastic behaviour plays afundamental role in biomedical applications. Moreover,hydrogels are also extensively used in laboratory tests. Forinstance, they are used as versatile platform in the study ofcell–substrate interactions as well as tissue-mimicking mate-rials (TMMs) in the investigation of mechanical and thermaleffects in tissues due to ultrasounds.

As hydrogels show both elastic and viscoelastic behaviour,their mechanical properties are influenced by strain-rate andtemperature. In this work the dependence on strain-rate andtemperature of Young's modulus and relaxation time of ninehydrogel samples (Agar and Phytagel based) has been quan-tified on the basis of accurate experimental data. Limited tothis case study, a constitutive model of Young's modulus, asa function of temperature and strain-rate, have been alsodefined, in order to highlight the magnitude of mechanicalproperties fluctuations. Moreover, the presence of solid par-ticles into the hydrogel matrix has been observed to greatlymodify mechanical properties of the materials, revealing thata simple preparation procedure can change its elastic proper-ties according to its purpose.

Acknowledgements

The research leading to these results is conducted in the frameof the EMRP JRP HLT03 and partially in the frame of EMRP JRPIND05. The EMRP is jointly funded by the EMRP participatingcountries within EURAMET and the European Union. Thiswork has been partially performed at NanoFacility Piemonte,INRiM, a laboratory supported by Compagnia di San Paolo.

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