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Journal of the Mechanical Behavior ofBiomedical Materials

journal homepage: www.elsevier.com/locate/jmbbm

Effect of dissolution of magnesium alloy AZ31 on the rheological propertiesof Phosphate Buffer Saline

Usman Riaza, Leela Rakeshb, Ishraq Shabiba,c, Waseem Haidera,c,⁎

a School of Engineering and Technology, Central Michigan University, Mount Pleasant, MI 48859, USAbDepartment of Mathematics, Center for Applied Mathematics & Polymer Fluid Dynamics, Central Michigan University, Mount Pleasant, MI 48859, USAc Science of Advanced Materials, Central Michigan University, Mount Pleasant, MI 48859, USA

A R T I C L E I N F O

Keywords:BiodegradationImplantsStentMagnesiumPhosphate Buffer SalineRheologyViscosity

A B S T R A C T

The issue of long-term incompatible interactions associated with the permanent implants can be eliminated byusing various biodegradable metal implants. The recent research is focusing on the use of degradable stents torestore most of the hindrances of capillaries, and coronary arteries by supplying instant blood flow with constantmechanical and structural support. However, internal endothelialization and infection due to the corrosion ofimplanted stents are not easy to diagnose in the long run. In the recent past, magnesium (Mg) has been widelyinvestigated for the cardiovascular stent applications. Here we made an attempt to understand the biode-gradation process of Mg alloy stent by studying the degradation of Mg alloy AZ31 (3 wt% Aluminum, 1 wt% Zn)powder at various time-intervals in simulated blood fluid using the Rheological methods. The degradability ofthe Mg stent in the arteries affects the stress-strain properties of blood plasma and the subsequent flow condi-tions. Blood and plasma viscosities alter due to the degradation of Mg resulting from the stress-strain experi-enced in the blood vessels, in which the stent is inserted. Here our objective was to explore the influence of Mgdegradation on the blood plasma viscosity by studying the viscoelastic properties. In this work, the effect ofdissolution of Mg alloy AZ31 on the rheological properties of Phosphate Buffer Saline (PBS) at various timeintervals have been investigated. The viscosity of the PBS-AZ31 solution increased with the dissolution of bothslurries and percolated clear solution. The only exception was day-7 of the percolated clear solution, whereviscosity was decreased showing a reduction in viscosity at initial stages of dissolution. The frequency sweepshowed the tendency of the PBS-AZ31 gelation up to 100 rad/s frequency.

1. Introduction

In the 21st century, various metallic biomaterials and polymershave been significantly used in the medical devices and implants due tothe advancement in the material properties such as strength, wear, tear,and corrosion resistance (Walker et al., 2014; Witte, 2015; Son et al.,2015; Zheng et al., 2014; Im et al., 2017; Zartner et al., 2005; Lim,2013; Bowen et al., 2013; Eliaz, 2012; Pompa et al., 2015; Khalajabadiet al., 2017). The approach of using biodegradable metallic materialsmay revolutionize a variety of biomedical implants currently in clinicalusage. Of these implants, cardiovascular stents are of immense im-portance owing to their effectiveness in the treatment of heart pro-blems. A stent is a tiny tubular mesh-like scaffold, that is used to fa-cilitate the flow of blood in the blocked or narrowed arteries (Groganet al., 2011). The stent is deployed in the body by an angioplasty pro-cedure, in which the stent is first positioned and then expanded in therespective artery/capillaries to open the blocked area. During such

procedure, the stent is first secured on the balloon. The stent is thenstretched and expanded by inflating the balloon in the respective po-sition until the obstruction is completely eliminated. The recovery timeis estimated to be approximately six months (Gastaldi et al., 2011). Thepermanent stents can lead to various unwanted complications such asin-stent restenosis in case of unprotected metallic stents, and the pos-sibility of thrombosis in drug-eluting stents (Gastaldi et al., 2011). Theuse of biodegradable stents can effectively eliminate such complica-tions. However, it is extremely challenging to discover and address theissues associated with the use of biodegradable implants. In the recentpast, several issues regarding the use of biodegradable implants havebeen identified and rigorous research is going on to address these is-sues.

Mg found appreciation in the field of biomaterials and biomedicalimplants because of its biodegradability (Rahman et al., 2015). Thebetter mechanical strength of Mg as compared to polymeric materialsalong with its biodegradation and biocompatibility are the prime

https://doi.org/10.1016/j.jmbbm.2018.06.002Received 26 February 2018; Received in revised form 19 April 2018; Accepted 1 June 2018

⁎ Corresponding author at: School of Engineering and Technology, Central Michigan University, Mount Pleasant, MI 48859, USA.E-mail address: haide1w@cmich.edu (W. Haider).

Journal of the Mechanical Behavior of Biomedical Materials 85 (2018) 201–208

Available online 05 June 20181751-6161/ © 2018 Elsevier Ltd. All rights reserved.

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reasons for the extensive investigation of Mg as a biomaterial. Mg hasbeen proved non-toxic in nature (Chen et al., 2014) with daily re-commended intake of 240–420mg/day for adults (Chen et al., 2014).The degradation of the Mg content in the physiological solutions leadsto release of Mg2+ and formation of Mg(OH)2. Mg ions are required bythe body and hence pose no threat (within tolerance limits) to thenormal functioning of the body. The Mg(OH)2 is not stable underphysiological conditions and undergoes reversible reactions to releaseMg2+ and OH-. The excessive OH- can lead to the alkalization of thetissues surrounding the Mg implant. The tolerance limit of OH- has notbeen defined, limiting the knowledge on the effects of OH- in the humanbody (Seitz et al., 2014). Similarly, Mg ions can react with chlorides andphosphates to form MgCl2 and Mg3(PO4)2. However, these products arenegligible because of their extremely low quantity. Another importantconsideration in the degradation of Mg is the evolution of H2 gas. TheH2 gas can damage the tissues surrounding the implant (Riaz et al.,2018). Moreover, the evolution of gas bubbles can disrupt the regularblood flow (Riaz et al., 2018). In the case of Mg alloy AZ31, the smallcontent of Al (3 wt%) and Zn (1 wt%) leads to the formation of Al3+,Al2O3, Zn2+ and Zn(OH)2. The effects of Al depends on its concentra-tion in the body. At higher concentration, the Al can cause Alzheimer(Perl and Moalem, 2006) and may also lead to neuronal injuries (El-Rahman, 2003). On the other hand, Zn is one of the essential elementsin the body with no negative effect (Zhang et al., 2010).

Historically, Mg has been investigated for a number of biomedicalapplications (Witte, 2015). Even though exploration of Mg alloys asimplant materials started in 1878 by the physician Edward C. Huse, itwas Erwin Payr, an Austrian physician, who took the research of Mg inbiomedical industry to next level (Witte, 2015). Since then many sur-geons and physicians used Mg implants in cardiovascular, muscu-loskeletal and general surgery without serious side effects for a briefperiod. Although the issue of fast degradation is still a barrier in thecommercial use of Mg in the biomedical industry, the current researchon Mg heavily focusing on the improvement of corrosion resistance mayhelp to realize the dream of biodegradable implants

One of the primary application of Mg as biomaterial is in vascularstenting (Zartner et al., 2005; Lim, 2013; Bowen et al., 2013). Severalresearchers studied the possibility of Mg as stent material and foundthat Mg can be used as an alternative to permanent stent materials(Zartner et al., 2005). Although Mg was under research as stent mate-rial for a long period, it was 2005 when the Mg stent was implantedsuccessfully for the very first time (Zartner et al., 2005). Mg stents havebeen under review for different properties including degradation, bio-compatibility, and coatings (Lim, 2013; Bowen et al., 2013; Groganet al., 2011; Wu et al., 2013). The effect of stenting on the fluid patternof blood has been studied in the literature (Kabinejadian et al., 2015;Zhang et al., 2017; Mut et al., 2014; Chiastra et al., 2014). Computa-tional fluid dynamics has also been used extensively to study the flowpattern of blood as a result of stenting in the carotid (Kabinejadianet al., 2015; Zhang et al., 2017; Mut et al., 2014) and in the cardiac(Chiastra et al., 2014). Moreover, there are some studies that in-vestigated the rheological properties of body fluids under the influenceof foreign materials, which affects the entire physiological system(Friederichs and Meiselman, 1994; Cengiz et al., 2016). The rheologicalproperties of blood under different conditions have been explored in theliterature (Bäumler et al., 1996; Kayar et al., 2001; Schmid-Schönbein,1988; Baieth, 2008; Merrill et al., 1963; Brust et al., 2013; Jeong andRosenson, 2013). Although the effect of varying fluid conditions on thedegradation of Mg stents has been investigated (Wang et al., 2014),surprisingly there is not much work on the effects of dissolution of Mgon related flow conditions of simulated body fluids. In this work, theefforts have been made to explore the effect of Mg degradation on thefluid properties of PBS, a commonly used fluid to simulate body fluids.

1.1. General theory of rheology and measurements

Rheology is a study of the deformation process occurring in any typeof materials. The extent of deformation with respect to steady strainrate is often defined as a measurable quantity: viscosity. The degree ofeasiness/springiness is the measure of the solid-like response to strainrate; hence rheology and viscosity are two different concepts sinceviscosity is the resistance to flow. The ability of a material to thin orstiffen/gels with growing stress, or the amount of force exerted in therespective direction, and the point where the material begins to move isoften quantified as yield stress (Walter, 1975; Morrison, 2010;Batchelor, 2000).

Generally, the fluids are divided into two types, Newtonian fluidsand non-Newtonian fluids. Newtonian fluids like water, alcohol, andsome oils obey the Newtonian equation and have a constant viscosity.On the other hand, the viscosity of the fluid/suspensions varies withstress in case of non-Newtonian fluids, violating the Newtonian fluidflow equation. One of the foremost interests in rheology is the study ofthe unusual flow behavior of non-Newtonian constituents and theirconcentrated suspensions/mixtures under various operating conditions.Fig. 1 is a representation of the velocity gradient generated in a fluidbetween two parallel plates. The lower plate is located at y= 0, and theupper plate is kept at a distance, y= d. The upper plate moves with alocal velocity, U while the lower plate remains stationary. The force, Fexerted on the fluid produces a velocity gradient where the arrows areproportionate to local velocity within the area, which in turn developsinternal friction within the fluid. Such resistance to the force is themeasure of fluid shear viscosity. Shear strain is the movement of a layerof fluid relative to parallel adjacent layers (Walter, 1975; Morrison,2010; Batchelor, 2000; Likhtman and Graham, 2003; Bird, 1987; Masaoand Frederick, 1986; Larson, 1988), which is a measure of zero shearviscosity.

Shear rate ( ′γ ) is defined as the rate of change of shear, and is re-sponsible for the velocity gradient. On the other hand, shear stress (σ) isthe force parallel to the upper plate at d. One of the most importantmaterial properties is the steady shear measurement, which can befundamentally obtained from the mathematical definition of velocitygradient. The constitutive equation relates shear rate and shear stressfor non-Newtonian fluids, exhibits viscous modulus and elastic mod-ulus, and is known as viscoelasticity. The equation is given as:

=η γσγ

( ̇)̇

xy

(1)

Elasticity modulus is the ability of a material to store mechanicalenergy during deformation, and viscous modulus is the opposite ofelastic modulus, exhibiting lost energy. Viscoelasticity is recognized asthe breakage and remaking process of the complex structure networkduring applied shear stress loading and unloading periods. Linearityproperty of viscoelasticity is based on the superposition concept thatthe strain at a given period is proportional to stress exerted upon thematerial. In order to determine the linear viscoelastic region (LVER),small amplitude oscillatory shear (SAOS) flow is the typical methodapplied at deformation mode in which the lower plate is fixed, and theupper plate oscillates back and forth in the direction of flow at smallamplitudes.

Fig. 1. Simple shear fluid flow velocity gradient generated by the parallel platesmovement at U velocity along x-direction (Walter, 1975).

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Different models exist to measure the oscillatory shear rate.Based on the Maxwell theory, the shear strain can be defined as

=γ γ ωtcos ( )0 (2)

From the above equation, the complex shear modulus (G′) is definedas:

∫= − ′ ′∞

− − ′G iω φ t t e dt* ( ) iω t t0

( )(3)

where (t − t′) is rheological history, φ is relaxation function dependson relaxation time τ once the shear flow stops.

The above equation is equivalent to

= +G G iG* ’ " (4)

where G′ is storage modulus/dynamic rigidity, G′′ is loss modulus/orimaginary part of the G*.

G′ is the quotient of the stress that is in-phase with the strain underoscillatory conditions, whereas G′′ is the quotient of the stress that isout-of-phase with strain, that is

′ =+

Gητω

τ ω1

2

2 2 (5a)

′ =+

′Gηω

τ ω1

2

2 2 (5b)

From the above equations, shear stress can be rewritten as

=σ t G γ t( )̇ * ( ) (6)

The phase angle gives the information about the viscous to elasticnature of the material, & is defined as

= ′′ ′tanδ G G/ (7)

Its graphical representation during rheological measurements isshown in Fig. 2 with a difference in both the curves (δ π/2 ).

Larger values of tan δ indicate that the flow is primarily viscous andthe relationship is weak between the suspended particles. Under gravityconditions, the sedimentation process occurs by the inter-particleforces. However, at low tan δ, strong inter-particle interaction (higherelasticity) can occur, which results in skirting, and generates large ag-gregation, which leads to settling in due course. The constitutivemodeling is explained in detail in the literature (Walter, 1975;Morrison, 2010; Larson, 1988).

As discussed above, the materials that undergo a change in viscositywith the shear rate are termed as non-Newtonian fluids. However, theNewtonian constitutive equation is limited to purely Newtonian fluidsand is unable to explain the phenomenon of non-Newtonian fluids.Depending upon the nature of materials and the particles in the mix-ture, various mathematical equations have been developed, verified byexperimental data, and reported in the literature. For example, the in-elastic models such as the Power-Law model and the Carreau-Yassudamodel are most commonly used to explain the behavior of non-Newtonian fluids. The Carreau-Yassuda model is the most commonlyemployed model to study the fluids undergoing shear thinning, as

Power law is limited to higher shear rates. It defines the viscosity byinterpolating the viscosities between the zero shear rate and the infiniteshear rate (Morrison, 2010; Morozov and Spagnolie, 2014). The equa-tion of Carreau-Yassuda model is,

= + − +∞ ∞

−

η η η n λγ( )[1 ( )̇ ]a na

0

1(8)

where ∞η is infinite shear viscosity, η0 is zero shear viscosity, λ is therelaxation time (consistency), n is the Power law index (rate index) anda is the size parameter. The fluids in this article are following the trendsof the Carreau-Yassuda model (Morrison, 2010).

Here we investigate the effects of dissolution of Mg alloy AZ31powder in PBS solution at various time intervals by stress-strain steadyand oscillatory rheological experiments.

2. Significance of the study

Monitoring the degradation of Mg and its alloys in PBS/bloodsubstitute is an important criterion for prospective applications insustainable biomedical implants. Such degradation diminishes themechanical characteristics of the implant and increases the alkalinity ofthe local blood plasma, which in turn warrants further medical onset topatients. Mg degradation is affected by various intermingling factors,which includes its microstructure, compositions of alloys at the surface,and the surrounding fluids. Thus, understanding the interactions amongsuch factors during the flow conditions is very important. Secondly, theviscosity of blood or blood substitute is dependent on the shear rate anddissolved particles, and needs to be monitored when a biodegradableimplant is introduced into the body.

If the surrounding fluid (blood) is mixed with the degraded Mg, itwill exert many complications, including faster red cell aggregation andflow instability, which can be studied using anomalous rheologicalbehavior of fluid (blood/blood substitute). If the degradation of Mg ishigher in the blood, it would increase the sedimentation rate of red cell/erythrocyte which would disrupt the suspension stability of blood. Insuch situations, a certain critical shear stress (yield stress) must apply tomake the fluid flow. Such critical stresses can be evaluated usingrheological methods. Also, often Lewis negative patients show symp-toms due to anomalous hemorheological characteristics, and protractedlow-grade contaminations that eventually lead to premature athero-sclerosis and cardiovascular disease progression (Alexy et al., 2015).Many experimental results showed that these rheological variationshave circulatory and metabolic significance (Charm and Kurland, 1965;Dintenfass, 1963; Merrill et al., 1966). Therefore, understanding theimportant rheological parameters could provide valuable informationto the medical practitioners.

The rheological behavior of blood greatly influences the degrada-tion of Mg at medium to high-speed shear rate fluid flow. It couldeventually increase the viscosity of the suspension of blood and derailthe normal blood flow through the blood vessels. The complicationsoccurring due to this increased suspension viscosity could be preventedby studying the viscosity and viscoelasticity of the blood on a continualbasis. Therefore, we attempted to study the degradation process usingrheological properties of the percolated clear solution and the slurryafter incorporating the Mg alloy AZ31 powder in pure PBS at varioustime intervals under stress-strain conditions. Present investigation notonly enhanced our understanding of Mg/Mg alloy degradation underphysiological conditions, but also covered some crucial factors to reflectin order to fulfill the degradation predictabilities for other biodegrad-able implants and devices.

3. Materials and methods

Mg alloy AZ31 powder was obtained by smoothing a Mg AZ31 rod.The outer rod surface was first ground using Silicon Carbide grindingpapers and then cleaned by sonicating it in acetone for 10min. After

Fig. 2. Graphical form of oscillatory strain–stress input and output (Walter,1975).

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grinding and cleaning, it was smoothed with a flat 2nd cut steel file toobtain fine size powder. The commercially available PBS pallets weremixed in water. 3 pallets were used for PBS of 600ml. 0.6 g of AZ31powder was mixed in 200ml of PBS. AZ31 rod was obtained fromsource1metals and PBS was obtained from Sigma-Aldrich.

Two types of sample testing were performed. In the first type, theMg powder was allowed to settle at the bottom and the percolated clearsolution was collected. The percolated clear samples were named asPBS-AZ31(C) in the study. In the second type, the solution was stirredusing a magnetic stirrer and the slurry was collected from the stirredsolution. The slurry samples were termed as PBS-AZ31(S) in the study.40 mm 2° Steel cone-plate was used to do experiments on the clearsolution and the 40mm parallel plate with 100-micron gap was used toperform experiments on the slurry using AR 2000 Rheometer (TAInstruments).

3.1. Rheological measurements

Dynamic and steady shear flow measurements were conductedusing an AR 2000 Rheometer (TA instrument, New Castle, DE) andanalyzed with commercial computer software (Rheology AnalysisAdvantage Software Version 5.7.2, TA Instruments). Samples fromvarious sets were subsequently stirred for more than ½ h to avoid airbubbles and were then stored at room temperature for various daysbefore rheological measurements were performed. In order to carry outthese experiments, a 40mm 2° Steel cone-plate was used to do ex-periments on the clear solution and a 40mm parallel plate was used toperform experiments on slurry. The respective samples were loadedonto the plate for 3–5min to avoid residual shear history and thenexperiments were carried out instantaneously. The rheometer isequipped with a high-to-low temperature unit with a solvent-trap thatprovided very good temperature control (37 ± 0.05 °C) over an ex-tended period of time in this work. Steady shear and oscillatory ex-periments were conducted at 37 °C.

The linear viscoelastic region was found to be within 0.5–2% strain.We used 1% strain and 1 Hz frequency with heating and cooling rates of1 °C/min to obtain the oscillatory measurement data. Three types ofexperiments were performed.

In the first type, steady-state experiments were performed at a shearrate of 10−3–1000/s for PBS and 1–1000/s for all the other solutions.The range in literature is found to be 1–1000/s (Brust et al., 2013). Thereason for going to lower shear rates in case of PBS is to define themodel with certainty. Steady state tests were performed on the 7th,15th, and 24th day of mixing for both the percolated solutions andslurries. The second type of experiment is strain sweep that was per-formed over a range of 1–5 strain % at 1 Hz. The frequency sweep wasperformed at frequencies 0.1–100 rad/s at a strain % of 1. All tests wereperformed at 37 °C.

In general, the rheological characteristics of slurries depend on thesolid concentrations and interactions of solid-particles. Often it is ob-served that some fluids show Newtonian behavior at low concentrationof solid, and shear dependent non-Newtonian at high solid concentra-tions. Again, the non-Newtonian characteristics will not only depend onthe solid concentration, but also depend on particle shape, size, dis-tribution and the suspending fluid rheological properties. The sus-pended Mg-slurry could develop a yield-stress along with time de-pendency due to the development of structures within the fluid as thesolid concentration increases, which we are planning to study in thefuture. However, here we focus mainly on the steady and oscillatorymeasurements of rheological properties, where we assume a fullysheared fluid, thus the time dependency in rheological properties isunlikely. The aim is to investigate the clear solution (which may con-tain extremely fine particles) and Mg-slurry at various time intervals forsteady state and oscillatory measurements.

4. Results and discussion

4.1. Steady shear rheological behavior of PBS pure solution

Fig. 3 shows the relationship between viscosity and shear rate ofPBS at 37 °C. The viscosity is not constant with varying shear rate in-dicating that PBS is a non-Newtonian fluid. The viscosity vs shear rateshows a downward trend with an increase in shear rate from 10−3 to1000/s. The downward trend with increased shear rate proves that PBSexhibits shear thinning. Many shear-thinning fluids often demonstrateNewtonian like characteristics at low and high shear rates, which re-presented as zero-shear viscosity (low shear rate region) and followedby shear thinning region at the intermediate shear rate and infiniteviscosity region at high shear.

4.2. Steady shear rheological behavior of PBS-AZ31 clear solution andslurry

Fig. 4 shows the shear viscosity with increasing shear rate for thePBS-AZ31(C) with pure PBS. The alloy powder was settled at thebottom with some content dissolved in the PBS. The clear solution atthe top was collected on 7th, 15th and 24th day to study the transfor-mation in percolated clear solution in comparison to pure PBS solution.The percolated solution still exhibited the shear thinning behavior on

Fig. 3. Shear rate vs viscosity of pure PBS at 37 °C.

Fig. 4. Shear rate vs viscosity of pure PBS, percolated clear solutions of PBS-AZ31 at 7th, 15th and 24th day.

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7th, 15th and 24th day. The viscosity showed a direct relationship withthe time. With the increase in the number of days, the viscosity ex-hibited upward trend at low shear rates except for day-7. However, thedifference in the viscosity value seems to be dropped to low values athigher shear rates. The time of degradation appeared to have not sosignificant impact on the viscosities at higher shear rates. The value ofviscosity of the percolated solution at day 7 appeared to be less than thevalue of viscosity of PBS indicating a drop in the viscosity at the initialstage. The apparent reason for the decreased viscosity on day 7 isboundary lubrication. The change in viscosity from 7th to 24th day issignificant at lower shear rates. At a shear rate of 0.90/s the value ofviscosity after 7th day is approximately 8.16× 10−3 Pa s that increasedto 7.51×10−2 Pa s after the 15th day and further increased to1.19 Pa s after the 24th day. In short, the viscosity value of pure PBSwas higher than the viscosity of PBS-AZ31(C) for 7th day, we mayconjecture that initially degraded Mg particles lubricated with PBSsolution and set up in an arrangement that offers less resistance ascompared to pure PBS. As the number of days increased, the Mg par-ticles clustered and showed resistance to flow, hence the viscosityclearly increased in the order of 2–3 magnitudes at low to intermediateshear rate. However, at the high shear rate, this difference decreased.

Often aorta and veins experience the shear in the range of 1–300/sat normal conditions and vary depending upon the abnormality con-dition. The results proved the increase in viscosity of PBS with the in-crease in time (days) of dissolution of Mg alloy AZ31 in PBS based onthis preliminary study.

Fig. 5 represents the relationship between the shear rate and shearstress for PBS-AZ31(C) at different time intervals. The shear stress re-quired to flow the fluid decreases on the 7th day as was expected fromthe shear rate vs viscosity trends. The shear stress increased on day 15and 24 as compared to pure PBS. On 15th and 24th day, the change inshear stress with shear rate was marginal and can be termed as constantshear stress with changing shear rate. For day 15 and day 24, the shearstress was approximately same at any given shear rate.

Apparently, the clear solution is still very similar to the pure PBS inappearance, but the dissolved salts can significantly alter the rheolo-gical properties of fluids (Lalko et al., 2009; Almeida et al., 2017). Theeffect of dissolved Mg is clearly visible from the steady-state experi-ments.

Fig. 6 presents the values of viscosity for PBS-AZ31(S) on 7th, 15thand 24th day by using the parallel plate with a gap of 100 μm. Theviscosity values for slurry were significantly higher than that of a clearsolution. The values of viscosity increased with every reading. Amongthree readings, the 7th-day sample showed lowest viscosities and 24th-day samples showed the highest. This shows a gradual increase in theviscous behavior of solution with the degradation time. The slurry data

presents a better picture of the problem as particles degrade from thestent will be added directly to the bloodstream before dissolution in reallife cases.

Fig. 7 represents the relationship of the shear rate with shear stressfor PBS-AZ31(S) on different days. The results verified the trends ofviscosity vs shear rate. The shear stress to make the fluid flow increasedwith the increasing number of days. This increasing viscosity with thenumber of days is directly affecting the shear rate trends.

Fig. 8 represents the trend line between the number of days andviscosity at approximately zero shear rates. Based on the steady-stateexperiments and from the graph presented in Fig. 8, we conjecture thatthe powder degradation of AZ31 in PBS has the following mathematicalmodel proposed for viscosity vs time in days;

= + −η η t324276o0.699 (9)

Further investigation is required with experiments stretching to alonger span (3–6 months) to predict the above model more precisely.

4.3. Small amplitude: rheological behavior of PBS-AZ31

Various classes of the general oscillatory rheological response of anyliquid to semi-solid materials can be understood from the dynamicexperiments. Therefore, the effect of AZ31 dissolution for clear andslurry samples were further investigated using oscillatory conditions asdescribed in the following section.

Fig. 5. Shear rate vs Shear stress curves for pure PBS and PBS-AZ31(C) on day7, 15 and 24.

Fig. 6. Shear rate vs viscosity of pure PBS, slurry of PBS-AZ31 at 7th, 15th and24th day.

Fig. 7. Shear rate vs Shear stress curves for pure PBS and PBS-AZ31(S) on day 7,15 and 24.

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4.3.1. Linear viscoelastic region test: critical strain and strain sweepStrain sweep tests were performed before every test to evaluate the

critical strain. Fig. 9 illustrates G′ (storage/elastic modulus), and G′′(viscous/loss modulus) of the PBS-AZ31(C) on day 24 as a function of %strain. Often rheological characteristics of viscoelastic material do notdepend on strain % up to a certain range of critical strain, above thislevel, the material shows the non-linearity and storage modulus de-creases. Therefore, measuring the strain amplitude percentage depen-dence of module would give the best possible characteristics of vis-coelasticity. Fig. 9 shows a strain % sweep for the clear solution at37 °C. In the present case, 0.5–3% is the critical strain and the structureis undamaged below this strain. Moreover, this solution exhibits anelastic behavior as G′ is greater than G′′. G′′< G′ signifies that thematerial is highly structured without any breakage due to shear.

4.3.2. Dynamic oscillatory test: structure and frequency sweepFig. 10 represents G′ and G′′ of the PBS, and PBS-AZ31(C) on Day 7,

15 and 24 as a function of angular frequency at 1% strain rate. Once thelinear viscoelastic region (LVE) has been located by strain sweep, itsstructure-property can be identified using a frequency- sweep below thecritical % strain, which provides more information about the variousforces acting on it. During the frequency sweep experiments, at variousoscillation frequencies with constant oscillation amplitude and tem-perature, we can identify various characteristics of the fluid and theparticles. If the elastic modulus G′ is nearly independent of frequency,

then it projects the behavior of solid-like materials, otherwise, it wouldbehave as fluid-like material. Fig. 10 depicts the transition of solid-fluidwith frequency sweep data measured on PBS and PBS-AZ31(C) at dif-ferent time intervals. It can be seen in the Fig. 10 that the G′ and G′′ incase of pure PBS is almost independent of the angular frequency. Fur-thermore, with the increase of time, the increase in viscous modulus isevident except for day 7. The frequency sweep results of PBS-AZ31(C)suggest the tendency of PBS-AZ31(C) gelation up to 100 rad/s. Thetrends are inclined towards the formation of semi-gel instead of perfectgel.

A semi-solid behavior, i.e. G′′ ~ ω−0.08 to 0.33, G′ ~ ω−0.01 to 0.35,which deviates from typical fluid-like behavior, i.e., G′′ ~ ω1 and G′ ~ω2 was observed. This clearly indicated that there were microstructuresof the fluid-solid associations and gel-like behavior.

Fig. 11 represents the frequency sweep of PBS-AZ31(S) on day 07,day 15 and day 24. PBS-AZ31(S) in all cases showed a trend that wasnearly independent of the frequency. The elastic modulus G' is in-dependent of the frequency in all 3 cases proving a more structuredfluid in slurry cases. A slight increase in viscous modulus with respect toa number of days can be observed. Similar to PBS-AZ31(C), the slurriesshowed the trends of gelation up to frequencies of 100 rad/s. Further-more, at this concentration G' and G'' are much higher than the purePBS solution and PBS-AZ31 clear solutions.

Like clear solution dynamics, the slurry also exhibited the semi-solidbehavior with G′ ~ ω0.025–0.057 and G′′ ~ ω−0.08−(−0.02).

In conclusion, these experiments have given the following scientificconclusions: (i) Viscosity of the PBS-AZ31 degraded clear solution andslurry increased more than one to four orders of magnitude, at varioustime intervals (ii) As the number of days progressed, the viscosity in-crease was dramatic at low shear rates. This study proved that theviscosity of PBS will increase with the increase in time (days) of dis-solution of Mg alloy AZ31 in PBS.

5. Conclusion and remarks

Improvement of metallic biomaterials has modernized the percep-tion of bio-implants from permanent to more degradable products, toresolve the biological issues encountered in patient care. As we dis-cussed above, there are certain issues related to the use of biodegrad-able implants including losing mechanical strength with corrosion, in-sufficient support to arteries, and restenosis. The degraded material inthe body should be non-toxic and should not altercate the fluid prop-erties of blood. This article evaluated the biodegradability of Mg in thesimulated blood with subsequent changes in the fluid using the rheo-logical experiments. The rationale of the current research was to un-derstand the blood-related complications during the stent introductionperiod. This study concluded that PBS with and without Mg degradedparticle exhibited shear-thinning non-Newtonian flow characteristics. Itwas observed that a smaller quantity of Mg degraded particles producedremarkable shear thinning. The effect caused by the degraded Mgparticles could create an increase in the apparent viscosity, which cansubsequently increase patient-related complications. Obviously, anychange in the pure PBS generally will have a profound effect, especiallyon solution viscosity. The experiments with PBS-AZ31 (percolated clearand slurry) in the oscillatory regime showed that the mixture exhibitedtypical viscoelastic characteristics.

Hence this article explored the basic rheological properties of thepure PBS and PBS-AZ31 matrix mixture at various time intervals usingthe percolated clear solution and the respective Mg alloy slurries. Theviscosity of the PBS-AZ31 degraded clear solution and the slurry in-creased more than an order of magnitude, at various time intervals.From oscillatory results, we may conjecture that AZ31 degradation inblood plasma (PBS) at high frequency has the tendency to gel and couldthreaten the blood flow in the aorta, arteries, and vein.

In the present study, authors suggest that an independent relation-ship between viscosity and related complications cannot be explained

Fig. 8. Degradation quantification – viscosity vs number of days at zero shearviscosity.

Fig. 9. Strain sweep for PBS-AZ31 clear solution after 24 days at 37 °C.

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by a single parameter, but other parameters such as blood consistency,and power-law index measured from the rheological experimentsshould be considered for in-depth knowledge of the problem. Therefore,medical practitioners should consider the pathophysiological

significance of blood viscosity before and after the stent implementa-tion into the cardiovascular system at a regular interval to reduce therisk associated with the stent insertion.

Further experiments are desired to investigate the consequences of

Fig. 10. Frequency sweep for PBS (a) and PBS-AZ31 clear solution after (b) 7 day, (c) 15 days and (d) 24 days at 37 °C.

Fig. 11. Frequency sweep for PBS (a) and PBS-AZ31 slurry after (b) 7 day, (c) 15 days and (d) 24 days at 37 °C.

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Mg and its alloy's degradation on gelation characteristics at variousfrequencies and temperatures, which will offer valuable understandingtowards the physical and mechanical fluctuations of the clear solutionand slurry, and the effect on blood flow conditions near the stent andperipherals. Moreover, the relationship between the viscosity and dis-solved Mg ions should be considered in future works for better under-standing of the subject. Future work includes but not limited to (i)Effect of composition of Mg alloy (at various dimensions) on therheological properties of PBS-Mg solution (ii) Use of dynamic flowsystem to investigate the rheological changes of PBS-Mg solution.

Acknowledgments

Authors are grateful to College of Science and Engineering, Schoolof Engineering and Technology and Department of Mathematics atCentral Michigan University. Special thanks to Mr. H. Flores, an un-dergraduate student in Engineering Technology for reconfirming someof the rheological experiments. We are also thankful to Mr. HassnainAsgar and Mr. Syed Nabeel Ahmed, graduate students in Engineering,for their support in compiling and plotting data. In addition, we thankall the students and faculty involved in Dr. Rakesh's rheology laboratoryfor suggestions and support. We also acknowledge the financial supportgiven by Office of Research and Graduate Studies at Central MichiganUniversity, and many thanks to the school of graduate studies at CMU,for this research.

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