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Monitoring and modelling of oxygen transport through un-crosslinked and crosslinked gelatine gels
Polymer Testing 40 (2014) 106e115
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
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Monitoring and modelling of oxygen transport through un-crosslinked and crosslinked gelatine gels Y. Elsayed a, *, C. Lekakou a, P. Tomlins b a b
Division of Mechanical, Medical and Aerospace Engineering University of Surrey, Guildford GU2 7XH, UK National Physical Laboratory (NPL), Teddington, Middlesex, TW11 0LW, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 July 2014 Accepted 27 August 2014 Available online 6 September 2014
A non-invasive, luminescence quenching technique is developed for continuous monitoring of oxygen spatial-temporal concentration distribution in fully hydrated gelatine gels, intended for use as scaffolds in tissue engineering. Two mass transfer-diffusion models were used to simulate the unsteady-state oxygen mass transport in the system. Oxygen diffusion coefficient and mass transfer coefficient at the water-gel interface were determined for un-crosslinked gelatine, as well as gelatine crosslinked with 1 and 1.5% w/v glutaraldehyde. While crosslinking and increased concentration of the crosslinking agent reduced oxygen mass transfer across the gel surface, both factors increased the diffusion coefficient of oxygen in the bulk of the gel. Voids in the gelatine's microstructure, which were generated during the crosslinking process due to shrinkage and associated internal stresses, were associated with both increasing the diffusion coefficient within the gel, as well as inhomogeneous diffusion of oxygen within the gel. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Crosslinked gelatine Oxygen diffusion coefficient Fluorescent quenching imaging Scanning electron microscopy
1. Introduction The success of scaffold-based tissue engineering has been always limited by the availability of nutrients, growth factors and sufficient oxygen exchange between the cell culture medium and the cells [2,22]. The optimisation of the design of the three-dimensional constructs and their environment in a tissue engineering bioreactor relies on the understanding and the monitoring of the transport of these nutrients to the cells. Oxygen supply to the cells has been shown to be the main limiting factor in their survival [17]. The two main success stories of tissue engineering, are skin [5] and cartilage [23], these examples had the advantage of not being limited by oxygen. The former is not required to be very thick allowing oxygen to diffuse along only a short distance to the cells, while for tissue engineering of * Corresponding author. E-mail addresses: [email protected], yahya_elsayed@hotmail. com (Y. Elsayed). http://dx.doi.org/10.1016/j.polymertesting.2014.08.016 0142-9418/© 2014 Elsevier Ltd. All rights reserved.
cartilage, chondrocytes naturally require less oxygen than other cells, which is why they are the only cells that exist further away than 100mm from the blood supply in the human body [7]. The dependence on oxygen of other cell types used in tissue engineering, such as vascular grafts, has led to research into methods of monitoring and modelling the oxygen transport across scaffold materials [4,12,14] as well as the quantification of the diffusion coefficient of oxygen and other nutrients to be used in mathematical modelling of the tissue engineering process [1,3,19]. One material commonly used to make scaffolds for tissue engineering applications is gelatine [9,10], a denatured form of collagen, a naturally occurring triple helix polymer that is abundant in the extracellular matrix that cells grow on. Gelatine is produced by destroying the hydrogen bond holding the collagen’s triple helix structure. Because there are no covalent bonds holding the polymer strands in gelatine, a triple helical fold is developed with segments of different strains of poly-proline II like helices. This leaves space
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within the hydrogel's structure which allows for fluid retention in these voids, something advantageous for tissue engineering. This however makes gelatine susceptible to dissolving in water and has one drawback, low mechanical strength. One common solution that is adopted when using gelatine for scaffolds in tissue engineering is to further chemically crosslink the polymer chains using organic compounds such as glutaraldehyde and formaldehyde [21] so that the gels do not dissolve in the water-based culture medium and in the organism when implanted. Studies of oxygen diffusion across gelatine films yielded values of the order of 108 cm2s1 [11], generally referring to the gelatine in dry conditions or at different humidity levels (53-84 RH%) for vitrified gelatine, sometimes with physical crosslinks [14] but without any chemical crosslinks. However, for tissue engineering applications, a fully hydrated chemically crosslinked gelatine structure is used to grow the cells, a state which lacks detailed study of its molecular mobility and diffusion properties. This means that the diffusion coefficient of oxygen in hydrogels used in tissue engineering is sometimes approximated to the value of the diffusion coefficient of oxygen in water [19] DO25 cm2s1. The approximation is justified Water ¼ 2.6 10 by the interstitial space within the gelatine's structure which allows for a large extent of filling and swelling of the hydrogels by water. While some tissue engineering applications can justify such an approximation, for example oxygen diffusion coefficient in collagen-hepatocyte gels was measured to be DO2 ¼ 2.99 105 cm2s1 [13], on the other hand a relatively lower diffusion coefficient was measured in an alginate gel DO2 ¼ 7 106 cm2s1, even if it was 95% swollen with water [8]. The need for quantification of oxygen mobility in bulk hydrated gelatine gels is emphasised when comparing the order of magnitude difference between water (105 cm2s1), alginate gels (106 cm2s1) and those of un-wetted gelatine films (108 cm2s1). Today, most commercially available oxygen sensing techniques revolve around probing (both electrochemical and luminescent based) which has the drawback of being invasive to the material under investigation, affecting the transport process in the vicinity of the probe and, in the case of the electrochemical sensors, consumption of oxygen can affect the results [14]. Imaging of the spatial-temporal oxygen concentrations across the hydrogel's depth is possible with the use of an appropriate phosphorescence or luminescent dye, and has been reported in literature to investigate the oxygen diffusion in gelatine films [11,18,20], as well as measuring the transport of oxygen across the boundary of two separate polymer films [16]. This is promising because of the low opacity, near transparency of gelatine hydrogels, even after crosslinking. One possibility is to use an oxygen quenched luminophore. Oxygen quenching is the decrease of luminescent intensity due to the presence of a quencher, such as oxygen, and is governed by the Stern-Volmer equation [15]:
to =t ¼ Io =I ¼ 1 þ K c
(1)
Io and I are the luminescent intensities in the absence and in the presence of the quenching substance of concentration c,
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respectively, to and t are the respective luminescent lifetimes, and K is the Stern-Volmer constant. The linear relationship between to/t or Io/I and the concentration of the quenching substance (oxygen in this case) provides the basis for the measurement of the oxygen concentration using a luminescence quenching technique. Assuming ideal Fickian diffusion, the ratio to/t is linked to the diffusion coefficient of oxygen [6]. The luminophore used in this study is the ruthenium complex: tris(4,7-diphenyl-1,10phenanthroline)ruthenium(II) dichloride complex, which has photo-stability, large Stokes shift enabling easy acquisition of intensity, and functionality across a large range of oxygen concentrations [14,26]. With maximum excitation wavelength of 455 nm, a blue light emitting diode (LED) can be used as the excitation light source. Using the above technique, oxygen transport from water to gelatine, for both un-crosslinked and chemically crosslinked gelatine, were examined. A mass transfer-diffusion numerical model was then used to fit the data and determine the oxygen diffusion coefficient in the different gelatine gels, as well as the mass transfer coefficient of oxygen at the water-gelatine interface. In order to determine what effect crosslinking has on the microstructure of gelatine gels, and relate that to the change in the gel’s oxygen diffusion properties, the gels were examined using scanning electron microscopy (SEM). 2. Materials and experimental methods 2.1. Preparation of ruthenium doped water solution Tris(4,7-diphenyl-1,10-phenanthroline)ruthenium(II) dichloride complex (Sigma Aldrich) was used as a luminophore. As the ruthenium complex is insoluble in water, ethanol, which is miscible with water, was used to dissolve the complex before being mixed with water. A solution for the ruthenium complex was made by dissolving 1 mg of the complex in 1 ml of ethanol; once the complex was dissolved, the solution was mixed with 100 ml deionised water to form a fully miscible system. The ruthenium solution was deoxygenated by bubbling nitrogen gas through it for a prolonged period (in excess of three hours for a 10 ml solution). The experimental procedures were carried out in an oxygen-free glove box, and the oxygen in the solution was monitored using a dissolved oxygen electrode meter (HI 9143 HANNA Instruments). All preparations and storage of the solution were undergone in a dark environment to prevent photobleaching. 2.2. Preparation of ruthenium doped gelatine gels 2% w/v porcine gelatine (Sigma Aldrich) solutions in deionised-deoxygenated water were prepared and then mixed with deoxygenated ruthenium complex solution under stirring for 3 min, the solution was poured into a clear glass square container of 13mm 13mm base and 16 mm height and was allowed to cool and gel. To crosslink the gel, 1% and 1.5% w/v of deoxygenated glutaraldehyde solution (Sigma Aldrich) was used to cover the gel for a period of 2 h, which was found to be the optimum
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concentration and time needed for the gel to reach an ideal strength without dissolving in water at 37 C. Each gel was cast into a clear glass container of a 13mm 13mm square base and a 7 mm gel height. The gel was preconditioned by covering it with 5 mm layer of deoxygenated, deionised water and left overnight in the oxygen free glove-box to ensure a fully swollen gel. Finally, oxygen transport from water to gelatine gel was measured by covering the gel with the ruthenium solution to a height of 5 mm; the solution would be either saturated with atmospheric oxygen or deoxygenated and the container would be subsequently opened to the air. The luminescent intensity of the gel and the solution was then monitored over time. For microstructure analysis, un-crosslinked, 1% and 1.5% w/v glutaraldehyde crosslinked gelatine were examined using SEM. The gelatine samples were placed in a freezer at -20 C overnight and then submerged in liquid nitrogen before being freeze-dried overnight. The dried samples were sputter coated with 3nm of gold and platinum (40/60) and fixed onto conductive platforms stubs using silver paste. The samples were then viewed using SEM (Hitachi S3200). 2.3. Monitoring luminescent intensity oxygen quenched ruthenium Fig. 1 shows the set up for the luminescence monitoring experiments. Each experiment involved two transparent glass containers, one in which the oxygen transport was monitored and a second container with a sealed deoxygenated system used as control. The two square containers were placed on a semi-transparent platform with 5 mm blue LEDs underneath, so that the semi-transparent platform would act as a light diffuser. A Lu105 1.3MPixel ½ inch CMOS-Sensor camera (FRAMOS imaging) was used for image acquisition. The containers were placed standing perpendicular to the camera used to capture the images.
The setup was inside a dark box eliminating any outside light, leaving the LED as the only excitation source for the ruthenium complex. The LEDs and the camera were connected to a DC power source and a computer, respectively, both placed outside the dark box so that they could be used to control the excitation and image acquisition remotely. To avoid photobleaching of the luminophore, the LEDs were switched on for an average of 10 seconds only when an image was taken, an image being taken approximately every 5 minutes. The LED voltage and current were set at 3.73 volts and 28 mA for all experiments and the images were taken with the autofocus and automatic image enhancements switched off. The software used to control the camera and capture the images was LuCAM Capture. The ruthenium complex absorbs blue light and emits red, hence each image was scanned and the red values were recorded for each pixel using MATLAB. Each image was meshed using a grid of 4 4 pixel squares (291 291 mm) and each square was allocated an average red value from its 16 pixels. Columns of single squares were then considered from the sample’s surface inwards towards the bulk of the sample for every image taken. Fig. 2 shows such a column of 4 100 pixels or of 25 4 4 pixel squares, and its colour map as a function of time every 50 min: at time ¼ 0 the gel is deoxygenated and then, as time passes, oxygen is transferred at the surface (top) of the gel and diffuses through the gel (downwards), which is illustrated in Fig. 2 by a high red intensity at time ¼ 0 emitted by the luminescent gel which decreases with time as oxygen concentration increases and quenches the luminescence, which means that there is less red intensity emitted, and a more bluish hue replaces the initial red tinge. For accurate spatial measurement of the oxygen concentration, the system needed to take into account a number of variables, namely, the optical density of the samples (which might change with experiment), as well as any inhomogeneity in light distribution across the depth of the sample (with the light source giving more light to the
Fig. 1. Diagram of the experimental set up for monitoring luminescence intensity.
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Fig. 2. Images of the same column (4 100 pixels) of the gel as a function of time at 50 minute intervals, where the initially deoxygenated gel was exposed to oxygen transport from the surface (top of the column).
bottom of the sample compared to the top). These issues were addressed by measuring the oxygen concentration using the normalised drop of intensity (I/I0) from the original intensity of every pixel, rather than an overall initial measurement. A calibration curve of the normalised red value against known oxygen concentrations in the water solution was established. First of all, the two extreme points of the range of any experiments were obtained: the normalised red value in ruthenium doped deoxygenated water and the normalised red value in ruthenium doped water fully saturated with oxygen. Using an oxygen probe (Hanna instruments HI9143), the intermediate points in the calibration curve were obtained by allowing the ruthenium doped deoxygenated water to absorb oxygen under normal atmospheric conditions at room temperature, while the oxygen concentration in the solution was monitored with the oxygen meter. The inter-sample variability for 5 columns in one sample, and the inter-sample variability for 3 independent experiments, were combined using the square root method to calculate the average combined standard deviation for oxygen concentration in un-crosslinked, and crosslinked gelatine gels. This error in incorporated in the error bar per each data point of the graphs for gels in Figs. 5e10.
Fig. 3. Calibration line (line of best fit) for the normalised red intensity values of the tris (4, 7-diphenyl-1, 10-phenanthroline) ruthenium (II) dichloride luminescent dye in water as a function of oxygen concentration, where oxygen acts as luminescence quencher. (Data points are the experimental data).
Fig. 4. Experimental data and numerical predictions of oxygen concentration across the water body as a function of time at different distances from the air-water interface, where the numerical model used a given boundary condition at x ¼ 0mm (which was the numerical fit of the experimental data at that position) and DO2-H2O ¼ 2 105 cm2 s1.
3. Numerical modelling A mass transfer-diffusion model has been used to model the unsteady-state oxygen mass transport across interfaces and in the bulk of materials. More specifically, Fick's second law of diffusion was used [24] to describe unsteady-state oxygen mass transport in the bulk of materials such as gel, water or air:
vc v2 c ¼D 2 vt vx
(2)
where c is the oxygen concentration, t is time, D the diffusion coefficient and x is the position. A mass transfer flux boundary condition was applied at fluid-gel interfaces, so that the mass transfer flux is equal to the diffusion flux in the gel at the interface:
vc kc cwater;bulk ci ¼ D vx i
(3)
kc is the mass transfer coefficient. The finite element analysis software COMSOL-Multiphysics was used for the numerical simulations of the oxygen mass transport to determine an appropriate diffusion coefficient and mass transfer coefficient so that the numerical results fit the experimental data. Equation (3) was suitable for the fitting of experimental data in the case of un-crosslinked gelatine but it was difficult to find a suitable mass transfer coefficient at the water-gel interface to best fit the experimental data in both cases of crosslinked gelatines. As a result, the thin boundary layer approach was used, where a third domain is assumed between the water and the gel. The domain has an initial concentration of oxygen saturated water on its top surface (in contact with water), and no oxygen at its bottom surface. This allows for mass flux continuity through the domain. The diffusion coefficient of the domain is changed using trial and error, until the best fit to the experimental data is achieved. The thin boundary layer had a thickness xlayer and diffusion coefficient Dlayer so that the mass transfer coefficient in Equation (3) could be expressed as:
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Fig. 5. Predictions and experimental data of unsteady-state oxygen transport in un-crosslinked gelatine from initially deoxygenated un-crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Un-crosslinked gelatine ¼ 0.75 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
kc ¼
Dlayer xlayer
(4)
4. Results and discussion To rule out the photobleaching effect as the cause of quenching of the luminophore, the red light intensity was
monitored in oxygen-free and fully saturated water bodies and gelatines subjected to continuous light excitation, using the blue LED, for periods over 100 minutes (considerably longer than the 10 second pulses used to capture the luminescence). The measured red light emission intensity (I/I0) showed no significant change in all four examples for the whole period, with an average fluctuation of ±3% for both water and gelatine gels.
Fig. 6. Predictions and experimental data of unsteady-state oxygen transport in un-crosslinked gelatine from initially deoxygenated un-crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Un-crosslinked gelatine ¼ 0.75 106 cm2/s and kc,O2-Un-crosslinked gelatine ¼ 2.9 106 cm s1at the air-gel interface.
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Fig. 7. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked with 1% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
A linear fit (R2 ¼ 0.96) of the red light emission intensity (I/I0) versus the known oxygen concentration range (no oxygen to fully saturated with oxygen) in the calibration curve was used to calculate the Stern-Volmer constant for oxygen in water as K ¼ 1.79 ± 0.01 l/mol (Fig. 3). This was
used to convert the normalised red intensity data, I/Io, into oxygen concentration curves across the length of the tested samples for both water and gelatine gels. Combined average standard deviations of 4.5% and 11% were found for un-crosslinked and crosslinked gelatine, respectively.
Fig. 8. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked using 1% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2/s and kc,O2-Crosslinked gelatine 1% 7 cm s1at the air-gel interface, using the thin boundary layer approach with a thin layer thickness of 3 103 cm and a thin layer diffusion Glutar. ¼ 5.5 10 coefficient of 1.65 109 cm2 s1.
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Fig. 9. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked with 1.5% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 7 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
coefficient in dilute solutions is established using the Wilke and Chang equation [25] which is based on the StokesEinstein equation for dilute solutions:
Before the numerical model or the experimental technique can be used to calculate the oxygen transfer through gelatine systems they were validated by measuring and predicting the oxygen concentration through a body of water in the same environment (zero oxygen at time ¼ 0 before allowing for atmospheric oxygen). Oxygen diffusion
D02 H2 o ¼ 7:4 108
Fig. 10. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked using 1.5% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1.5%Glutar. ¼ 7 106 cm2/s and kc,O2-Crosslinked gelatine 1.5%Glutar. ¼ 2 107 cm s1 at the air-gel interface, using the thin boundary layer approach with a thin layer thickness of 7 104 cm and a thin layer diffusion coefficient of 1.45 1010 cm2 s1.
where T is the absolute temperature, jH2o is a parameter for the solvent in this case water ¼ 2.26 [4], MH2 o is the molecular weight of water 18g/mol, m is the viscosity of water and VO2 is the molar volume of oxygen 25.6 cm3/gmol. According to Equation (5), the diffusion coefficient of oxygen in water is 2 105 cm2/s at room temperature of 23 C. Using this value of diffusion coefficient of oxygen in water, a computer simulation was carried out of the unsteady-state oxygen diffusion in water, where the water was initially deoxygenated and at time ¼ 0 its top surface was exposed to atmospheric oxygen. A dynamic boundary condition was used for the oxygen concentration at the water surface obtained from a best fit of the experimental concentration data at the surface. Fig. 4 presents the predicted concentration profiles at two positions away from the air-water interface as a function of time, and their comparison with the corresponding experimental data. The agreement is good and certainly within the fluctuations of the experimental data (it is believed that such fluctuations in water maybe due to natural convection given its fluid character). This demonstrates that the methodology developed in this study for the use of the luminescence quenching technique for monitoring oxygen concentration is suitable in the case of fast oxygen diffusion in water, and
T jH2 o MH2 o mVo0:6 2
1=2 (5)
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it is expected to be at least as equally reliable, if not more accurate, in the case of gelatine, which benefits from slower diffusion than water as well as the encapsulation of the luminophore. The next step was to monitor oxygen transport in un-crosslinked gelatine gels to determine the diffusion coefficient and mass transfer coefficient of oxygen in uncrosslinked gelatine. An initially deoxygenated uncrosslinked gelatine gel, cast in a clear glass container, was covered with oxygen saturated water at time ¼ 0, and the oxygen concentration was monitored at all points in the gel as a function of time on the basis of the red intensity map, as described in section 2.3. An initial set of numerical simulations was used to determine the diffusion coefficient of oxygen in un-crosslinked gelatine; this is achieved by using a prescribed boundary condition. The boundary condition was the oxygen concentration in the gel at the water-gel interface, calculated based on a numerical fit of the experimental data at a point in the gel that is closest to that boundary. This allows for the estimation of the diffusion coefficient along the gelatine body bulk. Finally, the bulk diffusion coefficient can be used in a following simulation to calculate the mass transfer across the boundary. Fig. 5 presents the experimental data and the corresponding predictions for a diffusion coefficient of DO2-Un6 cm2s1, which was the opticrosslinked gelatine ¼ 0.75 10 mum value (to ±0.25 106 cm2s1, the resolution in the values used for D in the trial-error-procedure of numerical simulations) for the best fit of the predictions to the experimental data. The next step was to use the full mass transferdiffusion numerical model with mass transfer at the watergel interface controlled by the mass transfer coefficient (Equation 3) determined by trial-and-error numerical simulations to fit the experimental data as best as possible. Fig. 6 presents the best predictions and their comparison with the experimental data, where the diffusion coefficient is DO2-Un6 cm2s1 and the mass transfer crosslinked gelatine ¼ 0.75 10 coefficient is kc,O2-Un-crosslinked gelatine ¼ 2.9 106 cm s1. This experimental and numerical process for monitoring oxygen transport and the determination of the diffusion coefficient and mass transfer coefficient of oxygen was then repeated for the chemically crosslinked gelatine samples. Figs. 7 and 8 refer to gelatine crosslinked using 1% glutaraldehyde for 2 hours. Fig. 7 presents the experimental data of the oxygen concentration profiles, and the best fitting predictions using a diffusion coefficient of 3.5 106 cm2s1. The boundary condition used as the approximate oxygen concentration at the gel surface was taken from the numerical fit of the experimental data at the closest point to the air-gel interface. Equation (3) using just the mass transfer coefficient of oxygen at the water-gel interface proved inadequate for best fitting the experimental data for both cases of crosslinked gelatine gels. As a result, the thin boundary layer approach (Equation 4) was used in both these cases. Fig. 8 shows the predictions using a diffusion coefficient DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2s1, a thin layer thickness of 3 103 cm and a thin layer diffusion coefficient of 1.65 109 cm2 s1, where the two latter parameters yield an equivalent mass transfer coefficient of kc,O2-Crosslinked gelatine 1%Glutar. ¼ 5.5 107 cm s1. Increasing
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the concentration of the crosslinking agent to 1.5% glutaraldehyde, again for 2 hours of crosslinking, doubles the rate of oxygen diffusion through the crosslinked gel to DO26 cm2s1 (Fig. 9) but reCrosslinked gelatine 1.5%Glutar. ¼ 7 10 duces the equivalent mass transfer coefficient to kc,O2-Cross7 cm s1. The thin boundary linked gelatine 1.5%Glutar. ¼ 2 10 layer approach yielded a thin layer thickness of 7 104 cm and a thin layer diffusion coefficient of 1.45 1010 cm2 s1 (Fig. 10). In general, the results show that crosslinking of gelatine and an increased concentration of the crosslinking agent lead to a reduction of the oxygen concentration in the gel, as expected. The results reveal that this is due to a decrease in the mass transfer of oxygen across the water-gel interface; once the oxygen has been transferred into the gel, crosslinking and an increase of the concentration of the crosslinking agent result in an increase in the diffusion coefficient of oxygen in the crosslinked gel. An increase of the diffusion coefficient with crosslinking has also been previously reported [18] for the diffusion of oxygen in crosslinked poly(vinyl alcohol) gels and in gelatine with physical crosslinks [11]. While the numerical model assumes a homogenous gel structure, and offers an approximate global oxygen diffusion coefficient calculation, the higher fluctuations of oxygen concentration profiles in crosslinked gelatine compared to their un-crosslinked counterparts, demonstrate heterogeneity of the crosslinked gelatine structure. Another indication of the heterogeneity of the gel after crosslinking is the reported sharp rise in oxygen concentration in crosslinked samples (Figs. 7e10) in the first 20 minutes of the experiment before a drop in the oxygen concentration. Higher oxygen mobility through physically crosslinked gelatine was similarly measured, and also believed to be due to heterogeneities in the matrix structure compared to uncrosslinked uniformly packed matrix in gelatine films, by Lukasik and Ludescher [11]. In their case, they detected such matrix heterogeneities in the factor of distribution of decay times of the phosphorescent dye. SEM was carried out for freeze-dried gels in this study to further elucidate this effect. Fig. 11 shows SEM images of a freeze-dried un-crosslinked gelatine gel. The cast gel is relatively dense and homogeneous, with tubular growth normal to the surface where the parallel tubular spaces are of about 3 mm diameter. For gelatine crosslinking using 1% glutaraldehyde for 2h, the bulk of the crosslinked gel has regular large spaces of an average 140 mm length (Fig. 12), which become even larger, averaging 400 mm in length for crosslinked gelatine using 1.5% glutaraldehyde for 2 h. It seems that crosslinking pulls the gelatine chains and gelatine fibres together in a random manner, disturbing the original parallel tubular orientation perpendicular to the surface, and resulting in a more random crosslinked structure. The shrinkage induced by the crosslinking generates internal stresses which lead to tears in the gel and generates large free spaces that accelerate oxygen diffusion, now water filled voids in the crosslinked gelatine structure. It is believed that this causes preferential wide pathways for oxygen transport. On the other hand, the crosslinking at the gel free surface is dense as it is exposed directly and fully to the crosslinking agent, so the equivalent mass
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Fig. 11. SEM of freeze-dried uncrosslinked gelatin gel; the low magnification image displays the surface of the cast gel, the higher magnification of the gelatine demonstrated its homogenous structure.
Fig. 12. SEM of freeze-dried crosslinked gelatin gel, where crosslinking was carried out using 1% glutaraldehyde for 2 h; the lower magnification image displays the heterogeneity of the gelatine microstructure, the higher magnification image demonstrates the pores created by the stresses caused because of crosslinking.
transfer coefficient of oxygen at the gel surface is reduced with crosslinking. 5. Conclusions A simple, low cost, non-invasive oxygen monitoring technique has been developed based on luminescence quenching of oxygen in gelatine. The experimental technique was combined with numerical modelling, using unsteady state diffusion in the bulk of the gel and mass transfer at the gel surface to determine the diffusion coefficient and mass transfer coefficient of oxygen. The methodology was validated by monitoring dynamically unsteady-state oxygen transport in water and determining the diffusion coefficient of oxygen in water as 2 105 cm2s1. The results of oxygen diffusion across bulk fully hydrated gelatine gels was determined to be 0.7 106 cm2s1 and 3.5-7 106 cm2s1 for un-crosslinked and crosslinked gelatine, respectively, about two orders of magnitude faster than those measured in dry gelatine films. SEM of freeze-dried gels revealed the densely packed, homogeneous, tubular structure of the uncrosslinked gelatine gel with the parallel tubular spaces of about 3 mm diameter perpendicular to the gel surface. Crosslinking and increased concentration of crosslinking agent lowered mass transfer across the gel surface, whereas
both factors increased the diffusion coefficient of oxygen in the crosslinked gel. This is explained by crosslinking induced shrinkage in the gelatine's structure, creating large free spaces in the gelatine structure that caused multiscale diffusion and accelerated the overall diffusion process. Acknowledgements The authors would like to gratefully acknowledge the funding of this project by the University of Surrey-NPL Partnership (2008-PhD1). References [1] O.A. Boubriak, J.P. Urban, Z. Cui, Monitoring of metabolite gradients in tissue-engineered constructs, Journal of The Royal Society, Interface/The Royal Society 3 (10) (2006) 637e648. [2] L. Corstorphine, M.V. Sefton, Effectiveness factor and diffusion limitations in collagen gel modules containing HepG2 cells, Journal of Tissue Engineering and Regenerative Medicine 5 (2) (2011) 119e129. [3] T.I. Croll, S. Gentz, K. Mueller, M. Davidson, A.J. O'Connor, G.W. Stevens, J.J. Cooper-White, Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications, Chemical Engineering Science 60 (17) (2005) 4924e4934. [4] J.L. Drury, D.J. Mooney, Hydrogels for tissue engineering: scaffold design variables and applications, Biomaterials 24 (24) (2003) 4337e4351.
Y. Elsayed et al. / Polymer Testing 40 (2014) 106e115 [5] W.H. Eaglstein, V. Falanga, Tissue engineering and the development of Apligraf a human skin equivalent, Advances in Wound Care: The Journal for Prevention and Healing 11 (Suppl. 4) (1998) 1e8. [6] S. Fischkoff, J.M. Vanderkooi, Oxygen diffusion in biological and artificial membranes determined by the fluorochrome pyrene, The Journal of General Physiology 65 (5) (1975) 663e676. [7] A.C. Guyton, J.C. Hall, Textbook of Medical Physiology, 1996. [8] H. Hiemstra, L. Dijkhuizen, W. Harder, Diffusion of oxygen in alginate gels related to the kinetics of methanol oxidation by immobilized Hansenula polymorpha cells, European Journal of Applied Microbiology and Biotechnology 18 (4) (1983) 189. [9] D. Lamprou, P. Zhdan, F. Labeed, C. Lekakou, Gelatine and gelatine/ elastin nanocomposites for vascular grafts: processing and characterization, Journal of Biomaterials Applications 26 (2) (2011) 209e226. [10] C. Lekakou, D. Lamprou, U. Vidyarthi, E. Karopoulou, P. Zhdan, Structural hierarchy of biomimetic materials for tissue engineered vascular and orthopedic grafts, Journal of Biomedical Materials Research. Part B, Applied Biomaterials 85 (2) (2008) 461e468. [11] K.V. Lukasik, R.D. Ludescher, Molecular mobility in water and glycerol plasticized cold- and hot-cast gelatin films, Food Hydrocolloids 20 (1) (2006) 96e105. [12] J. Malda, T.B. Woodfield, F. van der Vloodt, F.K. Kooy, D.E. Martens, J. Tramper, C.A. van Blitterswijk, J. Riesle, The effect of PEGT/PBT scaffold architecture on oxygen gradients in tissue engineered cartilaginous constructs, Biomaterials 25 (26) (2004) 5773e5780. [13] S. Nyberg, S. Santilli, R. Shatford, F. Cerra, D. Knighton, W. Hu, Microelectrode measurement of oxygen tensions in collagenhepatocyte gels, Biotechnology Techniques 5 (6) (1991) 449. [14] D.P. O'Neal, M.A. Meledeo, J.R. Davis, B.L. Ibey, V.A. Gant, M.V. Pishko, G.L. Cote, Oxygen sensor based on the fluorescence quenching of a ruthenium complex immobilized in a biocompatible poly(ethylene glycol) hydrogel, Sensors Journal, IEEE 4 (6) (2004) 728e734. [15] E. Permyakov, Luminescent Spectroscopy of Proteins, CRC Press, 1992.
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[16] L. Poulsen, I. Zebger, P. Tofte, M. Klinger, O. hassager, P.R. Ogilby, Oxygen diffusion in bilayer polymer films, The Journal of Physical Chemistry B 107 (50) (2003) 13885. [17] E. Sachlos, J.T. Czernuszka, Making tissue engineering scaffolds work. Review: the application of solid freeform fabrication technology to the production of tissue engineering scaffolds, European Cells & Materials 5 (2003) 29e39 discussion 39e40. [18] N.B. Schack, C.L. Oliveira, N.W. Young, J.S. Pedersen, P.R. Ogilby, Oxygen diffusion in cross-linked, ethanol-swollen poly(vinyl alcohol) gels: counter-intuitive results reflect microscopic heterogeneities, Langmuir: The ACS Journal of Surfaces and Colloids 25 (2) (2009) 1148e1153. [19] B.G. Sengers, C.C. van Donkelaar, C.W. Oomens, F.P. Baaijens, Computational study of culture conditions and nutrient supply in cartilage tissue engineering, Biotechnology Progress 21 (4) (2005) 1252e1261. [20] K.V. Simon-Lukasik, R.D. Ludescher, Erythrosin B phosphorescence as a probe of oxygen diffusion in amorphous gelatin films, Food Hydrocolloids 18 (4) (2004) 621e630. [21] K. Sisson, C. Zhang, M.C. Farach-Carson, D.B. Chase, J.F. Rabolt, Evaluation of cross-linking methods for electrospun gelatin on cell growth and viability, Biomacromolecules 10 (7) (2009) 1675e1680. [22] B. Starly, A. Choubey, Enabling sensor technologies for the quantitative evaluation of engineered tissue, Annals of Biomedical Engineering 36 (1) (2008) 30e40. [23] G. Vunjak-Novakovic, L.E. Freed, Culture of organized cell communities, Advanced Drug Delivery Reviews 33 (1-2) (1998) 15e30. [24] J. Welty, C. Wicks, G. Rorrer, R. Wilson, Fundamentals of Momentum, Heat and Mass Transfer, fifth ed., Wiley, 2008. [25] C.R. Wilke, P. Chang, Correlation of diffusion coefficients in dilute solutions, AIChE Journal 1 (2) (1955) 264e270. [26] X. Xiong, D. Xiao, M.M.F. Choi, Dissolved oxygen sensor based on fluorescence quenching of oxygen-sensitive ruthenium complex immobilized on silicaeNieP composite coating, Sensors and Actuators B: Chemical 117 (1) (2006) 172e176.
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
Monitoring and modelling of oxygen transport through un-crosslinked and crosslinked gelatine gels Y. Elsayed a, *, C. Lekakou a, P. Tomlins b a b
Division of Mechanical, Medical and Aerospace Engineering University of Surrey, Guildford GU2 7XH, UK National Physical Laboratory (NPL), Teddington, Middlesex, TW11 0LW, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 July 2014 Accepted 27 August 2014 Available online 6 September 2014
A non-invasive, luminescence quenching technique is developed for continuous monitoring of oxygen spatial-temporal concentration distribution in fully hydrated gelatine gels, intended for use as scaffolds in tissue engineering. Two mass transfer-diffusion models were used to simulate the unsteady-state oxygen mass transport in the system. Oxygen diffusion coefficient and mass transfer coefficient at the water-gel interface were determined for un-crosslinked gelatine, as well as gelatine crosslinked with 1 and 1.5% w/v glutaraldehyde. While crosslinking and increased concentration of the crosslinking agent reduced oxygen mass transfer across the gel surface, both factors increased the diffusion coefficient of oxygen in the bulk of the gel. Voids in the gelatine's microstructure, which were generated during the crosslinking process due to shrinkage and associated internal stresses, were associated with both increasing the diffusion coefficient within the gel, as well as inhomogeneous diffusion of oxygen within the gel. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Crosslinked gelatine Oxygen diffusion coefficient Fluorescent quenching imaging Scanning electron microscopy
1. Introduction The success of scaffold-based tissue engineering has been always limited by the availability of nutrients, growth factors and sufficient oxygen exchange between the cell culture medium and the cells [2,22]. The optimisation of the design of the three-dimensional constructs and their environment in a tissue engineering bioreactor relies on the understanding and the monitoring of the transport of these nutrients to the cells. Oxygen supply to the cells has been shown to be the main limiting factor in their survival [17]. The two main success stories of tissue engineering, are skin [5] and cartilage [23], these examples had the advantage of not being limited by oxygen. The former is not required to be very thick allowing oxygen to diffuse along only a short distance to the cells, while for tissue engineering of * Corresponding author. E-mail addresses: [email protected], yahya_elsayed@hotmail. com (Y. Elsayed). http://dx.doi.org/10.1016/j.polymertesting.2014.08.016 0142-9418/© 2014 Elsevier Ltd. All rights reserved.
cartilage, chondrocytes naturally require less oxygen than other cells, which is why they are the only cells that exist further away than 100mm from the blood supply in the human body [7]. The dependence on oxygen of other cell types used in tissue engineering, such as vascular grafts, has led to research into methods of monitoring and modelling the oxygen transport across scaffold materials [4,12,14] as well as the quantification of the diffusion coefficient of oxygen and other nutrients to be used in mathematical modelling of the tissue engineering process [1,3,19]. One material commonly used to make scaffolds for tissue engineering applications is gelatine [9,10], a denatured form of collagen, a naturally occurring triple helix polymer that is abundant in the extracellular matrix that cells grow on. Gelatine is produced by destroying the hydrogen bond holding the collagen’s triple helix structure. Because there are no covalent bonds holding the polymer strands in gelatine, a triple helical fold is developed with segments of different strains of poly-proline II like helices. This leaves space
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within the hydrogel's structure which allows for fluid retention in these voids, something advantageous for tissue engineering. This however makes gelatine susceptible to dissolving in water and has one drawback, low mechanical strength. One common solution that is adopted when using gelatine for scaffolds in tissue engineering is to further chemically crosslink the polymer chains using organic compounds such as glutaraldehyde and formaldehyde [21] so that the gels do not dissolve in the water-based culture medium and in the organism when implanted. Studies of oxygen diffusion across gelatine films yielded values of the order of 108 cm2s1 [11], generally referring to the gelatine in dry conditions or at different humidity levels (53-84 RH%) for vitrified gelatine, sometimes with physical crosslinks [14] but without any chemical crosslinks. However, for tissue engineering applications, a fully hydrated chemically crosslinked gelatine structure is used to grow the cells, a state which lacks detailed study of its molecular mobility and diffusion properties. This means that the diffusion coefficient of oxygen in hydrogels used in tissue engineering is sometimes approximated to the value of the diffusion coefficient of oxygen in water [19] DO25 cm2s1. The approximation is justified Water ¼ 2.6 10 by the interstitial space within the gelatine's structure which allows for a large extent of filling and swelling of the hydrogels by water. While some tissue engineering applications can justify such an approximation, for example oxygen diffusion coefficient in collagen-hepatocyte gels was measured to be DO2 ¼ 2.99 105 cm2s1 [13], on the other hand a relatively lower diffusion coefficient was measured in an alginate gel DO2 ¼ 7 106 cm2s1, even if it was 95% swollen with water [8]. The need for quantification of oxygen mobility in bulk hydrated gelatine gels is emphasised when comparing the order of magnitude difference between water (105 cm2s1), alginate gels (106 cm2s1) and those of un-wetted gelatine films (108 cm2s1). Today, most commercially available oxygen sensing techniques revolve around probing (both electrochemical and luminescent based) which has the drawback of being invasive to the material under investigation, affecting the transport process in the vicinity of the probe and, in the case of the electrochemical sensors, consumption of oxygen can affect the results [14]. Imaging of the spatial-temporal oxygen concentrations across the hydrogel's depth is possible with the use of an appropriate phosphorescence or luminescent dye, and has been reported in literature to investigate the oxygen diffusion in gelatine films [11,18,20], as well as measuring the transport of oxygen across the boundary of two separate polymer films [16]. This is promising because of the low opacity, near transparency of gelatine hydrogels, even after crosslinking. One possibility is to use an oxygen quenched luminophore. Oxygen quenching is the decrease of luminescent intensity due to the presence of a quencher, such as oxygen, and is governed by the Stern-Volmer equation [15]:
to =t ¼ Io =I ¼ 1 þ K c
(1)
Io and I are the luminescent intensities in the absence and in the presence of the quenching substance of concentration c,
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respectively, to and t are the respective luminescent lifetimes, and K is the Stern-Volmer constant. The linear relationship between to/t or Io/I and the concentration of the quenching substance (oxygen in this case) provides the basis for the measurement of the oxygen concentration using a luminescence quenching technique. Assuming ideal Fickian diffusion, the ratio to/t is linked to the diffusion coefficient of oxygen [6]. The luminophore used in this study is the ruthenium complex: tris(4,7-diphenyl-1,10phenanthroline)ruthenium(II) dichloride complex, which has photo-stability, large Stokes shift enabling easy acquisition of intensity, and functionality across a large range of oxygen concentrations [14,26]. With maximum excitation wavelength of 455 nm, a blue light emitting diode (LED) can be used as the excitation light source. Using the above technique, oxygen transport from water to gelatine, for both un-crosslinked and chemically crosslinked gelatine, were examined. A mass transfer-diffusion numerical model was then used to fit the data and determine the oxygen diffusion coefficient in the different gelatine gels, as well as the mass transfer coefficient of oxygen at the water-gelatine interface. In order to determine what effect crosslinking has on the microstructure of gelatine gels, and relate that to the change in the gel’s oxygen diffusion properties, the gels were examined using scanning electron microscopy (SEM). 2. Materials and experimental methods 2.1. Preparation of ruthenium doped water solution Tris(4,7-diphenyl-1,10-phenanthroline)ruthenium(II) dichloride complex (Sigma Aldrich) was used as a luminophore. As the ruthenium complex is insoluble in water, ethanol, which is miscible with water, was used to dissolve the complex before being mixed with water. A solution for the ruthenium complex was made by dissolving 1 mg of the complex in 1 ml of ethanol; once the complex was dissolved, the solution was mixed with 100 ml deionised water to form a fully miscible system. The ruthenium solution was deoxygenated by bubbling nitrogen gas through it for a prolonged period (in excess of three hours for a 10 ml solution). The experimental procedures were carried out in an oxygen-free glove box, and the oxygen in the solution was monitored using a dissolved oxygen electrode meter (HI 9143 HANNA Instruments). All preparations and storage of the solution were undergone in a dark environment to prevent photobleaching. 2.2. Preparation of ruthenium doped gelatine gels 2% w/v porcine gelatine (Sigma Aldrich) solutions in deionised-deoxygenated water were prepared and then mixed with deoxygenated ruthenium complex solution under stirring for 3 min, the solution was poured into a clear glass square container of 13mm 13mm base and 16 mm height and was allowed to cool and gel. To crosslink the gel, 1% and 1.5% w/v of deoxygenated glutaraldehyde solution (Sigma Aldrich) was used to cover the gel for a period of 2 h, which was found to be the optimum
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concentration and time needed for the gel to reach an ideal strength without dissolving in water at 37 C. Each gel was cast into a clear glass container of a 13mm 13mm square base and a 7 mm gel height. The gel was preconditioned by covering it with 5 mm layer of deoxygenated, deionised water and left overnight in the oxygen free glove-box to ensure a fully swollen gel. Finally, oxygen transport from water to gelatine gel was measured by covering the gel with the ruthenium solution to a height of 5 mm; the solution would be either saturated with atmospheric oxygen or deoxygenated and the container would be subsequently opened to the air. The luminescent intensity of the gel and the solution was then monitored over time. For microstructure analysis, un-crosslinked, 1% and 1.5% w/v glutaraldehyde crosslinked gelatine were examined using SEM. The gelatine samples were placed in a freezer at -20 C overnight and then submerged in liquid nitrogen before being freeze-dried overnight. The dried samples were sputter coated with 3nm of gold and platinum (40/60) and fixed onto conductive platforms stubs using silver paste. The samples were then viewed using SEM (Hitachi S3200). 2.3. Monitoring luminescent intensity oxygen quenched ruthenium Fig. 1 shows the set up for the luminescence monitoring experiments. Each experiment involved two transparent glass containers, one in which the oxygen transport was monitored and a second container with a sealed deoxygenated system used as control. The two square containers were placed on a semi-transparent platform with 5 mm blue LEDs underneath, so that the semi-transparent platform would act as a light diffuser. A Lu105 1.3MPixel ½ inch CMOS-Sensor camera (FRAMOS imaging) was used for image acquisition. The containers were placed standing perpendicular to the camera used to capture the images.
The setup was inside a dark box eliminating any outside light, leaving the LED as the only excitation source for the ruthenium complex. The LEDs and the camera were connected to a DC power source and a computer, respectively, both placed outside the dark box so that they could be used to control the excitation and image acquisition remotely. To avoid photobleaching of the luminophore, the LEDs were switched on for an average of 10 seconds only when an image was taken, an image being taken approximately every 5 minutes. The LED voltage and current were set at 3.73 volts and 28 mA for all experiments and the images were taken with the autofocus and automatic image enhancements switched off. The software used to control the camera and capture the images was LuCAM Capture. The ruthenium complex absorbs blue light and emits red, hence each image was scanned and the red values were recorded for each pixel using MATLAB. Each image was meshed using a grid of 4 4 pixel squares (291 291 mm) and each square was allocated an average red value from its 16 pixels. Columns of single squares were then considered from the sample’s surface inwards towards the bulk of the sample for every image taken. Fig. 2 shows such a column of 4 100 pixels or of 25 4 4 pixel squares, and its colour map as a function of time every 50 min: at time ¼ 0 the gel is deoxygenated and then, as time passes, oxygen is transferred at the surface (top) of the gel and diffuses through the gel (downwards), which is illustrated in Fig. 2 by a high red intensity at time ¼ 0 emitted by the luminescent gel which decreases with time as oxygen concentration increases and quenches the luminescence, which means that there is less red intensity emitted, and a more bluish hue replaces the initial red tinge. For accurate spatial measurement of the oxygen concentration, the system needed to take into account a number of variables, namely, the optical density of the samples (which might change with experiment), as well as any inhomogeneity in light distribution across the depth of the sample (with the light source giving more light to the
Fig. 1. Diagram of the experimental set up for monitoring luminescence intensity.
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Fig. 2. Images of the same column (4 100 pixels) of the gel as a function of time at 50 minute intervals, where the initially deoxygenated gel was exposed to oxygen transport from the surface (top of the column).
bottom of the sample compared to the top). These issues were addressed by measuring the oxygen concentration using the normalised drop of intensity (I/I0) from the original intensity of every pixel, rather than an overall initial measurement. A calibration curve of the normalised red value against known oxygen concentrations in the water solution was established. First of all, the two extreme points of the range of any experiments were obtained: the normalised red value in ruthenium doped deoxygenated water and the normalised red value in ruthenium doped water fully saturated with oxygen. Using an oxygen probe (Hanna instruments HI9143), the intermediate points in the calibration curve were obtained by allowing the ruthenium doped deoxygenated water to absorb oxygen under normal atmospheric conditions at room temperature, while the oxygen concentration in the solution was monitored with the oxygen meter. The inter-sample variability for 5 columns in one sample, and the inter-sample variability for 3 independent experiments, were combined using the square root method to calculate the average combined standard deviation for oxygen concentration in un-crosslinked, and crosslinked gelatine gels. This error in incorporated in the error bar per each data point of the graphs for gels in Figs. 5e10.
Fig. 3. Calibration line (line of best fit) for the normalised red intensity values of the tris (4, 7-diphenyl-1, 10-phenanthroline) ruthenium (II) dichloride luminescent dye in water as a function of oxygen concentration, where oxygen acts as luminescence quencher. (Data points are the experimental data).
Fig. 4. Experimental data and numerical predictions of oxygen concentration across the water body as a function of time at different distances from the air-water interface, where the numerical model used a given boundary condition at x ¼ 0mm (which was the numerical fit of the experimental data at that position) and DO2-H2O ¼ 2 105 cm2 s1.
3. Numerical modelling A mass transfer-diffusion model has been used to model the unsteady-state oxygen mass transport across interfaces and in the bulk of materials. More specifically, Fick's second law of diffusion was used [24] to describe unsteady-state oxygen mass transport in the bulk of materials such as gel, water or air:
vc v2 c ¼D 2 vt vx
(2)
where c is the oxygen concentration, t is time, D the diffusion coefficient and x is the position. A mass transfer flux boundary condition was applied at fluid-gel interfaces, so that the mass transfer flux is equal to the diffusion flux in the gel at the interface:
vc kc cwater;bulk ci ¼ D vx i
(3)
kc is the mass transfer coefficient. The finite element analysis software COMSOL-Multiphysics was used for the numerical simulations of the oxygen mass transport to determine an appropriate diffusion coefficient and mass transfer coefficient so that the numerical results fit the experimental data. Equation (3) was suitable for the fitting of experimental data in the case of un-crosslinked gelatine but it was difficult to find a suitable mass transfer coefficient at the water-gel interface to best fit the experimental data in both cases of crosslinked gelatines. As a result, the thin boundary layer approach was used, where a third domain is assumed between the water and the gel. The domain has an initial concentration of oxygen saturated water on its top surface (in contact with water), and no oxygen at its bottom surface. This allows for mass flux continuity through the domain. The diffusion coefficient of the domain is changed using trial and error, until the best fit to the experimental data is achieved. The thin boundary layer had a thickness xlayer and diffusion coefficient Dlayer so that the mass transfer coefficient in Equation (3) could be expressed as:
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Fig. 5. Predictions and experimental data of unsteady-state oxygen transport in un-crosslinked gelatine from initially deoxygenated un-crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Un-crosslinked gelatine ¼ 0.75 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
kc ¼
Dlayer xlayer
(4)
4. Results and discussion To rule out the photobleaching effect as the cause of quenching of the luminophore, the red light intensity was
monitored in oxygen-free and fully saturated water bodies and gelatines subjected to continuous light excitation, using the blue LED, for periods over 100 minutes (considerably longer than the 10 second pulses used to capture the luminescence). The measured red light emission intensity (I/I0) showed no significant change in all four examples for the whole period, with an average fluctuation of ±3% for both water and gelatine gels.
Fig. 6. Predictions and experimental data of unsteady-state oxygen transport in un-crosslinked gelatine from initially deoxygenated un-crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Un-crosslinked gelatine ¼ 0.75 106 cm2/s and kc,O2-Un-crosslinked gelatine ¼ 2.9 106 cm s1at the air-gel interface.
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Fig. 7. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked with 1% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
A linear fit (R2 ¼ 0.96) of the red light emission intensity (I/I0) versus the known oxygen concentration range (no oxygen to fully saturated with oxygen) in the calibration curve was used to calculate the Stern-Volmer constant for oxygen in water as K ¼ 1.79 ± 0.01 l/mol (Fig. 3). This was
used to convert the normalised red intensity data, I/Io, into oxygen concentration curves across the length of the tested samples for both water and gelatine gels. Combined average standard deviations of 4.5% and 11% were found for un-crosslinked and crosslinked gelatine, respectively.
Fig. 8. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked using 1% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2/s and kc,O2-Crosslinked gelatine 1% 7 cm s1at the air-gel interface, using the thin boundary layer approach with a thin layer thickness of 3 103 cm and a thin layer diffusion Glutar. ¼ 5.5 10 coefficient of 1.65 109 cm2 s1.
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Fig. 9. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked with 1.5% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1%Glutar. ¼ 7 106 cm2/s and dynamic surface boundary condition fitted according to the experimental data at the surface of the gel.
coefficient in dilute solutions is established using the Wilke and Chang equation [25] which is based on the StokesEinstein equation for dilute solutions:
Before the numerical model or the experimental technique can be used to calculate the oxygen transfer through gelatine systems they were validated by measuring and predicting the oxygen concentration through a body of water in the same environment (zero oxygen at time ¼ 0 before allowing for atmospheric oxygen). Oxygen diffusion
D02 H2 o ¼ 7:4 108
Fig. 10. Predictions and experimental data of unsteady-state oxygen transport in gelatine crosslinked using 1.5% glutaraldehyde, from initially deoxygenated crosslinked gelatine gel where at time ¼ 0 the top gel surface was covered with fully saturated water: oxygen concentration in the gel as a function of time for different distances from the water-gel interface. Numerical simulations with DO2-Crosslinked gelatine 1.5%Glutar. ¼ 7 106 cm2/s and kc,O2-Crosslinked gelatine 1.5%Glutar. ¼ 2 107 cm s1 at the air-gel interface, using the thin boundary layer approach with a thin layer thickness of 7 104 cm and a thin layer diffusion coefficient of 1.45 1010 cm2 s1.
where T is the absolute temperature, jH2o is a parameter for the solvent in this case water ¼ 2.26 [4], MH2 o is the molecular weight of water 18g/mol, m is the viscosity of water and VO2 is the molar volume of oxygen 25.6 cm3/gmol. According to Equation (5), the diffusion coefficient of oxygen in water is 2 105 cm2/s at room temperature of 23 C. Using this value of diffusion coefficient of oxygen in water, a computer simulation was carried out of the unsteady-state oxygen diffusion in water, where the water was initially deoxygenated and at time ¼ 0 its top surface was exposed to atmospheric oxygen. A dynamic boundary condition was used for the oxygen concentration at the water surface obtained from a best fit of the experimental concentration data at the surface. Fig. 4 presents the predicted concentration profiles at two positions away from the air-water interface as a function of time, and their comparison with the corresponding experimental data. The agreement is good and certainly within the fluctuations of the experimental data (it is believed that such fluctuations in water maybe due to natural convection given its fluid character). This demonstrates that the methodology developed in this study for the use of the luminescence quenching technique for monitoring oxygen concentration is suitable in the case of fast oxygen diffusion in water, and
T jH2 o MH2 o mVo0:6 2
1=2 (5)
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it is expected to be at least as equally reliable, if not more accurate, in the case of gelatine, which benefits from slower diffusion than water as well as the encapsulation of the luminophore. The next step was to monitor oxygen transport in un-crosslinked gelatine gels to determine the diffusion coefficient and mass transfer coefficient of oxygen in uncrosslinked gelatine. An initially deoxygenated uncrosslinked gelatine gel, cast in a clear glass container, was covered with oxygen saturated water at time ¼ 0, and the oxygen concentration was monitored at all points in the gel as a function of time on the basis of the red intensity map, as described in section 2.3. An initial set of numerical simulations was used to determine the diffusion coefficient of oxygen in un-crosslinked gelatine; this is achieved by using a prescribed boundary condition. The boundary condition was the oxygen concentration in the gel at the water-gel interface, calculated based on a numerical fit of the experimental data at a point in the gel that is closest to that boundary. This allows for the estimation of the diffusion coefficient along the gelatine body bulk. Finally, the bulk diffusion coefficient can be used in a following simulation to calculate the mass transfer across the boundary. Fig. 5 presents the experimental data and the corresponding predictions for a diffusion coefficient of DO2-Un6 cm2s1, which was the opticrosslinked gelatine ¼ 0.75 10 mum value (to ±0.25 106 cm2s1, the resolution in the values used for D in the trial-error-procedure of numerical simulations) for the best fit of the predictions to the experimental data. The next step was to use the full mass transferdiffusion numerical model with mass transfer at the watergel interface controlled by the mass transfer coefficient (Equation 3) determined by trial-and-error numerical simulations to fit the experimental data as best as possible. Fig. 6 presents the best predictions and their comparison with the experimental data, where the diffusion coefficient is DO2-Un6 cm2s1 and the mass transfer crosslinked gelatine ¼ 0.75 10 coefficient is kc,O2-Un-crosslinked gelatine ¼ 2.9 106 cm s1. This experimental and numerical process for monitoring oxygen transport and the determination of the diffusion coefficient and mass transfer coefficient of oxygen was then repeated for the chemically crosslinked gelatine samples. Figs. 7 and 8 refer to gelatine crosslinked using 1% glutaraldehyde for 2 hours. Fig. 7 presents the experimental data of the oxygen concentration profiles, and the best fitting predictions using a diffusion coefficient of 3.5 106 cm2s1. The boundary condition used as the approximate oxygen concentration at the gel surface was taken from the numerical fit of the experimental data at the closest point to the air-gel interface. Equation (3) using just the mass transfer coefficient of oxygen at the water-gel interface proved inadequate for best fitting the experimental data for both cases of crosslinked gelatine gels. As a result, the thin boundary layer approach (Equation 4) was used in both these cases. Fig. 8 shows the predictions using a diffusion coefficient DO2-Crosslinked gelatine 1%Glutar. ¼ 3.5 106 cm2s1, a thin layer thickness of 3 103 cm and a thin layer diffusion coefficient of 1.65 109 cm2 s1, where the two latter parameters yield an equivalent mass transfer coefficient of kc,O2-Crosslinked gelatine 1%Glutar. ¼ 5.5 107 cm s1. Increasing
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the concentration of the crosslinking agent to 1.5% glutaraldehyde, again for 2 hours of crosslinking, doubles the rate of oxygen diffusion through the crosslinked gel to DO26 cm2s1 (Fig. 9) but reCrosslinked gelatine 1.5%Glutar. ¼ 7 10 duces the equivalent mass transfer coefficient to kc,O2-Cross7 cm s1. The thin boundary linked gelatine 1.5%Glutar. ¼ 2 10 layer approach yielded a thin layer thickness of 7 104 cm and a thin layer diffusion coefficient of 1.45 1010 cm2 s1 (Fig. 10). In general, the results show that crosslinking of gelatine and an increased concentration of the crosslinking agent lead to a reduction of the oxygen concentration in the gel, as expected. The results reveal that this is due to a decrease in the mass transfer of oxygen across the water-gel interface; once the oxygen has been transferred into the gel, crosslinking and an increase of the concentration of the crosslinking agent result in an increase in the diffusion coefficient of oxygen in the crosslinked gel. An increase of the diffusion coefficient with crosslinking has also been previously reported [18] for the diffusion of oxygen in crosslinked poly(vinyl alcohol) gels and in gelatine with physical crosslinks [11]. While the numerical model assumes a homogenous gel structure, and offers an approximate global oxygen diffusion coefficient calculation, the higher fluctuations of oxygen concentration profiles in crosslinked gelatine compared to their un-crosslinked counterparts, demonstrate heterogeneity of the crosslinked gelatine structure. Another indication of the heterogeneity of the gel after crosslinking is the reported sharp rise in oxygen concentration in crosslinked samples (Figs. 7e10) in the first 20 minutes of the experiment before a drop in the oxygen concentration. Higher oxygen mobility through physically crosslinked gelatine was similarly measured, and also believed to be due to heterogeneities in the matrix structure compared to uncrosslinked uniformly packed matrix in gelatine films, by Lukasik and Ludescher [11]. In their case, they detected such matrix heterogeneities in the factor of distribution of decay times of the phosphorescent dye. SEM was carried out for freeze-dried gels in this study to further elucidate this effect. Fig. 11 shows SEM images of a freeze-dried un-crosslinked gelatine gel. The cast gel is relatively dense and homogeneous, with tubular growth normal to the surface where the parallel tubular spaces are of about 3 mm diameter. For gelatine crosslinking using 1% glutaraldehyde for 2h, the bulk of the crosslinked gel has regular large spaces of an average 140 mm length (Fig. 12), which become even larger, averaging 400 mm in length for crosslinked gelatine using 1.5% glutaraldehyde for 2 h. It seems that crosslinking pulls the gelatine chains and gelatine fibres together in a random manner, disturbing the original parallel tubular orientation perpendicular to the surface, and resulting in a more random crosslinked structure. The shrinkage induced by the crosslinking generates internal stresses which lead to tears in the gel and generates large free spaces that accelerate oxygen diffusion, now water filled voids in the crosslinked gelatine structure. It is believed that this causes preferential wide pathways for oxygen transport. On the other hand, the crosslinking at the gel free surface is dense as it is exposed directly and fully to the crosslinking agent, so the equivalent mass
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Fig. 11. SEM of freeze-dried uncrosslinked gelatin gel; the low magnification image displays the surface of the cast gel, the higher magnification of the gelatine demonstrated its homogenous structure.
Fig. 12. SEM of freeze-dried crosslinked gelatin gel, where crosslinking was carried out using 1% glutaraldehyde for 2 h; the lower magnification image displays the heterogeneity of the gelatine microstructure, the higher magnification image demonstrates the pores created by the stresses caused because of crosslinking.
transfer coefficient of oxygen at the gel surface is reduced with crosslinking. 5. Conclusions A simple, low cost, non-invasive oxygen monitoring technique has been developed based on luminescence quenching of oxygen in gelatine. The experimental technique was combined with numerical modelling, using unsteady state diffusion in the bulk of the gel and mass transfer at the gel surface to determine the diffusion coefficient and mass transfer coefficient of oxygen. The methodology was validated by monitoring dynamically unsteady-state oxygen transport in water and determining the diffusion coefficient of oxygen in water as 2 105 cm2s1. The results of oxygen diffusion across bulk fully hydrated gelatine gels was determined to be 0.7 106 cm2s1 and 3.5-7 106 cm2s1 for un-crosslinked and crosslinked gelatine, respectively, about two orders of magnitude faster than those measured in dry gelatine films. SEM of freeze-dried gels revealed the densely packed, homogeneous, tubular structure of the uncrosslinked gelatine gel with the parallel tubular spaces of about 3 mm diameter perpendicular to the gel surface. Crosslinking and increased concentration of crosslinking agent lowered mass transfer across the gel surface, whereas
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