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ZERO- ORDER KINETIC RELEASE FROM CAPSULE RESERVOIRS THROUGH SEMI-PERMEABLE MEMBRANES

Denise Bion, Matthew Blank, Dylan Freas, Craig Gambogi,

Demetris Rotsides, Sadik Shahidain, Daniel Ye, Barbara Zhan

Advisor: Dr. David Cincotta Assistant: Amanda Garfinkel

ABSTRACT

A vital goal of recent drug-delivery technology research involves inducing zero-order controlled-release, in which a liquid diffuses from the system into the surroundings at a constant rate. Based on the principle of drug-delivery microspheres embedded in a polymer matrix, a model was developed in which liquid-filled capsules in a membrane-covered Petri dish demonstrated pseudo-zero-order release across the semi-permeable membrane. Two organic liquids (acetone and pentane) were tested with two different capsule types (gelatin and pullulan) and three different polymer membranes (12% and 10% ethylene-vinyl acetate and polyethylene), with the diffusion accelerated by increasing the temperature in an oven. This research demonstrated that pseudo-zero order release can be achieved through a practical, medically-feasible approach. This lays the foundation of future studies in a novel zero-order release mechanism applied in drug transportation. INTRODUCTION Reaction Rates Most chemical reactions proceed at rates that are dependent on the concentrations of the reactants and catalysts involved. For the reaction aA + bB ==> cC, the rate can be readily calculated.

Rate Law of a Chemical Reaction:

where r is the rate, [A] and [B] represent the concentrations of A and B, respectively, and k is the rate constant of the reaction. x and y are not the coefficients of the balanced equation; rather, they are indicators of rate and must be determined experimentally.

A first-order reaction proceeds at a rate proportional to the concentration of one reactant. A second-order reaction proceeds at a rate proportional to the square of one reactant’s concentration or the product of two reactants’ concentrations, and so on. Zero-Order Reactions Unlike first and second order reactions, a zero-order reaction proceeds at a constant rate; its rate is thus independent of the reactant concentrations. Very few zero-order reactions occur in nature, and most known zero-order reactions are actually pseudo-zero-order reactions. These

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types of reactions may appear to proceed in a linear fashion, as shown in Figure 1, but are not truly zero-order.

Figure 1: This graph shows the linear change of concentration in a zero-order reaction

Though zero-order processes do not occur naturally, they have become a popular subject

of science research due to their potential influence in real-world applications. For example, current treatments involve the first-order delivery of toxins or enzymes into a patient’s bloodstream.1 Accordingly, immediately after injection, the drugs invade at near-toxic concentrations. As the injected concentration decreases, the bloodstream drug concentration rapidly decreases until the next infusion. This disastrous drug delivery method is used most often on cancer patients, where the toxicity of chemotherapeutic treatments causes deleterious side-effects.1 If a zero-order release mechanism were to be developed, the concentration of drugs inside the body could be delivered at a constant rate and thus maintained at safe and effective levels. Microspheres The application of zero-order release mechanisms to drug delivery systems was recently studied by a research team at Nanyang Technological University.2 The researchers attempted to achieve zero-order release by loading the experimental solute into microspheres and controlling the rate that solute diffused from the microspheres. Microspheres are composed of a hardened alginate solution with drug particles dissolved throughout the alginate. In this experiment, the drug tested was Bovine Serum Albumin (BSA) and the researchers attempted to control the rate of its release by immobilizing some BSA in a polyethylene-glycol (PEG) membrane. This immobilized drug would significantly limit the amount of BSA able to diffuse from the microspheres, making the microsphere act as an effectively unlimited drug source with only a limited rate of release.2 The researchers hypothesized that this would cause the drug to be released in a near zero-order rate. Without the BSA- immobilizing membrane, BSA was released from the microspheres in less than six hours at a first-order rate. However, when the microspheres were embedded in the

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membrane, the drug exhibited near- zero-order release over the course of approximately 70 hours. Immobilizing 5g/5ml of the drug in the membrane resulted in 170 hours of near-zero-order release, thus preventing the drug from coming close to the toxic levels found in contemporary medical treatment. In the experiment to be described in this paper, the original intention was to determine if the same results of the Nanyang lab’s BSA investigation could be achieved on a macro scale, with cheaper and more accessible vegetable (pullulan) and gelatin capsules representing the microspheres. However, due to time and resource constraints, the researchers involved with the present experiment were forced to utilize vapor pressure instead of drug immobilization to control the rate of diffusion through the capsules. Capsules In order to apply the foundational concepts behind the microsphere experiment to a model involving capsules, it is necessary to first gain a greater understanding of the properties of the capsules involved. Two types of capsules were utilized in this experiment: vegetable capsules and gel capsules.

The vegetable capsules used in this project were made of a polysaccharide called pullulan. Pullulan is a white, odorless, water-soluble powder that makes a clear and viscous solution.3 The polymer is highly adhesive and can form films. The hydroxyl -OH groups found throughout the molecule cause it to be moderately polar. This polarity enabled the vegetable capsules to allow similarly polar solvents to diffuse through them at quicker rates than non-polar capsules. The vegetable capsules were very easy to purchase, as they were found in most pharmacies in the area. Also, pullulan’s relatively high melting point, due to its hydrogen bonding, enables it to be used in a variety of temperatures without concern of the capsules melting.

The other type of capsule was composed of gelatin, a translucent protein substance derived from animal collagen. Gelatin’s solubility in hot water, its ability to cross-link, and its frequent use in strong, transparent gels, make it a very popular commodity in food processing and pharmaceuticals.4 Though the gelatin capsules’ usefulness in this experiment was limited by its low melting point along with its high degree of solubility in most polar solvents, it was included because of its strong structure; the gelatin capsules are much more durable than the pullulan capsules, and were thus much easier to work with and more reliable. Polymer Membranes

While the capsule membranes served to represent the microsphere component of the Nanyang BSA experiment, the research project described in this paper sought to mimic the occurrence of membrane-based diffusion through the use of various polymer membranes. A polymer is a macromolecule that consists of many smaller, chemically-bonded monomer units. The different morphologies, or molecular structures, of polymers account for their largely diverse physical properties. One clear example is found in the arrangement of monomer chains in the polymer. Generally, the monomers pack together in a non-uniform fashion, though some

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order is found in the “crystalline-like” sections, where linear polymer chains are structurally oriented in a uniform pattern. These “linear” polymers tend to be stronger and stiffer than those with more distorted and highly branched chains.

The structures of polymers are instrumental in determining a given polymer membrane’s permeability to specific molecules. In general, molecules cannot enter the linear, crystalline regions of a polymer but readily diffuse through the amorphous, highly-branched areas.5 This is because the tangled areas allow for greater transparency and flexibility, making it very easy for chemicals to enter and exit. A molecule’s ability to diffuse through a membrane is also determined by the polymer’s chain length. A general rule-of-thumb states that as chain size decreases, its ability to allow diffusion increases. The last factor that influences the polymer’s degree of crystallinity is the presence of inter-chain bonding. Polymers are much more likely to be crystalline with the presence of strong, polar bonds and intermolecular forces.6 In essence, a polymer with short, highly-branched chains and weak inter-chain bonds will barely be crystalline in structure, and will therefore allow for great diffusion through the membrane. Fick’s Law

Fick’s Law, the equation that summarizes most natural diffusion trends, states:

where D is the diffusivity coefficient, R is the universal gas constant, c is the concentration, u is the chemical potential, x is distance, and J is the diffusion flux or diffusion through a small area. Considering that most of the factors in the equation will remain constant over the course of the release across the membrane, concentration and diffusion flux will have an essentially linear relationship.7 This means that as concentration decreases over the course of the reaction the diffusion flux will decrease as well.

Noting this linear relationship between reactant concentration and diffusion flux, the challenge in keeping the rate of diffusion constant relates to keeping the reactant concentration constant as the process occurs.7 Thus, to achieve zero-order-release, it is necessary to maintain a constant reactant concentration. Solubility Parameters Acknowledging that the zero-order kinetics model used in this experiment depends on the movement of gaseous particles through polymer membranes, it was necessary to gain a qualitative understanding of the interactions of these two substances. The chance of a certain molecule passing through a specific membrane can be easily predicted through solubility parameters, mathematical tools that provide insight into the solubility of some material as it moves across a polymer membrane. There are two popular methods for finding the solubility parameters: Hildebrand’s model and Hansen’s model.

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The Hildebrand solubility parameter is a quantitative scale that estimates the extent of interaction between two or more different materials. This standard of measurement applies specifically to non-polar materials, such as polymers, and can be used to predict the solubility of one material in another.8 The Hansen solubility parameter is based upon Hildebrand’s model, but specifically tailored for polar materials, which made it more applicable for this experiment than the Hildebrand solubility parameter. The Hansen Solubility Parameters, is based on the principle of “like likes like.”9 There are three points that represent specific solvents and act as coordinates in a three dimensional space forming the radius of a sphere. The parameters are the energy from dispersion bonds ( 0) can be used to verify the range of parameters of the solvent and polymer. The distance formula used to calculate the space between the parameters is:

The interaction radius and the distance between parameters can be used to calculate the

relative energy difference, or RED, where 2. The similarity between parameters of two materials determines the degree of the interactions. The aggressiveness of organic liquids vary when diffusing through various polymers.9 This experiment applies Hansen Solubility parameters to predict how well the solvents in use can diffuse through a given polymer

(Hansen Book). For example, Table 1 illustrates the different polymers used during the experiment. Using the limits for RED, where if Ra/R0 is less than one, then the product is insoluble and if Ra/R0 is greater than one, then the product is soluble, one can calculate the parameter of the given liquid and the gel along with the liquid and membrane.

Table 1. This table shows the solubility parameters for the polymers and some solvents use during the experiment.

.

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HYPOTHESIS The goal of this experiment is to develop an apparatus for zero-order release based on controlled approaches of diffusion across capsule and polymer membranes. The major dependent variables that affect the rate of zero-order release are: the temperature of the apparatus used, the polymer membrane used, the polarity of the solvent used, and the capsule being used. This experiment aims to test if zero-order release across a polymer membrane is possible from a reservoir of liquid inside capsules. By having a reservoir of gas particles, equilibrium between the gaseous and liquid phases will be created, causing a constant vapor pressure. We hope that this data can later be used as a model for zero-order release mechanisms in the pharmaceutical industry. METHODS AND MATERIALS Finding a Solvent that Diffuses Through the Capsules The initial step of this experiment involved finding a solvent that would not break down the capsules but whose gaseous particles would diffuse across the capsule surface. To test the first requirement --that the solvent would not dissolve the capsules-- the capsules were placed inside vials filled with different kinds of liquids, including ethanol, acetone, propanol, pentane, heptane, and n-octane. The capsules didn’t dissolve in most of these solvents, so each remaining solvent was subject to further testing for its ability to diffuse through the capsules. Gel and vegetable capsules were then filled with the different types of the liquid mentioned. Afterwards, the capsules were filled with the candidate solvents and sealed with cyanoacrylate, which was experimentally determined to be the best method of capsule sealing. A group of vegetable and gel capsules were weighed initially and then let to sit in room temperature. Another batch of capsules was subjected to the same procedure and conditions, except they were placed in an oven at 37 °C. All of the capsules were massed periodically for the next two days. The results of this test revealed that the majority of the alcohols leaked through the capsules rather than exhibiting gaseous diffusion. However, acetone and pentane did diffuse through the capsules as gases, and thus were selected as the best solvents for the experiment. Determining Which Semi-Permeable Membranes to Use

A separate experiment was then conducted to test which membranes would be most likely to promote zero-order release in our final apparatus. Three different membranes were initially tested: Polyethylene, Ethylene Vinyl Acetate (EVA) with 10% Vinyl Acetate, and Ethylene Vinyl Acetate with 12% Vinyl Acetate. Ten milliliters acetone and pentane were added to Petri dishes. These Petri dishes were covered with the three different membranes and then massed periodically for one day. The Petri dish apparatus gradually decreased in mass due to diffusion. Final Experiment After collecting data about solvent characteristics, gluing technique, and membrane capabilities, an apparatus was designed to put our zero-order kinetics hypothesis to the test. The

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most volatile solvents were determined to be pentane and acetone, because from preliminary experiments, they diffused the quickest. Each liquid was tested with two different types of capsules, gel and pullulan. Each liquid was also tested with three different membranes, EVA 12%, EVA 10%, and polyethylene sheets. The apparatus was set up so that the gel capsules filled with liquid were put into a Petri dish with a membrane covering on top. The membrane was secured with a rubber band, creating a tight seal so that the only liquid leaving the system would be through the semi-permeable membrane.

Figure 4: The apparatus used in this experiment included the membrane, rubber band, a Petri dish, and acetone/pentane contained in gel/vegetable capsules.

Each Petri dish contained several capsules that in total held 2 mL of the solvent being tested. For trials with vegetable capsules, each capsule was filled with 0.4 mL of liquid, which was standardized using a micro-pipette, and 5 capsules were used per Petri dish. For trials with gel capsules, which were larger in volume, each capsule was filled with 0.5 mL of liquid, and 4 capsules total were used per Petri dish. First, a small beaker or Erlenmeyer flask containing the liquid was put on the balance and massed. After using a micro-pipette to draw exactly 2 mL of liquid and filling the capsules, the capsules were glued with Krazy Glue. Then, the beaker containing the liquid was weighed so that the mass of the liquid used could be determined by the difference. The filled capsules were put on the balance and massed as well. For each trial, the Petri dish, membrane, and rubber band were also weighed separately. Then, the entire system consisting of the Petri dish, membrane, rubber band, and filled capsules was massed. All of the Petri dishes were put into the oven at the same time to ensure equal time lapse for each trial. Then, over the course of a 14 hour period, the Petri dishes were massed every two hours to determine the amount of liquid that diffused through. For each liquid-capsule-membrane combination, there were two trials (A and B) to ensure that the data was accurate.

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The compiled data consisted of a list of the masses of the apparatus at two-hour intervals over a cumulative 14-hour period. The difference in mass for each apparatus between each time interval indicated the mass of the liquid that had diffused across the semi-permeable polymer membrane. Plotting the mass of each system over time demonstrated the order and pattern of the solvent’s diffusion. Each scatter plot was given a trend line through linear regression in order to exemplify the extent of its pseudo-zero-order diffusion. The slope of each trend line was the rate of diffusion in grams/hour and the linear nature of each line demonstrated that the rate of diffusion was relatively constant, and thus, indicative of a zero-order process.

RESULTS Below are the results concerning the diffusion rates of the two trials of our liquid,

capsule, and polymer membrane combinations. There were a total of 9 combinations that were each tried twice over the same 14-hour period under the same conditions.

Combinations Involving Acetone

Figure 5. A: Diffusion of Acetone Across Gelatin Capsules and Various Polymer Membranes (Trial A), B: Diffusion of Acetone Across Gelatin Capsules and Various Polymer Membranes (Trial B). The above figures display the diffusion plots of the acetone in the gelatin capsules through each of the three polymer membranes, each of which are represented by a different color, for both trials. EVA=Ethylene Vinyl Acetate, PE= Polyethylene

For the modified data from Trial A, least squares regression lines were plotted for each

set of data and coefficients of determination, indicators of how well the trend line fits the data, were subsequently calculated for each as well. As one can see above, after removing outliers and influential data points, the resulting best-fit line modeled the data very well for all three polymer membranes, as the coefficients of determination were all over .985, which is very close to 1, an indicator of perfect linearity.

For the data from Trial B, least squares regression lines were plotted for each set of data

and coefficients of determination were subsequently calculated for each as well. For this trial, the first data point was excised as the systems had not yet reached equilibrium. Upon visual inspection, all of the linear regression lines appear to fit the data very well, and the r2 values support this conclusion, as for all of the membranes, they were over .970 and very close to 1.

A. B.

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Combinations Involving Pentane

Combinations Involving Pentane

For Trial A, least squares regression lines were plotted for each set of data and coefficients of determination were subsequently calculated as well. One should note that four of the data points were removed from the 12 % EVA graph as they were outliers and the initial points from the other two data sets were removed as the systems had not yet reached equilibrium. Upon initial inspection, all of the regression lines appeared to fit the data very well, but the coefficient of determination of the 10 % EVA data was only .967, which was not as exemplary as previously mentioned results. However, the 12 % EVA and the polyethylene data exhibited strong, zero-order release, which is bolstered by the fact that their r2 values were both over .985.

Figure 6. A. Diffusion of Pentane Across Gelatin Capsules and Various Polymer Membranes (Trial A). B. Diffusion of Pentane Across Gelatin Capsules and Various Polymer Membranes (Trial B): The above figures display the diffusion plots of the pentane in the gelatin capsules through each of the three polymer membranes, each of which are represented by a different color, for both trials. EVA=Ethylene Vinyl Acetate, PE= Polyethylene

A.

B.

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For Trial B, least squares regression lines were plotted for each set of data and coefficients of determination were subsequently calculated as well. One should note that the initial data points for each membrane and an additional one for the 12 % EVA were removed as they were outliers. After these modifications, all three of the membranes displayed very strong, linear releases as each of their coefficients of determination were over .990.

Figure 7. A: Diffusion of Pentane Across Pullulan Capsules and Various Polymer Membranes (Trial A). B: Diffusion of Pentane Across Pullulan Capsules and Various Polymer Membranes (Trial B). The above figures display the diffusion plots of the pentane in the pullulan capsules through each of the three polymer membranes, each of which are represented by a different color, for both trials. EVA=Ethylene Vinyl Acetate, PE= Polyethylene

For Trial A, least squares regression lines were plotted for each set of data and coefficients of determination were subsequently calculated as well. One should note that the initial data points for each of the three data sets was removed as the systems had not yet reached equilibrium. On this occasion with the pentane and the pullulan capsules, the 10 % EVA did not display excellent linearity, as one can observe by noting the slight concavity of the data points and the relatively low r2 value of .9015. On the contrary, the 12 % EVA and the polyethylene both exhibited very strong, zero-order releases, as there were only slight variations about the regression line and both of their coefficients of determination were over .980.

A.

B.

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For Trial B, least squares regression lines were plotted for each set of data and coefficients of determination were subsequently calculated as well. One should note that the initial data points for each of the three data sets was removed as the systems had not yet reached equilibrium. Furthermore, one immediately notices that the diffusion of the pentane through the pullulan capsules and the 10% EVA membrane was clearly not linear, which is supported by the extremely low r2 value of .769. However, the 12 % EVA and the polyethylene membranes both exhibited good linear releases, as both of their coefficients of determination were over .950 and they did not have much variation about the best-fit line.

DISCUSSION This research has demonstrated that in a system where vapor pressure is a factor, pseudo-zero order release can be achieved as long as extraneous factors are kept constant. In most of the set-ups, the solvent diffused in a linear fashion with a few exceptions. In all of our graphs we removed the first point of data when making linear trend lines. This was done to account for the period of time where the vapor pressure has not yet reached an equilibrium. The results of each variable system of the experiment will be considered in detail in the following paragraphs. Acetone Acetone gave a very accurate model for zero order diffusion. Acetone diffused much slower than Pentane in our capsule membrane experiment. This was expected, as in the tests where only capsules were used, the heated acetone was only 29% diffused at the completion of the experiment. However, the small mass loss of acetone is still surprising when one considers its high volatility. The low amounts of Acetone release made it difficult to distinguish through which membrane the release rate was highest as both tests had different results. Despite the small amounts of diffusion the extremely high r2 values are great enough to still give researchers confidence in the zero-order nature of Acetone’s diffusion. Pentane

Pentane also worked as a strong model for demonstrating a constant release of fluid, with several tests resulting in linear graphs with r-squared values greater than .95. Considering that pentane completely diffused from each capsule in tests where only capsules were used, the considerably faster diffusion rate was to be expected. Pentane experienced the greatest diffusion from the polyethylene vegetable capsules, which agreed with this experiment’s hypotheses as pentane shares non-polar properties with polyethylene. In both EVA 10% and EVA 12%, the amounts diffused were extremely close, suggesting that the additional vinyl acetate was not enough to have a major impact on pentane diffusion. Overall, Pentane acted as an excellent model for demonstrating zero-order diffusion. Error Analysis An experiment that demands such precision and accuracy is bound to produce some error. Sources of error were encountered in the preparation and in the subsequent massing of the systems. First, the membranes covering the Petri dishes may have not been fully restricting air

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flow into and out of the dish throughout the experiment. This may have caused the linear zero-order release to become an exponential first-order reaction. Moreover, the systems were taken out of the oven every two hours to be massed. This constant removal from heat slowed down and sped up the diffusion because the oven had to reheat each time that it was opened. In addition, the scales were fluctuating on the thousandth place due to the heat emanating from the systems and slight air movement around the scale. Furthermore, some of the capsules became stuck to the Petri dish, which decreased the surface area of the capsule, causing slower diffusion. An error also occurred with the original masses of the systems due to an excess amount of membrane that extended over the edge of the scale that was not accounted for. A trimming was needed in order to produce accurate results, though unrecorded diffusion occurred while adjustments were being made. Also, the diffusion took a very long time, which led to a fewer number of recordable data points. With very few data points, it is difficult to accurately assess whether the release was zero-order or first-order. Future Studies

This experiment showed that pseudo-zero-order reactions can be created through the use of gel capsules that release chemicals at a constant rate. However, in order for this concept to become effective in any real world application researchers will need to find a chemical that is more suitable for use in the composition of the capsules. The capsules that the researchers used were extremely soluble in a number of solutions, causing the capsule to deform and the liquid to diffuse directly without evaporating first. Furthermore, the vegetable and gelatin capsules used are both soluble in water, meaning that they would be unable to slowly partition substances in a biological system. Future studies should attempt to produce a capsule that consists of a material that is not easily dissolved, but that still allows specific drugs to diffuse through it.

Future studies could also attempt to replicate this experiment over a longer period of

time, running the experiment for long enough time for solvent to finish diffusing from the capsules. This would give researchers a better understanding of the effects of the concentration on solvent diffusion. Conclusion Our experiment has shown that pseudo-zero-order release via capsules and a polymer membrane is possible. Many of the polymer, capsule, and liquid combinations that were tested exhibited strong, linear releases over the observed time period. Therefore, since this experiment served as a cost-effective model for a previously outlined more complex system that involves microspheres and pharmokinetics, our results suggest that research into that type of system is warranted and should be pursued. REFERENCES 1. Kibanov A. Controlled Release Technology: Polymeric Delivery Systems for

Pharmaceuticals, Proteins, and Other Agents [home page on the Internet]. Cambridge (MA): Massachusetts Institute of Technology; 2011 July 18. [cited 2011 July 20].

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7. Hansen CM. HSP for Beginners [home page on the Internet]. Hansen Solubility Parameters; n.d. [cited 2011 July 18]. Available from: http://http://hansen-solubility.com/index.php?id=19.

8. Belmares M, Blanco M, Goddard WA III, Ross RB, Caldwell G, Chou SH, Pham J, Olofson PM, Thomas C. Hildebrand and Hansen Solubility Parameters from Molecular Dynamics with Applications to Electronic Nose Polymer Sensors [home page on the Internet]. Pasadena (CA): Wiley Interscience; 2004 June 4. [cited n.d.]. Available from: http://http://www.wag.caltech.edu/publications/sup/pdf/587.pdf.

9. Hansen CM. Hansen Solubility Parameters: A User’s Handbook. Boca Raton (FL): CRC Press; 2007. 520 p.