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Transport characteristics using nor-dihydroguaiaretic acid (NDGA)-polymerized collagen fibers as a local drug delivery system

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Transport characteristics using nor-dihydroguaiaretic acid (NDGA)-polymerized collagen fibers as a local drug delivery system
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Guegan, Eric
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Dexamethasone
Dexamethasone 21-phosphate
Diffusion coefficient
Mathematical model
Polylactic-co-glycolic acid (PLGA)
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Dexamethasone and dexamethasone 21-phosphate were loaded into NDGA-polymerized collagen fibers and release rate studies were performed to calculate their diffusion coefficients. Dexamethasone loaded fibers were placed in a PBS solution for specified time intervals (1, 3, 6, 7, 12, 24, 30, and 48 hours) after which the eluant was removed and analyzed by capillary zone electrophoresis (CZE). CZE is a tool that can be utilized for quantitative analysis of chemical compounds. This data was incorporated into mathematical models to determine the diffusion coefficient. The diffusion coefficient (D) for dexamethasone in NDGA-polymerized collagen fibers is D = 1.86 x 10^-14 m2/s. Similarly, dexamethasone 21-phosphate loaded fibers were placed into a PBS solution and analyzed using CZE at these specified intervals (15, 30, 45, 60, and 75 minutes). Applying this data to the mathematical model provided a diffusion coefficient for dexamethasone 21-phosphate in NDGA-polymerized collagen fibers of D = 2.36 x 10^-13 m2/s. In an effort to control drug delivery from these fibers a polylactic-co-glycolic acid (PLGA) coating was applied to the fibers. This coating helped sustain delivery of dexamethasone 21-phosphate for over a 100 day period. CZE experiments were again conducted in conjunction with another mathematical model to characterize release. A semi steady-state diffusion coefficient was estimated to be D = 4.59 x 10^-14 m2/s.
Thesis:
Thesis (M.S.)--University of South Florida, 2007.
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by Eric Guegan.
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Transport Characteristics Using Nor-Di hydroguaiaretic Acid (NDGA)-Polymerized Collagen Fibers as a Local Drug Delivery System by Eric Guegan A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Co-Major Professor: Yvonne Moussy, Ph.D. Co-Major Professor: Francis Moussy, Ph.D. Frank Pyrtle, Ph.D. Date of Approval: June 5, 2007 Keywords: dexamethasone, dexamethasone 21-phosphate, diffusion coefficient, mathematical model, polylact ic-co-glycolic acid (PLGA) Copyright 2007, Eric Guegan

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Acknowledgements I would like to personally thank Yvonne Moussy, Ph.D. for all her support and guidance on this project. I would like to also thank Th omas J. Koob, Ph.D. for the development of the NDGA collagen fibers and fo r collaborating with our lab. As well, I would like to acknowledge Tian Davis for her ro le in collecting the experimental data. I would also like to thank Leigh West for his patience and assistance in the laboratory. Finally, I would like to thank all of my colleagues in the Biosensors and Biomaterials Laboratory; I truly appr eciate all the support.

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i Table of Contents List of Tables iii List of Figures iv Abstract vi Chapter 1 Background 1 1.1 Diabetes 1 1.2 Glucose Sensor 4 1.3 Sensor Complications 5 1.4 Control Inflammation by Using a Drug Delivery System 7 1.5 Purpose 8 Chapter 2 NDGA Collagen Fibers 10 2.1 Background 10 2.2 Fiber Fabrication Process 12 2.3 Dexamethasone Loading 13 2.4 Dexamethasone 21-phosphate Loading 13 2.5 PLGA Coating of NDGA Collagen Fibers 14 Chapter 3 Capillary Zone Electrophoresis 15 Chapter 4 Mathematical Model 17 4.1 Transient Mathematical Model 17 4.2 Composite Mathematical Model 19 Chapter 5 Dexamethasone Loaded Fiber Results 24 Chapter 6 Dexamethasone 21-phospha te Loaded Fiber Results 30 Chapter 7 Dexamethasone 21phosphate Loaded PLGA Coated Fiber Results 36 Chapter 8 Discussion 42 8.1 Dexamethasone 42 8.2 Dexamethasone 21-phosphate 43 8.3 PLGA Coated Dexamethasone 21-phosphate Loaded Fibers 44

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ii Chapter 9 Conclusion 46 9.1 Summary 46 9.2 Future Works 47 References 48 Appendices 50 Appendix A: Additional Information and Figures 51 Appendix B: Maple Programs 57

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iii List of Tables Table 1. The numerous compli cations diabetics may face 4 2 Table 2. Diffusion coefficients of de xamethasone in various media. 43

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iv List of Figures Figure 1. Implantable glucose sensor 9 5 Figure 2. NDGA collagen fibers. 8 Figure 3. SEM image of two NDGA collagen fibers side by side. 11 Figure 4. 10x magnification of H & E stained cross-section of implanted fibers at 6 weeks. 11 Figure 5. Diagram of the fiber and the model parameters. 21 Figure 6. Standard curve for dexamethasone. 24 Figure 7. CZE data obtained from each incubation time. 25 Figure 8. Relationship between dexamethasone concentration and time. 26 Figure 9. Cumulative concentration release against time for dexamethasone. 27 Figure 10. (A) The cumulative percent of dexamethasone released per fiber into PBS versus time. (B) The cumulative percent of dexamethasone released per fiber into PBS versus the square root of time. 28 Figure 11. Standard curve for dexamethasone 21-phosphate. 30 Figure 12. CZE data obtained from each incubation time for dexamethasone 21-phosphate. 31 Figure13. Relationship between dexamethasone 21-phosphate concentration and time. 32 Figure 14. Cumulative concentration release against time for dexamethasone 21-phosphate. 33

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v Figure 15. (A) The cumulative percent of dexamethasone 21-phosphate released per fiber into PBS ve rsus time. (B) The cumulative percent of dexamethasone 21-phosphate released per fiber into PBS versus the square root of time. 34 Figure 16. CZE data obtained fo r each incubation period. 37 Figure 17. Concentration eluted at each time interval for the dexamethasone 21-phosphate loaded PLGA coated fibers. 38 Figure 18. Cumulative concentratio n release against time for PLGA coated fibers. 39 Figure 19. The cumulative percentage of dexamethasone 21-phosphate released from the PLGA membrane surrounding the fiber into PBS versus time. 40 Figure 20. Diffusion rates at each time interval for dexamethasone 21-phosphate through a PLGA membrane. 41 Figure 21. This figure illustrates th e process at which the agents are diffusing from the fibers. 51 Figure 22. Cross-section of PLGA coated fiber. 52 Figure 23. Fabricati on procedure. 56

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vi Transport Characteristics Using Nor-Dihy droguaiaretic Acid (NDGA)-Polymerized Collagen Fibers as a Local Drug Delivery System Eric Guegan ABSTRACT Dexamethasone and dexamethasone 21-phosphate were loaded into NDGApolymerized collagen fibers and release rate studies were performed to calculate their diffusion coefficients. Dexamethasone loaded fibers were pl aced in a PBS solution for specified time intervals (1, 3, 6, 7, 12, 24, 30, and 48 hours) af ter which the eluant was removed and analyzed by capillary zone electrophoresis (CZE) CZE is a tool that can be utilized for quantitative analysis of chemical com pounds. This data was incorporated into mathematical models to determine the diffusion coefficient. The diffusion coefficient (D) for dexamethasone in NDGA-polymerized collagen fibers is D = 1.86 x 10 -14 m 2 /s. Similarly, dexamethasone 21-phosphate load ed fibers were pl aced into a PBS solution and analyzed using CZE at thes e specified intervals (15, 30, 45, 60, and 75 minutes). Applying this data to the mathematical model provided a diffusion coefficient for dexamethasone 21-phosphate in NDGA-polymerized collag en fibers of D = 2.36 x 10 13 m 2 /s. In an effort to control drug delivery from these fibers a polylactic-co-glycolic acid (PLGA) coating was applied to the fibers. This coating helped sustain delivery of dexamethasone 21-phosphate for over a 100 day period. CZE experiments were again

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vii conducted in conjunction with another mathematical model to characterize release. A semi steady-state diffusion coefficient was estimated to be D = 4.59 x 10 -14 m 2 /s.

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1 Chapter 1 Background 1.1 Diabetes Diabetes is a disease that affects th e blood glucose levels. These levels are augmented to a higher state because of a defi ciency in insulin pr oduction and utilization. In 2002, the 6 th leading cause of death in the United States was diabetes. This disease afflicted 20.8 million Americans in 2005. Diabetes can cause serious complications in the human body, and people of similar age with this dis ease are twice as likely to experience premature death. Every day 613 Americans will die from this disease. Regrettably, the cause for diabetes is still unknown; however, genetics and environmental factors such as health and diet contribute greatly to this disease 3 Diabetes mellitus is a chronic metabolic disorder affecting the way the body uses glucose. When food is consumed and digested it is broken down into glucose, a simple sugar that is the main source of energy fo r the body. Glucose is absorbed into the blood stream where cells utilize it for energy and growth. However, glucose alone cannot be absorbed into the cells; it re quires the presence of insulin. Insulin is a hormone produced by the pancreas whose primary function is to help the cells metabolize and use glucose. During the digestion phase the body produces th e appropriate amount of insulin required to move glucose from the bloodstream to our cells. However, this systemic disease can limit or cause no insulin production to occur a nd can even alter the cells response to the

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2 insulin. When this happens there is nothing present to fuel the cells or metabolize the excess glucose, result ing in Hyperglycemia 7 This can lead to numerous potential problems throughout the body (Table 1). Table 1. The numerous compli cations diabetics may face 4 Complications Hypertension Affects more than 70% of all diabetics Heart disease and stroke 2 to 4 times as likely to experience than someone who does not have this disease Diabetic retinopathy, blindness Leading cause of blindne ss (ages 20-74) Diabetic nephropathy, kidney failure Leading cause of kidney failure Nervous system disease (digestion problems, Carpal Tunnel Syndrome, lack of feeling or pain in appendages, etc) Affects more than 60% of all diabetics Lower-extremity amputations 60% of all cases are diabetics Pregnancy 15-20% increased chance of miscarriage 5-10% will have major birth defects Biochemical imbalances can lead to: Diabetic ketoacidosis Hyperosmolar (nonketonic) comas Acute life threatening events Since diabetes primarily targets insulin production and influences glucose levels it is evident that maintaining and monitoring thes e levels is of the utmost of importance. There are two main types of blood tests ad ministered: the A1c blood test and selfmonitoring of blood glucose (SMBG) test. Both of these are used to monitor glucose levels and provide vital results to aid in th e adjustment of treatments. The A1c blood test measures the glycerated hemoglobin per centage. The protein, hemoglobin, is a component in red blood cells that transfer s oxygen from the lungs to the body. The excess presence of glucose caused from diabetes links up and glycates with the molecules of the

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3 hemoglobin. This forms a compound known as HbA 1c that can be measured by the A1c test as a percentage, which shows an average of the glucose control over a two to three month period 7 The second method, the SMBG test, is self-a dministrated about two to four times a day. This provides the patient with a bett er understanding of how their bodies glucose levels fluctuate. Changes in medicine, diet, stress, physical activity, health, or routines can alter the state of your blood glucose. By monitoring these levels the diabetic patient will learn how their body reacts and can make self-adjustments when needed. These daily results are compared to the physicians A1c test to see if accuracy is being achieved. This also allows the physician to see possible trends and to adjust treatments appropriately. However, both test methods are fairly e ffective for the monitoring of glucose but each presents limitations. The A1c is by far the most accurate method of the two but must be administered by a physician and then sent to a lab for analysis. It is only taken every two to three months and within this time frame drastic changes in glucose levels may occur. In most cases SMBG test would pick up these changes; however studies show that patient testing techniques are not without error. An estimated 31% of SMBG users, due to improper testing techniques, have results that vary by 10-20% of the actual glucose value and 53% perform errors that cause results to be off up to 10%. Furthermore, FDA guidelines allow glucose meters on the market to vary up to 20% of actual blood glucose levels. So, with all this variation how accurate are the readings patients are receiving? It seems a better monitoring technique is need ed, one which has the accuracy of the A1c testing but the frequency of SM BG testing. A technique to monitor glucose levels without the influence of human error 1, 15

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4 1.2 Glucose Sensor A possible solution to the inadequacies of the SMBG and A1c tests would be to develop an implantable glucos e sensor for the body (figur e1). This biosensor would revolutionize current monito ring techniques and significantly contribute to the control and understanding of diabetes. Current monitori ng techniques use discrete measurement methods collecting data points from a system that is constantly changing. These test methods contribute to delays from the acquired level to actual glucose level due to the setup and test time. Similarly, pa tterns or rapid fluctuations in the patients glucose levels will not show. To develop an effective means to continuously monitor glucose levels would be of great benefit to the medical community. Through continuous monitoring of blood glucose levels diabetics would be able to administer insulin in a timely manner, knowing precisely when levels are not where th ey should be. This in itself would be a great tool furthering th e effectiveness of insulin delivery and proactively preventing the frequencies of attacks from occu rring. It is clear there is a need for these sensors, and there is a potential market. In 2002 the American Diabetes Association reported that U.S. healthcare costs for diabetes exceeded 132 billion dollars. According to Business Communications Company Inc. who performed a market study in 2002, predicted that by 2007 glucose monitor market will exceed 8 billio n dollars worldwide. Clearly, the need for improvement is present and with in creasing technological advancements an implantable glucose sensor is a feasible solution. In general, this sensor will need to be tiny, as it is to be implanted in human tissue; it will need to provide accurate read ings with a rapid response-time; and also be biocompatible with the human body. Miniat urization is no longer an issue as

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technological advancements have lead to s ubstantial improvements in sensor designs. Current glucose sensor elements occupy an area in the rang e of less than 1mm 2 These sensors can accurately provide continuous response times given that the sensor is intact and not influenced by outside factors. Furt hermore, sensors are becoming increasingly more biocompatible as our understanding of material properties and the human response to these increases. However, the bodys greatest ally is th e enemy to the biosensor; the human bodys complex defense and healing mech anisms. This intricate system has lead to substantial failures in designing an effective implantable glucose sensor. Figure 1. Implantable glucose sensor 9 1.3 Sensor Complications These failures often occur due to the in teraction between th e biosensor and the bodys immune system response. There are two reactions that occur when implanting sensors that contribute to their failure: the implantation process and the foreign body response. During the implantation phase a wound is created at the surgical site. Various 5

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6 techniques have been studied to minimize ti ssue and cell damage from surgical incisions to insertion using small gauge needles. However, all these techniques will contribute to a certain amount of damage at the insertion si te that cannot be avoi ded. When thinking of the biosensors size one must consider that al though it is very small, it is much larger than the cells and blood capillaries from which it will need to acquire data making insertion damage inevitable. Consequently, one must minimize the implantation site as much as possible and ensure th e sensor is contaminant free to eliminate risk of infection. Similarly, one must prevent the bodys defens es from rejecting the sensor. As the body begins the wound-healing phase, trying to stop loss of blood, prev ent infection and restore function to the injured implantation s ite; inflammatory cells like neutrophils and macrophages detect the presence of a forei gn body. Since phagocytos is, the breakdown of foreign objects, is nearly impossible the macrophages form into giant cells encapsulating the site. The giant cells will form a collage n shell around the implant preventing normal interaction with the body by is olating it from surrounding tissue This will lead to chronic inflammation resulting in potential sensor failure and inaccurate sensor readings. There is a viable solution to this problem, which deals primarily with the biocompatibility of materials. Biocompatible materials are ideally ones, which are not rejected by the body, ones that elicit very litt le foreign body response and cause little to no irritation in the body. However, no current implant materials have been developed that will not induce some sort of biological response. Since this cannot be avoided, the only answer is to reduce the re action that will occur. If one can modify the outer layer of the biosensor to a more tolerable material th en there will be less interaction between the bodys defenses and the device. Essentiall y, the body would be deceived into accepting

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7 the device as normal. However, this is a very complicated task. It would be even more effective to combine a special outer layer to the sensor, which coul d lessen the foreign body response through the use of preventive ag ents to help the sensor gain acceptance 6 1.4 Control Inflammation by Using a Drug Delivery System The use of preventive agents could s ubstantially improve the function of the sensor. By combining the sensor with a drug delivery coating one, could use the medicinal properties of the agent to prev ent the bodys foreign body response. Dr. T.J. Koob has developed a biocompatible fiber that ideally suits this purpose (figure 2). By surrounding the sensor with a collagen base d nor-dihydroguaiaretic acid (NDGA) fiber potential negative interaction between the body and sensor co uld be limited. Using this fiber as a delivery system an anti-inflamma tory agent could be administered by the process of diffusion. A substantial candidate for this is dexamethasone. This synthetic glucocorticoid is widely used as an antiinflammatory and an immunosuppressive drug. Therefore, surrounding the fiber with de xamethasone loaded NDGA fibers should provide an effective means fo r controlling inflammation and drastically increase the life of the sensor.

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Figure 2. NDGA collagen fibers. 1.5 Purpose Now that an effective system has been hypothesized to help extend biosensor function the mechanisms that control our process must be understood. Diffusion is a passive transport process where the driving potential is due to the species concentration gradient. The higher concentration of dexamethasone will diffuse to the lower concentration until a balance is achieved (f igure 21 appendix. page 51). Diffusion will occur until the drug is depleted from the fiber 8 The dexamethasone loaded NDGA collagen fibers will administer the drug at a specific rate. This diffusion coefficient will help one understand how much of the drug c ould potentially be de livered into the body for a certain length of time. However, calculatio ns of this rate have never been performed in this media. This paper aims to illustrate a novel drug delivery system and model transport characteristics for three different cases presenting the various analytical and 8

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9 experimental techniques performe d to obtain these rates. The three cases examined were: i.) dexamethasone diffusing through the NDGA collagen fiber ii.) dexamethasone-21 phosphate disodium diffusing through NDGA collagen fibers iii.) dexamethasone-21 phosphate disodium diffusing through a polylac tic-co-glycolic acid (PLGA) coating that surrounds the fiber. Understanding these rate s will help to optimize an effective drug deliver system.

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10 Chapter 2 NDGA Collagen Fibers 2.1 Background In attempt to produce a material for us e in tendon repair, Dr. Thomas J. Koob developed NDGA collagen based fibers. Thes e fibers were created with similar mechanical properties to the actual hu man tendon, modeling an elastic solid. More significantly to this research, the fibers are biologically ba sed and biocompatible 10 ; a key factor in their potential use as a sensor coating and drug delivery tool. The main component of these fibers is collagen, a chemical protei n found throughout the body that aids in strengthening and connecting tissues Since this protein is found throughout the body it is a prime candidate as a potential biomat erial. Extracted fetal bovine collagens at 37 C in physiological buffers will re-nature into collagen fibrils (figure 3). These synthetic fibrils are weak because native cross-linking pathways do not manifest in vitro formation. A cross-linking agent is needed for the collagen fibers to increase the tensile strength and to lower the potential inflammatory res ponse. The anti-oxidant, NDGA meets these criteria (figure 4). NDGA is a di-c atechol extracted from the creosote bush and when cross-linked resolved strength and biocompatibility issues 11

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Figure 3. SEM image of two NDGA collagen fibers side by side. Figure 4. 10x magnification of H & E stained cross-section of implanted fibers at 6 weeks. These were implanted in the paravertebral musculature of rabbits. It is evident that the control fiber (non cross-linked collagen fiber) has well-organized capsules of cells surrounding it. It is also fragmented and has begun to degrade. The NDGA fiber has barely any encapsulating cells surrounding it, with the exception of the right corner. It is completely int act except for fragmentation that was caused during sectioning 10 Any biomaterial incorporated into a host must not elicit harm to the body or cells. However, during the fabrication process, NDGA and residual products from cross-linking were found to be cytotoxic in vitro. However, by washing the fibers in 70% ethanol cytotoxicity can be eliminated 12 To ensure that non-cytotoxic and biologically based biocompatible fibers are fabricated, an intricate protocol must be followed. 11

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12 2.2 Fiber Fabrication Process The fiber fabrication process (figure 23 appendix, page 56) is a very delicate and intricate procedure. It is essential to fo llow the required steps to produce high strength, biocompatible fibers. The entire process take s four days and can be broken up into daily procedures. Refer to appendix (Detaile d Fiber Fabrication Protocol, page 53) for a more detailed procedure. The fibers were made using purified pe psin-solubilized type I fetal bovine tendon collagen. The 0.13% w/v collagen solution was placed in 0.32-ml/cm dialysis tubing and then washed every 30 minutes in de-ionized water for at least 7 hours. The tubing assemblies were then transferred to a PBS solution of pH level 7.4 and incubated at 37 C for 16 hours. This extrusion process permits th e collagen to re-nature and promotes fibril alignment. Following this step, the fibers were then hung dry; strengthening the weakened fibers. Once the fibers are dry, NDGA cross-linking can occur. Oxidized sodium phosphate buffer, having a pH level of 9.0, is combined with NDGA (Cayman Chemical, Ann Arbor, MI) to form the cross-linking agent. The amount of oxygen present accelerates the cross-linking reaction. The fibers are then agitated in this NDGA solution overnight. The final day encomp asses washing and drying the NDGA treated fibers. The fibers are washed in 70% et hanol to remove any un-reacted, soluble NDGA intermediates. The procedure is sufficien tly repeated to ensure all unbound NDGA is removed. The fibers are finally straightened and hung vertically in tension to dry overnight, completing the fabrication process.

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13 2.3 Dexamethasone Loading With the fabrication process complete the fibers are ready to be loaded with a drug agent. The drug loading procedure is fair ly simple and could pot entially be applied to other drug agents. In the first case, ten dried fibers were load ed with dexamethasone. These samples (diameter of 0.08 mm) were cut into 10 mm lengths and placed into 1.5 ml tubes. These tubes contained 200 l of 10 mg/ml of dexameth asone (SIGMA, St. Louis, MO) in a 70% ethanol solution ( 10 fibers/tube, number of tube s, n = 10). The fibers were incubated in this mixture for 18 hours at room temperature. The solution was then removed and the fibers were allowed to air dry for 24 hours. Once dried, the fibers were washed in 200 l of PBS, with pH level of 7.4, to remove any residual dexamethasone left from drying. The fibers were then incubated at 25 C in 200 l of PBS in the dark, as it is light sensitive. The PBS was removed at specific time periods (1, 3, 6, 7, 12, 24, 30, and 48 hours) and replaced with fresh PBS. This removed dexamethasone was analyzed by Capillary Zone Electrophoresis (CZE) for drug elution amounts (refer to ch.3). 2.4 Dexamethasone 21-phosphate Loading In the second case, ten dried fibers of length 10 mm and di ameter of 0.08 mm were placed into a 1.5 ml tubes. These tubes contained 200 l of 10 mg/ml of dexamethasone 21-phosphate disodium salt (SIG MA, St. Louis, MO) in a 3% acetic acid solution (10 fibers/tube, number of tubes, n = 10). The fibers were then incubated at room temperature for 18 hours in this solution. The mixture was discarded and the fibers were air dried for 24 hours. The dried fibers were th en washed with PBS, with a pH level of 7.4, to remove any residual dexamethasone 21-p hosphate not incorporated into the fibers.

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14 The fibers were then stored in the dark at 25 C, in 200 l of PBS. The PBS was removed at specific time intervals (15, 30, 45, 60, and 75 minutes) and analyzed on the CZE. Fresh PBS replaced the removed solution, which was analyzed on the CZE for dexamethasone 21-phosphate content (refer ch.3). 2.5 PLGA Coating of NDGA Collagen Fibers In the third examined case dexamethasone 21-phosphate loaded fibers (n = 15) were coated with PLGA (figure 22 appendix, page 51). To coat the fibers, 0.5g of PLGA crystals, which were stored at Celsius, were dissolved in 1g of chloroform. The chloroform had a purity of 99% and is a nhydrous. Place the solution on a rocker for at least 2 hours to ensure complete PLGA cr ystal breakdown. Allow the solution to sit overnight to dissipate any ai r bubbles from the mixture. On the following day, dip coat the fibers in PLGA (50:50) in chloroform (PLGA/chloroform = 54%) uniformly. Remove them from the solution and hang them to air dry at 25 C for 5 days. This will provide a PLGA coating to the fibers with an average diameter of 0.306 mm (n = 30). The coated fibers were then incubated in 200 l of PBS (3 fibers/tube). The PBS was removed at varying time intervals and examined on the CZE for dexamethasone 21-phosphate content (refer to ch.3). The PBS was repla ced with fresh PBS after every analysis.

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15 Chapter 3 Capillary Zone Electrophoresis Capillary zone electrophoresis (CZE) is a t ool that can be utilized for quantitative analysis of chemical compounds. The system ha s the ability to separa te analytes based on their charge and size. The CZE machine usually consists of two reservoirs and a capillary filled with a homogeneous buffer solution. S upplying a high-voltage across the capillary creates an electric field. This electric field produces an electro-osmotic flow in the capillary causing the cations in the solvent to migrate towards the cathode. This migration also allows separation of the chemical co mpound because of the electrophoretic mobility of the analyte. Using various wavelengths, depending on your sample, the migration rates can be detected and quantified using UV methods of detection. This data is then sent to a computer and displayed as an electropher ogram, which displays the response as a function of time. The output is displayed as peaks based of the analytes retention times. The consequential profile provides a very fast, highly efficient separation method. By taking the drug loaded fi bers and analyzing them in vitro, in sink conditions, concentration levels can be found. Since the fi bers are in sink condi tions, the PBS washes described earlier, provide a solution containi ng PBS and the eluted dexamethasone agents. Using the CZE machine the amount of eluted dr ug can be calculated at each time interval. The PBS eluant was analyzed on a Dionex Capillary Electrophoresis System I. Using a sodium borate buffer (10 mM of sodium borate, 50 mM of boric acid, pH 8.0) the eluant

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16 was diluted (2 fold). It was then loaded from a height of 50 mm for 10 s by gravity into a 75 m inner diameter x 80 cm long hollow gl ass capillary. This capillary was then electrophoresed at 20,000 V. Dexamethasone agents can be detected at 246 nm 13 Prior to loading samples, calibration of the C ZE was performed for dexamethasone and dexamethasone 21-phosphate. Standards were di ssolved directly into the CZE buffer at increasing concentrations providing a rela tionship between peak area output and concentration. Running each of the experimental samples in the CZE provided the elution amounts determined from peak area. This provided data for the amount of dexamethasone and dexamethasone-21 phosphate released with respect to each time interval.

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17 Chapter 4 Mathematical Model 4.1 Transient Mathematical Model From a research standpoint, it is v ital to understand how various chemicals and agents react within other medi a. When there is a different species concentration in a mixture, mass transfer will occur. The prim ary mechanism governing this mass transfer or drug release from the fibers is diffusion. In the first two examined cases fibers were placed into a well-stirred reservoir of PBS. This represents a sink condition as would occur in the body. The sink condition ensure s a balance will not be achieved between concentrations inside and outsi de the fibers, as the volume is sufficiently large allowing complete diffusion. To understand this better one can use mathematical models to help illustrate the occurring process. To begin a few assumptions must be made to properly model the specified case. The formations of the fibers are solid and uniform in nature, meaning there is no other material inside th e fibers to warrant a composite case. The fibers are cylindrical in formation having a length of 10 mm. The hydrated radius of the fibers is on average 0.058 mm. The length to radius ratio is sufficiently large enough to assume the case of diffusion through a cylinder of infinite length. Secondly, this ratio also means diffusion through the cylinder will happen radially; diffusion with respect to length is insubstantial. Also, diffusion here is a transient process, thus is time dependent. Based off these assumptions and simplificati ons, a governing equation can be formulated

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that describes the concentra tion of a diffusing substance from a long cylinder with a uniform distribution under steady-state conditions: r c r r c D t c 12 2 (1) Here, c is the concentration of the drug in the fiber, t is the time following immersion into the reservoir, D is the diffusion coefficient of the dr ug in the fiber, and r is the radial distance within the fiber. Ce rtain boundary conditions must be assumed to solve this equation: 1) the drug distribution is initially uniform in the fiber (c = c i at t = 0 for 0 < r < R where R is the radius of the fiber and c i is the initial concentration); and 2) the drug concentration at the su rface of the fiber is zero thro ughout the release (c = 0 for t > 0 at r = R). The solution for equation (1) is 19 : ) exp( )( )(2 ),(2 1 1 0Dt RJ rJ R c trcn n nn n i (2) This solution provides an expression where c oncentration is a functi on of radial distance and time. This allows concen tration profiles to be formul ated for dexamethasone and dexamethasone 21-phosphate eluted from the NDGA collagen fibers. The amount of diffusing substance per unit area, M t, which has left the cylindrical fibers in time, t equals: 18

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dt r c DMRr t t 0 (3) If M is the amount of diffusing substance per unit area that is left as t approaches infinity, then for short times this equation becomes: 5.04 Dt RM Mt (4) The amount, M is also the same as th e initial amount loaded into the fibers. The amount, M is also the same as the initial amount lo aded into the fibers. By combining equation (4) with the slope from expe rimental data plots for M t /M vs. t 1/2 (cumulative drug release versus the square root of time), the diffusion coefficient, D, can be calculated 5 4.2 Composite Mathematical Model For the 3 rd case in which diffusion occurs from the NDGA fibers through the PLGA membrane, a different mathematical model was used. Since the PLGA coating degrades with time, a steady diffusion coe fficient cannot be calculated using the previously mentioned method. Instead, an analysis must be used that looks at each time interval independently to solve for a time dependent diffu sion coefficient. This model uses the assumption that the PLGA coating is the main factor controlling diffusion of dexamethasone 21-phos phate; the NDGA collagen fiber acts only as a storage vessel for the drug. This assu mption is valid as the diffusion rate for 19

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dexamethasone 21-phosphate in the fiber is mu ch greater than in PLGA, which will be discussed later in chapter 5. To solve for the time dependent diffusion rate, each time interval was viewed as an individual diffusion case. Since each time interval was relatively short, a quasi-steady-state assump tion was made. The mathematical model was assumed to be for a hollow cylinder of infi nite length under steady state conditions with constant drug concentrations on each surface: r c r r c 1 02 2 (5) Two boundary conditions were assumed here: 1) the inner surface of the PLGA coating has a concentration equal to th e fibers concentration (c = c i at r =R i where c i is the concentration in the fiber and R i is the inner radius, that of the fiber); and 2) the outer surface of the PLGA coating ha s a concentration (c = c e at r = R e where R e is the outer radius of the coated fiber and c e is the concentration in the PLGA coating ) (see figure 5). Applying these boundary conditions and solvin g equation (5) leaves an expression for concentration as a function of radius: i e e ie eR R R r cc crc ln ln)( )( (6) 20

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PLGA coating Ri Re ceciFiber Figure 5. Diagram of the fiber and the model parameters. Ficks 1 st Law, denoted below, relates the rate of diffusion to the concentration gradient as the driving force behind mass transfer. d r dc DJ (7) Here, J represents mass flux. This expression can be related to the fibers geometry through the cross-s ectional area, A. A d r dc DJ AM (8) By integrating equation (8) w ith respect to time, an e xpression for the amount of diffusing substance, M t, which diffuses through the length, L, of the cylindrical fibers in time, t, can be obtained: 21

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trc dr d LDRMeRr e t )( 2 (9) Taking the derivative of equation (6) provides an expression for: e i e ieR R R cc rc dr d ln ) ( (10) If we assume perfect sink conditions, the con centration in the PLGA me mbrane will go to zero. Applying this simplification to equation (10) and substituting this new expression into equation (9) yields: R R ln 2i e tLDc Mi t (11) This formula can be re-arranged into a numer ical expression to calculate the diffusion coefficient at each time interval The fibers concentration, c i will now be a function of the total concentration left in the fiber at the specific time being examined. Similarly, M t will be a function for the amount of diffusing s ubstance at each time. Lastly, the time, t, will be the time period. This leads to an expression for the individual diffusion coefficient at each specific elution period: 22

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i e i tR R tLc M tD ln )(2 )( (12) Refer to appendix (Program Diffusion th rough PLGA membrane Pr ogram, page 86) for calculations and for a more in de pth derivation of formulas. 23

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Chapter 5 Dexamethasone Loaded Fiber Results Using the CZE machine a standard cu rve for dexamethasone was created by dissolving varying concentrations of dexamethasone in PBS. The different concentrations were diluted (2 fold) into a sodium borate buffer and then electrophoresesed as described in chapter 3. The obtained peak areas provi ded a linear relations hip for concentration (figure 6). 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 500 1000 1500 2000 2500 3000 Concentration (mg/ml)Area Units y = 14501*x 33.932 Figure 6. Standard curve for dexamethasone. The dexamethasone-loaded fibers were placed in a PBS solution for specified time intervals (1, 3, 6, 7, 12, 24, 30, and 48 hours). After each incubation period the 24

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eluant was removed and analyzed using CZE. This provided an accurate method for determining the dexamethasone content, which was eluted into the PBS solution at each period (figure 7). 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 10 20 30 40 50 60 70 80 Time (hours)Area Units Figure 7. CZE data obtained from each incubation time. Using the standard curve (f igure 6) with the above figures data provides a direct correlation between time and concentration leve ls. The peak areas for each sample were converted to their equivale nt concentration using this relationship (figure 8). 25

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0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 2 3 4 5 6 7 8 x 10-3 Time (hours)Concentration (mg/ml) Figure 8. Relationship between dexamethasone concentration and time. Simply taking the corresponding concentra tion at each time interval and adding the following concentration can form a cumulative relationship. This shows the cumulative release of dexamethasone concen tration for each time until depletion (figure 9). The outlying bars represent standard deviation. Refer to appendix (Program Dexamethasone Concentrations, page 57) for calculations. 26

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0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 0.005 0.01 0.015 0.02 0.025 0.03 Time (hours)Cumulative Concentration (mg/ml) Figure 9. Cumulative concentration release against time for dexamethasone. The fibers on average were loaded with a concentration of 0.021 mg/ml of dexamethasone as verified by CZE. Based off the release data the fiber segments were loaded with 4.2 g of dexamethasone. Knowing the in itial concentration allows the previous figure to be conve rted to a cumulative mass release versus time plot. The cumulative mass release plot is then taken ag ainst the square root of time (figure 10). This ensures the data is in the proper format to apply equation (4) from the mathematical model. Taking the slope for the short times from this plot satisfies, t MM slopet (12) which allows one to solve for the diffusion coefficient. 27

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0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 0 20 40 60 80 100 120 Time (hours)Cumulative Mass Release (%)A 0 50 100 150 200 250 300 350 400 450 0 20 40 60 80 100 120 Time (sec1/2)Cumulative Mass Release (%)B Figure 10. (A) The cumulative percent of dexamethasone released per fiber into PBS versus time. (B) The cumulative percent of dexamethasone releas ed per fiber into PBS versus the square root of time. Dashed line indicates the slope for short times. The rather large standard deviation is probably because of th e insolubility of dexamethasone in PBS. The first 6 hours of release of dexamethasone was linear with 28

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29 respect to the square root of time. Approximately 60% of the drug was released in the first 3 hours; by 6 hours nearly 77% had been released. Using the slope the diffusion coefficient was estimated to be D = 1.86 x 10 -14 m 2 /s. Refer to appendix (Program Diffusion Coefficient for Dexameth asone Calculations, page 84).

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Chapter 6 Dexamethasone 21-phosphate Loaded Fiber Results Using the CZE machine a standard curve for dexamethasone 21-phosphate was created by dissolving varying concentrations of dexameth asone 21-phosphate in PBS. The different concentrations were diluted (2 fold) into a sodium borate buffer and then electrophoresesed as described in chapter 3. The obtained pe ak areas provided a linear relationship for concentr ation (figure 11). 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7 x 104 Concentration (mg/ml)Area Units y = 13571*x + 328.71 Figure 11. Standard curve for dexamethasone 21-phosphate. The dexamethasone 21-phosphate loaded fibe rs were placed in a PBS solution for specified time intervals (15, 30, 45, 60, and 75 minutes). After each incubation period the 30

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eluant was removed and analyzed using CZE. This provided an accurate method for determining the dexamethasone 21-phosphate content, which was eluted into the PBS solution at each period (figure 12). 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 500 1000 1500 Time (minutes)Area Units Figure 12. CZE data obtained from each incubation time for dexamethasone 21-phosphate. Using the standard curve (f igure 11) with the above figures data provides a direct correlation between time and elution concentration levels. The peak areas for each sample were converted to their equivalent concentration using this relationship (figure 13). 31

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Time (minutes)Concentration (mg/ml) Figure 13. Relationship between dexamethasone 21-phosphate concentration and time. Taking the corresponding concentration at each time interval and adding the following concentration a cumulative relationship can be formed. This shows the cumulative release of dexamethasone 21-phosphate concentration for each time until depletion (figure 14). The outlying bars repres ent standard deviation. Refer to appendix (Program Dexamethasone 21-phosphate Con centrations, page 63) for calculations. 32

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 0.05 0.1 0.15 0.2 Time (minutes)Cumulative Concentration (mg/ml) Figure 14. Cumulative concentration release against time for dexamehatsone 21-phosphate. The fibers on average were loaded with a concentration of 0.222 mg/ml of dexamethasone 21-phosphate as verified by CZ E. Based off the release data the fiber segments were loaded with 44.4 g of dexamethasone 21-phosphate. Knowing the initial concentration allows the previous figure to be converted to a cumulative mass release versus time plot. The cumulative mass release plot is then taken agains t the square root of time (figure 15). This ensures the data is in the proper format to apply equation (4) from the mathematical model. Taking the slope for the short times from this plot satisfies equation (11) from chapter 4. With this sl ope, the diffusion coefficient can be solved. 33

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 10 20 30 40 50 60 70 80 90 100 Time (minutes)Cumulative Mass Release (%)A 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 80 90 100 Time (sec1/2)Cumulative Mass Release (%) B Figure 15. (A) The cumulative percent of dexamethasone 21-phosphate released per fiber into PBS versus time. (B) The cumulative percent of dexamethasone 21-phosphate released per fiber into PBS versus the square root of time. Da shed line indicates the slope for short times. The standard deviation is substantially smaller than for the dexamethasone in PBS case. This is most likely due to the solubility of dexa methasone 21-phosphate in PBS. 34

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35 During the first 45 minutes release of dexa methasone 21-phosphate with respect to the square root of time was fairly linear. Approximately 60% of the drug was released in the first 15 minutes; by 45 minutes nearly 95% had been released. Using the slope the diffusion coefficient was estimated to be D = 2.36 x 10 -13 m 2 /s. Refer to appendix (Program Diffusion Coefficient for Dexameth asone 21-phosphate Calculations, page 85).

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36 Chapter 7 Dexamethasone 21-phosphate Loaded PLGA Coated Fiber Results For this 3 rd case dexamethasone 21-phosphate was diffusing through a PLGA membrane into PBS. Since the same agent was being analyzed us ing the CZE machine, as in chapter 5, the same standard curve was used (refer to figure 11). The dexamethasone 21-phosphate loaded PLGA coated fibers were again placed in a PBS solution and analyzed at various time periods (1, 2, 5, 8, 12, 17, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, 93, 100, and 107 days). After each incubation period the eluant was removed and analyzed using CZE and then replaced wi th fresh PBS. This provided an accurate method for determining the dexamethasone 21-p hosphate content, which was eluted into the PBS solution during each period (figure 16).

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0 10 20 30 40 50 60 70 80 90 100 110 0 50 100 150 200 250 300 350 400 Time (days)Area Units Figure 16. CZE data obtained for each incubation period. To use the mathematical model described in chapter 4 it is necessary to calculate the concentration and the cumulative concentrat ion levels at each ti me period. This can be achieved as in the previous chapters usi ng the standard curve (figure 11). Forming a relationship between the two sets of data provides a direct correlation between time and concentration levels. The peak areas for each sample were converted to their equivalent concentration using this relationship (figure 17). The outlying bars in the figures represent standard deviation for the data sets. 37

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0 10 20 30 40 50 60 70 80 90 100 110 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time (days)Concentration (mg/ml) Figure 17. Concentration eluted at each time interval for the dexamethasone 21-phosphate loaded PLGA coated fibers. Taking the corresponding concentration at each time interval and adding the following concentration a cumulative rela tionship was formed. This shows the cumulative release of dexamethasone 21-phosphate concentration for each time until depletion from the coated fiber (figure 18) Refer to appendix (Program PLGA DEX21 Concentrations, page 68) for calculations. 38

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0 10 20 30 40 50 60 70 80 90 100 110 0 0.05 0.1 0.15 0.2 0.25 Time (days)Cumulative Concentration (mg/ml) Figure 18. Cumulative concentration releas e against time for PLGA coated fibers. On average the fibers were loaded wi th a concentration of 0.222 mg/ml of dexamethasone 21-phosphate as verified by CZE having an equivalent mass of 44.4 g per fiber segment. Knowing the initial concen tration allows the previous figure to be converted to a cumulative mass release versus time plot (figure 19). This set of data is not necessary in the calculation of the diffusion coefficient; howev er, this plot helps provides a better understanding of the diffusion proce ss. By day 17, approximately 52% of the drug was released from the fiber through th e PLGA membrane. Release was measured till day 107 at which time ~98% of the agent had b een released. Due to th e increasing rate of release in the later time intervals it is safe to assume that the fibers were very near to complete elution by 107 days. This can be verified below by the diffusion rate trends. 39

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0 10 20 30 40 50 60 70 80 90 100 110 0 10 20 30 40 50 60 70 80 90 100 Time (days)Cumulative Mass Release (%) Figure 19. The cumulative percentage of dexamethasone 21-phosphate released from the PLGA membrane surrounding the fiber into PBS versus time. Using the concentration and cumulative concentration data with chapter 4s equation (12) individual time in terval diffusion coefficients can be calculated. Refer to the program (Program Diffusion through PL GA membrane Program, page 86) in the appendix. Plotting these coefficients illustrate s how diffusion is varying with respect to time (figure 20). 40

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0 10 20 30 40 50 60 70 80 90 100 110 0 1 2 3 4 5 6 7 x 10-13 Time (days)Diffusion Rate (m2/s) Figure 20. Diffusion rates at each time interval for dexamethasone 21-phosphate through a PLGA membrane. Analyzing (figure 20), it is evident that for a sustained period dexamethasone 21phoshate is diffusing through the PLGA membrane at an almost steady rate. From day 5 until day 58 it appears that nearly steady-state diffusion occurred. This model was linearized and the steady-state diffusion coefficient for dexamethasone 21-phosphate through a PLGA membrane was es timated to be D = 4.59 x 10 -14 m 2 /s, a value not previously reported. For the first two days the diffusion rate was faster because there is an initial burst of releas e for the dexamethasone 21-phosphate This is mainly due to the residual drug left on the outside of the fiber. After 58 days the fibe rs coating began to degrade releasing the agent at an increasing rate as time progressed. These two results seem quite accurate and follow what was exp ected for release from the polymer, PLGA. 41

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42 Chapter 8 Discussion 8.1 Dexamethasone The dried NDGA collagen fibers wei gh on average 0.169 mg/fiber, have a diameter of ~0.08 mm, and a length of 10 mm. When placed in a dexamethasone solution overnight the fibers swell and absorb the drug. The hydrated fibers diameter increases to 0.117 mm on average. After 2 days nearly all of the dexamethasone was released into the PBS solution, an estimated 0.021 mg/ml of dexamethasone (figure 9). The diffusion coefficient of dexamethasone in the NDGA collagen fibers was found to be D = 1.86 x 10 -14 m 2 /s, a value that has not been previously reported. The diffusion coefficient of dexamethasone in the NDGA collagen fiber was compared to the diffusion coefficient for dexamethasone in other media from the literature. The diffusion coefficient of dexamethasone in the NDGA collagen fiber is less than that in cellulose acetate but greater than in the poly(ether ur ethane), Tecoplast (Table 2).

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43 Table 2. Diffusion coefficients of dexamethasone in various media. Medium D [m 2 /s] Reference Water 6.82x10 -10 Stokes-Einstein equation Subcutaneous tissue 4.111.77 x10 -10 Moussy et al. 2006 16 Subcutaneous tissue 4.012.01 x10 -10 Moussy et al. 2006 17 Brain 2.0x10 -10 Saltzman and Radomsky, 1991 18 Cellulose acetate membrane 3.15x10 -11a Barry and Brace, 1977 2 NDGA collagen fibers 1.86 x 10 -14 This study. Tecoplast 7.0 x 10 -17 Lyu et al., 2005 14 PTMC 2.26 x 10 -21b Zhang et al., 2006 21 mPEG 3 -PTMC 11 4.8 x 10 -22c Zhang et al., 2006 21 Tecothane75D 3.0 x 10 -23 Lyu et al., 2005 14 a Interpolated for 37 C b poly(trimethylene carbonate) c monomethoxy poly(ethylene glycol)block -poly(trimethylene carbonate) 8.2 Dexamethasone 21-phosphate The dexamethasone 21-phosphate loaded NDGA collagen fibers were of the same dimensions as the dexamethasone loaded fibers when hydrated. The primary difference between these two agents is their capability for loading and their solubility. Protonated free amines in the collagen phase bind with the negatively charged phosphate groups in the dexamethasone 21-phosphate. This binding process enables the fibers to be loaded with an estimated 0.222 mg/ml of drug when lo aded in a 3% acetic acid solution. This is

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44 nearly 11 times greater than when the fibers are loaded with dexamethasone in ethanol. The two agents are loaded using different so lvents (ethanol versus 3% acetic acid). In water dexamethasone is nearly insoluble havi ng a solubility of 10 mg/100 ml. However, it is highly soluble in ethanol 3 On the other hand, dexamethasone 21-phosphate is watersoluble. However, dexamethasone 21-phosphate is loaded in the 3% acetic acid (v/v, in water) because it alters the pH levels causi ng the collagen phase to become positively charged favoring ionic interaction with the negatively charged phosphate groups increasing the loading potential. When examining the data for dexamethasone 21phosphate elution, it is evident that the release rate is much faster than for dexamethasone. After 75 minutes the dexameth asone 21-phosphate had left the fiber. This rapid elution is due to the solubility of this drug in PBS and the neutralization of the collagen in PBS. The diffusion coefficient of dexamethasone 21-phosphate in the NDGA collagen fibers was found to be D = 2.36 x 10 -13 m 2 /s, a value that has not previously been reported. The diffusion coefficient for dexamethasone 21-phosphate in the NDGA collagen fiber is approximately 12 times greater than for dexamethasone in the NDGA collagen fiber. 8.3 PLGA Coated Dexamethasone 21-phosphate Loaded Fibers Clearly, dexamethasone 21-phosphate shows a greater capacity for loading in the NDGA collagen fibers. However, since this agen t is water-soluble the release rate is too rapid and does not demonstrate substantial be nefit for drug delivery applications. To use this anti-inflammatory drug the release rate must be controlled in a sustained manner,

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45 which is why a PLGA membrane was applied to the fibers. This membrane increased the fibers average diameter to 0.306 mm (n =30). The preliminary results for the 3 rd case show that after 100 days the coated fibe rs continue to release dexamethasone 21phosphate (figure 18). The PLGA membrane also sustains a nearly st eady state rate of release for the first 58 days. This steady state diffusion coefficient was estimated to be D = 4.59 x 10 -14 m 2 /s, a value not previously reported. This rate is approximately 5 times slower than that of the unco ated fiber loaded with dexame thasone 21-phosphate. The rate is based off of the diffusional distance, whic h corresponds to the thickness of the fibers coating. These preliminary results illust rate the potential that PLGA coated NDGA collagen fibers possess for a drug delivery system.

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46 Chapter 9 Conclusion 9.1 Summary It is evident that there is a substantial need for a method to continuously monitor blood glucose levels via an implantable se nsor. Applying an effective drug delivery system for anti-inflammatory and immunosuppresant agents in vivo will increase the biosensors acceptance by the host, increase functionality and lifespan 20 This paper has shown that NDGA collagen fibers can be loaded with a therapeutic agent and release of this agent can be determined and controll ed. The loading process is principally a mechanical process. Therefore, loading the fi bers with other agents (or combinations of agents) should be a viable option. By a ltering the fiber length or thickness during fabrication potential loading volumes can be increased and by utilizing different chemistries drug retention in the fibers can be improved. If further control of release is required different biopolymer me mbranes could be applied. Similar to the fibers, the thickness of the coatings can be adjusted to promote the optimum rate of diffusion. Previous studies have demonstrated that the NDGA collagen fibers are biocompatible in vitro and in vivo 12 Thus, NDGA collagen fibers exhibit a great deal of potential for in vivo applications and clearly repres ent a novel drug delivery system.

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47 9.2 Future Works Now that an effective system has been proposed to deliver anti-inflammatory agents, the next step will be to incorporate these fibers into the implantable glucose sensor. The next proposed project would be to apply these fibers to glucose sensors, which our lab has developed, and implant these for in vivo testing. This will hopefully provide insight into how effective the de xamethasone 21-phosphate is at reducing inflammation and fibrosis around the implante d sensor and show if the sensitivity and lifespan of the sensor is improved. If the resu lts from this experiment show promise, drug loading amounts and diffusion rates may be adju sted during fabricati on to model the most efficient system for use with the sensor. Further studies may include the loading of different agents into the fibers, such as Vascular Endothelial Growth Factor (VEGF). VEGF should increase blood vessel growth; t hus, has potential for in creasing sensitivity in the sensor.

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48 References 1. Alto, William A., Daniel Meyer, James Schneid, Paul Bryson, and Jon Kindig. Assuring the Accuracy of Home Glucose Monitoring. JABFP 15 (2002): 1-6. 2. Barry, B.W. and A.R. Brace. Permeation of oestrone, oestradiol, oestriol and dexamethasone across cellulose acetate membrane. The Journal of pharmacy and pharmacology 29 (1997): 397-400. 3. Budarari, Susan, ed. The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals. Rahyway, NJ: Merck & Co., Inc., 1989. 4. Centers for Disease Control and Prevention. National diabetes fact sheet: general information and national estimates on diab etes in the United St ates, 2005. Atlanta, GA: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, 2005. 5. Dang, Wenbin and W. Mark Saltzman. Dextran Retention in the Rat Brain Following Release from a Polymer Implant. Biotechnol. Prog. 8 (1992): 527-532. 6. Fraser, David M., Biosensors in the Body, Continuous in vivo Monitoring. Chichester, England: John Wiley & Sons, 1997. 7. Galleti, Pierre M., Clark K. Colton, Mich ael Jaffrin, and Gerard Reach. Artificial Pancreas. The Biomedical Engineeri ng Handbook. Ed. Joseph Bronzino. Hartford, CT: CRC Press, 1995. 1968-1978. 8. Incropera, Frank and David Dewitt. Fundame ntals of Heat and Mass Transfer. New York: John Wiley & Sons, 1996. 9. Ju, Young Min, Bazhang Yu, Yvonne Moussy and Francis Moussy. Preparation of 3D Porous Collagen Scaffold around Implantable Biosensor for Improving Biocompatibility in 2006 Society for Biomater ials Annual Meeting, Pittsburgh, 2006. 10. Koob, Thomas J. Biomimetic a pproaches to tendon repair. Comparative Biochemistry and Physiology Part A 133 (2002): 1171-1192. 11. Koob, Thomas J. and Daniel Hernandez. Material properties of polymerized NDGAcollagen composite fibers: development of biologically based tendon constructs. Biomaterials 23 (2002): 203-212.

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49 12. Koob, Thomas J., Toni A. Willis, Yu Sh an Qiu, and Daniel J. Hernandez. Biocompatibility of NDGA-polymerized collagen fibers. I. Evaluation of cytotoxicity with tendon fibroblasts in vitro . J Biomed Mater Res. 56 (2001): 31-39. 13. Lamiable D., R. Vistelle, H. Millart, V. Sulmont, R. Fay, J. Caron, and H. Choisy. High-performance liquid chromatographic determination of dexamethasone in human plasma. J Chromatography. 378 (1986): 486-491. 14. Lyu, Su-Ping, et al. Adjusting drug diffusivity using miscible polymer blends. Journal of Controlled Release 102 (2005): 679-687. 15. Mayfield, Jennifer and Stephen Havas. S elf-control: A Physicians Guide to Blood Glucose Monitoring in the Management of Diabetes, An American Family Physician Monograph. American Academy of Family Physicians, 2004. 16. Moussy, Yvonne, Lawrence Hersh and Pa ul Dungel. Distribution of [ 3 H] dexamethasone in rat subcutaneous tissue after delivery from osmotic pumps. Biotechnology. Prog. 22 (2006): 819-824. 17. Moussy, Yvonne, Lawrence Hersh and Paul Dungel. Diffusion of [ 3 H] Dexamethasone in rat subcut aneous Slices after Inj ection Measured by Digital Autoradiography. Biotechnology. Prog. 22 (2006): 1715-1719. 18. Saltzman, W.M. and M.L. Radomsky. Dr ugs Released from Polymers: Diffusion and Elimination in Brain Tissue. Chem. Eng. Sci. 46 (1991): 2429-2444. 19. Vergnaud, J.M. Liquid Transport Processes in Polymeric Materials. Englewood Cliffs, NJ: Prentice Hall, 1991. 20. Wisniewski, N., F. Moussy, and W.M. Reic hert. Characterization of Implantable Biosensor Membrane Biofouling. Fresenius J. Anal. Chem. 366 (2000): 611-621. 21. Zhang, Zheng, Dirk W. Grijpma, and Jan Feijen. Poly(trimethylene carbonate) and monomethoxy poly(et hylene glycol)block-poly(trimethylene carbonate) nanoparticles for the controlled release of dexamethasone. Journal of Controlled Release 111 (2006): 263-270.

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50 Appendices

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Appendix A: Additional Information and Figures Diffusion Diffusion is a passive transport process in which the driving potential is the species concentration gradient. The higher concentration will permea te through the fiber to the lower concentration until a balance is achieved. Figure 21. This figure illustrates the process at which the agents are diffusing from the fibers. 51

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Appendix A: (Continued) NDGA collagen fiber PLGA coating Figure 22. Cross-section of PLGA coated fiber. 52

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53 Appendix A: (Continued) Detailed Fiber Fabrication Protocol The fiber fabrication process is a very delicate and intricate procedure. It is essential to follow the required steps to produce high strength, biocompatible fibers. The entire process takes four days and can be broken up into daily procedures. The following is a more detailed account of the fabrication procedure. The first day covers initial setup a nd collagen production. To begin attach 0.32ml/cm hydrated dialysis tubing to the end of a 5 ml Ependorf Repeater pipet tips. It is essential not to crimp or hit the dialysis tubi ng on any sharp edges, as it is very fragile and important to the collagen formation pro cess. Use a piece of silicon tubing to hold the 41.5cm length dialysis tubing ont o the repeater tip. The colla gen solution used is 0.13% w/v in 3% acetic acid. This 0.13% w/v yields the strongest fibers feasible, w ith around a 250 Newton tensile strength. Load the collagen solution into the dialysis tubing. Make sure to seal the end of the tubing, so as not to lose the solution. As pirate any air bubbles, as this will weaken the collagen fibril form ation. Make sure the tubing assemblies are hung in tension to prevent imperfections in fibril alignment and place them in a 4-liter graduated cylinder of de-ionized water. Change the water every 30 minutes for at least 7 hours. This washing step is necessary as it dialyses the acetic acid from the collagen solution. Any remaining acetic acid left in the tubing will breakdown the collagen preventing fibril alignment and formation. Once the washing is complete transfer the tubing assemblies into 4-liters of freshly made PBS, pH 7.4. Place this into a 37 C incubator overnight.

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54 Appendix A: (Continued) The second day encompasses drying th e fibers. After 16 hours of incubation remove the PBS filled graduated cylinder. During this time period the collagen will have re-natured and formed fibrils. Once again, tr ansfer the tubing assembly into a 4-liter graduated cylinder filled with de-ionized water for 30 minutes to remove any salt that was absorbed during incubation. Transfer the fibers to a flat pan filled with 1cm of deionized water. At this stage in fabrication the fibers are extremely fragile. Ensure the fibers will not twist or kink, as this will promote weaknesses in the drying phase. The drying device is essentially a motor drive the lifts a jack at variable speeds. Attached to the jack is a Styrofoam block that overhangs the pan. Attach the fiber ends to a bamboo toothpick by overlapping them. Place the toot hpick approximately 4cm out of the water into the Styrofoam block. Allow the fibers to dry here for about 2 hours, until their diameter is about 1mm. Once the fiber is dr y the strength will increase dramatically. Running the lifting device at rate of 1.4m m/min ensures exposed fibers will dry and strengthen enough to su pport the hydrated fibers that ar e being lifted from the pan. On the third day NDGA cross-linking takes place. Remove the dried fibers from the lifting device and use sewing thread to bunc h the fibers together at one end. Making sure the fibers remain aligned and in slight tension using the thread. Place the fibers into a long glass tube with stoppers at each end. Create a 27ml solution of 0.1 M sodium phosphate buffer increase the pH level to 9.0 using NaOH. Sparge th is solution for two minutes. While the buffer is sparging, di ssolve 90mg of NDGA in 0.4 M NaOH. Mix both of these solutions together and place conten ts inside the glass tube that houses the

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55 Appendix A: (Continued) fibers. Set glass tube on a rocker overnight. Th is step will help th e fibers to cross-link evenly with the NDGA. The final day is used to wash the fi bers and dry them. Begin by removing the NDGA solution and briefly wash the fibers w ith 5ml of 70% ethanol. Empty contents of the glass tube and then fill 2/3 of tube with ethanol again. Seal the tube and replace it back onto the rocker for about 20 minutes. Dr ain again and perform final wash refilling tube with ethanol and placing on rocker fo r 60 minutes. Finally, drain the tube and remove fibers carefully. Hang vertically for dr ying. Ensure the fibers are separated while drying and in tension. Allo w fibers to dry overnight.

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Appendix A: (Continued) Figure 23. Fabrication procedure. Top panel: 1) Ta ke 0.13%(w/v) collagen in 3% acetic acid and place in dialysis tubing. 2) Dialyze in de-ionized H 2 O for ~7 hrs. 3) Incubate at 37 C for 16 hrs in 4L of PBS solution 4) Dialyze in de-ionized H 2 O again. 5) Extrude and dry fibers; NDGA Cross-linking. Middle panel: 6) Place the dry fibers into a glass tube with NDGA/sodium phosphate buffer solution. 7) Cap tube and place on rocker overnight. 8) Wash fibers in 70% EtOH to remove unbound NDGA. 9) Remove NDGA treated fibers and hang to dry. 10) NDGA cross-linked collagen fibers; Drug Loading and Elution. Bottom panel: 11) Dexamethasone loaded in 70% EtOH solution or dexamethasone 21-phosphate loaded in 3% acetic acid overnight. 12) Discard solution and dry fibers for one day. 13) Place drug loaded fibers in PBS solution and use Capillary Zone Electrophoresis to measure drug elution at specified time intervals. 56

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Appendix B: Maple Programs > restart; Program Dexamethasone Concentrations This program calculates first the concentrations at co rresponding times (a), then the cumulative concentrations (b ) including standard deviations. This equation was obtained from the standa rd curve of DEX in PBS calculated by Tian Davis' experiments. Using data provided by her June 5th, 2006 excel sheet. This formula represents how much DEX is eluted (y in area units) depending on the concentration loaded into the fibers (x in mg/ml). y:=14501*x-33.932 This equation is then rewritten in terms of x: > x:=(y+33.932)/14501; := x y 14501 0.002339976553 This equation was then used with corresponding data from Tian Davis' experiment 6 from June 1st, 2006 email. In experiment 6 Tian found a relationship between the DEX eluted in PBS to the time. Using the data from this experiment we shall formulate a relationship between the concentration (mg/ml) vs. time (hours). case 1: at time 0 there was no area units present. > y:=0; := y 0 > Concentration[time=0]:=evalf(x); := Concentration time 00.002339976553 case 2: at time = 1 hr, 78.81 area units were eluted. > y:=78.81; Concentration[time=1]:=(y+33.932)/14501; := y 78.81 := Concentration time 10.007774774153 case 3a: at time = 3 hr, 69.8 area units were eluted. 57

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Appendix B: (Continued) > y:=69.8; Concentration[time=3]:=(y+33.932)/14501; := y 69.8 := Concentration time 30.007153437694 case 4a: at time = 6 hr, 49.34 area units were eluted. > y:=49.34; Concentration[time=6]:=(y+33.932)/14501; > := y 49.34 := Concentration time 60.005742500517 case 5a: at time = 9 hr, 33.81 area units were eluted. > y:=33.81; Concentration[time=9]:=(y+33.932)/14501; := y 33.81 := Concentration time 90.004671539893 case 6a: at time = 12 hr, 12.91 area units were eluted. > y:=12.91; Concentration[time=12]:=(y+33.932)/14501; := y 12.91 := Concentration time 120.003230259982 case 7a: at time = 24 hr, 10.74 area units were eluted. > y:=10.74; Concentration[time=24]:=(y+33.932)/14501; := y 10.74 := Concentration time 240.003080615130 case8a: at time = 30 hr, 3.7 area units were eluted. 58 > y:=3.7;

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Appendix B: (Continued) Concentration[time=30]:=(y+33.932)/14501; := y 3.7 := Concentration time 300.002595131370 case9a: at time = 48 hr, 8.27 area units were eluted. > y:=8.27; Concentration[time=48]:=(y+33.932)/14501; := y 8.27 := Concentration time 480.002910282049 These are the cumulative concentrations : case 1: at time 0 there was no area units present. case 2: at time = 1 hr, 78.81 area units were eluted. > y:=78.81; CumulativeConcentration[time=1]:=(y+33.932)/14501; dev:=78.81+(7.485608414); UpperStd[time=1]:=(dev+33.932)/14501; DevDiff:=.8290987408e-2-.7774774153e-2; := y 78.81 := CumulativeConcentration time 10.007774774153 := de v 86.29560841 := UpperStd time 10.008290987408 := D evDif f 0.000516213255 case 3b: at time = 3 hr, 69.8 mo re area units were eluted. > y:=78.81+69.8; CumulativeConcentration[time=3]:=(y+33.932)/14501; dev:=148.61+(23.99038928); UpperStd[time=3]:=(dev+33.932)/14501; DevDiff:=.1424263080e-1-.1258823529e-1; := y 148.61 59

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Appendix B: (Continued) := CumulativeConcentration time 30.01258823529 := dev 172.6003893 := UpperStd time 30.01424263080 := D evDiff 0.00165439551 case 4b: at time = 6 hr, 49.34 more area units were eluted. > y:=78.81+69.8+49.34; CumulativeConcentration[time=6]:=(y+33.932)/14501; dev:=197.95+(42.08267656); UpperStd[time=6]:=(dev+33.932)/14501; DevDiff:=.1889281267e-1-.1599075925e-1; := y 197.95 := CumulativeConcentration time 60.01599075925 := de v 240.0326766 := UpperStd time 60.01889281267 := D evDif f 0.00290205342 case 5b: at time = 9 hr, 33.81 more area units were eluted. > y:=78.81+69.8+49.34+33.81; CumulativeConcentration[time=9]:=(y+33.932)/14501; dev:=231.76+(64.53328512); UpperStd[time=9]:=(dev+33.932)/14501; DevDiff:=.2277258707e-1-.1832232260e-1; := y 231.76 := CumulativeConcentration time 90.01832232260 := de v 296.2932851 := UpperStd time 90.02277258707 := D evDif f 0.00445026447 case 6b: at time = 12 hr, 12.91 mo re area units were eluted. 60

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Appendix B: (Continued) > y:=78.81+69.8+49.34+33.81+12.91; CumulativeConcentration[time=12]:=(y+33.932)/14501; dev:=244.67+(71.77189252); UpperStd[time=12]:=(dev+33.932)/14501; DevDiff:=.2416205037e-1-.1921260602e-1; := y 244.67 := CumulativeConcentration time 120.01921260602 := de v 316.4418925 := UpperStd time 120.02416205037 := D evDif f 0.00494944435 case 7b: at time = 24 hr, 10.74 mo re area units were eluted. > y:=78.81+69.8+49.34+33.81+12.91+10.74; CumulativeConcentration[time=24]:=(y+33.932)/14501; dev:=255.41+(82.22359015); UpperStd[time=24]:=(dev+33.932)/14501; DevDiff:=.2562344598e-1-.1995324460e-1; := y 255.41 := CumulativeConcentration time 240.01995324460 := de v 337.6335902 := UpperStd time 240.02562344598 := D evDif f 0.00567020138 case 8b: at time = 30 hr, 3.7 mo re area units were eluted. > y:=78.81+69.8+49.34+33.81+12.91+10.74+3.7; CumulativeConcentration[time=30]:=(y+33.932)/14501; dev:=259.11+(82.27916504); UpperStd[time=30]:=(dev+33.932)/14501; DevDiff:=.2588243328e-1-.2020839942e-1; 61

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Appendix B: (Continued) := y 259.11 := CumulativeConcentration time 300.02020839942 := de v 341.3891650 := UpperStd time 300.02588243328 := D evDif f 0.00567403386 case 9b: at time = 48 hr, 8.27 mo re area units were eluted. > y:=78.81+69.8+49.34+33.81+12.91+10.74+3.7+8.27; CumulativeConcentration[time=48]:=(y+33.932)/14501; dev:=267.38+(77.96223872); UpperStd[time=48]:=(dev+33.932)/14501; DevDiff:=.2615504025e-1-.2077870491e-1; := y 267.38 := CumulativeConcentration time 480.02077870491 := de v 345.3422387 := UpperStd time 480.02615504025 := D evDif f 0.00537633534 An average of 267.38 area units eluted wh ich is equivalent to a total of 0.02077870491 mg/ml 62

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Appendix B: (Continued) > restart; Program Dexamethasone 21-phosphate Concentrations This program calculates first the concentrations at co rresponding times (a), then the cumulative concentrations (b) and standard deviations. This equation was obtained from the sta ndard curve of dexamethasone 21-phosphate (DEX21) in PBS calculated by Ti an Davis' experiments. Usi ng data provided by her June 13, 2006 excel sheet called 'Exp 15 std'. This formula represents how much DEX21 is eluted (y in area units) depending on the concentration loaded into the fibers (x in mg/ml). y:=13571*x-328.71 This equation is then rewritten in terms of x: > x:=(y+328.71)/13571; := x y 13571 0.02422150173 This equation was then used with corresponding data from Tian Davis' experiment 8 from July 7th, 2006 email. In experiment 8 Tian found a relationship between the DEX21 eluted in PBS to the time. Using the data from this experiment we shall formulate a relationship between the concentrat ion (mg/ml) vs. time (minutes). case 1: at time 0 there was no area units present. > y:=0; := y 0 > Concentration[time=0]:=evalf(x); := Concentration time 00.02422150173 case 2: at time = 15 minutes, 1498.27 area units were eluted. > y:=1498.27; Concentration[time=15]:=(y+328.71)/13571; := y 1498.27 := Concentration time 150.1346238302 case 3a: at time = 30 minutes, 727.55 area units were eluted. > y:=727.55; 63

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Appendix B: (Continued) Concentration[time=30]:=(y+328.71)/13571; := y 727.55 := Concentration time 300.07783214207 case 4a: at time = 45 minutes, 317.15 area units were eluted. > y:=317.15; Concentration[time=45]:=(y+328.71)/13571; > := y 317.15 := Concentration time 450.04759118709 case 5a: at time = 60 minutes, 106.52 area units were eluted. > y:=106.52; Concentration[time=60]:=(y+328.71)/13571; := y 106.52 := Concentration time 600.03207059170 case 6a: at time = 75 minutes, 35.5 area units were eluted. > y:=35.5; Concentration[time=75]:=(y+328.71)/13571; := y 35.5 := Concentration time 750.02683737381 Here, case 2 is redone because the standard deviation was needed. case 2: at time = 15 minutes, 1498.27 area units were eluted. > y:=1498.27; Concentration[time=15]:=(y+328.71)/13571; dev:=1498.27+142.4087626; UpperStd[time=15]:=(dev+328.71)/13571; 64 devDiff:=.1451174388-.1346238302;

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Appendix B: (Continued) := y 1498.27 := Concentration time 150.1346238302 := de v 1640.678763 := UpperStd time 150.1451174388 := devDif f 0.0104936086 These are the cumulative concentrations (b) and also the standard deviations for the data. Notice case 1 and 2 were omitted because they are the same. case 3b: at time = 30 minutes, 727. 55 more area units were eluted. > y:=1498.27+727.55; CumulativeConcentration[time=30]:=(y+328.71)/13571; dev:=2225.82+151.9352698; UpperStd[time=30]:=(dev+328.71)/13571; devDiff:=.1994300545-.1882344705; := y 2225.82 := CumulativeConcentration time 300.1882344705 := de v 2377.755270 := UpperStd time 300.1994300545 := devDif f 0.0111955840 case 4b: at time = 45 minutes, 317. 15 more area units were eluted. > y:=1498.27+727.55+317.15; CumulativeConcentration[time=45]:=(y+328.71)/13571; dev:=2542.97+159.5902465; UpperStd[time=45]:=(dev+328.71)/13571; devDiff:=.2233638085-.2116041559; 65

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Appendix B: (Continued) := y 2542.97 := CumulativeConcentration time 450.2116041559 := de v 2702.560246 := UpperStd time 450.2233638085 := devDif f 0.0117596526 case 5b: at time = 60 minutes, 106. 52 more area units were eluted. > y:=1498.27+727.55+317.15+106.52; CumulativeConcentration[time=60]:=(y+328.71)/13571; dev:=2649.49+168.421221; UpperStd[time=60]:=(dev+328.71)/13571; devDiff:=.2318636225-.2194532459; := y 2649.49 := CumulativeConcentration time 600.2194532459 := de v 2817.911221 := UpperStd time 600.2318636225 := devDif f 0.0124103766 case 6b: at time = 75 minutes, 35.5 more area units were eluted. > y:=1498.27+727.55+317.15+106.52+35.5; CumulativeConcentration[time=75]:=(y+328.71)/13571; dev:=2684.99+171.8312121; UpperStd[time=75]:=(dev+328.71)/13571; devDiff:=.2347307650-.2220691179; := y 2684.99 := CumulativeConcentration time 750.2220691179 := de v 2856.821212 := UpperStd time 750.2347307650 := devDif f 0.0126616471 66

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67 Appendix B: (Continued) An average of 2684.99 area units were eluted which is equivale nt to a total of 0.2220691179 mg/ml

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Appendix B: (Continued) > restart; Program PLGA DEX21 Concentrations This program calculates the concentrations at corresponding times (a), and the cumulative concentrations at corresponding times (b). Both include standard deviation calculations. This equation was obtained from the standard curve of DEX21 in PBS calculated by Tian Davis' experiments. Using data provided by her June 13, 2006 excel sheet called 'Exp 15 std'. This formula represents how much DE X21 is eluted (y in area units) depending on the concentration level (x in mg/ml). y:=13571*x-328.71 This equation is then rewritten in terms of x: > x:=(y+328.71)/13571; := x y 13571 0.02422150173 This equation was then used with corresponding data from Tian Davis' experiment 14. In experiment 14 Tian found a relationship be tween the DEX21 eluted from the PLGA coated fibers into PBS with respect to time. Using the data from this experiment we shall formulate a relationship between the c oncentration (mg/ml) vs. time (days). case 1: at time 0 there was no area units present. case 2: at time = 1 day, 371. 2 area units were eluted. > y:=371.2; Concentration[time=1]:=(y+328.71)/13571; dev:=254.0424943+371.2; UpperStd[time=1]:=(dev+328.71)/13571; devDiff:=.7029345621e-1-.5157394444e-1; := y 371.2 := Concentration time 10.05157394444 := de v 625.2424943 := UpperStd time 10.07029345621 := devDif f 0.01871951177 68

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Appendix B: (Continued) case 3a: at time = 2 days, 136.33333 area units were eluted. > y:=136.333333; Concentration[time=2]:=(y+328.71)/13571; dev:=91.40963966+136.333333; UpperStd[time=2]:=(dev+328.71)/13571; devDiff:=.4100309282e-1-.3426743298e-1; := y 136.333333 := Concentration time 20.03426743298 := de v 227.7429727 := UpperStd time 20.04100309282 := devDif f 0.00673565984 case 4a: at time = 5 days, 221.93333 area units were eluted. > y:=221.9333333; Concentration[time=5]:=(y+328.71)/13571; dev:= 124.4473115+y; UpperStd[time=5]:=(dev+328.71)/13571; devDiff:=.4974509209e-1-.4057500061e-1; := y 221.9333333 := Concentration time 50.04057500061 := de v 346.3806448 := UpperStd time 50.04974509209 := devDif f 0.00917009148 case 5a: at time = 8days, 146.66667 area units were eluted. > y:=146.6666667; Concentration[time=8]:=(y+328.71)/13571; dev:= 59.99907407+y; UpperStd[time=8]:=(dev+328.71)/13571; devDiff:=.3944998458e-1-.3502886056e-1; 69

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Appendix B: (Continued) := y 146.6666667 := Concentration time 80.03502886056 := de v 206.6657408 := UpperStd time 80.03944998458 := devDif f 0.00442112402 case 6a: at time = 12days, 175. 266667 area units were eluted. > y:=175.2666667; Concentration[time=12]:=(y+328.71)/13571; dev:= 85.8860356+y; UpperStd[time=12]:=(dev+328.71)/13571; devDiff:=.4346494011e-1-.3713629553e-1; := y 175.2666667 := Concentration time 120.03713629553 := de v 261.1527023 := UpperStd time 120.04346494011 := devDif f 0.00632864458 case 7a: at time = 17days, 178. 733333 area units were eluted. > y:=178.7333333; Concentration[time=17]:=(y+328.71)/13571; dev:= 93.18154324+y; UpperStd[time=17]:=(dev+328.71)/13571; devDiff:=.4425796747e-1-.3739174219e-1; := y 178.7333333 := Concentration time 170.03739174219 := de v 271.9148765 := UpperStd time 170.04425796747 := devDif f 0.00686622528 case 8a: at time = 23days, 199. 333333 area units were eluted. 70

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Appendix B: (Continued) > y:=199.3333333; Concentration[time=23]:=(y+328.71)/13571; dev:= 81.15999288+y; UpperStd[time=23]:=(dev+328.71)/13571; devDiff:=.4489008372e-1-.3890968486e-1; := y 199.3333333 := Concentration time 230.03890968486 := de v 280.4933262 := UpperStd time 230.04489008372 := devDif f 0.00598039886 case 9a: at time = 30days, 210. 8 area units were eluted. > y:=210.8; Concentration[time=30]:=(y+328.71)/13571; dev:= 74.98762861+y; UpperStd[time=30]:=(dev+328.71)/13571; devDiff:=.4528020253e-1-.3975462383e-1; := y 210.8 := Concentration time 300.03975462383 := de v 285.7876286 := UpperStd time 300.04528020253 := devDif f 0.00552557870 case 10a: at time = 37days, 141.266667 area units were eluted. > y:=141.2666667; Concentration[time=37]:=(y+328.71)/13571; dev:= 47.21487525+y; UpperStd[time=37]:=(dev+328.71)/13571; devDiff:=.3811005394e-1-.3463095326e-1; 71

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Appendix B: (Continued) := y 141.2666667 := Concentration time 370.03463095326 := de v 188.4815420 := UpperStd time 370.03811005394 := devDif f 0.00347910068 case 11a: at time = 44days, 108.133333 area units were eluted. > y:=108.1333333; Concentration[time=44]:=(y+328.71)/13571; dev:= 44.58985934+y; UpperStd[time=44]:=(dev+328.71)/13571; devDiff:=.3547514498e-1-.3218947265e-1; := y 108.1333333 := Concentration time 440.03218947265 := de v 152.7231926 := UpperStd time 440.03547514498 := devDif f 0.00328567233 case 12a: at time = 51days, 91.8 area units were eluted. > y:=91.8; Concentration[time=51]:=(y+328.71)/13571; dev:= 53.45226323+y; UpperStd[time=51]:=(dev+328.71)/13571; devDiff:=.3492463806e-1-.3098592587e-1; := y 91.8 := Concentration time 510.03098592587 := de v 145.2522632 := UpperStd time 510.03492463806 := devDif f 0.00393871219 72

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Appendix B: (Continued) case 13a: at time = 58days, 76. 933333 area units were eluted. > y:=76.93333333; Concentration[time=58]:=(y+328.71)/13571; dev:= 57.3349806+y; UpperStd[time=58]:=(dev+328.71)/13571; devDiff:=.3411526887e-1-.2989045268e-1; := y 76.93333333 := Concentration time 580.02989045268 := de v 134.2683139 := UpperStd time 580.03411526887 := devDif f 0.00422481619 case 14a: at time = 65days, 129.466667 area units were eluted. > y:=129.4666667; Concentration[time=65]:=(y+328.71)/13571; dev:= 102.1144782+y; UpperStd[time=65]:=(dev+328.71)/13571; devDiff:=.4128591444e-1-.3376145212e-1; := y 129.4666667 := Concentration time 650.03376145212 := de v 231.5811449 := UpperStd time 650.04128591444 := devDif f 0.00752446232 case 15a: at time = 72days, 133. 66667 area units were eluted. > y:=133.6666667; Concentration[time=72]:=(y+328.71)/13571; dev:= 69.89714666+y; UpperStd[time=72]:=(dev+328.71)/13571; devDiff:=.3922141429e-1-.3407093557e-1; 73

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Appendix B: (Continued) := y 133.6666667 := Concentration time 720.03407093557 := de v 203.5638134 := UpperStd time 720.03922141429 := devDif f 0.00515047872 case 16a: at time = 79days, 107. 4666667 area units were eluted. > y:=107.4666667; Concentration[time=79]:=(y+328.71)/13571; dev:= 43.57279987+y; UpperStd[time=79]:=(dev+328.71)/13571; devDiff:=.3535107705e-1-.3214034829e-1; := y 107.4666667 := Concentration time 790.03214034829 := de v 151.0394666 := UpperStd time 790.03535107705 := devDif f 0.00321072876 case 17a: at time = 86days, 76.7333333 area units were eluted. > y:=76.73333333; Concentration[time=86]:=(y+328.71)/13571; dev:= 47.03568385+y; UpperStd[time=86]:=(dev+328.71)/13571; devDiff:=.3334161205e-1-.2987571537e-1; := y 76.73333333 := Concentration time 860.02987571537 := de v 123.7690172 := UpperStd time 860.03334161205 := devDif f 0.00346589668 74

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Appendix B: (Continued) case 18a: at time = 93days, 57.0666667 area units were eluted. > y:=57.06666667; Concentration[time=93]:=(y+328.71)/13571; dev:= 39.87368946+y; UpperStd[time=93]:=(dev+328.71)/13571; devDiff:=.3136470091e-1-.2842654680e-1; := y 57.06666667 := Concentration time 930.02842654680 := de v 96.94035613 := UpperStd time 930.03136470091 := devDif f 0.00293815411 case 19a: at time = 100days, 35.5333333 area units were eluted. > y:=35.53333333; Concentration[time=100]:=(y+328.71)/13571; dev:= 28.39268294+y; UpperStd[time=100]:=(dev+328.71)/13571; devDiff:=.2893198852e-1-.2683983003e-1; := y 35.53333333 := Concentration time 1000.02683983003 := de v 63.92601627 := UpperStd time 1000.02893198852 := devDif f 0.00209215849 case 20a: at time = 107days, 30.8666667 area units were eluted. > y:=30.86666667; Concentration[time=107]:=(y+328.71)/13571; dev:= 38.54694108+y; UpperStd[time=107]:=(dev+328.71)/13571; devDiff:=.2933635014e-1-.2649595952e-1; 75

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Appendix B: (Continued) := y 30.86666667 := Concentration time 1070.02649595952 := de v 69.41360775 := UpperStd time 1070.02933635014 := devDif f 0.00284039062 These are the cumulative concentrations at corresponding times (b) with standard deviations. Note that case 1 and 2 are omitted because they were already solved in part (a). case 3b: at time = 2 days, 136.3333 more area units were eluted. > y:=507.5333333; CumulativeConcentration[time=2]:=(y+328.71)/13571; dev:=507.5333333+298.679929; UpperStd[time=2]:=(dev+328.71)/13571; devDiff:=.8362856549e-1-.6161987571e-1; := y 507.5333333 := CumulativeConcentration time 20.06161987571 := de v 806.2132623 := UpperStd time 20.08362856549 := devDif f 0.02200868978 case 4b: at time = 5 days, 221.9333 more area units were eluted. > y:=729.4666667; CumulativeConcentration[time=5]:=(y+328.71)/13571; dev:=729.4666667+357.1519751; UpperStd[time=5]:=(dev+328.71)/13571; devDiff:=.1042906670-.7797337460e-1; 76

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Appendix B: (Continued) := y 729.4666667 := CumulativeConcentration time 50.07797337460 := de v 1086.618642 := UpperStd time 50.1042906670 := devDif f 0.02631729240 case 5b: at time = 8 days, 146.6667 more area units were eluted. > y:=876.1333333; CumulativeConcentration[time=8]:=(y+328.71)/13571; dev:=876.1333333+396.7563344; UpperStd[time=8]:=(dev+328.71)/13571; devDiff:=.1180163340-.8878073342e-1; := y 876.1333333 := CumulativeConcentration time 80.08878073342 := de v 1272.889668 := UpperStd time 80.1180163340 := devDif f 0.02923560058 case 6b: at time = 12 days, 175.2667 more area units were eluted. > y:=1051.4; CumulativeConcentration[time=12]:=(y+328.71)/13571; dev:=1051.4+443.6188554; UpperStd[time=12]:=(dev+328.71)/13571; devDiff:=.1343842646-.1016955272; := y 1051.4 := CumulativeConcentration time 120.1016955272 := de v 1495.018855 := UpperStd time 120.1343842646 := devDif f 0.0326887374 77

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Appendix B: (Continued) case 7b: at time = 17 days, 178.73333 more area units were eluted. > y:=1230.133333; CumulativeConcentration[time=17]:=(y+328.71)/13571; dev:=1230.133333+513.1005749; UpperStd[time=17]:=(dev+328.71)/13571; devDiff:=.1526743724-.1148657677; := y 1230.133333 := CumulativeConcentration time 170.1148657677 := de v 1743.233908 := UpperStd time 170.1526743724 := devDif f 0.0378086047 case 8b: at time = 23 days, 199.3333 more area units were eluted. > y:=1429.466667; CumulativeConcentration[time=23]:=(y+328.71)/13571; dev:=1429.466667+562.1573327; UpperStd[time=23]:=(dev+328.71)/13571; devDiff:=.1709773782-.1295539508; := y 1429.466667 := CumulativeConcentration time 230.1295539508 := de v 1991.624000 := UpperStd time 230.1709773782 := devDif f 0.0414234274 case 9b: at time = 30 days, 210.8 more area units were eluted. > y:=1640.266667; CumulativeConcentration[time=30]:=(y+328.71)/13571; dev:=1640.266667+619.3419178; UpperStd[time=30]:=(dev+328.71)/13571; devDiff:=.1907242344-.1450870729; 78

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Appendix B: (Continued) := y 1640.266667 := CumulativeConcentration time 300.1450870729 := de v 2259.608585 := UpperStd time 300.1907242344 := devDif f 0.0456371615 case 10b: at time = 37 days, 141.2667 more area units were eluted. > y:=1781.533333; CumulativeConcentration[time=37]:=(y+328.71)/13571; dev:=1781.533333+610.5314898; UpperStd[time=37]:=(dev+328.71)/13571; devDiff:=.2004844759-.1554965244; := y 1781.533333 := CumulativeConcentration time 370.1554965244 := de v 2392.064823 := UpperStd time 370.2004844759 := devDif f 0.0449879515 case 11b: at time = 44 days, 108.1333 more area units were eluted. > y:=1889.666667; CumulativeConcentration[time=44]:=(y+328.71)/13571; dev:=1889.666667+593.91928; UpperStd[time=44]:=(dev+328.71)/13571; devDiff:=.2072283506-.1634644954; := y 1889.666667 := CumulativeConcentration time 440.1634644954 := de v 2483.585947 := UpperStd time 440.2072283506 := devDif f 0.0437638552 79

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Appendix B: (Continued) case 12b: at time = 51 days, 91.8 more area units were eluted. > y:=1981.466667; CumulativeConcentration[time=51]:=(y+328.71)/13571; dev:=1981.466667+558.2319112; UpperStd[time=51]:=(dev+328.71)/13571; devDiff:=.2113630961-.1702289195; := y 1981.466667 := CumulativeConcentration time 510.1702289195 := de v 2539.698578 := UpperStd time 510.2113630961 := devDif f 0.0411341766 case 13b: at time = 58 days, 76.9333 more area units were eluted. > y:=2058.4; CumulativeConcentration[time=58]:=(y+328.71)/13571; dev:=2058.4+521.9679322; UpperStd[time=58]:=(dev+328.71)/13571; devDiff:=.2143598800-.1758978704; := y 2058.4 := CumulativeConcentration time 580.1758978704 := de v 2580.367932 := UpperStd time 580.2143598800 := devDif f 0.0384620096 case 14b: at time = 65 days, 129.4667 more area units were eluted. > y:=2187.866667; CumulativeConcentration[time=65]:=(y+328.71)/13571; dev:=2187.866667+506.5052703; UpperStd[time=65]:=(dev+328.71)/13571; devDiff:=.2227604404-.1854378208; 80

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Appendix B: (Continued) := y 2187.866667 := CumulativeConcentration time 650.1854378208 := de v 2694.371937 := UpperStd time 650.2227604404 := devDif f 0.0373226196 case 15b: at time = 72 days, 133.6667 more area units were eluted. > y:=2321.533333; CumulativeConcentration[time=72]:=(y+328.71)/13571; dev:=2321.533333+481.014241; UpperStd[time=72]:=(dev+328.71)/13571; devDiff:=.2307315285-.1952872546; := y 2321.533333 := CumulativeConcentration time 720.1952872546 := de v 2802.547574 := UpperStd time 720.2307315285 := devDif f 0.0354442739 case 16b: at time = 79 days, 107.4667 more area units were eluted. > y:=2429; CumulativeConcentration[time=79]:=(y+328.71)/13571; dev:=2429+442.8970284; UpperStd[time=79]:=(dev+328.71)/13571; devDiff:=.2358416497-.2032061012; := y 2429 := CumulativeConcentration time 790.2032061012 := de v 2871.897028 := UpperStd time 790.2358416497 := devDif f 0.0326355485 81

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Appendix B: (Continued) case 17b: at time = 86 days, 76.73333 more area units were eluted. > y:=2505.733333; CumulativeConcentration[time=86]:=(y+328.71)/13571; dev:=2505.733333+405.2431643; UpperStd[time=86]:=(dev+328.71)/13571; devDiff:=.2387212804-.2088603148; := y 2505.733333 := CumulativeConcentration time 860.2088603148 := de v 2910.976497 := UpperStd time 860.2387212804 := devDif f 0.0298609656 case 18b: at time = 93 days, 57.06667 more area units were eluted. > y:=2562.8; CumulativeConcentration[time=93]:=(y+328.71)/13571; dev:=2562.8+377.4835979; UpperStd[time=93]:=(dev+328.71)/13571; devDiff:=.2408808192-.2130653599; := y 2562.8 := CumulativeConcentration time 930.2130653599 := de v 2940.283598 := UpperStd time 930.2408808192 := devDif f 0.0278154593 case 19b: at time = 100 days, 35.53333 more area units were eluted. > y:=2598.333333; CumulativeConcentration[time=100]:=(y+328.71)/13571; dev:=2598.333333+355.7691199; UpperStd[time=100]:=(dev+328.71)/13571; devDiff:=.2418990828-.2156836882; 82

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Appendix B: (Continued) := y 2598.333333 := CumulativeConcentration time 1000.2156836882 := de v 2954.102453 := UpperStd time 1000.2418990828 := devDif f 0.0262153946 case 20b: at time = 107 days, 30.86667 more area units were eluted. > y:=2629.2; CumulativeConcentration[time=107]:=(y+328.71)/13571; dev:=2629.2+337.9609281; UpperStd[time=107]:=(dev+328.71)/13571; devDiff:=.2428613166-.2179581460; := y 2629.2 := CumulativeConcentration time 1070.2179581460 := de v 2967.160928 := UpperStd time 1070.2428613166 := devDif f 0.0249031706 An average of 2629.2 area units were eluted which is equivalent to a total of mg/ml. .2179581460 83

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Appendix B: (Continued) 84

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Appendix B: (Continued) 85

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Appendix B: (Continued) > restart; > unprotect(D); Program Diffusion through PLGA membrane Program This program goes through the derivations nece ssary to obtain equation (12) and the diffusion coefficient at each time interval. case: Hollow cylinder of Infinite Length under steady state conditions with constant concentration on each surface. Boundary Condi tions: @ r = Ri, C = Ci @ r = Re, C = Ce > Variable declarations: Ri is the inner radius, th e radius of the fiber. Re is the outer radius, the ra dius of the PLGA coating. r is the radius at any location in the com posite, depends on time. D is the diffusion coefficient L is the length of the coated fiber t is the time Mt is the amount of diffusing substance V is the volume of the fiber Ci is the dex21 fibers concentration Ce is the concentration in the PLGA coated fiber Steady State equations: > Eq1:=diff(r*diff(C(r),r),r); := Eq1 d d r () C rr d d2r2() C r > Eq2:=dsolve(Eq1,C(r)); := Eq2 () C r _C1_C2 () ln r > Eq3:=diff(Eq2,r); := Eq3 d d r () C r _C2 r Solving for using the boundary conditions previously stated. > bc1:=_C2*ln(R[i])+_C1-C[i]; := bc1 C2 () ln R i C1 C i > bc2:=_C2*ln(R[e])+_C1-C[e]; := bc2 C2 () ln R e C1 C e 86

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Appendix B: (Continued) > Eq4:=bc2-bc1; := E q4 C2 () ln R e C e C2 () ln R i C i > solve(Eq4,_C2); CeCi () ln Re() ln Ri Rewriting this result still in terms of what _C2 equals. > _C2:=(C[e]-C[i])/ln(R[e]/R[i]); := _C2 C e C i ln ReRi Substituting _C2 back into bc2 to solve for _C1. > solve(bc2,_C1); () ln ReCe() ln ReCiCe ln R eRi ln ReRi Assigning these constants and substituting them into our intial Con centration equation. > assign(_C1,_C2); > Eq2; () C r C e C i ln ReRi () C e C i() ln r ln ReRi Rewriting these results yields: > Eq2:=C(r)=C[e]+((C[e]-C[i])/ln(R[e]/R[i]))*ln(r/R[e]); 87

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Appendix B: (Continued) := Eq2 () C r Ce () CeCi ln r Re ln ReRi > The amount of a diffusing substance, M[t], diffuses through the le ngth of the tubing in time, t can be calculated by integrating Fick's 1st Law w.r.t time. > Eq4:=lhs(Eq3)=subs(r=R[e],rhs(Eq3)); := Eq4 d d r () C r C e C i ln ReRiRe > Ficks:=-2*pi*R[e]*L*int((D*diff(C(r),r)),t); := Ficks 2 ReL D d d r () C rt > M[t]:=subs(Eq4,Ficks); := Mt 2 L D() C e C it ln ReRi Since we have perfect sink conditions, Ce goes to 0. > M[t]:=subs(C[e]=0,M[t]); := Mt 2 L D C it ln ReRi > The purpose is to calculate D, the diffusion coefficient, so rearranging these equations: > M[t]:=unapply(M[t]); 88

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Appendix B: (Continued) := Mt () 2 L D C it ln ReRi > D:=(M[t]*ln(R[e]/R[i]))/(2*Pi*L*C[i]*t); := D 1 2 Mt ln R eRi LCit We shall now simplify this expression by ma king it a numerical expression and set it up for each time interval by taking out the constants not affected by each interval. The time for each case will be represented here by the variable n; however, the specific cases do not follow a specific interval and therefore must be calculated individually. Hours will be what n represents. > D[n]:=A*M[t](n)/(C[i](n)*(t(n)-t(n-1))); := Dn A M t () Cin () () t n () t n 1 Defining what variable A represents. > A:=ln(R[e]/R[i])/(2*Pi*L); := A 1 2 ln R eRi L Declaring the consta nts: Inner Radius, Ri; PLGA coated Radius, Re; L, length of the coated fiber. The inner radius, Ri is equal to the radius of the De x21 collagen fiber before the coating. This value was obtained from the volume frac tion program for dexamethasone (the units are in mm). > R[i]:=0.05832; := R i0.05832 89

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Appendix B: (Continued) The outer radius, Re is equal to the total radius with coating. Using the average of 30 fiber measurements we were able to obt ain a total diameter average of 0.372333mm. Therefore the radius would be 0.1861655mm. > R[e]:=0.305667; := R e0.305667 The length of the coated fiber will be equal to the length of our fibers 10mm, plus the thickness of the coating on the top and bottom of the fibers. The thickness is equal to the radius of the PLGA. Solving for thickness (in mm), then length of the coated fiber, L yields: > PLGAthickness:= R[e]-R[i]; := PLGAthickness 0.247347 > L:= (PLGAthickness*2)+10; := L 10.494694 Now we have all the components needed to solve for A (units are 1/mm). > A:=ln(R[e]/R[i])/(2*evalf(Pi)*L); := A 0.02512205784 I shall now convert this to centime ters for easier calculations later. > A:=A/10; := A 0.002512205784 The dex21 fibers concentration, Ci, is equal to the total concentration, Ct, minus the dex21 eluted from the fibers. Note: The total concentration was obtained from our previous experiments with just Dex21 loaded fibers. This value is assumed to be the same since the fibers were loaded exactly the same; the only difference is after loading they were coated with PLGA. Here I will declare the total concentration > C[tot]:=0.2220691179; := C tot0.2220691179 90

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Appendix B: (Continued) To calculate Mt, the amount of diffusing substance at each time, we must multiply the concentration at that time (which has been previously calculated, refer to maple program, Program Dexamethasone 21-phosphate Concentrations) by the volume of our PBS solution, V[PBS] declared here. Units are milliliters. > V[pbs]:=0.2; := V pbs0.2 Diffusion calculations at each time interval. Units: Mt is in mg Ci is in mg/ml t is in seconds D is in cm^2/sec > unprotect(Ci); Case1: At time 1 day. > Mt[1]:= V[pbs]*.5157394444e-1; := Mt 10.01031478889 > Ci[1]:= C[tot]-.5157394444e-1; := Ci10.1704951735 > t[1]:=24*60*60; := t186400 > D[1]:=(A*Mt[1])/(Ci[1]*t[1]); := D10.175909673810-8 Case2: At time 2 days. > Mt[2]:= V[pbs]*.3426743298e-1; := Mt 20.006853486596 91

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Appendix B: (Continued) > Ci[2]:= C[tot]-.6161987571e-1; := Ci20.1604492422 > t[2]:=86400; := t286400 > D[2]:=(A*Mt[2])/(Ci[2]*t[2]); := D20.124198218510-8 Case3: At time 5 days. > Mt[3]:= V[pbs]*.4057500061e-1; := Mt 30.008115000122 > Ci[3]:= C[tot]-.7797337460e-1; := Ci30.1440957433 > t[3]:=(86400*5-86400*2); := t3259200 > D[3]:=(A*Mt[3])/(Ci[3]*t[3]); := D30.545830240410-9 Case4: At time 8 days. > Mt[4]:= V[pbs]*.3502886056e-1; := Mt 40.007005772112 > Ci[4]:= C[tot]-.8878073342e-1; := Ci40.1332883845 92

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Appendix B: (Continued) > t[4]:=(86400*8-86400*5); := t4259200 > D[4]:=(A*Mt[4])/(Ci[4]*t[4]); := D40.509429295510-9 Case5: At time 12 days. > Mt[5]:= V[pbs]*.3713629553e-1; := Mt 50.007427259106 > Ci[5]:= C[tot]-.1016955272; := Ci50.1203735907 > t[5]:=(86400*12-86400*8); := t5345600 > D[5]:=(A*Mt[5])/(Ci[5]*t[5]); := D50.448516925910-9 Case6: At time 17 days. > Mt[6]:= V[pbs]*.3739174219e-1; := Mt 60.007478348438 > Ci[6]:= C[tot]-.1148657677; := Ci60.1072033502 > t[6]:=(86400*17-86400*12); := t6432000 93

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Appendix B: (Continued) > D[6]:=(A*Mt[6])/(Ci[6]*t[6]); := D60.405666180610-9 Case7: At time 23 days. > Mt[7]:= V[pbs]*.3890968486e-1; := Mt 70.007781936972 > Ci[7]:= C[tot]-.1295539508; := Ci70.0925151671 > t[7]:=(86400*23-86400*17); := t7518400 > D[7]:=(A*Mt[7])/(Ci[7]*t[7]); := D70.407628921310-9 Case8: At time 30 days. > Mt[8]:= V[pbs]*.3975462383e-1; := Mt 80.007950924766 > Ci[8]:= C[tot]-.1450870729; := Ci80.0769820450 > t[8]:=(86400*30-86400*23); := t8604800 > D[8]:=(A*Mt[8])/(Ci[8]*t[8]); := D80.429014162410-9 94

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Appendix B: (Continued) Case9: At time 37 days. > Mt[9]:= V[pbs]*.3463095326e-1; := Mt 90.006926190652 > Ci[9]:= C[tot]-.1554965244; := Ci90.0665725935 > t[9]:=(86400*37-86400*30); := t9604800 > D[9]:=(A*Mt[9])/(Ci[9]*t[9]); := D90.432157838110-9 Case10: At time 44 days. > Mt[10]:= V[pbs]*.3218947265e-1; := Mt 100.006437894530 > Ci[10]:= C[tot]-.1634644954; := Ci100.0586046225 > t[10]:=(86400*44-86400*37); := t10604800 > D[10]:=(A*Mt[10])/(Ci[10]*t[10]); := D100.456305195310-9 Case11: At time 51 days. 95

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Appendix B: (Continued) > Mt[11]:= V[pbs]*.3098592587e-1; := Mt 110.006197185174 > Ci[11]:= C[tot]-.1702289195; := Ci110.0518401984 > t[11]:=(86400*51-86400*44); := t11604800 > D[11]:=(A*Mt[11])/(Ci[11]*t[11]); := D110.496559444910-9 Case12: At time 58 days. > Mt[12]:= V[pbs]*.2989045268e-1; := Mt 120.005978090536 > Ci[12]:= C[tot]-.1758978704; := Ci120.0461712475 > t[12]:=(86400*58-86400*51); := t12604800 > D[12]:=(A*Mt[12])/(Ci[12]*t[12]); := D120.537816729810-9 Case13: At time 65 days. > Mt[13]:= V[pbs]*.3376145212e-1; := Mt 130.006752290424 96

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Appendix B: (Continued) > Ci[13]:= C[tot]-.1854378208; := Ci130.0366312971 > t[13]:=(86400*65-86400*58); := t13604800 > D[13]:=(A*Mt[13])/(Ci[13]*t[13]); := D130.765671082310-9 Case14: At time 72 days. > Mt[14]:= V[pbs]*.3407093557e-1; := Mt 140.006814187114 > Ci[14]:= C[tot]-.1952872546; := Ci140.0267818633 > t[14]:=(86400*72-86400*65); := t14604800 > D[14]:=(A*Mt[14])/(Ci[14]*t[14]); := D140.105685813510-8 Case15: At time 79 days. > Mt[15]:= V[pbs]*.3214034829e-1; := Mt 150.006428069658 > Ci[15]:= C[tot]-.2032061012; := Ci150.0188630167 97

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Appendix B: (Continued) > t[15]:=(86400*79-86400*72); := t15604800 > D[15]:=(A*Mt[15])/(Ci[15]*t[15]); := D150.141550971310-8 Case16: At time 86 days. > Mt[16]:= V[pbs]*.2987571537e-1; := Mt 160.005975143074 > Ci[16]:= C[tot]-.2088603148; := Ci160.0132088031 > t[16]:=(86400*86-86400*79); := t16604800 > D[16]:=(A*Mt[16])/(Ci[16]*t[16]); := D160.187900645210-8 Case17: At time 93 days. > Mt[17]:= V[pbs]*0.2842654680e-1; := Mt 170.005685309360 > Ci[17]:= C[tot]-.2130653599; := Ci170.0090037580 > t[17]:=(86400*93-86400*86); := t17604800 98

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Appendix B: (Continued) > D[17]:=(A*Mt[17])/(Ci[17]*t[17]); := D170.262285158410-8 Case18: At time 100 days. > Mt[18]:= V[pbs]*.2683983003e-1; := Mt 180.005367966006 > Ci[18]:= C[tot]-.2156836882; := Ci180.0063854297 > t[18]:=(86400*100-86400*93); := t18604800 > D[18]:=(A*Mt[18])/(Ci[18]*t[18]); := D180.349191012910-8 Case19: At time 107 days. > Mt[19]:= V[pbs]*.2649595952e-1; := Mt 190.005299191904 > Ci[19]:= C[tot]-.2179581460; := Ci190.0041109719 > t[19]:=(86400*107-86400*100); := t19604800 > D[19]:=(A*Mt[19])/(Ci[19]*t[19]); := D190.535437233010-8 99

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Appendix B: (Continued) Displaying all the diffusion coeffici ents up to day 107 (Units m^2/s). > for i from 1 by 1 to 19 do D[i]*10^(-4); end do; 0.175909673810-12 0.124198218510-12 0.545830240410-13 0.509429295510-13 0.448516925910-13 0.405666180610-13 0.407628921310-13 0.429014162410-13 0.432157838110-13 0.456305195310-13 0.496559444910-13 0.537816729810-13 0.765671082310-13 0.105685813510-12 0.141550971310-12 0.187900645210-12 0.262285158410-12 0.349191012910-12 0.535437233010-12 > Using Matlab to plot the diffu sion coefficients versus time (figure 20), we were able to calculate the steady-state diffusion rate. After 5 days the diffusion rate stabilizes till day 58, from here a linearization was taken. This provided us with an equation of: y = 3.17e-22*x+4.59e-14 100

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101 Appendix B: (Continued) where y is the diffusion coefficient and x is th e time in seconds. The slope of the line can be cancelled out since it is so minute. This provides us with a steady-state diffusion coefficient of 4.59e-14 m^2/sec for diffusion of dexame thasone 21-phosphate through the PLGA coating. Note: The experimental data we used to calcula te these results was only tested for 107 days. According to the data and trend the coat ed fibers should last slightly longer than this. At 107 days, 98% of the dexamethasone 21-phosphate was eluted. Theoretically, as the experiment continues to progress, the PLGA coating should begin to degrade more rapidly allowing the remaining dexamethasone 21-phosphate to diffuse quicker. From the diffusion results it appears this occurs. At about 65 days the PLGA coating may start to degrade increasing the rate of diffusion. It seems shortly after 107 days all the dexamethasone 21-phosphate loaded should have left the fiber.


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Transport characteristics using nor-dihydroguaiaretic acid (NDGA)-polymerized collagen fibers as a local drug delivery system
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by Eric Guegan.
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[Tampa, Fla.] :
b University of South Florida,
2007.
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ABSTRACT: Dexamethasone and dexamethasone 21-phosphate were loaded into NDGA-polymerized collagen fibers and release rate studies were performed to calculate their diffusion coefficients. Dexamethasone loaded fibers were placed in a PBS solution for specified time intervals (1, 3, 6, 7, 12, 24, 30, and 48 hours) after which the eluant was removed and analyzed by capillary zone electrophoresis (CZE). CZE is a tool that can be utilized for quantitative analysis of chemical compounds. This data was incorporated into mathematical models to determine the diffusion coefficient. The diffusion coefficient (D) for dexamethasone in NDGA-polymerized collagen fibers is D = 1.86 x 10^-14 m2/s. Similarly, dexamethasone 21-phosphate loaded fibers were placed into a PBS solution and analyzed using CZE at these specified intervals (15, 30, 45, 60, and 75 minutes). Applying this data to the mathematical model provided a diffusion coefficient for dexamethasone 21-phosphate in NDGA-polymerized collagen fibers of D = 2.36 x 10^-13 m2/s. In an effort to control drug delivery from these fibers a polylactic-co-glycolic acid (PLGA) coating was applied to the fibers. This coating helped sustain delivery of dexamethasone 21-phosphate for over a 100 day period. CZE experiments were again conducted in conjunction with another mathematical model to characterize release. A semi steady-state diffusion coefficient was estimated to be D = 4.59 x 10^-14 m2/s.
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Dexamethasone.
Dexamethasone 21-phosphate.
Diffusion coefficient.
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Polylactic-co-glycolic acid (PLGA).
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Dissertations, Academic
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