Application of Chemical Structure-Based Parameters of Drug Substances and Polymers to Predict Kinetics of Drug Release from Polymer Coated Pellets By

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Application of Chemical Structure-based Parameters of Drug Substances and Polymers to Predict Kinetics of Drug Release from Polymer Coated Pellets

Stephanie Kwan

A thesis submitted in conformity with the requirements for the degree of Master of Science Leslie Dan Faculty of Pharmacy University of Toronto

Application of Chemical Structure-based Parameters of Drug Substances and Polymers to Predict Kinetics of Drug Release from Polymer Coated Pellets

Stephanie Kwan

Degree of Master of Science

Leslie Dan Faculty of Pharmacy University of Toronto

2016 Abstract

The purpose of this thesis is to correlate drug substance properties that are easily calculated or obtained in literature with drug-polymer partition and permeability values.

Initially, partition and permeability values were determined experimentally using a side- by-side diffusion cell and values were correlated with drug substance properties mentioned above. The drug-polymer squared solubility parameter, aqueous solubility and molar volume resulted in the best correlations. The empirical correlations, paracetmaol dissolution data (obtained from literature) and AP-CAD© software were utilized to predict the release profile of a similarly coated metoprolol pellet. Verification took place with a comparison of the predicted metoprolol AP-CAD© release profile and metoprolol dissolution data obtained from literature. Results met equivalence criteria outlined by the

F1 and F2 difference and similarity factor. Therefore, the methodology and correlations identified could be used as a starting point in formulation studies, thus eliminating various experiments.

Acknowledgments

First and foremost, I’d like to thank my parents and brother for their help and support.

Next, I’d like to thank Dr. Wu and members of my advisory committee-both past and present (Dr. Heerklotz, Dr. Macgregor and Dr. Lee) for providing me with guidance during my research.

And last but not least, I’d like to thank all the members of Dr. Wu’s lab. I’ve learned a lot from all of you and had some fun times when I came to the lab. It wouldn’t have been the same without any of you!

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Table of Contents

Acknowledgments ...... iii

Table of Contents ...... iv

List of Tables ...... vii

1 Introduction ...... 1

1.1 Background ...... 1

1.2 Rationale for the Project ...... 2

1.3 Purpose of the Thesis and Objectives ...... 3

2 Literature Review ...... 4

2.1 Diffusion ...... 4

2.2 Permeation through Polymer Membranes and Drug Release Modeling in the Pharmaceutical Industry ...... 4

2.3 Drug Partitioning between Polymer and Medium ...... 9

2.4 Permeability and Partition Case Studies ...... 9

2.4.1 Permeability ...... 10

2.4.2 Partition ...... 12

2.5 Polymers in the Pharmaceutical Industry ...... 13

2.5.1 Polymer Solubility ...... 14

2.6 Drug Substance Characterization ...... 16

2.6.1 Aqueous Solubility ...... 16

2.6.2 The Solubility Parameter ...... 17

2.6.3 Hydrophilicity/Hydrophobicity ...... 18

2.6.4 Acidic/Basic Characterization ...... 18

2.7 Mathematical Modeling and AP-CAD© Simulations ...... 18

2.7.1 Computer Aided Design ...... 18

2.7.2 Verification of Computer Aided Design ...... 20 iv

3 Methods ...... 21

3.1 Identification of Drug Substances ...... 21

3.2 Identification of Polymers ...... 21

3.3 Characterization of Drug Polymer Compatibility ...... 21

3.4 Experimental Design ...... 22

3.5 Materials ...... 26

3.6 Preparation of Polymer Membranes ...... 26

3.7 Drug Polymer Partition Studies ...... 26

3.8 Drug Permeation Studies ...... 27

3.9 Computer Simulation: Predicting Release Behavior in Coated Pellet Systems ...... 28

3.9.1 Model Development ...... 30

3.9.2 Model Verification ...... 31

4 Results ...... 33

4.1 Partition between the Polymer and Phosphate Buffer Solution ...... 33

4.1.1 The Polymer-Phosphate Buffer Solution Partition Coefficient and Δδ ...... 34

4.1.2 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Aqueous Solubility ...... 36

4.1.3 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Octanol Water Partition Coefficient ...... 38

4.1.4 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Molecular Weight ...... 39

4.1.5 The Partition Coefficient and the Molar Volume ...... 41

4.1.6 Interacting Effects ...... 42

4.2 Drug Permeation through the Polymer Films ...... 44

4.2.1 Drug Release Profiles ...... 44

4.2.2 Time Lag ...... 46

4.2.3 Permeability/Diffusivity coefficients ...... 47

4.2.4 Correlations ...... 49

4.3 Predicting Drug Release Behavior in Drug Layered, Eudragit® NE Pellet Coated Systems ...... 52

4.3.1 Obtaining a Model ...... 52

4.3.2 Applying the Model for Metoprolol Layered, Eudragit® NE Coated MCC Pellets ...... 54

5 Discussion and Conclusions ...... 57

5.1 Partition Coefficient Results ...... 57

5.1.1 Correlations ...... 57

5.1.2 Improvements ...... 60

5.2 Side-by-Side Diffusion Results ...... 61

5.2.1 Release Curves ...... 61

5.2.2 Time Lag ...... 61

5.2.3 Permeability and Diffusion Coefficients ...... 62

5.2.4 Correlations ...... 62

5.2.5 Improvements ...... 65

5.3 Drug release kinetics AP-CAD© model ...... 66

5.3.1 Developing a Model ...... 66

5.3.2 Applying the Model ...... 67

5.3.3 Improvements ...... 68

5.4 Conclusions ...... 69

References ...... 71

Appendices-Table and Data ...... 79

List of Tables

Table 1: A summary of the average partition coefficients for the 6 drug substances investigated ...... 33

Table 2: The average permeability calculated via the bass balance and lag time methods...... 48

Table 3: The average diffusion coefficient results ...... 48

Table 4: A summary of the calculated/determined values associated with Figure 35...... 54

Table 5: A summary of the calculated/determined values associated with Figure 36...... 56

Table 6: The calculated solubility parameter and squared difference for various drug substances and polymers ...... 79

Table 7: The calculated partition coefficient for various drug substances and the Eudragit® NE polymer ...... 80

Table 8: The wavelength used to obtain absorbance readings for each drug substance studied. . 81

Table 9: The calculated partition coefficient results ...... 81

Table 10: A summary of the calculated permeability values, obtained via the mass balance and time lag methods...... 81

Table 11: The calculated diffusion coefficient values using the time lag and Permeability/Partition Values ...... 82

Table 12: A comparison of the % released profiles for Paracetamol ...... 83

Table 13: Summary of calculated partition coefficient values for Metoprolol ...... 84

Table 14: Summary of calculated drug diffusivity values for Metoprolol ...... 85

Table 15: Summary of calculated drug dissolution rate for Metoprolol ...... 85

Table 16: A comparison of the % released profiles for Metoprolol ...... 86

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List of Figures

Figure 1: A schematic diagram of a coated matrix pellet (left) and a cross section of the coated matrix pellet (right, obtained from Wu, X. Y., 2016)...... 19

Figure 2: The structure of Eudragit® NE (Evonik Industries, n.d.) ...... 23

Figure 3: The structure of valproic acid (DrugBank, n.d.) ...... 24

Figure 4: The structure of theophylline (DrugBank, n.d.) ...... 24

Figure 5: The structure of caffeine (DrugBank, n.d.) ...... 25

Figure 6: The structure of niacin (DrugBank, n.d.) ...... 25

Figure 7: The structure of Carbamazepine (DrugBank, n.d.) ...... 25

Figure 8: The structure of Naproxen (DrugBank, n. d.) ...... 26

Figure 9: A schematic diagram showing the process used to determine the correction factor between the lab scale empirical correlations and the enteric coated pellet...... 28

Figure 10: A schematic diagram showing the process used to determine the dissolution profile via lab scale empirical correlations and the correction factor...... 29

Figure 11: The relationship between the experimentally determined partition coefficient and Δδ...... 34

Figure 12: The relationship between the experimentally determined partition coefficient and Δδ, excluding values for niacin and theophylline...... 35

Figure 13: The relationship between the experimentally determined partition coefficient and Δδ, excluding values for niacin and theophylline; but showing calculated partition coefficient data and its relationship with Δδ...... 35

Figure 14: The relationship between the experimentally deermined partition coefficient and the experimental aqueous solubility values of the drug substance (obtained from the drug bank database (DrugBank, n.d.))...... 36 viii

Figure 15: The relationship between the experimentally determined partition coefficient and the experimental aqueous solubility values of the drug substance (obtained from the drug bank database (DrugBank, n.d.)), excluding values for niacin and theophylline...... 37

Figure 16: The relationship between the experimentally determined partition coefficient and the experimental aqueous solubility values of the drug substance (obtained from the drug bank database (DrugBank, n.d.)), excluding values for niacin and theophylline; but showing calculated partition coefficient data and its relationship with the experimental aqueous solubility values. . 37

Figure 17: The relationship between the experimentally determined partition coefficient and the octanol-water partition coefficient results of the drug substance (obtained from the drug bank database (DrugBank, n.d.))...... 38

Figure 18: The relationship between the experimentally determined partition coefficient and the experimental octanol-water partition coefficient values of the drug substance (obtained from the drug bank database (DrugBank, n.d.)), excluding values for niacin, theophylline and caffeine; but showing calculated partition coefficient data and its relationship with the experimental octanol water partition coefficient values...... 39

Figure 19: The relationship between the experimentally determined partition coefficient and the molecular weight of the drug substance...... 40

Figure 20: The relationship between the experimentally determined partition coefficient and the molecular weight of the drug substance, excluding values for niacin and theophylline; but showing calculated partition coefficient data and its relationship with the molecular weight. .... 40

Figure 21: The relationship between the experimentally determined partition coefficient and the molar volume of the drug substance...... 41

Figure 22: The relationship between the experimentally determined partition coefficient and the molar volume of the drug substance, excluding values for niacin and theophylline; but showing calculated partition coefficient data and its relationship with the molar volume...... 42

Figure 23: The interaction plot for theoretical partition coefficient values...... 43

Figure 24: The interaction plot for theoretical partition coefficient values, excluding pseudoephedrine and verapamil...... 43

Figure 25: The percent released curves for caffeine, carbamazepine, niacin, naproxen, valproic acid, and theophylline...... 45

Figure 26: A zoomed view of the percent released curves for carbamazepine & naproxen (top) and caffeine, niacin, and theophylline (bottom) ...... 45

Figure 27: The frequency distribution curve of the Eudragit® polymer and the Eudragit® + niacin mixture...... 47

Figure 28: The relationship between the obtained partition coefficient values and the pKa of the drug substance...... 49

Figure 29: The correlation developed between the permeability (obtained using the time lag method) and the calculated Δδ term...... 50

Figure 30: The correlation developed between the permeability (obtained using the time lag method) and the drug substance’s molar volume...... 50

Figure 31: The relationship developed between the permeability (obtained using the time lag method) and the molecular weight of the drug substance...... 51

Figure 32: The relationship developed between the permeability (obtained using the time lag method) and the aqueous solubility of the drug substance ...... 51

Figure 33: The relationship developed between the permeability (obtained using the time lag method) and the drug substance’s octanol water partition coefficient ...... 52

Figure 34: The relationship developed between the permeability (obtained using the time lag method) and the predicted pKa value of the drug substances...... 52

Figure 35: The dissolution profiles generated from AP-CAD© and obtained from literature (Mota, J., 2010) for paracetamol layered, Eudragit® NE MCC coated pellets...... 53

Figure 36: The dissolution profiles obtained from the AP-CAD© "drug release kinetics prediction coating” and literature (Mota, J., 2010) for Metoprolol-layered, Eudragit® NE coated MCC pellets obtained ...... 56

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1 Introduction 1.1 Background

The pharmaceutical industry is a 23.3 billion dollar industry and the generic drug industry represents 22.6% of that industry (Canadian Generic Pharmaceutical Association, 2015a). In 2014, the generic drug industry saved the pharmaceutical industry $14.8 billion dollars (Canadian Generic Pharmaceutical Association, 2015b). A generic drug may take 2-3 years to develop and can require $3-10 million dollars of research and development costs (Science Media Centre of Canada, n.d.). Consequently, reducing the time and subsequently the cost to develop a new drug formulation is advantageous. The FDA’s guidance for the industry (Q11 Development and Manufacture of Drug Substances) and the ICH Q8 indicates “that a greater understanding of the drug substance and its manufacturing process can create the basis for more flexible regulatory approaches.” (U.S. Department of Health and Human Services, et al., 2012)

Controlled release formulations is the most commonly used formulation in the pharmaceutical industry (Wen, H., et. al, 2010). Oral controlled release formulations consists of delayed release, sustained release and repeat action formulations (Wen, H., et. al, 2010). A delayed release formulation is developed so that the drug substance will not release in the acidic, gastric environment, but rather in the intestine (Wen, H., et. al, 2010). In sustained release formulations, drug substances are released over a prolonged period of time, which can range from a 12-18 hour time period (Wen, H., et. al, 2010). Consequently, the different release profiles of the various oral controlled release formulations will have several advantages such as an improvement in the tolerability, reduced adverse side effects, increased therapeutic effect duration and increased patient comfort and compliance (since the patient will have to take fewer doses) (Wen, H., et. al, 2010). One of the most effective methods for achieving controlled release formulations is through the coating with polymeric material (McGinity, J. W., 1989).

It has been reported that polymer-drug or drug-polymer interactions can influence the properties, functionality and permeability of the applied film (McGinity, J. W., et al., 2008) thus affecting the controlled release profile and consequently resulting in additional time and costs to develop a new drug formulation. For the generic drug industry, several drug substances are developed simultaneously and when several patents expire in a similar time frame, developing a thorough

2 understanding of the properties of a drug substance that influence the rate of permeation through polymer films will save time and development costs.

1.2 Rationale for the Project

Despite the importance of oral controlled release formulations and the amount of time, energy and money (development costs) put forth by the generic drug industry to develop various products (and formulations), a correlation between polymer drug interactions and the drug release rate has not been well established (Sawant, P. D., et al., 2010). Even though the polymer drug interactions is only one aspect of the finished drug product formulation, developing a fundamental understanding of the relationship between various drug substances and polymeric material is important, particularly in the generic drug industry where several controlled release drug formulations are being developed simultaneously.

Subsequently, since this project would be beneficial to those working in the generic drug industry, the method of analyzing or establishing a correlation between properties of the drug substance and partition/release behavior into/through polymers must utilize information that is readily available through literature or easily calculated. Some properties that are readily available for generic drug substances include the aqueous solubility, the octanol-water partition coefficient, the molecular weight and molar volume. In addition, as discussed in the literature review, various functional groups can affect the drug partition between the polymer/medium and subsequent permeation through the polymer membrane. Consequently, the solubility parameter considers various functional groups and accounts for its influence to the dipole, polar and hydrogen bond effects. There are several methods to calculate or determine the solubility parameter and each method typically involves the use of complex thermodynamic equations or an experimental approach; however, the most simplistic method of predicting the solubility parameter is an additive approach, defined by the group contribution method and introduced by Fedor and Van Krevelen (Krevelen, D., 1990).

Based on the empirical correlations and utilizing the AP-CAD© software, a simplistic method for predicting the release behavior of generic drug substances could be determined and utilized in the pharmaceutical industry.

1.3 Purpose of the Thesis and Objectives

The purpose of the study is to develop an understanding of specific drug substance characteristics that result in interactions with the polymer and subsequently influence the permeation of the drug substance through the polymeric film. The objectives of the study are as follows:  Identify drug substances and polymers suitable for study  Demonstrate that various drug substances can affect the release rate through polymeric films  Determine how properties (that are easily obtainable through simplistic calculations or literature) of the drug substances affect the diffusion/permeation of the drug substance into and through the polymeric film  Based on observations, develop an empirical correlation that can predict a relative partition/permeability coefficient value  Apply the knowledge gained between easily obtainable or calculated properties of the drug substance and their permeability through polymer membranes to predict the release kinetics of coated pellets using AP-CAD© computer software

2 Literature Review 2.1 Diffusion

At its most basic definition, “diffusion is the process by which matter is transported from one part of a system to another…” (Crank, J., 1975). When discussing the mathematics of diffusion, the discussion frequently starts by discussing Fick’s law of diffusion. Fick’s first law of diffusion assumes the rate at which a substance diffuses through a medium (the flux) is proportional to the concentration gradient in which it is diffusing through (Crank, 1968). Fick’s first law of diffusion assumes the concentration does not vary with time and the diffusion coefficient is constant. The equation shown below represents Fick’s first law of diffusion in one direction. F=Flux ∂C D=Diffusion Coefficient F = −D ∂x (1) C=Concentration x=Distance

In Fick’s second law of diffusion, concentration varies with time and space. Subsequently, Fick’s second law of diffusion is represented using the equation below, again assuming diffusion takes place in one direction. D=Diffusion Coefficient ∂C 휕2C C=Concentration = D (2) ∂t ∂x2 x=Distance t=time 2.2 Permeation through Polymer Membranes and Drug Release Modeling in the Pharmaceutical Industry

In the pharmaceutical industry, the use of pellet technology has been applied towards modified release dosage forms. The pellets are typically spherical in shape with a diameter that is usually no more than 1.7 mm (Harris, M. R., et al., 1997). Pellets can be loaded with the drug substances through a wet granulation process or via layering onto sugar spheres (Harris, M. R., et al., 1997). Polymers are generally incorporated into the pellets to control the release of the drug substance into the media and this can be accomplished with an outer membrane or incorporated as part of the pellet matrix.

Subsequently, in the pharmaceutical industry, while diffusion would describe how a drug substance migrates or moves within the polymer membrane, permeation would describe how the drug substances migrates through the polymer membrane (Griskey, R. G., 1995). Higuchi used Fick’s law of equation and combined it with a moving boundary layer mass balance to obtain the equation shown below (Higuchi, T., 1961). The equation represents the relationship between the amount of drug that has been depleted and the drug substance’s diffusivity, initial concentration and solubility in the matrix. D=Diffusion Coefficient Q = Dt(2C0 − Cs)CS Co=Concentration of drug loaded in the matrix (3) Cs=Saturated Drug concentration in the matrix x=Distance t=time

In order to develop the mass balance and obtain a simplified equation, several assumptions are used in the Higuchi equation (Siepmann, J., et al., 2011 and Lee, P. I., 2011). First, it is assumed that the initial concentration of the drug substance in the matrix is evenly distributed and much higher compared to the solubility of the drug substance in the matrix. Second, it is assumed that the dissolution rate of the drug particles is much faster than the drug diffusion and thus release kinetics is determined by diffusion (i.e. a diffusion-controlled process). In terms of the receiving end, it is assumed that a “perfect sink” is maintained so that the concentration in this region is negligible. Moreover, it is assumed that the diffusion coefficient of the drug within the matrix is constant. For the slab geometry of the matrix or film (as the equation was originally developed to describe a drug layered film that is diffusing into the skin) it is assumed that the edge effects are negligible because the surface of the matrix layer is large compared to the thickness. In addition, a semi-infinite geometry applies and erosion or swelling does not apply. Lastly, to minimize the lag time effect, it is assumed that the drug particles are finely dispersed and much smaller than the thickness of the matrix.

However, due to the various assumptions used in developing the Higuchi equation, several approaches have been utilized to create a more rigorous solution (Paul, D. R., 2011). For example, one of Higuchi’s key assumptions is that the drug dissolution rate is rapid or negligible compared to the diffusion of the drug particles; however, this assumption would not hold true in scenarios where drugs have low solubility/dissolves slowly in the matrix or if diffusion in the matrix is fast (Paul, D. R., 2011). Subsequently, for low soluble drugs or when the dissolution is

6 extremely slow, a separate form of Fick’s second law can be applied where a “solute dissolution rate constant” is added (Paul, D. R., 2011).

Another key assumption from the Higuchi equation is that the initial drug loading is much higher compared to the drug substance’s solubility in the matrix. While this assumption may hold true during the initial stages, eventually the concentration will change because the concentration in the reservoir does not remain constant. Subsequently, release of the drug substance can be described as taking place in two steps. The first step will mimic the constant reservoir system and will occur when the concentration is much greater than the solubility of the drug resulting in a portion of drug that will be dispersed. Such a system can be characterized by a zero-order release profile (Zhou, Y., 2010). However, once the entire dispersed drug is dissolved, the system becomes a non-constant reservoir system. In the second system, the drug concentration is less than the solubility of the drug substance and could be solved using a moving boundary condition (Zhou, Y., 2010). Subsequently, two different distinct equations are required to describe both the constant reservoir and non-constant reservoir systems and the combined analytical solution is presented in Zhou’s paper (Zhou, Y., 2010).

Other models have also been built to take other considerations into account. For example, Zhou et al. (Zhou, Y., 2005) considered the effect of non-uniformity or anisotropic conditions where differences can occur in the radial and axial directions. In this particular instance, two separate diffusion coefficients were considered for two different directions. Results were verified by experimental conditions and it was determined that the influence of radial and axial conditions does affect the diffusion coefficient and subsequently the shape of the release profile.

In another case, Zhou et al. (Zhou, Y., 2004) also tried modeling analytical solutions that analyzed analytical heterogeneous sphere ensembles where spheres varied in size distribution and initial drug loading. In the study, it was determined that as the distribution of spheres increases, the release rate decreases. For the effect of varying the initial drug loading, it was found that a uniform initial loading resulted in the fastest release rate compared to those with non-uniform drug loading and in fact, it was further identified that non-uniform drug loading reduced the initial burst release and created release rates that were more steady (Zhou, Y., 2004). In addition to diffusion and drug dissolution, other mechanisms are also utilized to modulate drug release profiles including ion exchange, swelling, erosion, and osmosis pressure.

Comprehensive review of various release mechanisms and mathematical models can be found from recent books, book chapters and review articles (e.g. Amidon, L., et al., 2000; Siepmann 2001; Thombre 2011)

Experimentally, the side-by-side diffusion cell can be used to determine the effect of drug diffusivity (Wang, D., 2000) and permeability. The side-by-side diffusion cell contains a receptor cell and donor cell, where concentrated drug solution is placed into the donor cell and the cast polymeric membrane is placed between the donor cell and receptor cell. As drug diffuses from the donor cell to the receptor cell, it can be modeled as a device where the drug has not initially partitioned into the polymer and as the drug concentration gradually increases in the polymer, a delayed concentration in the receptor cell will be observed, until steady state conditions are reached in the polymer. The amount of time required for the polymer to reach steady state is known as the lag effect (Comyn, J., 1985).

The release kinetics from the side-by-side diffusion cell could be modelled by equations that were derived from a combination of Fick’s law/mass balance equations and used to describe the release kinetics from controlled release dosage forms (Comyn, J., 1985; Ende, D. J., 2010). At steady state, the relationship used to describe the amount of drug released (or the concentration in the receptor cell) versus time is shown in equation (4) (Ende, D. J., 2010) and the lag effect is shown in equation (5) (Comyn, J., 1985).

q = the amount of penetrant in the receptor cell t = time (4) D = Diffusion coefficient Cr = Reservoir Concentration h = polymer membrane thickness tlag = the lag time or the time to reach steady state

(5)

Using the mass balance method, the membrane permeability can be calculated, as shown in equation (6) and equation (7) approaches (Chen, Y., 2010).

2C 2PA Vd=Volume r h-polymer thickness  ln(1 )  t (6) C Vh Cr=Concentration in the Receptor Cell 0 A=Surface Area CD=Concentration in the Donor Cell Co=Initial Concentration in the Receptor Cell (7) t=time P= permeability of drug through the membrane Q=total amount of permeate passing through the membrane

Alternatively, if steady state has not been reached, then Fick’s 2nd law of diffusion (described in equation (8)) can be used to obtain the diffusion coefficient. By integrating Fick’s 2nd law and using Laplace transforms, equation (9) is obtained. Upon re-arranging equation (10), equation (16) is obtained.

C - concentration t - time (8) x - distance

C - concentration C0 - Initial Reservoir Concentration (9) D - diffusion coefficient t - time x - distance C - concentration C0 - Initial Reservoir Concentration (10) D - diffusion coefficient t - time x - distance

As a result, results from will provide values for the term which could subsequently be used to determine the diffusion coefficient at specified time and distance values. For instance, if erf(B)=A, and upon obtaining a value for A and applying the inverse function, then the value B could be determined.

In addition, the relationship between the diffusion coefficient and the membrane permeability can be described by equation (11) (Baker, R., 2004).

P - permeability of drug through the membrane P = D · K (11) D - Diffusion coefficient K - equilibrium term between liquid and polymer

The equilibrium term in equation (11) can be obtained from other studies that investigate transport in polymeric systems. In a side-by-side diffusion cell where diffusion has not taken place the equilibrium term or the partition coefficient can be defined as the ratio of the reservoir concentration to the polymer concentration as described in equation (12) (Amidon, G., et al., 2000).

K - partition coefficient C0 - Initial Reservoir Concentration (12) Cf - Final Reservoir Concentration Cp - Polymer Concentration Vs - Reservoir Volume Vp - Polymer Volume

2.3 Drug Partitioning between Polymer and Medium

The partition coefficient describes the ability of a substance to distribute itself between two immiscible systems (Sangster, J., 1997). It has been studied as a physicochemical phenomenon that has been linked with biological action. In the pharmaceutical industry, early studies linked narcotic activity with the organic compound’s oil-water partition coefficient (Sangster, J., 1997). Consequently, several industries have studied the science of partitioning and for solute-polymer partitioning; theories derived from various industries could be applied to the pharmaceutical industry and a drug-polymer partition system.

The polymer-water partition coefficient could be obtained by dividing the drug’s solubility in the polymer by the drug substance’s aqueous solubility. The drug solubility in the polymer can be determined from the following equation:

3 Cm - drug solubility in the polymer (g/cm ) Ρ - the density of the drug (g/cm3)=molar weight/molar volume 2  - V(δd- δp) /RT; where V=molar volume δd - the total solubility parameter of the drug substance (13) δp - the total solubility parameter of the polymer ΔSf - the entropy of fusion of the drug substance R is the gas law constant=8.314 J/K·mol T - environmental temperature, in K Tm - melting point temperature of the drug substance, in K

The entropy of fusion could be determined using Yalkowsky’s method (Yalkowsky, S. H., 1979) where the entropy of fusion=56.484 J/mol·K for rigid molecules and (13.5+ 2.5(n-5)) × 4.184 J/mol·K for flexible molecules, where n is the number of carbon atoms. Rigid molecules are molecules that have 5 or less carbon atoms; however for most drug substances, the estimation used for rigid molecules is not applicable (Yalkowsky, S. H., 1979). The melting point temperature was obtained from the drug bank database (DrugBank, n.d.) and an environmental temperature of 310 K was used to simulate the conditions of the experimentally determined partition coefficients.

2.4 Permeability and Partition Case Studies

Section 2.1, 2.2 and 2.3 describe the theory and mathematics behind diffusivity, permeability and the partition coefficient. However, several case studies have been conducted to analyze various properties that could influence the permeability, diffusion and partition coefficient.

2.4.1 Permeability

In one study, the release of various drug substances through poly D-L lactic acid (PLA) was investigated and it was determined that 3 factors influence the rate of drug release (Proikakis, C. S., et al., 2006). The three factors that influenced the rate of release was the high degree of polymeric swelling, changes in the solubility of the drug substance and the degradation of the polymer. The degree of polymeric swelling was largely dependent on the pH of the solution as more basic conditions resulted in the dissociation of the carboxylic end group and caused more repulsive forces amongst the carboxyl anions, which led to more polymeric swelling. The solubility of some of the drug substances was influenced by changes in pH and in one case, an increase in the pH resulted in a decrease in the solubility of the drug substance and consequently resulted in a slower dissolution profile. Finally, the direct interaction of acid/basic drugs resulted in the acid/base catalysis of the ester bond resulting in hydrolysis or cleavage of the ester bond and thus degradation of the polymeric membrane itself. The results from Proikakis’ study (Proikakis, C. S., et al., 2006) were in good agreement with Miyajima’s study (Miyajima, M., et al, 2006) where the release profiles of basic, acid and neutral drug substances from copoly (L- lactic/glycolic acid) (PLGA) were investigated. However, in this particular case, the slow release profile of the basic drug substances was also attributed to the high partition coefficient of the basic drug substance, which indicated the presence of ionic interactions with the polymer.

In another study, it was determined that the diffusivity of drug substances from hydroxyproylmethylcellulose (HPMC) was largely controlled by the swelling of the polymeric matrix and other factors such as the solubility of the drug substance (Siepmann, J., 2001). In contrast, Sawant (Sawant, P. D., et al., 2010) found that a variety of factors contributed to the drug release from a similar polymer hydroxpropyl cellulose (HPC). For HPC, a slow release profile was observed when a hydrophobic drug substance, lidocaine was used; however, a burst release was observed for a hydrophilic drug substance, lidocane hydrochloride. The slow release of the hydrophobic drug substance was attributed to drug-polymer interactions (as characterized using FTIR) and it was concluded that the lipophilic nature of the drug substance (characterized by the octanol water partition coefficient) influences the drug’s release rate. The study was further expanded to investigate drug release kinetics from hydrophobic polymers and it was found that the hydrophobic drug substance, lidocaine, resulted in a burst effect when the

11 hydrophobic Eudragit® polymer was used. The author was unable to account for the unexpected burst release.

The release kinetics associated with the Eudragit® polymer was studied extensively. It was determined that the faster release profile of chlorpheniramine was due to the highe aqueous solubility of chlorpheniramine (Jenquin, M. R., et al, 1990). Lin (Lin, S., et al., 1995) studied the release of piroxicam from piroxicam loaded Eudragit® E films and found that the release was dependent on the amount of drug loaded in the polymer. Further, it was found that while the release did follow Higuchi’s equation for matrix controlled release, the drug-polymer interactions (the intermolecular hydrogen bonding between piroxicam and the Eudragit® E polymer) resulted in a delayed release of the piroxicam. Similarly, Lin (Lin, et al., 1994) investigated the interaction between Euragit® E, RL and S resins and found that the molecular interaction between warfarin and Euragit® E resulted in a delayed release.

Wang C. et al. (Wang, C., et al, 2007) used experiments, free volume theory and molecular dynamic simulations to assess the molecular movement of aspirin and theophylline drug substances through polyvinyl acetate (PVA) molecules. Even though both aspirin and theophylline had the similar van der Waal volume and molecular weight, it was found that between the two drug substances, a lower diffusion coefficient was observed for aspirin. The low diffusion coefficient was attributed to the drug-polymer interaction and the hydrophobicity of aspirin. The drug polymer interaction was verified using polymer-ethanol partition studies and both the experimental and theoretical simulations were in agreement and concluded that aspirin should have a lower diffusion coefficient.

In the above case studies, various polymers (PLA, PLGA, HPC, HPMC, Eudragit®, and PVA) and various drug substances were used to study the release rate. While the above studies investigated various factors that influenced the release of drug substance through different polymers, some commonalities could be seen amongst each of the studies. For example, some common influencing factors include:

 Polymeric swelling, which resulted in an increased release rate

 Different aqueous solubility values for various drug substances, where high soluble drug substances would result in a faster release

 Higher Partition/Absorption into/by the polymer, which resulted in retention of the drug substance into the polymer and consequently slower release rates

 Drug-Polymer Interactions (characterized by FTIR, hydrogen bonding)

 Hydrophobic/Hydrophilic nature of the drug substance, which resulted varying effects and was also dependent on the hydrophobic/hydrophilic nature of the polymer

Even though the nature of the polymer does influence the release rate of a drug substance, the above studies demonstrate that the nature of the drug substance plays an important role in the drug release kinetics. Costa (Costa, P., 2001) concluded that in general, drug release kinetics are influenced by the particle size, solubility and polymorphic form of the drug substance. As a result, in addition to some of the factors identified above, the influence of a drug substance’s physicochemical properties must be considered and may include factors such as the solubility, water content, particle size, crystal properties, biological activity, and permeability.

2.4.2 Partition

Learnings from other industries could be applied towards the pharmaceutical industry. In the food industry, polymers are used as packaging material and can result in the loss of flavors that are absorbed by the polymer. In those particular studies, the partition coefficient between the food and polymer was studied. The findings from some of the studies are shown below; but in summary, it was determined that the partition coefficient is dependent on the solubility coefficient, temperature, and the chemical structure/molecular size of the migrant (Tehrany, 2004).

 The solubility coefficient has been used to determine polymer solubility and is defined in section 2.5.1. In the food industry, it has been used as a tool to screen and rank solute- polymer thermodynamic affinity (Bacon, S., et al., 2014).

 Higher temperatures results in an increased mobility of molecules and subsequently, the partition coefficient increases with temperature (Tehrany, 2004).

 For the chemical structure, it was found that alcohols and short-chained esters have a high affinity for the polymer in oil solution compared to an aqueous solution; however,

aldehydes have a lower affinity for the polymer in oil solution compared to an aqueous solution. Further, within the same functional group (ester, aldehyde, alcohol), it was found that a longer chain length resulted in an increased partition coefficient even though small molecules should be absorbed by the polymer more quickly compared to larger molecules (Tehrany, 2004). In another study that looked at the release of various steroids from polymer films (Roseman, T. J., 1972) it was determined that the molecular structure of the steroid group directly impacted the partition coefficient, where the hydroxyl group decreased the solubility of the steroid in the silicone polymer.

In addition, the partition coefficient of other systems have been used to interpret or predict the polymer partition coefficient. For example the partition coefficients of hydrophobic polymers (polypropylene, polyethylene and poly-ehthylene-co-buytl acrylate) have been correlated with the octanol-water partition coefficient and other partition coefficient systems such as the hexane- water partition coefficient (Gasslander, U., et al, 2007).

2.5 Polymers in the Pharmaceutical Industry

The use of pharmaceutical polymers in the development and manufacture of pharmaceutical dosage forms is advantageous to the pharmaceutical scientist because of the various options of physical and chemical properties available from the selection of pharmaceutical polymers (Jones, D., 2004).

The pharmaceutical polymers used for controlled release formulations can be categorized into three different groups (Wen, H., et al., 2010). The first group is the class of synthetic polymers and for oral controlled release formulations includes poly(vinyl acetate), poly(ethylene oxide), poloxamers, Pluronics® and poly(methacrylates). The next 2 groups consist of natural polymers and cellulose derivatives. Polysaccharides is an example of a natural polymer commonly used for controlled release dosage formulations whereas hydroxypropylmethylcellulose, hydroxypropylcellulose and hydroxyethylcellulose are common cellulose based polymers used for oral controlled release formulations (Wen, H., et al., 2010).

Specific properties of the polymer can affect the diffusion and dissolution drug release mechanisms. For example, for cellulose based systems, the molecular weight, viscosity, and solubility in water affect the drug release dissolution mechanism and for the synthetic polymer

14 poly(methylmethacrylate) factors such as the molecular weight, viscosity and lipophilicity affect the diffusion of the drug through the polymer membrane.

2.5.1 Polymer Solubility

A polymer will be more soluble in a solvent if the chemical structure of the polymer and solvent are similar (Krevelen, D., 1990). Hildebrand identified the relationship between the solubility of a solute and internal pressures of corresponding solvents (Krevelen, D., 1990). An increase in the internal energy is used to define the cohesive energy of a substance and the square root of the cohesive energy density is the solubility parameter (Krevelen, D., 1990).

However, Hildebrand’s approach to defining the solubility parameter was based on the dispersion forces between structural units and did not account for the polar and hydrogen bonding (Krevelen, D., 1990). Subsequently, several methods have been proposed to indirectly determine the dipole, polar and hydrogen solubility parameters. One method to study the hydrogen solubility parameter was proposed by Beebower and later quantified by Gordy and Stanford where shifts in the infrared absorption band were graphed to identify solvents that would solubilize various polymers. Another method, to determine the partial solubility parameters, was proposed by Hansen where the solubility of polymers in various solvents were determined experimentally and required a trial and error approach to fit the resulting polymer solubility data (Hansen, C. M., 2007). An alternative method to predict the partial solubility parameter components was identified by Hoftyzer-Van Krevelen and utilizes a group contribution method that sums either the molar attraction constants (Fdi or Fpi) or the cohesive energy (Eh) from functional atomic groups and utilizes the molar volume to determine the partial solubility parameter components (Krevelen, D., 1990) using the equations shown below.

δd=Solubility parameter from dispersion forces δp=Solubility parameter from polar forces ; δd=Solubility parameter from hydrogen bonding (14) Fdi=Molar attraction constant-dispersion forces Fpi=Molar attraction constant-polar forces

E=Cohesive energy-hydrogen bonding Δt=Total solubility parameter

Upon determining the contributions of each partial solubility parameter, Hoftyzer-Van Krevelen provided a full equation (15) that will determine the solubility of a polymer in an organic liquid.

The squared difference (Δδ) between the dispersion forces, polar interactions and hydrogen bonds are calculated using the equation below. For good solubility, Δδ must be less than 5 (Krevelen, D., 1990).

= Compatibility term

δd,d= dispersion forces from the polymer (15) δd,p= dispersion forces from the drug δp,p = polar interactions from the polymer δp,d = polar interactions from the drug δh,d = hydrogen bonds from the polymer δh,d = hydrogen bonds from the drug

Flory and Huggins also provided an equation to define the solubility of a polymer in a solvent and developed a polymer-solvent interaction parameter (Krevelen, D., 1990). The interaction parameter is the sum of the enthalpic and entropic interactions, where the entropic contribution is generally 0.35±0.1. The equations below define the Flory-Huggins interaction parameter.

χ= χh + χs χ= Flory-Huggins interaction parameter

(16) χh=Enthalpic contributions of the Flory Huggins interaction parameter

χs=Entropic contributions of the Flory Huggins interaction parameter Vs=molar volume R=molar gas constant T=temperature δp=solubility parameter of the polymer δs=solubility parameter of the solvent

The Flory-Huggins parameter predicts that high molecular weight polymers will be soluble in a solvent if the interaction parameter is less than or equal to 0.5; however for low molecular weight polymers, the interaction parameter can be less than or equal to 2 (Krevelen, D., 1990).

For the Flory-Huggins parameter the solubility parameters will have to be determined from the cohesive energy or the molar attraction constant. However, for the Hoftyzer-Van Krevelen method the solubility parameter could be determined from the structure of the molecule. In fact, it was noted that the solubility parameter components are known for only a small number of polymer solvent combinations and as a result, a useful method to predict the solubility parameter must be based on the molecular structure (Krevelen, D., 1990).

2.6 Drug Substance Characterization

As previously mentioned in section 2.4, several case studies identified various factors that could affect the permeability of a drug substance. From the perspective a drug substance, non-covalent bonds, conjugate acids/bases, the aqueous solubility, the hydrophobicity and subsequently the octanol water partition coefficient are factors that can be used to characterize the permeability of a drug substance.

As a result, the following sections discuss various drug substance properties, starting with the aqueous solubility and usage of the solubility parameter to characterize the non-covalent bonds (since the solubility parameter can be used to account for the various dispersive forces, hydrogen bonds and polar groups). The subsequent section discusses the hydrophobicity of a drug substance, its characterization and subsequent importance and the last section discusses methods for acid/base characterization.

2.6.1 Aqueous Solubility

“Solubility is one of the most important physicochemical properties studied during pharmaceutical preformulation.” (Tong, W., 2007) and it is defined as the “maximum quantity of a substance that can be completely dissolved in a solvent” (Gong, Y., et al., 2007). A critical step in the pharmaceutical pre-formulation activity is the screening of various active substances for its solubility. In fact, the aqueous solubility has been used as part of the biopharmaceutic classification system (BCS) to define/identify drug substances that can qualify for an in-vivo bioavailability/bioequivalence study waiver. In recent years, the shift towards formulating Class II drug substances (which have high permeability/low solubility and will be limited by the dissolution or solubility rate (Dahan, A. S., et al., 2009)) has been made (Bai, J., et al, 2006). While the BCS classification defines permeability in the body, the shift towards low soluble drug substances further defines the need to identify the influence of drug substances that have low aqueous solubility on the permeability of the drug substance through the polymer. In fact, it has been said that the drug release via diffusion is strongly dependent on the drug solubility (Zuleger, et al., 2001). In addition, for drug substances that have low aqueous solubility, inadequate release rates are obtained (Zuleger, et al., 2001).

If experimental aqueous solubility data is not available, estimated solubility data can be used. Jain and Yalkowsky analyzed 580 compounds and proposed a mathematical formula to predict the aqueous solubility using the melting point temperature and the octanol-water partition coefficient (O’Donnell, K. P., et al, 2012). Though the equation has been referred to as a general solubility equation; there have been numerous articles that both support and disagree with the equation (O’Donnell, K. P., et al, 2012). Despite all of the available methods of calculation, experimental values are widely available for the majority of drug substances that have already been marketed.

As a result, based on the shift to use drug substances with low aqueous solubility values and based on the effects of varying the aqueous solubility values on the diffusion and subsequent drug release rates, studying the influence of a drug substance’s aqueous solubility value will prove to be quite advantageous.

2.6.2 The Solubility Parameter

As previously mentioned, it was found from various case studies that non-covalent bonds and various functional groups can influence the drug substance’s permeability and partition coefficient. A method of characterizing the non-covalent bonds and contributions from various functional groups is by determining the partial solubility parameters (discussed in section 2.5.1). While the Hoftyzer-Van Krevelen group contribution method was utilized to determine the solubility of the polymer in the solvent, the same solubility parameter could be applied towards a drug substance and polymer to deduce the contributions from the dispersion forces (δd), polar groups (δp) and from hydrogen bonding (δh). Further, the partial solubility values could be collectively assessed with the total solubility parameter (δt). Results from the total solubility parameter can be verified using Fedor’s method (Krevelen, D., 1990) where the solubility parameters are calculated directly from the cohesive energy density (Ecoh) of each group composing of the molecule. Again, specific cohesive energy density values for each group have been predetermined and can be obtained from Krevelen (Krevelen, D., 1990). The following equation is used:

t = solubility parameter

(17) Ecoh = cohesive energy density V = molar volume

In addition, the squared difference (Δδ) between the dispersion forces, polar interactions and hydrogen bonds could also be calculated and while it was determined that good polymer-solvent solubility would occur when Δδ is less than 5 (Krevelen, D., 1990), it is suspected that drug- polymer values that are less than 5 will affect the drug partition/permeation results through the polymer membrane.

2.6.3 Hydrophilicity/Hydrophobicity

Molecules that contain only hydrocarbons are non-polar and are usually soluble in non-polar solvents such as benzene and chloroform (Sangster, J., 1997). In contrast, water is a good solvent for polar molecules which will contain functional groups such as hydroxyl, aldehyde and carboxylic functional groups (Sangster., J., 1997).

The octanol water partition coefficient provides an indication of the hydrophobicity of the drug substance and as previously mentioned, the aqueous solubility can be predicted from the octanol water partition coefficient (O’Donnell, K.P., et al., 2012). Therefore, if the drug release via diffusion is strongly dependent on the drug substance’s solubility and if the octanol water partition coefficient can be used to predict both hydrophobicity and aqueous solubility, then naturally, the octanol water partition coefficient should provide a measure of drug permeation rates.

2.6.4 Acidic/Basic Characterization

Acid and basic drug substances were analyzed in chitosan matrix films and it was found that the acidic drug substance (salicylic acid) interacted with the polymer film and affected the release of the drug substance from the polymer film (Puttipipatkhachorn, S., et al., 2001). Drug substances can be subsequently characterized with the acid dissociation constant or the logarithmic form, pKa. Large pKa values will indicate a weak acid and smaller values will indicate a strong acid.

2.7 Mathematical Modeling and AP-CAD© Simulations

2.7.1 Computer Aided Design

Computer aided design (CAD) to model drug release kinetics saves time and costs during the drug development phase (Wen, H., et al., 2010). Siepman (Siepman, J., et al., 2001) has stated that the benefit of a mathematical model is to be able to predict the release profile from various

19 design parameters, thereby reducing the number of experiments required during the initial development phase and further optimizing the development process of new pharmaceutical products.

The Advanced Pharmaceutics Computational Analysis & Design (AP-CAD©) is software that can be used to generate release profiles from known parameters (such as the drug dissolution rate, the partition coefficient, and drug diffusivity in the matrix and coating). However, from a release profile and other known parameters, it can also determine predicted parameters for the partition and drug diffusivity in the matrix and in the coating.

The “Drug Release Kinetics Prediction Coating Systems” module within the AP-CAD© software predicts the release behavior of diffusion controlled or diffusion/dissolution controlled pellets, tablets, capsules, slabs and cylinders. For a diffusion/dissolution pellet with variable material properties (see Figure 1), the software requires certain parameters to be entered to generate a release profile. The radius of the pellet and coating thickness represent the dimensions of the pellet. The drug diffusion/dissolution mechanisms are represented by the drug diffusivity in the matrix/coating, the partition coefficient between the coating and the matrix, the solubility of the drug in the matrix and the initial quantity of drug loaded/dissolved in the matrix/coating.

Figure 1: A schematic diagram of a coated matrix pellet (left) and a cross section of the coated matrix pellet (right, obtained from Wu, X. Y., 2016).

Utilizing the parameters mentioned above, the AP-CAD© software is a mechanistic model-based computer simulation that utilizes the finite element, finite difference and optimization methods (Wu, S., 2016) to solve Fick’s laws of equations. The AP-CAD© software utilizes the following equations to generate drug release profiles.

Cw - Water drug concentration Cd - dissolved drug concentration Csd - dispersed drug concentrations. Cs - drug solubility Dw - water diffusivity (18) Dd - drug diffusivity K - drug dissolution rate constant C- - drug concentration (left interface) D− - drug diffusivity (left interface) C+ - drug concentration (right interface) D+ - drug diffusivity (right interface)

However, identifying values for specific parameters, such as the diffusion or partition coefficient can be identified through specific experiments or theoretical calculations (Wu, X. Y., 2012). Amongst the theoretical calculations, the effective diffusion coefficient is defined as the product of the diffusion coefficient of the solute through pores filled with solvent and the porosity divided by the tortuosity (Zhou, Y., 2005). However, an empirical approach could be applied to determine those values.

2.7.2 Verification of Computer Aided Design

Once models have been generated, the resulting dissolution profile needs to be compared with the actual experimental dissolution profile. The FDA guidance documents describe several methods to compare dissolution data in an attempt to reduce the number of bioequivalence studies and FDA prior approval changes (O’Hara, T., 1998). Both model independent and dependent approaches have been established to show similarity between two dissolution profiles. Some of those methods will be discussed below and can be applied to compare actual experimental data with dissolution profiles generated from the AP-CAD© software.

Within the model independent approaches, there are two mathematical methods that have been recommended within the FDA guidance documents (O’Hara, T, 1998). These mathematical methods include the F1 difference factor and the F2 similarity factor. The equations are calculated using the approach below, where R1 and T1 represent the dissolution result from the reference and test curves at various time points, t.

F1=Difference Factor (19) R=Reference dissolution value T=Test dissolution value n=no. of dissolution time points

F2=Similarity Factor (20) Wt=weighting factor (optional)

In addition, the FDA guidance documents has provided criteria to ‘ensure sameness or equivalence’ between dissolution profiles (O’Hara, T., 1998). For the F1 difference factors, values should be close to zero and values between 0 and 15 will ensure sameness (O’Hara, T., 1998 and US Department of Health and Human Services, 1997b). For the F2 similarity factor, values should be close to 100 and values between 50 and 100 will ensure equivalence (O’Hara, T., 1998 and US Department of Health and Human Services, 1997b).

3 Methods 3.1 Identification of Drug Substances

Drug substances that were previously marketed as extended release dosage forms were selected for study. Approved extended release drug substances were identified through a search of the drug bank database (DrugBank, n.d.). 63 drug substances were identified as being previously marketed as an extended release dosage form.

3.2 Identification of Polymers

The common synthetic and natural polymers commonly used in oral controlled release formulations are: poly vinyl alcohol (PVA), poly(acrylic acid) (Carbopol®), poly(ethylene oxide) (PEO), poloxamers, pluronics, polymethacrylates (Eudragit®), and cellulose derivatives (HPMC, HPC, MC) (Wen, H, et al., 2010). At least one polymer was selected from each class for further study and evaluation.

3.3 Characterization of Drug Polymer Compatibility

The solubility parameter was calculated for the various polymer and drug substances using equation (14) which is defined from Hoftyzer-Van Krevelen’s group contribution method (Krevelen, D., 1990) and from the Fedor method which is defined using equation (17). The

22 solubility parameter was confirmed using Fedor’s method (Krevelen, D., 1990). After determining the dispersive, polar group and hydrogen bond contributions, the compatibility between each drug substance and polymer was determined from the squared difference term, defined in equation (15)). For good solubility, Δδ must be less than 5 (Krevelen, D., 1990).

3.4 Experimental Design

For each of the 63 drug substances, the squared difference (∆δ) between each drug substance and polymer was calculated and is shown in Appendix 1-Table 6. Since ionic electrostatic interactions are not part of the calculated squared difference term and because salt forms of the drug substance improve the aqueous solubility, drug substances available as salt forms were not investigated. Subsequently, the list of 63 drug substances was narrowed to 16 drug substances and due to the lack of charge associated with the Eudragit® NE polymer, the Eudragit® NE polymer was chosen as the polymer to be studied. For each of the 16 drug substances, a comparison of the squared difference term (Δδ) and USP solubility class is summarized in the table below. Molecule Δδ (E. E/NM) USP Class Levonorgestrel & Norgestrel 1.91 practically insoluble in water Valproic Acid 2.21 slightly soluble in water Naproxen 4.77 practically insoluble in water Nifedipine 4.89 practically insoluble in water Ethinyl Estradiol 5.10 Insoluble in water Carbamazepine 5.28 practically insoluble in water Indomethacin 6.40 practically insoluble in water Budesonide 6.67 practically insoluble in water Felodipine 7.08 Insoluble in water Cyanocobalamin 8.80 Sparingly soluble in water Clarithromycin 9.56 practically insoluble in water Pentoxifylline 12.22 soluble in water Caffeine 17.43 Sparingly soluble in water Potassium Chloride 18.98 freely soluble in water Theophylline 21.90 slightly soluble in water Niacin 42.10 Sparingly soluble in water

The Eudragit® NE polymer is used for sustained release formulations and releases the active ingredient in a time-controlled environment. The structure is shown below. It has low permeability, does not require any plasticizer and is insoluble in water. (Evonik Industries, n.d.)

Figure 2: The structure of Eudragit® NE (Evonik Industries, n.d.)

Valproic acid, carbamazepine, and naproxen were selected for further characterization because the squared solubility value (Δδ) was less than or equal to 5 and good solubility occurs when Δδ is less than 5. As a point of comparison, the drug substances with the small squared solubility values were compared with drug substances that have much larger Δδ values. Caffeine, theophylline and niacin were selected for further study because they had much larger squared solubility values. Within the group of drug substances that have a much smaller Δδ value, naproxen and carbamazepine have a similar USP solubility class and could be compared with valproic acid, which is in a class that is more soluble. Amongst the group of drug substances that have a larger Δδ value, caffeine and niacin have a similar solubility class and could be compared with theophylline. Between the group of drug substances that have smaller and larger squared solubility values, valproic acid and theophylline could be compared with each other since they are part of a similar solubility class.

The structure of valproic acid is shown in Figure 3. The 7-carbon chain will increase the London dispersion forces, whereas the carboxylic acid group will increase the polar forces. The interactions between the London dispersion forces the polar forces results in a compound that is slightly soluble in water. The total solubility value, using the van Krevelen and Fedor method is 17.98 and 19.47. The squared solubility value between valproic acid and the Eudragit® NE polymer is 2.21.

Figure 3: The structure of valproic acid (DrugBank, n.d.)

The structure of theohpylline is shown below. Theophylline is an aromatic purine ring that consists of two ketone groups and two methyl groups. According to the USP pharmacopeia, theophylline is slightly soluble. Evaluation of the theophylline molecule using the van Krevelen and Fedor method resulted in total solubility value of 39.35 and 26.32. The squared solubility value between theophylline and the Eudragit® NE polymer is 21.90.

Figure 4: The structure of theophylline (DrugBank, n.d.)

The structure of caffeine is shown below. Caffeine is similar in structure to theophylline because it is an aromatic purine ring containing methyl and ketone groups; however, the key difference is observed in the number of methyl groups. Three methyl groups are observed for theophylline; while two methyl groups are observed in caffeine. While the additional methyl group should increase the London dispersion forces, according to the USP pharmacopeia the compound is sparingly soluble in water. The van Krevelen and Fedor methods resulted in total solubility parameters of 34.90 and 25.60. The squared solubility value between caffeine and the Eudragit® NE polymer is 17.43.

Figure 5: The structure of caffeine (DrugBank, n.d.)

The structure of niacin is shown below. Niacin is a pyridine ring that contains one carboxylic acid group. According to the USP pharmacopeia, Niacin is considered to be a freely soluble in boiling water and sparingly soluble in water. Evaluation of the niacin molecule using the van Krevelen and Fedor method will result in total solubility value of 59.84 and 37.87. The squared solubility value between niacin and the NE polymer is 42.10.

Figure 6: The structure of niacin (DrugBank, n.d.)

The structure of carbamazepine is shown below. According to the US pharmacopeia, carbamazepine is very slightly soluble in water. Evaluation of carbazepine using the van Krevelen and Fedor method results in total solubility values of 21.97 and 23.54. The squared solubility value between carbamazepine and the Eudragit® NE polymer is 5.28.

Figure 7: The structure of Carbamazepine (DrugBank, n.d.)

The structure of naproxen is shown below. According to the US Pharmacopeia, naproxen is practically insoluble in water. Evaluation of narproxen using the van Krevelen and Fedor method

26 resulted in total solubility value of 20.85 and 22.65. The squared solubility value between naproxen and the Eudragit® NE polymer is 4.77.

Figure 8: The structure of Naproxen (DrugBank, n. d.)

3.5 Materials

Valproic acid, naproxen, carbamazepine, caffeine, theophylline, and niacin were purchased from

Sigma Aldrich. Phosphate buffer solution was prepared by mixing 0.1387 g of K2HPO4, 0.5786 g of Na2HPO4, 4.5865 g of NaCl and 500 mL of DDI water. 0.1M HCl was added until a pH of 6.8 was obtained. Eudragit® NE 30D was kindly provided from Evonik Canada Inc.

3.6 Preparation of Polymer Membranes

Eudragit® NE 30D (ethyl acrylate and methyl methacrylate copolymer dispersion) polymer membranes were cast using 35.2 cm2 Teflon plates. Approximately 2.15 g of liquid Eudragit® was weighed and diluted with 15 mL of distilled, de-ionized water to obtain an even film layer across the Teflon plate. The polymer films were dried in the oven at 37°C for at least 24 hours before being removed and soaked in phosphate buffer solution 24 hours prior to starting the diffusion experiments or partition coefficient studies.

3.7 Drug Polymer Partition Studies

The affinity of the various drug substances to the polymer was determined by the quantity of drug partitioning into the polymer. 20-35 cast polymeric membranes (with thicknesses ranging from 70-140 µm and diameters ranging from 1.7-2.0 cm) were submersed into various concentrated drug solutions (from 0.028 mg/mL to 5 mg/mL). Next, the polymer membranes were removed and the difference in concentration (before and after submersing the polymer) provided an indication of the portion absorbed by the polymer. Drug concentrations were obtained from UV-VIS absorption, where readings were taken at the wavelengths described in Appendix 1-Table 8. Equation (12) was used to calculate the partition coefficient. The partition

27 coefficient results were compared with the squared solubility value (between the drug substance and the polymer) in addition to various properties of the drug substance including the aqueous solubility of the drug substance and the octanol water partition coefficient molecular weight and the molar volume.

In addition, the experimentally determined partition data was complemented with calculated partition coefficient values. The calculated partition coefficient values were determined from the ratio of the drug solubility in the polymer (as determined from equation (13)) and the experimentally determined aqueous solubility of the corresponding drug substance, obtained from the drug bank database (Drug Bank, n.d.).

3.8 Drug Permeation Studies

Drug permeation studies were completed through a side-bi-side® diffusion cell, obtained from Permegear©. The side-bi-side® diffusion cell is a set of side-by-side diffusion cells that contains a receptor cell and donor cell, where a concentrated drug solution is placed into the donor cell and the cast polymeric membrane is placed in-between the donor cell and receptor cell. Cast polymeric membranes were submersed in phosphate buffer solution for a period of 24 hours before being placed between two water jacketed cells. Each cell was maintained at 37°C. Phosphate buffer solution was placed in the receptor cell and the concentrated drug solutions (with concentrations ranging from 0.125 mg/mL to 5 mg/mL) were placed in the donor cell. Upon reaching steady state in the polymeric film, equations (4) and (5) were used to determine the diffusion coefficient and the lag time. Equation (4) demonstrates a linear equation of the form [f(x) = (slope) x + intercept] where after determining the slope and y intercept, the x intercept or lag time was determined. Using equation (5) the lag time was used to determine the diffusivity. The membrane permeability was determined using the lag time/partition coefficient values and mass balance methods described in equations (6) and (7). Drug concentrations were obtained from UV-VIS absorption readings, using the wavelengths described in Appendix 1- Table 8. The permeability results were compared with the square solubility value (between the drug substance and the polymer), the drug substance’s aqueous solubility, molar volume, molecular weight, octanol-water partition coefficient and predicted pKa values.

3.9 Computer Simulation: Predicting Release Behavior in Coated Pellet Systems

The empirical correlations developed in the lab scale were applied to predict the release behavior of enteric coated pellet dosage forms. Dissolution profiles of two model drugs (paracetamol and metoprolol tartrate) were obtained from literature (Mota, J., 2010) and used to elucidate the release behavior of enteric coated pellet dosage forms.

Drug-Binder Solution (Mota, J., 2010) Insoluble MCC Core Drug Layer: Ingredients % Paracetamol Paracetamol 15.0

Polymeric Coating- HPMC E5 3.8 Eudragit NE® Isopropanol 71.5 Water 9.8

Paracetamol Determine Model Values (pellet) Dissolution Drug dissolution rate, drug Curve (Mota, J., diffusivity in the matrix/coating, Correction 2010) partition coefficient (Trial & Error) Factor (Pellet & Determine Model Values (lab) Lab) Empirical Drug diffusivity in the Correlations matrix/coating, partition coefficient (via Δδ, aq. solubility, molar volume)

Figure 9: A schematic diagram showing the process used to determine the correction factor between the lab scale empirical correlations and the enteric coated pellet.

To correlate lab scale empirical correlations with the enteric coated pellet dosage form, a correction factor was determined by dividing the later by the former. As illustrated in Figure 9, model values such as the drug dissolution rate, drug diffusivity in the matrix/coating and the partition coefficient for the enteric coated pellet dosage form were predicted through trial and error and the AP-CAD© “dosage form parameter identification” simulation. Paracetmaol was chosen as the starting drug substance and the dissolution profile obtained from literature (Mota, J., 2010) was entered into the AP-CAD© software. Section 3.9.1 provides additional details

29 about the use of paracemtaol for model development and details the source of the other parameters required in the AP-CAD© software.

After determining the enteric coated pellet system parameters and with the use of a correction factor, the lab scale empirical correlations could be applied to another enteric coated pellet system for a different drug substance. Metoprolol was used to verify the model developed from paracetamol and additional details are provided in section 3.9.2. Figure 10 displays the process used to determine the parameters that would be entered into the AP-CAD© “release kinetics prediction coating systems” simulation software to generate a release profile. The generated release profile was compared with the metoprolol dissolution profile obtained from literature (Mota, J., 2010).

Drug-Binder Solution (Mota, J., 2010) Insoluble MCC Core Drug Layer: Ingredients % Metoprolol Metoprolol Tartrate 15.0 Tartrate Polymeric Coating- HPMC E5 3.8 Eudragit NE® Isopropanol 71.5 Water 9.8 Determine Model Result: Model Values (lab): Values (pellet) Drug diffusivity in Correction Drug dissolution Empirical the matrix/coating, Factor rate, drug diffusivity Correlations partition coefficient (Pellet + in the (via Δδ, aq. Lab) matrix/coating, solubility, molar partition coefficient volume)

Compare with Metoprolol Tartrate Dissolution curve (Mota, J., 2010) F1/F2 Sim/Diff.

Figure 10: A schematic diagram showing the process used to determine the dissolution profile via lab scale empirical correlations and the correction factor.

In both types of simulations, the diffusion + dissolution controlled coating matrix/pellet bead system was used because drug-binder (hydroxypropyl methylcellulose) solutions were layered on insoluble microcrystalline cellulose (MCC) cores to a 33% w/w followed by an aqueous dispersion of the Eudragit® NE 30D polymer (Mota, J., 2010). Figure 9 and Figure 10 also details the drug-binder solution formulation used by Mota (Mota, J., 2010).

The paracetamol and metoprolol tartrate dissolution curves obtained from the literature (Mota, J., 2010) were extracted using the Engauge Digitizer software©, version 4.1 (Mitchell, M., 2002). The resulting dissolution profiles obtained from the AP CAD© software were compared with the dissolution profiles generated from the AP-CAD© software. The root mean squared error (where the error was represented by the mean of the squared residuals) F1 difference and F2 similarity factors were used as a basis to demonstrate similarity between the predicted release curves and those obtained from literature.

3.9.1 Model Development

Paracetamol was used as a starting drug to develop a relationship between the lab-scale predicted diffusivity/partition coefficient and the dissolution profiles of the enteric coated pellet bead system. The text below describes how each parameter was obtained for the “dosage form parameter identification” simulation.  The radius of the pellet: Since Celphere-MCC spheres 500-850 µm were used as the base for drug layering (Mota, J., 2010), the minimum radius (250µm) was used to model the drug release curves.  Coating Thickness: The coating thickness was determined by the AP-CAD© using the Eudragit® NE weight gain (16%), the density of the pellet (the bulk density of the MCC bead is 0.97 g/cm3 for CP-507 (Asahi Kasei Chemicals Corporation, n.d.)) and the density of the coating solution (1.047 g/cm3 for Eudragit® NE (Evonik Nutrition & Care GmbH, 2015)). The coating thickness was determined to be 12.35 microns.  Drug dissolution rate: Various drug simulations were completed using the “drug release kinetics prediction coating system.” Using a trial and error approach, 1.5×10-2 sec-1 was determined to provide optimal results.  Drug diffusivity in the matrix: Various drug simulations were completed using the “drug release kinetics prediction coating system.” Using a trial and error approach, a value of 3.5×10-8 cm2/s was determined to provide optimal results.  Drug diffusivity in the coating was determined through the AP-CAD© dosage form parameter identification module  Partition Coefficient was determined through the AP-CAD© dosage form parameter identification module

 Drug solubility in the matrix was determined from the aqueous solubility of the drug substance, paracetamol. According to literature (Mota, J., 2010) paracetamol has an aqueous solubility value of 0.017 g/cm3 and this value was used to represent the drug solubility in the matrix.  The initial drug loading in the matrix was determined from the drug concentration used in the literature (Mota, J., 2010). Since the minimum radius of Celphere-MCC spheres 500-850 were used in the simulation, the minimum radius of the pellet (250 µm) was used to calculate the volume of one pellet and based on the bulk density of the pellets (0.97 g/cm3 (Celphere)), the weight of one pellet was determined to be 6.54×10-5 g. Since the drug substance was applied with an HPMC coating solution (33w/w% drug loading), the final weight of the pellet would be 9.48×10-5g or the weight of the applied drug would be 3.13×10- 5g. Consequently, the weight of drug substance/volume of pellet was determined to be 0.478 (3.13×10-5 g/6.54×10-5 cm3)  The initial drug loading in the coating, dissolved drug in the matrix and dissolved drug in the coating were 0 g/cm3. The theoretical drug diffusivity values and partition coefficient values, obtained from the empirical lab scale correlations were divided by the ideal drug diffusivity and partition coefficient values for the pellet coating systems, resulting in a correction factor between the two systems.

For the drug dissolution rate, an inverse relationship was developed between the aqueous solubility value and the drug dissolution rate. Through this relationship (e.g. solubility=constant/drug dissolution rate) a correction factor was determined from the predicted paracetamol model.

3.9.2 Model Verification

The theoretical partition and diffusion coefficients for metoprolol tartrate in the lab scale system were predicted/calculated using the empirical correlations determined from the side-by-side/lab scale experiments. The lab scale empirical correlations used to predict the partition coefficient involved the squared solubility term (Δδ) and the aqueous solubility; whereas the empirical correlations used to predict the diffusivity involved the squared solubility term (Δδ) and molar volume. Upon obtaining lab scale partition coefficient and diffusivity values, the correction

32 factor (which was determined from the paracetamol model) was applied to translate the lab scale values to values used for the enteric coated pellet coated system. A summary of the correlations obtained from the small scale experiments and used to predict theoretical partition and permeability or diffusion coefficient values are summarized Appendix 1-Table 13, Table 14, and Table 15.

Since the coated pellet system is the same system that was used for paracetmaol, the radius of the pellet, coating thickness, initial drug loading in the matrix, the initial drug loading in the coating, dissolved drug in the matrix and dissolved drug in the coating were determined as outlined in section 3.9.1. The aqueous solubility value (3630 mg/mL) cited in literature (Mota, J., 200) was used as the drug solubility in the matrix. In addition, the drug dissolution rate was determined through the inverse relationship developed from paracetamol. Subsequently, parameters were entered into the AP-CAD© “Drug Release Kinetics Prediction Coating System” simulation and dissolution profiles were generated.

Results from the actual dissolution curves (obtained from Mota, J., 2010) were compared with the predicted dissolution curves. The root mean squared error (where the error was represented by the mean of the squared residuals) F1 difference and F2 similarity factors were used as a basis to demonstrate similarity between the predicted release curves and those obtained from literature.

4 Results 4.1 Partition between the Polymer and Phosphate Buffer Solution

Of the six drug substances that were studied, carbamazepine had the highest affinity for the Eudragit® NE polymer, followed by naproxen, valproic acid, caffeine, theophylline and niacin. A summary of the average results is shown in the table below and Appendix 1-Table 6 shows all of the results obtained.

Table 1: A summary of the average partition coefficients for the 6 drug substances investigated Average Partition Drug Substance Coefficient Results Niacin ~0 Theophylline ~0 Caffeine 0.311 Valproic Acid 1.341 Naproxen 3.482 Carbmazepine 13.173

It should be noted that valproic acid resulted in absorbance readings that correlated to concentrations that were higher than the starting concentrations and it was determined that a compound from the Eudragit® NE polymer was contributing to the higher absorbance values. Even though the higher valproic acid absorbance values were corrected using baseline results, where the peak from the Eudragit® NE polymer was subtracted based on the weight of polymer used, data from the valproic acid compound was not used to further elucidate a correlation. For Niacin and theophylline, negative or near zero partition coefficient values were obtained. Based on the UV spectrum obtained from the Eudragit® NE polymer and phosphate buffer solution, there was no interference from the polymer resulting in higher absorbance readings in that region. The higher absorbance readings were attributed to analytical variability.

The partition coefficient results from the remaining drug substances were compared with the square solublity (δΔ), aqueous solubility, octanol water partition coefficient, molecular weight and molar volume values. The results are further discussed in the subsequent sections.

4.1.1 The Polymer-Phosphate Buffer Solution Partition Coefficient and Δδ

The partition coefficient values followed a somewhat logarithmic curve where low Δδ would indicate better solubility or more interactions; thus, resulting in a higher affinity of the drug substance for the polymer. In fact, with the exception of the valproic acid, approximately half of the partition coefficient values could be predicted through the Δδ term. Figure 11 depicts the graphical representation and shows the correlation (y = -4.611ln(x) + 15.206 and the R2=0. 0.5648) established between the partition coefficient and the calculated Δδ term.

Figure 11: The relationship between the experimentally determined partition coefficient and Δδ.

It should be noted that two of the drug substances (niacin and theophylline) resulted in average negative or near zero partition coefficient values. The negative partition coefficient values indicate a higher final concentration compared to the starting concentration and as previously mentioned, even though it was found that a compound from the Eudragit® NE polymer was contributing to the higher absorbance readings for valproic acid, the same phenomenon was not observed for niacin and theophylline. A wavelength of 263nm and 272 nm was used and these wavelengths are similar to the wavelengths used for carbamazepine, caffeine and naproxen (285nm, 272nm, 271nm). From the blank cell, it was determined that the Eudragit® compound would not interfere at that wavelength.

It should be noted that upon removal of the negative partition coefficient values, an improved correlation could be developed between the partition coefficient and Δδ. The data was complimented with calculated

35 partition coefficient values and both sets of data are presented in Figure 12and Figure 13. By adding the calculated partition coefficient values, the relationship between the partition coefficient and the squared solubility parameter could be easily improved. The asymptotic function of 1/(x-3.5) easily fits several of the data points and shows that for good solubility to occur, the squared solubility term must be less than 3.5.

Figure 12: The relationship between the experimentally determined partition coefficient and Δδ, excluding values for niacin and theophylline.

4.1.2 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Aqueous Solubility

Figure 14 shows the correlation between the partition coefficient and the aqueous solubility of the drug substance. Similar to the relationship developed between the partition coefficient and Δδ, as depicted in Figure 15 and Figure 16, removal of the negative partition coefficient values resulted in a better exponential correlation and the data was complemented with calculated partition coefficient data.

4.1.3 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Octanol Water Partition Coefficient

Figure 17 shows the correlation between the partition coefficient and the octanol-water partition coefficient of the drug substance. Though a linear correlation is shown, the R2 value (which is less than 0.5) shows the correlation is not strong.

In this particular case, it should be noted that the experimental octanol water partition coefficient obtained from the DrugBank database (DrugBank, n.d.) was negative for caffeine and removing the negative partition coefficient values (for niacin and theophylline) resulted in only two data points. Calculated partition coefficient values were added to the two data points; however, a clear relationship between the polymer-phosphate buffer solution partition and octanol-water partition coefficients could not be established. The data are shown in Figure 18.

4.1.4 The Polymer-Phosphate Buffer Solution Partition Coefficient and the Molecular Weight

Figure 19 shows the correlation between the polymer-phosphate buffer solution partition coefficient and the molecular weight. Based on the correlation shown below, it would appear that higher molecular weight molecules appear to be retained or trapped in the polymer more so compared to drug substances of lower molecular weight. Though a quadratic correlation was utilized, the correlation was limited because drug substances with a molecular weight that is less than 100 g/mol were not used and therefore, the quadratic correlation could not be verified for drug substances with a molecular weight less than 100 g/mol.

Upon removal of the negative partition coefficient values, it would appear that a power correlation could be generated amongst the three data points; however the addition of calculated partition coefficient values disproves or invalidates a power correlation. However, it should be noted that in some cases, drug substances with a molecular weight between 230-260 g/mol appeared to result in higher partition coefficient values. Higher partition coefficient values are

40 also observed for a drug substance with a molecular weight of 144 g/mol and another drug substance with a molecular weight of 384 g/mol. The results are shown in Figure 20.

Figure 19: The relationship between the experimentally determined partition coefficient and the molecular weight of the drug substance.

4.1.5 The Partition Coefficient and the Molar Volume

While the molecular weight of a drug substance provides an indication of the size of the molecule, it does not take into account the stearic effects and actual size of the molecule. The molar volume was determined using the group contribution method and Figure 21 shows the relationship between the molar volume and the partition coefficient. Similar to the molecular weight correlation, smaller molecules did result in a smaller partition coefficient; however, due to the negative partition coefficients a quadratic correlation had to be used.

Upon removal of the negative partition coefficient values, similar to the molecular weight correlation, it would appear that a power correlation could be generated amongst the three data points; however addition of the calculated partition coefficient values, again disproves or invalidates any correlation between the partition coefficient and the molar volume. Despite the fact that a strong correlation could not be developed between the molar volume and partition coefficient, similar to the molecular weight correlation, high partition coefficient values were obtained around a cluster of drug substances. In this case, some dug substances with a molar volume between 150 and 350 cm3/mol resulted in higher partition coefficient values. The results are shown in Figure 22.

Figure 21: The relationship between the experimentally determined partition coefficient and the molar volume of the drug substance.

4.1.6 Interacting Effects

The squared solubility term and the aqueous solubility values were determined to be the two main effects that significantly influence the partition coefficient. To determine if there were any interacting effects between the squared solubility term and the aqueous solubility, the values associated with the squared solubility and the aqueous solubility were grouped according to similar values. Drug substances with squared solubility values ranging from 0 to 5 and 5 to 10 were grouped, whereas aqueous solubility values were grouped by magnitudes of 10, in mg/L found in the drug bank database (DrugBank, n.d.). In an interacting effects plot, each grouping (i.e. each magnitude of 10 for aqueous solubility) is graphed as a series against the groupings created for the squared solubility term (i.e. between 0 to 5 and 5 to 10) and the average resulting partition coefficient data is plotted on the y-axis. Alternatively, the squared solubility groupings is graphed as a series against the groupings created for the aqueous solubility term (x-axis) and the average resulting partition coefficient data. Since each series is graphed against another effect and the average partition coefficient data, if the trend within one series changes and crosses the trend from another series, it will indicate an interacting effect. The near zero

43 calculated partition coefficient values (<0.02) were eliminated from the analysis. A summary of the interacting effects are shown in Figure 23.

Figure 23: The interaction plot for theoretical partition coefficient values.

Based on the interaction plot, it may appear that an interaction is present between the squared solubility term and the aqueous solubility term; however, a closer examination of the actual data shows that this is not the case. In fact, calculated partition coefficient data from pseudoephedrine and verapamil appear to skew the data as values exceeded 500. Excluding those values from the data set resulted in the interaction plot shown in Figure 24.

Interaction Plot for Theoretical Partition Values Data Means

25 Δδ (Grouped) 0-5 5-10

M 10

0.10 10.00 1000.00 10000.00 Aqueous Solubility (Grouped)

Figure 24: The interaction plot for theoretical partition coefficient values, excluding pseudoephedrine and verapamil.

Figure 24 clearly shows that when the squared solubility term is between 5 and 10, drug substances with an aqueous solubility values greater than 10 mg/L are not present. Similarly, when the squared solubility term is between 0 and 5, drug substances with an aqueous solubility value less than 10 mg/L does not exist. However at 10 mg/L, drug substances can fall on either side of the squared solubility term and be between 0 and 5 or 5 and 10. In this case, drug substances with a squared solubility term between 0 and 5 clearly demonstrated much higher calculated partition coefficient results compared to drug substances with a squared solubility term that ranged between 5 and 10. These data demonstrate that the aqueous solubility is interrelated with the squared solubility term associated with the drug substance and Eudragit® NE polymer; but in cases where the same aqueous solubility value is observed, the squared solubility term provides better insight into the partition coefficient value.

It should be noted that when the squared solubility term is between 0 and 5, high partition coefficient values exist when the aqueous solubility is approximately 10 mg/L; however, for drug substances with greater aqueous solubility values (approximately 1000 mg/L) the calculated partition coefficient values fall to near zero values. Therefore, it can be concluded that when the squared solubility is between 0 and 5, the calculated partition coefficient decreases with the increase in the aqueous solubility value. However, when the squared solubility term is between 5 and 10, a similar trend was not observed; but, there is also insufficient data to identify a trend.

4.2 Drug Permeation through the Polymer Films

4.2.1 Drug Release Profiles

Each drug substance resulted in different dissolution profiles. Due to the potential interference with the Eudragit® NE polymer, valproic acid had the highest % of drug released after 18 hours, followed by carbamazepine, naproxen, caffeine, niacin and theophylline. Figure 25 shows the percent released curves for each drug substance studied and Figure 26 provide a closer examination of the % released drug release profiles.

Figure 25: The percent released curves for caffeine, carbamazepine, niacin, naproxen, valproic acid, and theophylline.

Figure 26: A zoomed view of the percent released curves for carbamazepine & naproxen (top) and caffeine, niacin, and theophylline (bottom)

4.2.2 Time Lag

A close examination of the % released profiles shows that valproic acid demonstrated lag time where approximately 2.7 hours was required for the drug substance to accumulate into the polymer before reaching steady state in the polymeric membrane and obtaining a constant release profile. Naproxen also showed a similar delay where a time lag of approximately 5 hours was observed.

In contrast, unexpected initial burst effects were observed for carbamazepine, niacin and caffeine. Most notable is the burst effect observed for niacin, where, after the initial release or burst, the rate of release drastically slows where little or no drug is further released.

It was thought that the burst effect could be explained through drug polymer interactions where the drug substance was interacting with the polymer, quickly becoming entrapped into the Eudragit® NE polymer, and making the polymer membrane less permeable. If this were the case, the hydrodynamic radius of the polymer nanoparticles in the suspension Eudragit® NE would change. To test this hypothesis, Eudragit® NE polymer suspension was mixed with the same drug substance and the hydrodynamic diameter of the polymer nanoparticles was measured by dynamic light scattering method. Particle size distributions of the Eudragit® NE polymer and the mixture of niacin+Eudragit® NE polymer are shown in Figure 27. The frequency distribution curve did not show any significant shift in the hydrodynamic diameter of the polymer nanoparticles, suggesting that hydration of polymers in the presence of niacin may not be the contributing factor to the slow release after the initial burst presented in Figure 26. More investigations are required in future to explain the abnormal permeation curve of niacin.

Figure 27: The frequency distribution curve of the Eudragit® polymer and the Eudragit® + niacin mixture.

4.2.3 Permeability/Diffusivity coefficients

With the exception of valproic acid, from the drug release profiles, the calculated permeability from the time lag and the mass balance method were in agreement for all the drug substances studied. Amongst the drug substances studied, the average permeability had magnitudes of difference, ranging from 10-9 to 10-11. The highest permeability was obtained for carbamazepine followed by naproxen, caffeine, theophylline and niacin. A summary of the average permeability results are shown in Table 2.

Table 2: The average permeability calculated via the bass balance and lag time methods. Average Permeability (cm2/s)-Mass Average Permeability Drug Substance Balance Method (cm2/s) -Time Lag Method Niacin 4.028 × 10-11 4.026 × 10-11 Theophylline 5.670 × 10-11 5.701 × 10-11 Caffeine 1.444 × 10-10 1.443 × 10-10 Valproic Acid 1.093 × 10-7 9.903 × 10-8 Naproxen 1.739 × 10-9 1.734 × 10-9 Carbamazepine 5.207 × 10-9 5.119 × 10-9

Using the time lag method, the diffusion coefficient was determined through the x-intercept. However, due to insufficient lag time, in some cases, negative diffusion coefficient values were obtained. A summary of the calculated results are shown in appendix 1-Table 11.

The diffusion coefficient was also determined using the permeability and the partition coefficient. Exclusive of valproic acid, values ranged in magnitude from 10-10 to 10-12. However, since near zero or negative partition coefficient values were obtained for niacin and caffeine, this resulted in negative diffusion coefficients. A summary of the results are shown in appendix 1-Table 11.

Table 3: The average diffusion coefficient results Diffusion Coefficient (cm2/s) (via Diffusion Coefficient (cm2/s) Drug Substance the time lag method) (via partition studies) Niacin ~0 ~0 Theophylline 1.271× 10-3 ~0 Caffeine ~0 4.646 × 10-10 Valproic Acid 1.546 × 10-8 8.588 × 10--8 Naproxen 1.404 × 10-9 4.993 × 10-12 Carbamazepine ~0 2.681 × 10-10

In the last method, the diffusion coefficient was obtained through Fick’s law, shown in Equation 9 and Equation 10. In this case, the diffusion coefficient was calculated at 3, 6.8 and 16.7 hours. In all cases, as time progressed, the diffusion coefficient decreased. A summary of the calculated results are shown in Appendix 1-Table 11.

4.2.4 Correlations

A linear correlation was developed between the permeability and the partition coefficient, where approximately 95% of the data points could be explained. The linear correlation is shown in Figure 28.

Figure 28: The relationship between the obtained partition coefficient values and the pKa of the drug substance.

Consequently, the linear correlation would indicate that some of the empirical correlations developed for the partition coefficient would be applicable to predict the permeability. In fact, an empirical correlation between the permeability and the calculated Δδ term was well established, and predicts approximately 94% of the values. A graphical representation of the correlation is shown in Figure 29. In addition, 96% of the data points could be explained using the calculated molar volumes and the established correlation is shown in Figure 30.

Figure 29: The correlation developed between the permeability (obtained using the time lag method) and the calculated Δδ term.

Figure 30: The correlation developed between the permeability (obtained using the time lag method) and the drug substance’s molar volume.

For the molecular weight, aqueous solubility and the octanol water partition coefficient, strong correlations were not as well established compared to the previous correlations for the partition coefficient, squared solubility term and molar volume. The relationship between the drug substance’s pKa and the permeability was the worst correlation because only 60% of the data

51 points could be explained. Figure 31, Figure 32, Figure 33, and Figure 34show the relationships between the permeability and drug substance’s molecular weight, aqueous solubility, octanol water partition coefficient and the pKa.

Figure 31: The relationship developed between the permeability (obtained using the time lag method) and the molecular weight of the drug substance.

Figure 32: The relationship developed between the permeability (obtained using the time lag method) and the aqueous solubility of the drug substance

Figure 33: The relationship developed between the permeability (obtained using the time lag method) and the drug substance’s octanol water partition coefficient

Figure 34: The relationship developed between the permeability (obtained using the time lag method) and the predicted pKa value of the drug substances.

4.3 Predicting Drug Release Behavior in Drug Layered, Eudragit® NE Pellet Coated Systems

4.3.1 Obtaining a Model

The module “dosage form parameter identification” in the AP-CAD© software package was used to predict the partition and diffusivity values from a fractional release profile obtained in

53 literature. The fraction release profile was obtained for microcrystalline cellulose (MCC) beads layered with a paracetamol drug-binder solution and coated with Eudragit® NE. Using the method of trial and error, the optimal drug dissolution rate and drug diffusivity in the matrix was determined to be 1.5 × 10-2 1/sec and 3.5× 10-8 cm2/sec. Subsequently, the best-fit drug diffusivity in the coating and the partition coefficient was determined by the AP-CAD© software to be 5.00× 10-9 cm2/sec and 1.00. Using the parameters obtained via trial and error from the AP- CAD© simulations, a fractional release profile was generated and compared with the % released profile obtained from literature. A graphical comparison of the results is shown in Figure 35.

A comparison of the dissolution profile obtained in literature and from the AP-CAD© simulation was completed. The comparison between both dissolution profiles resulted in a root mean square error of 2.99%, an F1 similarity factor of 5.74 and the F2 result of 84.97, indicating a close match of the predicted curve with the experimental data.

Figure 35: The dissolution profiles generated from AP-CAD© and obtained from literature (Mota, J., 2010) for paracetamol layered, Eudragit® NE MCC coated pellets.

Table 4: A summary of the calculated/determined values associated with Figure 35. Parameter Value Comments Radius of pellet/bead 0.025 cm Calculated from literature values Coating thickness 12.35 microns Determined by Weight gain Drug Dissolution Rate 1.5 × 10-2 1/sec Determined via trial and error Drug Diffusivity in matrix 3.5 × 10-8 cm2/sec Determined via trial and error Drug Diffusivity in coating 5.00 × 10-9 cm2/sec Results from AP-CAD© Partition Coefficient 1.00 Results from AP-CAD© Drug Solubility in the Matrix 0.017 Aqueous solubility (Mota, J., 2010) Initial drug loading in matrix 0.478 g/cm3 Calculated from literature values Initial drug loading in coating 0 g/cm3 Set Initial dissolved drug in matrix 0 g/cm3 Set Initial dissolved drug in coating 0 g/cm3 Set

4.3.2 Applying the Model for Metoprolol Layered, Eudragit® NE Coated MCC Pellets

The theoretical drug diffusivity in the coating/matrix and the partition coefficient obtained from the Paracetamol AP-CAD© “dosage form parameter identification” simulation was divided by the permeability and partition coefficients obtained from the empirical lab scale correlations (developed from the lab scale partition/side-by-side diffusion cell experiments). The quotient was used to obtain a correction factor, which was subsequently used to develop a relationship between the enteric coated pellet system and the slab scale results. Please refer to Appendix 1- Table 13 for drug diffusivity and partition coefficient correction factors developed from paracetamol.

For the partition coefficient, two correlations were established in section 4.1 and the best parameters to predict the partition coefficient were the squared solubility term (Δδ) and the experimental aqueous solubility. When using the square solubility term (Δδ), the theoretical AP- CAD© values ranged from 0.09 to 3.62, whereas the experimental aqueous solubility correlations resulted in the smallest partition coefficient values. Please refer to Appendix 1- Table 13 for the calculated partition coefficient values obtained for metoprolol.

The empirical permeability correlations developed from the side-by-side diffusion experiments were used to predict values for the drug diffusivity in the matrix and in the coating. The best empirical correlations used the squared solubility term (Δδ) and the molar volume to predict permeability. Utilizing the empirical correlations and correction factor, values ranged from 1.30×10-8 to 6.85×10-7 cm2/sec if the squared solubility or the molar volume empirical

55 correlation were used. Similarly, drug diffusivity values ranged from 1.85×10-9 to 9.79×10-8 cm2/sec depending if the squared solubility or molar volume empirical correlation were used. Please refer to Appendix 1 - Table 14 for a complete list of calculated drug diffusivity values for metoprolol tartrate.

For the drug dissolution rate, a simple inverse relationship was developed with the aqueous solubility value cited in literature (Mota, J., 2010). An aqueous solubility value of 3.630 g/cm3 was used for metoprolol tartrate. Using paracetamol’s aqueous solubility value of 0.017 g/cm3 (Motal, J., 2010) and predicted drug dissolution rate of 1.5×10-2 sec-1 resulted in a predicted drug dissolution rate of 7.02 × 10-5 sec-1 for metoprolol tartrate; however, due to the limitations of the AP-CAD© software, where the minimum value of the drug dissolution rate is 1× 10-4 sec-1 caused a value of 1× 10-4 sec-1 to be used to generate the predicted model for metoprolol. It should be noted that the solubility value used in literature was for metoprolol as a salt (i.e. metoprolol tartrate); however, metoprolol as a free base has a much different experimental aqueous solubility value of 0.0169 g/mol.

After establishing diffusivity and partition coefficient parameters (as described above) the dissolution profiles for metoprolol tartrate were generated. The squared solubility term provided the best correlation and the resulting dissolution profile is shown in Figure 36. A comparison of the resulting dissolution profile and the profile obtained from literature (Mota, J., 2010) was completed. The comparison between both dissolution profiles resulted in a root mean square error of 9.46%, an F1 similarity factor of 13.21 and the F2 result of 74.51, demonstrating good agreement between the prediction and experimental result.

Compared to the squared solubility term, it should be noted that estimated the matrix and coating diffusivity values from the molar volume resulted in dissolution profiles that were extremely fast, even if the minimum partition coefficient of 0.09 was used. In that scenario practically all of the drug substance would be released within 1.5 hours.

Estimating the partition coefficient from the correlation developed from the aqueous solubility, resulted in extremely slow dissolution profiles when the drug diffusivity in the coating and matrix were estimated from the squared solubility term. Almost 70 hours was required for the drug substance to be fully released.

Table 5: A summary of the calculated/determined values associated with Figure 36. Parameter Value Comments Radius of pellet/bead 0.025 cm Calculated from literature values Coating thickness 12.35 micron Determined by Weight gain Drug Dissolution Rate 1×10-4 1/sec Determined from the inverse aqueous solubility Drug Diffusivity in matrix 1.30×10-8 cm2/sec Calculated from Δδ correlation & Correction factor Drug Diffusivity in coating 1.85×10-9 cm2/sec Calculated from Δδ correlation & Correction factor Partition Coefficient 2.07 Calculated from Δδ correlation & Correction factor Drug Solubility in the Matrix 3.630 g/cm3 Aqueous solubility (Mota, J., 2010) Initial drug loading in matrix 0.381 g/cm3 Calculated from literature values Initial drug loading in coating 0 g/cm3 Set Initial dissolved drug in matrix 0 g/cm3 Set Initial dissolved drug in coating 0 g/cm3 Set

5 Discussion and Conclusions 5.1 Partition Coefficient Results

It should be noted that two of the drug substances (niacin and theophylline) resulted in average negative partition coefficient values. The negative partition coefficient values indicate a higher final concentration compared to the starting concentration and as previously mentioned, for valproic acid, it was found that a compound from the Eudragit® NE polymer was contributing to the higher absorbance values at a wavelength of 202 nm. However, for niacin and theophylline, it was determined that the Eudragit® compound would not interfere at a wavelength of 263 nm and 272 nm. In addition, a wavelength of 263 nm and 272 nm are similar to the wavelengths used for carbamazepine, caffeine and naproxen (285 nm, 272 nm, 271 nm). As a result, in this case, since other values were positive, but near zero, the negative partition coefficient values were associated with analytical variability.

Subsequently, due to the limited partition coefficient results, calculated partition coefficient values supplemented the experimental values to verify the correlations. In some cases, the calculated partition coefficient values were in good agreement with the experimental results; but in other cases, the calculated partition coefficient values provided additional data to support the experimental results or disprove any potential correlation. The findings from each correlation are further discussed below.

5.1.1 Correlations

5.1.1.1 The Partition Coefficient and Δδ

The partition coefficient data provides an indication of the affinity of the drug substance for the polymer. The correlation developed in Figure 11 only explains approximately half the data points; however, by analyzing the actual experimental data results, it shows that when Δδ is less than 5, the drug substance partitions into the polymer, which is in good agreement with van Krevelen’s statement where good solubility occurs when Δδ is less than 5 (Krevelen, D., 1990). In this case, carbamazepine and naproxen had Δδ values that were less than 5 and resulted in partition coefficient values that were significantly higher than the drug substances that had Δδ

58 values greater than 5 (e.g. caffeine, theophylline and niacin). According to van Krevelen, for good solubility, ∆δ must be less than 5 (Krevelen, D., 1990).

It should be noted that upon removal of the negative partition coefficient values, an improved power correlation could be developed between the partition coefficient and Δδ. By adding calculated partition coefficient data, the asymptotic function of 1/(x-3.5) easily fits several of the data points and shows that for good solubility to occur, the squared solubility term must be less than 3.5. Therefore, the calculated results are consistent with van Krevelen’s estimation where good solubility occurs when Δδ is less than 5 (Krevelen, D., 1990). The empirical relationship provides an easier method of estimating the partition coefficient compared to the calculated values because the calculated values of the partition coefficient requires the use of predetermined experimental properties of the drug substance, such as the melting point temperature and the aqueous solubility of the drug substance, but the squared solubility difference could be easily calculated solely on the basis of the molecular structure.

5.1.1.2 The Partition Coefficient and the Aqueous Solubility

All of the experimental data resulted in a logarithmic correlation between the partition coefficient and the aqueous solubility. However, removal of the negative partition values resulted in a power correlation that is well complimented with the calculated partition coefficient results. The empirical power correlation of y=22.54x-0.428 indicates that soluble drug substances (more than 1500 mg/L) will result in very little partition into the polymer as the polymer-phosphate buffer solution partition coefficient will be less than 1.

The results indicate that highly soluble drug substances with high aqueous solubility values are less likely to partition into the polymer is in good agreement with literature because the Eudragit® NE polymer is neutral in nature and consists of alkyl or non-polar groups resulting in a molecule that is hydrophobic in nature. This provides supporting rationale for why highly soluble drug substances are less likely to partition into the polymer.

5.1.1.3 The Partition Coefficient and the Octanol Water Partition Coefficient

It was unexpected that a strong correlation could not be developed between the octanol-water partition coefficient of the drug substance and the experimentally determined polymer-buffer

59 solution partition coefficient. The results from the experimental data and calculated partition values were unexpected because the Eudragit® NE polymer is a neutral copolymer and substances that have non-polar groups are typically hydrophobic in nature, which is similar to octanol. In fact the octanol water partition coefficient has been used to represent the hydrophobic nature of a drug substance and linear relationships were developed between the polymer-water partition coefficient and the octanol water partition coefficient (Pitt, C. G., et al., 1988). However, for a good linear relationship to exist, there are two rules that need to be satisfied. The first rule says that the polar phase needs to be water; which, is satisfied for the case of the polymer-phosphate buffer solution partition coefficient and the octanol water partition coefficient. The second rule indicates that the non-polar phase needs to contain the same functional groups (Leo, A., et al., 1971). In this case, octanol consists of ethyl, methyl and a hydroxyl group and the Eudragit® NE polymer consists of ethyl and methyl groups; however, rather than a hydroxyl group, the Eudragit® NE polymer consists of short chained ester groups. As a result, it would appear that the presence of the short chained ester groups has a significant effect on the partitioning effects of the drug substance.

5.1.1.4 The Partition Coefficient and the Molecular weight

When experimentally determined data is used, a parabolic or exponential relationship could be developed between the polymer-buffer solution partition coefficient and the molecular weight of the drug substance; however the calculated polymer-water partition coefficient values resulted in a contradictory relationship where both high and low molecular weight drug substances resulted in low partition coefficient values. A cluster of drug substances that resulted in high partition coefficient values seemed to occur for drug substances with a molecular weight of around 250 g/mol; however other drug substances with similar molecular weight values resulted in near zero calculated polymer-phosphate buffer solution partition coefficient values as well.

5.1.1.5 The Partition Coefficient and the Molar Volume

Similar to the molecular weight, when experimentally determined data is used, a parabolic or exponential relationship could be developed between the polymer-phosphate buffer solution partition coefficient and the molar volume of the drug substance; however adding the calculated polymer-buffer solution partition coefficient values resulted in a contradictory relationship where drug substances with high and low molar volumes resulted in low partition coefficient values.

5.1.2 Improvements

Even though a linear calibration curve was obtained between the absorbance-concentration results, niacin and theophylline had negative polymer-phosphate buffer solution partition coefficient results and those results were attributed to analytical variability. However, to verify the results, an alternative method could be employed. Co-solvents have been used to enhance the solubility of drug substances (Smedes, F., et al., 2009) and a third system/solvent can skew the results so more drug partitions into the polymer rather than in the aqueous phase. Consequently, reducing the solubility in the co-solvent aqueous phase can result in an increase in the polymer solubility of a three component system. Therefore, the same theory can be applied to the hydrophilic drug substances, theophylline and niacin. By reducing the solubility or creating a larger difference between the polymer and aqueous phases, it may overcome the observed analytical variability or the product of the partition coefficient between Eudragit® NE/ethanol and ethanol/water could be used to determine the partition coefficient between Eudragit® NE and water. Therefore, the use of co-solvents provides an alternative method to determine the polymer-water partition coefficient (Smedes, F., et al., 2009).

From a thermodynamic perspective, the Flory-Huggins solution theory is used to describe the Gibb’s free energy of mixing between a polymer and a solvent. Several articles have used the Flory-Huggins equation as a predictive tool to interpret the partitioning of solutes in two phases of solvents. Usually, the activity coefficient has been used to quantify the Flory-Huggins theory, which could be interpreted as a system of three different contributions: the entropy of mixing, intermolecular interactions between the solute/polymer, and the free volume effect (Bacon, S., et al., 2014). The entropy of mixing is a measure of the potential molecular configurations that could stem from mixing the two systems. More configurations will result in increased entropic values. The intermolecular interaction can result in both positive and negative contributions towards Gibb’s free energy of mixing. For example, strong hydrogen bonding can result in negative or favourable conditions whereas dipole-dipole interactions can result in positive or unfavorable conditions. In terms of the free volume effect, the large polymeric molecules will have restricted movement since it will have less degrees of freedom compared to the small drug molecules. When the two substances are mixed together, the entropy will be positive, the enthalpy will be negative; however the net change in the Gibb’s free energy of mixing is a positive contribution or unfavorable results. The UNIFAC model uses a group contribution

61 method of the individual functional groups to predict the activity coefficient. As another area for improvement correlations between the partition and activity coefficient could be evaluated to determine if the empirical correlations are in agreement with theoretical predictions defined using activity coefficients.

5.2 Side-by-Side Diffusion Results

5.2.1 Release Curves

In the literature review, it was said that diffusion occurs through three mechanisms: Fickian diffusion through the polymer matrix, diffusion through water filled pores and by erosion of the polymer matrix (Kaith B. S., et al., 2011). However, the Eudragit® NE polymer is insoluble (Evonik, 2015) and therefore in phosphate buffer solution, diffusion will not be controlled by erosion of the polymer matrix. The influence of swelling was studied (Knop, K., 1996) and it was determined that Eudragit® NE polymers had the highest percentage of water uptake with distilled water (~36%) but had the lowest amount of swelling (~14%) when phosphate buffer 4.4 was used. Therefore, since Eudragit® NE polymers swell to a certain extent, the mechanisms controlling release of the drug substance include diffusion through the matrix and water filled pores.

For the six drug substances studied, the drug permeation kinetics demonstrates a difference in terms of the quantity of drug substance migrating through the polymer. Some issues were observed in some of the side-by-side diffusion experiments (for valproic acid, the polymer associated with cell 6 appears to have burst part way through the experiment; for caffeine, the polymer associated with cell 3 may have burst; for carbamazepine, air may have become entrapped in lines associated with cell 3; for niacin, cell 3 may have resulted in leakage near the end of the experiment and for naproxen, cell 1 & cell 3 resulted in leakage) but corresponding results were not included as part of the analysis. Despite the exclusion of some results, upon examining the release profiles of the remaining results, patterns could be obtained to deduce correlations described in the subsequent sections.

5.2.2 Time Lag

The diffusion of a drug substance through a polymeric membrane involves several steps. Initially, the polymeric membrane is free of the drug substance and enters one side of the

62 polymer and prior to steady state, the rate of flow and concentration varies within the polymeric sheet. As steady state is approached, the quantity of permeate passing through the polymer with regards to time will be constant. Subsequently, the burst profile, which was observed at the beginning of the release profile for carbamazepine, niacin and caffeine, was unexpected as it should take time for the quantity of drug substance to build in the polymeric film. The burst profile has been frequently observed in the pharmaceutical industry; but, a mechanism that fully explains or deduces the reason for the burst effect has not been determined (Huang, X., et al., 2001).

5.2.3 Permeability and Diffusion Coefficients

The mass balance and time lag methods were used to determine the permeability; but three methods were used to determine the diffusivity of the drug within the polymer film. In the first method, the lag time was used. However, due to insufficient lag times, in some cases, a negative diffusion coefficient value was obtained and the negative values could not be used. In the second method, diffusivity values were obtained through the use of the permeability and the partition coefficient; however since negative or near zero values were obtained for theophylline and niacin, a representative diffusion coefficient could not be obtained. In the last method, Fick’s equation (Equations 9 and 10) was used at various time points. It was observed that as time increased, the diffusion coefficient decreased or became smaller. In some cases, this explanation could be attributed to the burst effect observed in some drug substances. Subsequently, due to the issues observed with obtaining adequate diffusion coefficient results, permeability values obtained from the mass balance method were used to further identify potential empirical correlations.

5.2.4 Correlations

5.2.4.1 Permeability and the Partition Coefficient

The permeability is a product of the diffusion coefficient and the partition coefficient. The permeability describes how the drug substance diffuses through the polymer membrane while the movement of the drug substance within the polymer is related to the drug diffusivity (Griskey, R. G., 1995). A good linear correlation between the permeability and partition coefficient was obtained and the results indicate that the overall release mechanism or permeation of the drug

63 substance from the donor side through the polymer and into the receptor cell is dominated by the drug substance’s affinity for the polymeric membrane.

5.2.4.2 Permeability and Δδ

Similar to the drug partition studies, a correlation was developed between Δδ and the permeability. The retention of the drug substance in the polymer could be dictated by the drug’s solubility (Griskey, R. G., 1995) and in fact that statement agrees well with the correlation between the permeability and the squared solubility parameter because van Krevelen’s statement indicates good solubility occurs when Δδ is less than 5 (Krevelen, D., 1990). Consequently, in the developed correlation where drug substances had squared solubility terms equal to or less than 5, the permeability results were substantially higher. A power correlation was able to explain more than 95% of the data points and shows that solubility does play an important role in the permeability of a drug substance through the polymer.

5.2.4.3 Permeability and the Molar Volume

Unlike the drug partition studies, a good exponential correlation (R2=0.9641) was developed between the molar volume of the drug substance and the permeability.

5.2.4.4 Permeability and the Molecular Weight

A correlation was developed between the permeability results and the molecular weights of the drug substances; however the empirical correlation was not as strong compared to the empirical correlation developed with the molar volume (R2=0.9641 vs. R2=0.8088). Since the molecular weight is simply an indication of the number elements found in the drug substance, the difference is likely due to the stearic effects accounted for in the molar volume. It is likely that the size and shape of the molecule affects the retention and thus permeation of the drug substance through the polymer membrane.

5.2.4.5 Permeability and the Aqueous Solubility

A correlation was developed between the permeability results and the aqueous solubility; however, the correlation was not as strong compared to the empirical correlations developed with the squared solubility term and molar volume correlation (R2=0.8988 vs. R2≥0.94%). It should be noted that Jenquin (Jenquin, M. R., et al., 1990) had attributed the faster release profile of

64 chlorpheniramine to the aqueous solubility of the drug substance; however, other factors were also included such as the adsorption of the comparative drug substance, salicylic acid.

The FDA biopharmaceutical classification system (BCS), several articles study the effect of solubility and permeability of drug substances in a developmental setting; however the relationship between the aqueous solubility and permeability of the drug substance is not clearly highlighted. According to the BCS classification system, drug substances can exist with the various combinations of high/low aqueous solubility/permeability in the body and in fact, it was found that 23.6%, 17.1%, 31.7% and 10.6% of immediate release essential drug substances would be classified as Class I, II, III and IV type drug substances (Nehal A. K., et al., 2004). As a result, it is not surprising that the experimental results could not identify a relationship between the drug substance’s experimentally determined aqueous solubility values and permeability through polymer films.

Therefore, the results from Jenquin’s study (Jenquin, M. R., et al., 1990) and the FDA BCS classification system prove that the aqueous solubility does not necessarily translate into good permeability results and a comparison of the developed empirical correlations demonstrate that there are other factors that influence the permeability of the drug substance through the polymer membrane.

5.2.4.6 Permeability and logP

Unlike the partition coefficient correlations, a correlation (R2=0.8193) was developed between the octanol water partition coefficient and the permeability of the drug substance; however the correlation was not as strong compared to the other factors considered. The underlying reason for why a strong correlation was not developed between the permeability and the octanol-water partition coefficient is outlined in section 5.1.1.3. If the octanol water partition coefficient could not explain or predict how the drug substance will partition into the polymer, then naturally, it was expected that a strong correlation could not be developed between the permeability and the octanol-water partition coefficient, especially since a good correlation was developed between the permeability and partition coefficient.

Despite the case study that determined the hydrophobic/hydrophilic nature of the drug substance affected the release rate of the drug substance through HPC (Sawant, P. D., et al., 2010), it

65 should be noted the result was confounded with a drug polymer interaction and as a result, the role of interaction may have been more significant compared to the lipophilicity of the drug substance.

In addition, as previously mentioned, though a correlation was developed between the drug substance’s aqueous solubility and permeability, it was not strong compared to other factors. Subsequently, since the aqueous solubility of a drug substance could provide an indication of the drug substance’s lipophilicity, it is not surprising that a strong relationship could not be developed between the octanol water partition coefficient and permeability through the polymer films.

5.2.4.7 The Permeability and Acidic/Basic strength

A correlation between the permeability of the drug substance and the pKa was not established. Even though the acidic and basic groups could interact with the ester bond (through catalysis or hydrolysis) that process would not result in a breakdown of the hydrocarbon backbone chain that makes up the neutral Eudragit® NE polymer. In contrast, as previously mentioned, the acid/base interaction with poly (D,L-lactic acid) or copoly (l-lactic/glycolic acid) would result in the direct hydrolysis or cleavage of the ester bond, which is part of the underlying backbone of that polymeric structure and would consequently result in degradation of the polymer and increased release of the drug substances.

5.2.5 Improvements

Since the partition and permeability studies were performed separately, experiments could have been combined through a complete mass balance approach, which would allow for all parameters to be determined from one experiment. For instance, by determining the concentration in the donor cell and receptor cell and assuming any unaccounted drug substance is absorbed by the polymer substance, then the partition of the drug substance into the polymer could be determined. However, if the mass balance approach is used, additional studies need to be conducted to verify if absorption takes place at any drug substance contact surface. For instance, the tubing used to extract samples for analysis could result in absorption and consequently, separate tubing-phosphate buffer solution partition studies should be conducted.

5.3.1 Developing a Model

As part of the trial and error approach to develop the model relating lab scale empirical correlations with an enteric coated pellet system, predicted and experimental aqueous solubility values were used. For paracetmaol, the predicted aqueous solubility is 0.00415g/cm3 and the experimental aqueous solubility is 0.014g/cm3. Using the experimental aqueous solubility value, resulted in a decreased drug dissolution rate, drug diffusivity and partition coefficient values. However, it should be noted that the experimental aqueous solubility value of 0.014 g/cm3 closely reflects the aqueous solubility value (0.017 g/cm3) cited in literature (Mota, J., 2010). These results are in line with literature and an increase in the aqueous solubility can drastically alter the drug substance existing as a molecularly dissolved drug or a particle dispersed drug (Thombre, A. G., et al., 2011).

Using a trial and error approach and the AP-CAD© parameter identification simulation, parameters associated with the drug dissolution rate, drug diffusivity in the matrix/coating and the partition coefficient were identified. A dissolution profile was generated from the identified parameters and compared with the dissolution profile obtained from literature (Mota, J., 2010) and the generated drug dissolution profile closely reflects the dissolution profile found in literature (Mota, J., 2010). The root mean squared error was less than 3% and the F1/F2 difference/similarity factor was 5.74 and 84.97. According to the FDA guidance for the industry (US Department of Health and Human Services, 1997a) in-vitro dissolution profiles can be considered similar when the F2 value is between 50 and 100. In addition, criterion is provided that the average difference at any dissolution point should not be greater than 15%. In this particular case, both aspects were satisfied as the F2 value was 84.97 and the maximum difference found between both dissolution profiles was 5.5%. In addition, the guidance for the industry detailing dissolution testing of immediate release solid oral dosage forms (US Department of Health and Human Services, 1997b) details acceptance criterion for the F1 difference factor. It states that F1 values should be close to zero and be between 0 and 15 to be considered similar. For this particular case, the F1 difference factor was 5.74 which again shows similarity between the curve generated by AP-CAD© software and the dissolution profile observed in literature (Mota, J., 2010).

5.3.2 Applying the Model

When applying the model to Metoprolol, where the initial drug loading is significantly less than the aqueous solubility value (i.e. the initial drug loading is 0.381 g/cm3 and the aqueous solubility is 3.630 g/cm3) the drug release process is governed by the diffusion process and the drug dissolution rate should be sufficiently small. In the other scenario where the initial drug loading is greater than the aqueous solubility, the drug release process was governed by both the dissolution and diffusion process; however, as the drug is released and concentration in the polymer decreases, eventually the concentration will reach a point where the concentration is less than the aqueous solubility and will subsequently be governed by the diffusion process (Gurney, R., et al, 1982 and Harland, R. S., 1988). As a result, if the aqueous solubility is larger, the process will be more governed by the diffusion process and will have a smaller drug dissolution rate, which was reflected by the extremely small value obtained for Metoprolol.

The drug dissolution rate, diffusivity and partition coefficient parameters were identified through the use of lab scale empirical correlations and correction factors. After entering the metoprolol parameters, a dissolution profile was established and compared with the dissolution profile found in literature (Mota, J., 2010). The root mean square error was 9.46%, the F1 similarity factor was 13.21 and the F2 result was 74.51. The comparison of the dissolution curves are considered similar based on the criteria outlined by the FDA for the F1/F2 difference and similarity factor (US Department of Health and Human Services, 1997a), where F1 values between 0-15 and F2 values between 50-100 “ensures sameness or equivalence of the two curves” (US Department of Health and Human Services, 1997b). The similarity demonstrated in both dissolution curves shows that the lab scale empirical correlations could be extrapolated to predict dissolution profiles for enteric pellet coated systems using the AP-CAD© software. However, it should be noted that though the F1/F2 criteria were met, the guidance for the industry does outline recommendations that should be considered when applying the F1/F2 consideration. The guidance document associated with the dissolution testing of immediate release dosage forms (US Department of Health and Human Services, 1997b) states that “only one measurement should be considered after 85% dissolution of both the products,” which ended the comparison at the 4 hour time point, even though the dissolution profile continues to the 7 hour time point and consequently resulted in lower F1 and higher F2 results, which would show an improvement in similarity after the 4 hour time point. In addition, the guidance for the scale-up and post-

68 approval changes for modified release solid oral dosage forms (US Department of Health and Human Services, 1997a) states that “…the average difference at any dissolution sampling time point should not be greater than 15%” and this criteria was met for all dissolution time points except at the 1 hour and 1.5 hour dissolution time points where the difference between the AP- CAD© predicted result and literature value (the residual result) was 17.5 and 16.1%. Though these results are slightly higher than the stated 15%, the FDA only outlines that as a criteria to be considered and not requirement to identify sameness. In any case, the AP-CAD© simulation was meant to be used as a starting point to identify or provide an estimate of how the dissolution profile would look if a particular drug substance was coated with the same pellet coating system that was applied towards another drug substance. This will provide a starting criterion for formulation studies and can provide an estimate of whether more or less polymeric coating is required. The numerical simulation is not meant to replace the actual manufacture of pellets or to be used as a replacement for bio-equivalence studies, which is essentially what the FDA guidance documents and acceptance criteria for sameness is used for.

5.3.3 Improvements

In the AP-CAD© model, four parameters could not be calculated based on the dimensions or starting conditions (i.e. with the initial drug loading in the matrix and aqueous solubility of the drug substance) of the enteric coated pellet. The unidentified values included the drug dissolution rate, the drug diffusivity in the matrix, the drug diffusivity in the coating and the partition coefficient. Despite having four unknowns and only 2 model drug substances to work with, a single solution was presented to correlate lab scale diffusivity/partition coefficient date with data from the enteric coated pellet. Since a trial and error approach was utilized multiple combinations or variations amongst the four variables could take place and could result in a similar dissolution profile. However, the use or study of additional active pharmaceutical ingredients in a controlled environment could help to better characterize or accurately assess the correction factor or the relationship between the empirical lab scale correlations and the enteric coated pellet.

Similarly, several empirical correlations were found where various prediction models could be built for metoprolol tartrate. In this particular instance, the squared solubility term was able to provide the best correlation that closely matched the result found in literature. However, the use

69 of additional active ingredients and dissolution profiles will help to better verify the correlations, correction factors and prediction models built.

5.4 Conclusions

At the start of the study, several objectives were outlined. The first objective was to identify drug substances and polymers suitable for study. Initially, 63 drug substances and 7 polymers were identified; however, upon removal of drug substances listed as salt forms and selecting the Eudragit® NE polymer to avoid electrostatic interactions, the list was further reduced to 16 drug substances and 1 polymer. The list of 16 drug substances was further reduced to 6 drug substances based on the range of squared and aqueous solubility values.

The second objective was to understand or demonstrate the influence of various drug substances on its rate of permeation through polymer films. The second objective was completed through the lab scale side-by-side diffusion cell experiments that show the influence of various drug substances without the influence of additional formulating factors (such as plasticizers or use of other excipients). In addition, the partition studies demonstrated that some drug substances partition more into the polymer membrane compared to other drug substances and consequently result in different permeability values. The extent of affinity for the polymer was further extended to calculated partition coefficient values which demonstrated the effect of various drug substances because varying partition coefficient results were obtained.

The second objective was extended to understand the properties of the drug substances that caused the changes in the polymer-phosphate buffer solution partition coefficient, diffusivity or permeability values. Various properties of the drug substance were investigated and included the squared solubility term, the aqueous solubility term, the octanol water partition coefficient, molecular weight and molar volume. The squared solubility term and aqueous solubility appeared to provide the best empirical correlations to predict the polymer partition; while the squared solubility term and aqueous solubility resulted in the best empirical correlations or permeability of the drug substance through the polymer membrane.

The best correlations were extended to create a model that can be used in a formulation setting to understand the dissolution profile of different drug substances. The AP-CAD© software was designed to incorporate various theoretical analytical solutions, to predict drug release profiles or

70 estimate parameters from drug release profiles. However, obtaining a drug release profile requires the use of diffusivity or partition coefficient values, which can be determined from experimental data or experiments (Wu, X. Y., et al., 2010). However, by using the correlations, a calculation was created that could predict the diffusion or partition coefficients from properties of the drug substance and subsequently, a release profile was generated using the AP-CAD© software. The release profiles were compared to the actual release profiles and the generated dissolution profiles were within the F1/F2 acceptance criteria for equivalence as outlined in the guidance documents from the FDA (US Department of Health and Human Services, 1997a).

Several areas have been identified as areas for improvement. From a lab scale perspective, the use of co-solvents would improve the analytical variability and the study could be expanded to incorporate or compare empirical correlations with a theoretical thermodynamic perspective, where the Flory-Huggins solution theory and activity coefficients are predicted from the UNIFAC model. For the enteric coated pellets, the study of additional drug substances or the manufacture of additional small scale pellets will help validate empirical correlations and correction factors between lab scale empirical correlations and the enteric coated pellet system. Further, additional excipients and polymers could be used/further evaluated to understand its influence.

Despite the areas identified for improvement, the objectives set forth in this study were completed. Suitable drug substances and polymers were identified, the influence of easily obtainable properties of the drug substances on the diffusion/permeation of the drug substance into and through the polymeric film was identified, empirical correlations to predict a relative partition/permeability coefficient value were developed, and the knowledge gained between easily obtainable or calculated properties of the drug substance and their release behavior was applied to predict the release kinetics of coated pellets by computer simulations using specialized AP-CAD software. In conclusion, by utilizing information (such as chemical structure-based parameters) that is readily available, empirical correlations and computational software, a simplistic method for predicting the release behavior of generic drug substances was developed and can subsequently be used to save on development costs by reducing the number of iterative experiments required in the early stages of product formulation development.

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Appendices-Table and Data

Table 6: The calculated solubility parameter and squared difference for various drug substances and polymers

Molecule δd δp δh δt (Krevelen) δt (Fedor) Δδ (PVA) Δδ (PA) Δδ (PEO) Δδ (Plx.) Δδ (E. RS) Δδ (E. RL) Δδ (E. NE/NM) Salt? USP Class USP Sol Class Alfuzosin 20.25 4.03 8.77 22.43 23.90 25.21 8.49 7.50 9.99 5.17 5.15 5.08 Hydrochloride Soluble in water 10 Amphetamine 17.97 0.60 0.00 17.98 19.73 34.48 17.77 13.92 19.01 9.88 9.86 9.58 Sulfate freely soluble in water 1 Budesonide 20.17 4.58 12.71 24.28 25.46 21.93 5.61 7.83 6.26 6.60 6.60 6.67 same practically insoluble in water 10000 Buproprion 19.32 3.93 4.70 20.26 21.87 28.60 11.93 8.58 13.73 5.65 5.63 5.43 Hydrochloride very soluble in water 0 Caffeine 30.09 13.09 11.88 34.90 25.60 19.35 10.99 12.77 15.48 17.33 17.32 17.43 same Sparingly soluble in water 30 Carbamazepine 20.37 3.86 7.28 21.97 23.54 26.47 9.76 7.92 11.46 5.43 5.41 5.28 same practically insoluble in water 10000 Carbinoxamine 19.68 3.19 5.03 20.56 21.47 28.72 12.00 9.12 13.62 5.91 5.88 5.67 Maleate very soluble in water 0 Chlorpheniramine 24.42 3.60 4.46 25.08 22.35 28.91 12.98 11.06 15.52 10.14 10.12 9.98 Maleate freely soluble in water 1 Ciprofloxacin 25.52 9.49 12.83 30.11 29.60 18.87 5.82 8.74 10.01 12.13 12.12 12.24 Hydrochloride sparingly soluble in water 30 Clarithromycin 22.86 3.13 13.76 26.87 23.39 22.17 7.16 10.53 7.59 9.54 9.54 9.56 same practically insoluble in water 10000 Cyanocobalamin 21.39 3.68 14.43 26.06 29.27 21.33 6.12 9.82 5.97 8.74 8.75 8.80 same Sparingly soluble in water 30 Diclofenac 25.25 3.69 7.46 26.59 26.81 26.52 10.96 10.66 13.40 10.20 10.18 10.09 Sodium sparingly soluble in water 30 Diethylpropion 17.57 4.18 5.12 18.77 20.00 28.36 11.71 8.01 13.16 4.15 4.12 3.91 Hydrochloride freely soluble in water 1 Diltiazem 23.62 3.64 7.27 24.98 22.64 26.57 10.48 9.67 12.71 8.62 8.61 8.50 Hydrochloride freely soluble in water 1 Disopyramide 17.77 3.16 6.61 19.22 21.44 27.73 10.98 8.34 11.94 3.64 3.62 3.37 Phosphate freely soluble in water 1 Doxazosin 26.92 3.42 8.33 28.39 24.09 26.26 11.42 11.98 13.85 11.85 11.83 11.75 Mesylate very slightly soluble in water 1000 Ethinyl Estradiol 18.18 2.45 11.71 21.77 24.48 24.39 8.20 9.04 7.54 5.13 5.13 5.10 same Insoluble in water 10000 Felodipine 20.38 2.86 3.70 20.91 24.73 29.94 13.30 10.22 15.09 7.33 7.30 7.08 same Insoluble in water 10000 Fluvastatin 20.65 2.94 11.83 23.97 25.75 23.66 7.48 9.07 7.81 6.76 6.75 6.74 Sodium soluble in water 10 Galantamine 32.60 5.19 12.06 35.14 26.33 24.17 13.54 16.23 16.24 17.80 17.79 17.78 Hydrobromide sparingly soluble in water 30 Hydromorphine 34.94 5.55 11.38 37.17 26.01 25.50 15.77 18.18 18.65 19.99 19.98 19.97 Hydrochloride freely soluble in water 1 Indomethacin 21.60 4.09 7.78 23.32 24.59 25.87 9.33 8.11 11.32 6.52 6.50 6.40 same practically insoluble in water 10000 Isosorbide Dinitrate 26.92 3.42 8.33 28.39 24.09 26.26 11.42 11.98 13.85 11.85 11.83 11.75 diluted very slightly soluble in water 1000 Levonorgestrel & Norgestrel 16.31 3.28 8.87 18.86 22.25 26.22 9.73 7.97 9.82 2.09 2.08 1.91 same practically insoluble in water 10000 Lithium Carbonate 0.00 0.00 0.00 0.00 28.27 41.13 27.01 22.87 26.02 18.05 18.05 17.95 Carbonate sparingly soluble in water 30 Metformin 17.84 10.25 14.30 25.06 28.73 17.54 2.56 5.24 5.38 8.34 8.36 8.62 Hydrochloride freely soluble in water 1 Methylphenidate 22.89 1.91 5.95 23.72 20.36 28.65 12.30 10.99 14.00 8.65 8.63 8.45 Hydrochloride freely soluble in water 1 Metoprolol 18.83 2.82 10.19 21.59 22.62 25.10 8.53 8.42 8.78 4.60 4.59 4.51 Succinate & Tartrate freely soluble in water 1 Metronidazole 20.22 12.99 15.54 28.62 31.21 14.61 3.38 7.11 7.51 11.85 11.86 12.11 Benzoate practically insoluble in water 10000 Naproxen 19.35 2.46 7.36 20.85 22.65 27.38 10.62 8.97 11.59 4.99 4.97 4.77 same practically insoluble in water 10000 Niacin 50.72 21.96 22.94 59.84 37.87 28.97 33.84 37.33 36.93 41.99 41.98 42.10 same Sparingly soluble in water 30 Nifedipine 17.47 3.75 3.97 18.30 23.25 29.55 12.92 8.99 14.37 5.14 5.12 4.89 same practically insoluble in water 10000 Norepinephrine 26.24 6.28 22.18 34.92 34.74 15.44 9.87 16.28 9.59 17.71 17.71 17.84 Bitartrate freely soluble in water 1 Orphenadrine 18.89 2.56 4.75 19.64 20.59 29.41 12.65 9.68 13.96 5.75 5.72 5.48 Citrate sparingly soluble in water 30 Oxybutynin 21.04 2.74 9.06 23.07 21.79 25.78 9.24 8.99 10.36 6.31 6.29 6.18 Chloride freely soluble in water 1 Oxycodone 35.32 5.70 11.81 37.68 26.18 25.32 15.99 18.56 18.84 20.44 20.43 20.42 Hydrochloride Soluble in water 10 Paroxetine 28.43 2.49 6.38 29.25 24.05 28.61 13.99 13.98 16.45 13.64 13.62 13.50 Hydrochloride slightly soluble in water 100 Pentoxifylline 26.39 9.36 10.11 29.77 25.03 21.36 7.99 8.84 12.25 12.16 12.15 12.22 same soluble in water 10 Phentolamine 21.62 3.36 9.82 23.98 25.95 24.77 8.35 8.68 9.71 6.79 6.78 6.71 Mesylate free freely soluble in water 1 Potassium Chloride 18.75 22.92 4.08 29.89 21.94 24.59 17.35 12.88 21.66 18.80 18.80 18.98 same freely soluble in water 1 Procainamide 19.34 4.50 8.56 21.63 22.65 25.17 8.39 6.82 9.88 4.19 4.18 4.12 Hydrochloride very soluble in water 0 Procaine 18.90 3.70 8.94 21.24 21.85 25.43 8.67 7.49 9.64 3.97 3.96 3.87 Hydrochloride freely soluble in water 1 Propranolol 19.27 2.06 8.81 21.29 22.79 26.56 9.92 9.18 10.40 5.04 5.03 4.87 Hydrochloride Soluble in water 10 Pseudoephedrine 18.18 2.60 10.42 21.11 22.96 25.19 8.71 8.62 8.60 4.32 4.32 4.24 Hydrochloride very soluble in water 0 Pyridostigmine 23.91 5.39 8.30 25.88 18.40 24.71 8.87 8.42 11.71 8.74 8.73 8.69 Bromide freely soluble in water 1 Quinidine 20.00 2.92 8.89 22.08 23.68 25.85 9.18 8.49 10.15 5.26 5.25 5.13 Sulfate slightly soluble in water 100 Sumatriptan 19.21 3.23 6.49 20.53 27.23 27.58 10.81 8.43 12.15 4.79 4.77 4.57 Succinate freely soluble in water 1 Tamsulosin 21.63 2.10 7.63 23.04 27.30 27.24 10.73 9.91 12.03 7.11 7.09 6.93 Hydrochloride slightly soluble in water 100 Theophylline 34.40 14.45 12.49 39.35 26.32 20.58 15.24 17.28 19.46 21.81 21.81 21.90 same slightly soluble in water 100 Tramadol 24.48 3.72 10.05 26.72 22.48 24.44 8.91 10.02 10.94 9.53 9.51 9.47 Hydrochloride freely soluble in water 1 Valproic Acid 15.92 2.64 7.93 17.98 19.47 27.41 10.91 8.75 10.97 2.49 2.48 2.21 same slightly soluble in water 100 Venlafaxine 24.05 3.52 9.77 26.20 22.23 24.75 9.01 9.87 10.94 9.10 9.08 9.03 Hydrochloride Soluble in water 10 Verapamil 21.79 2.70 6.34 22.85 21.92 27.85 11.31 9.72 13.02 7.29 7.26 7.10 Hydrochloride Soluble in water 10

Polyvinyl Alchohol 22.31 19.92 28.23 41.13 39.00 Polyacrylic Acid/Carbomer/Carbopol 20.18 9.63 15.14 27.01 28.73 Polyethylene Oxide 17.78 11.11 9.13 22.87 19.17 Poloxamer (Pluronic) 17.57 6.44 18.09 26.02 26.55 Poloxamer (Pluronic) Grade 124 235.28 19.32 34.67 238.60 26.55 Poloxamer (Pluronic) Grade 188 897.65 39.12 65.22 900.87 26.55 Eudragit RS 15.18 4.98 8.41 18.06 18.24 Eudragit RL 15.19 4.97 8.39 18.06 18.21 Eudragit NE & NM 15.25 4.73 8.21 17.96 18.23 Water 21.00 35.36 44.72 60.75 54.59

Table 7: The calculated partition coefficient for various drug substances and the Eudragit® NE polymer

Theoretical δd δp δh δt (Krevelen) δt (Fedor) Δδ (E. NE/NM) Tm (DrugBank, AQ SOL (EXP, Partition Molecule Molecular Weight Molar Volume Density  (Krevelen)  (Fedor) in K) No. of Cs ΔS Fusion (Walden) Last Term Cm (Krevelen) Cm (Fedor) in g/cm3) Coefficient Acetaminophen (paracetamol) 19.28 7.28 13.88 24.85 26.61 7.41 151.163 130.2 1.161006 2.399654544 3.5476105 443 8 56.6 2.9207633 0.002088873 0.00066277 1.40E-02 0.15 0.50 0.05 0.16 Alfuzosin 20.25 4.03 8.77 22.43 23.90 5.08 389.449 382.3 1.0187 2.967052975 4.7730504 19 56.6 0.00 0.00 Amphetamine 17.97 0.60 0.00 17.98 19.73 9.58 135.20622 182 0.742891 2.99302E-05 0.1599676 9 56.6 0.00 0.00 Budesonide 20.17 4.58 12.71 24.28 25.46 6.67 430.534 309.4 1.391513 4.793478136 6.2776787 499 25 56.6 4.1505583 6.68108E-05 1.5145E-05 1.46 0.33 Buproprion 19.32 3.93 4.70 20.26 21.87 5.43 239.74 248.5 0.964748 0.513516184 1.2761829 506.5 13 56.6 4.315263 0.002837968 0.00132369 3.12E-01 0.01 40.95 0.00 19.10 Caffeine 30.09 13.09 11.88 34.90 25.60 17.43 194.19 134.6 1.442719 14.99084564 2.8347333 511 8 56.6 4.4140858 1.9835E-09 0.00037737 2.16E-02 0.00 0.00 0.02 0.03 Carbamazepine 20.37 3.86 7.28 21.97 23.54 5.28 236.269 290.6 0.813039 1.820310231 3.1824544 478 15 56.6 3.6893852 0.00121056 0.00031004 1.77E-05 68.39 7.96 17.52 2.04 Carbinoxamine 19.68 3.19 5.03 20.56 21.47 5.67 290.788 332.3 0.875077 0.875655212 1.3500334 298 16 56.6 -0.2635275 0.174545226 0.10861459 765.55 476.38 Chlorpheniramine 24.42 3.60 4.46 25.08 22.35 9.98 274.788 271.5 1.01211 5.350217812 1.7871691 16 56.6 5.50E-03 0.00 0.00 0.00 0.00 Ciprofloxacin 25.52 9.49 12.83 30.11 29.60 12.24 331.346 152.4 2.174186 8.727720216 7.6395646 529 17 56.6 4.8093771 1.05661E-06 3.1369E-06 3.00E-02 0.00 0.00 0.00 0.00 Clarithromycin 22.86 3.13 13.76 26.87 23.39 9.56 747.953 591.4 1.264716 18.21708468 6.1126607 493 38 56.6 4.0187946 1.02513E-10 1.8521E-05 3.30E-07 0.00 0.00 56.12 0.09 Cyanocobalamin 21.39 3.68 14.43 26.06 29.27 8.80 1355.38 704 1.925256 17.94656675 33.2985 573 63 56.6 5.7756447 3.52995E-11 7.5947E-18 1.25E-02 0.00 0.00 0.00 0.00 Diclofenac 25.25 3.69 7.46 26.59 26.81 10.09 296.148 249.9 1.185066 7.219680506 7.1410958 557 14 56.6 5.4242746 1.40685E-06 1.5219E-06 2.37E-06 0.59 0.31 0.64 0.34 Diethylpropion 17.57 4.18 5.12 18.77 20.00 3.91 205.3 266.9 0.769202 0.069282619 0.3260276 441 13 56.6 2.876842 0.014868263 0.01150157 12.19 9.43 Diltiazem 23.62 3.64 7.27 24.98 22.64 8.50 414.519 397.6 1.042553 7.607032462 2.9969553 460.5 22 56.6 3.3050742 6.99416E-06 0.00070286 4.65E-04 0.02 0.42 1.51 41.84 Disopyramide 17.77 3.16 6.61 19.22 21.44 3.37 339.475 352.9 0.961958 0.217615882 1.4126398 367.75 21 56.6 1.2682262 0.080088223 0.02424244 4.49E-05 1783.70 1624507570.53 539.92 491733114.02 Doxazosin 26.92 3.42 8.33 28.39 24.09 11.75 451.475 466.9 0.966963 19.7133939 6.2225477 562.5 23 56.6 5.5450581 3.81513E-12 2.7575E-06 2.40E-05 0.00 0.00 0.11 0.00 Ethinyl Estradiol 18.18 2.45 11.71 21.77 24.48 5.10 296.403 291.5 1.01682 1.642603106 4.4240822 416 20 56.6 2.3278264 0.0070569 0.00043715 1.13E-05 624.50 1042.38 38.69 64.57 Felodipine 20.38 2.86 3.70 20.91 24.73 7.08 384.259 284.6 1.350172 0.962579475 4.6720231 418 18 56.6 2.3717476 0.017701693 0.00043353 1.97E-05 898.56 2475.76 22.01 60.63 Fluvastatin 20.65 2.94 11.83 23.97 25.75 6.74 411.466 393.3 1.046189 5.525698865 8.6283784 469 24 56.6 3.4917395 4.66758E-05 2.0971E-06 4.60E-07 101.47 10.58 4.56 0.48 Galantamine 32.60 5.19 12.06 35.14 26.33 17.78 287.354 213.2 1.347814 24.43027852 5.4239583 542.5 17 56.6 5.1058456 7.37836E-14 1.3253E-05 1.00E-02 0.00 0.00 0.00 0.01 Hydromorphone 34.94 5.55 11.38 37.17 26.01 19.97 285.3 231.8 1.230802 33.18656856 5.4460933 539.5 17 56.6 5.0399637 1.13324E-17 1.2643E-05 0.00 0.00 Indomethacin 21.60 4.09 7.78 23.32 24.59 6.40 357.787 337 1.061682 3.763368171 5.2846533 424 19 56.6 2.5035114 0.00074136 0.00016194 9.37E-07 791.21 308.90 172.82 67.47 Isosorbide Dinitrate 26.92 3.42 8.33 28.39 24.09 11.75 236.136 466.9 0.505753 19.7133939 6.2225477 343 6 56.6 0.7247007 2.47453E-10 0.00017885 5.50E-04 0.00 0.00 0.33 0.19 Levonorgestrel & Norgestrel 16.31 3.28 8.87 18.86 22.25 1.91 312.446 279.5 1.117875 0.088381475 1.7558489 513 21 56.6 4.4580071 0.004361413 0.00082311 2.05E-06 2127.52 748.10 401.51 141.18 Lithium Carbonate 0.00 0.00 0.00 0.00 28.27 17.95 73.89 22 3.358636 2.752324148 0.8602296 0 56.6 #DIV/0! #DIV/0! Metformin 17.84 10.25 14.30 25.06 28.73 8.62 129.16364 80.7 1.600541 1.579072673 3.4509377 497.5 4 56.6 4.1176174 0.001976656 0.00030408 1.43 0.22 Methylphenidate 22.89 1.91 5.95 23.72 20.36 8.45 233.31 284.9 0.818919 3.677062699 0.5001917 498 14 56.6 4.1285977 0.000122741 0.00294231 1.26E-03 0.10 0.67 2.34 16.17 Metoprolol 18.83 2.82 10.19 21.59 22.62 4.51 267.364 280.4 0.953509 1.439819344 2.0934533 393 15 56.6 1.822732 0.013431435 0.00698639 1.69E-02 0.79 33.41 0.41 17.38 Metronidazole 20.22 12.99 15.54 28.62 31.21 12.11 171.15 109.8 1.558743 4.841354582 7.173076 433.5 6 56.6 2.7121373 0.000300635 2.92E-05 9.50E-03 0.03 0.05 0.00 0.00 Naproxen 19.35 2.46 7.36 20.85 22.65 4.77 230.259 240.3 0.958215 0.778805653 1.8205232 426 14 56.6 2.5474326 0.01266489 0.00446878 1.59E-05 796.53 247.85 281.06 87.45 Niacin 50.72 21.96 22.94 59.84 37.87 42.10 123.1094 41.8 2.945201 28.45258988 6.2548576 509.6 6 56.6 4.383341 5.94781E-15 2.5984E-05 1.80E-02 0.00 0.00 0.00 0.00 Nifedipine 17.47 3.75 3.97 18.30 23.25 4.89 346.335 292 1.186079 0.013365484 2.8512223 446 17 56.6 2.9866451 0.021723559 0.00127194 1227.32 71.86 Norepinephrine 26.24 6.28 22.18 34.92 34.74 17.84 169.18 139.1 1.216247 15.53707877 14.716879 490 8 56.6 3.9529127 1.53579E-09 3.4877E-09 0.00 0.00 Orphenadrine 18.89 2.56 4.75 19.64 20.59 5.48 269.381 355.3 0.758179 0.390368353 0.7660227 298 18 56.6 -0.2635275 0.245691988 0.16875101 8189.73 5625.03 Oxybutynin 21.04 2.74 9.06 23.07 21.79 6.18 357.486 390.2 0.916161 3.958140798 1.9194772 402.5 22 56.6 2.0313579 0.00084425 0.00648413 84.42 648.41 Oxycodone 35.32 5.70 11.81 37.68 26.18 20.42 315.364 236.4 1.334027 35.67619189 5.8007051 492 18 56.6 3.9968339 2.89131E-18 2.7281E-05 1.00E-01 0.00 0.00 0.00 0.00 Paroxetine 28.43 2.49 6.38 29.25 24.05 13.50 329.3 297.2 1.108008 14.69543465 3.9037933 421.5 19 56.6 2.4486098 1.46112E-08 0.00071029 1.00E-03 0.00 0.00 0.71 83.27 Pentoxifylline 26.39 9.36 10.11 29.77 25.03 12.22 278.31 205.4 1.354966 11.12054993 3.6832745 378 13 56.6 1.4933226 1.65767E-06 0.00281492 7.70E-02 0.00 0.00 0.04 0.54 Phentolamine 21.62 3.36 9.82 23.98 25.95 6.71 281.352 291.4 0.965518 4.104611295 6.740596 447.5 17 56.6 3.0195861 0.000286066 2.0496E-05 1.05 0.08 Potassium Chloride 18.75 22.92 4.08 29.89 21.94 18.98 74.5513 24 3.106304 1.32603802 0.128033 1043 0 56.6 16.097139 3.09856E-08 1.0267E-07 Procainamide 19.34 4.50 8.56 21.63 22.65 4.12 235.325 252.3 0.932719 1.318185281 1.9155779 440 13 56.6 2.8548814 0.00528587 0.00290852 5.05E-03 1.05 1.75 0.58 0.96 Procaine 18.90 3.70 8.94 21.24 21.85 3.87 236.31 255 0.926706 1.064602948 1.2961512 334 13 56.6 0.527055 0.069406343 0.05506036 9.45E-03 7.34 10.19 5.83 8.09 Propranolol 19.27 2.06 8.81 21.29 22.79 4.87 259.34 336.3 0.771157 1.446797868 2.7132459 369 16 56.6 1.2956769 0.018272858 0.00514986 6.17E-05 296.16 230.14 83.47 64.86 Pseudoephedrine 18.18 2.60 10.42 21.11 22.96 4.24 165.23 212.9 0.776092 0.822005069 1.8499561 392 10 56.6 1.8007713 0.020728193 0.00741529 7.00E-06 2961.17 2.51 1059.33 0.90 Pyridostigmine 23.91 5.39 8.30 25.88 18.40 8.69 181.212 174 1.041448 4.235382602 0.0020031 426 9 56.6 2.5474326 0.000434114 0.02993211 0.42 28.78 Quinidine 20.00 2.92 8.89 22.08 23.68 5.13 324.417 354.5 0.91514 2.338738393 4.0797959 447 20 56.6 3.0086058 0.001602769 0.00028102 1.40E-04 11.45 4.80 2.01 0.84 Sumatriptan 19.21 3.23 6.49 20.53 27.23 4.57 295.402 266 1.110534 0.685174443 8.3696484 443 14 56.6 2.9207633 0.011096818 5.1036E-06 2.14E-02 0.52 87.38 0.00 0.04 Tamsulosin 21.63 2.10 7.63 23.04 27.30 6.93 408.51 351.8 1.1612 3.520793772 11.228749 500 20 56.6 4.172519 0.000194737 8.7484E-08 29.73 0.01 Theophylline 34.40 14.45 12.49 39.35 26.32 21.90 180.164 109.6 1.643832 19.45682177 2.7854001 546 7 56.6 5.1827078 1.20435E-11 0.00020944 7.36E-03 0.00 0.00 0.03 0.01 Tramadol 24.48 3.72 10.05 26.72 22.48 9.47 263.4 277 0.950903 8.25615534 1.9372685 453.5 16 56.6 3.1513498 3.88709E-06 0.00215716 0.01 2.88 Valproic Acid 15.92 2.64 7.93 17.98 19.47 2.21 144.211 158.9 0.907558 4.66054E-05 0.0949892 398 8 56.6 1.9325351 0.04833597 0.04395795 1.30E-03 37.18 20.48 33.81 18.63 Venlafaxine 24.05 3.52 9.77 26.20 22.23 9.03 277.402 293.1 0.946441 7.728210285 1.8213493 489 17 56.6 3.9309521 3.00808E-06 0.00110562 5.72E-01 0.00 0.01 0.00 4.81 Verapamil 21.79 2.70 6.34 22.85 21.92 7.10 454.602 422.3 1.076491 3.925308447 2.2265556 298 27 56.6 -0.2635275 0.010172426 0.05561392 4.47E-06 2275.71 2581.83 12441.59 14115.21

Eudragit NE & NM 15.25 4.73 8.21 17.96 18.23

Table 8: The wavelength used to obtain absorbance readings for each drug substance studied. Drug Substance Wavelength Theophylline 272 nm Valproic Acid 202 nm Caffeine 272 nm Carbamazepine 285 nm Niacin 263 nm Naproxen 271 nm

Table 9: The calculated partition coefficient results

The Partition Studies The Calculated Partition Coefficient Results (Polymer:PBS) Solution 1 Solution 2 Solution 3 Solution 4 Solution 5 Solution 6 Solution 7 Average Caffeine -0.259 0.472 0.719 0.311 Carbmazepine 12.669 10.321 16.529 13.173 Naproxen 3.505 3.576 4.572 2.276 3.482 Niacin -0.864 -0.441 -0.269 -0.601 -0.544 Theophylline 0.083 0.165 -0.311 -0.021 Valproic Acid 0.848 0.618 0.954 1.907 1.482 1.411 2.169 1.341

Table 10: A summary of the calculated permeability values, obtained via the mass balance and time lag methods.

The Side bi Side Diffusion Cell Permeability Results: Mass Balance Method Cell 1 Cell 2 Cell 3 Cell 4 Average Average Caffeine 1.6565E-10 8.78861E-11 1.43937E-10 1.80004E-10 1.444E-10 1.444E-10 Carbamazepine 4.97449E-09 4.84497E-09 3.23724E-09 5.80008E-09 4.714E-09 5.207E-09 Naproxen 1.12771E-08 1.29923E-09 8.8333E-09 2.17813E-09 5.897E-09 1.739E-09 Niacin 4.66417E-11 3.20964E-11 3.6749E-11 4.56246E-11 4.028E-11 4.028E-11 Thoephylline 5.95258E-11 3.37042E-11 5.38821E-11 4.904E-11 5.670E-11 Valproic Acid 1.44955E-07 8.54004E-08 1.33287E-07 1.212E-07 1.093E-07

The Side bi Side Diffusion Cell Permeability Results: Time Lag Method Cell 1 Cell 2 Cell 3 Cell 4 Average Average Caffeine 1.65612E-10 8.78684E-11 1.4385E-10 1.79922E-10 1.443E-10 1.443E-10 Carbamazepine 4.89174E-09 4.78256E-09 3.21785E-09 5.6821E-09 4.644E-09 5.119E-09 Naproxen 1.10327E-08 1.29691E-09 2.3402E-07 2.17152E-09 6.213E-08 1.734E-09 Niacin 4.66233E-11 3.2087E-11 3.67319E-11 4.56046E-11 4.026E-11 4.026E-11 Thoephylline 5.99432E-11 3.2975E-11 5.408E-11 4.900E-11 5.701E-11 Valproic Acid 1.08793E-07 7.96025E-08 1.18459E-07 1.023E-07 9.903E-08

Table 11: The calculated diffusion coefficient values using the time lag and Permeability/Partition Values

The Side bi Side Diffusion Cell Diffusion Coefficient Results: Time Lag Method Cell 1 Cell 2 Cell 3 Cell 4 Average Average Caffeine 1.18131E-09 -1.26666E-09 -2.57248E-10 -8.87E-10 -3.074E-10 -3.074E-10 Carbamazepine -8.0792E-10 -1.36649E-09 1.16722E-09 -4.31587E-10 -3.597E-10 -8.687E-10 Naproxen 7.07091E-10 6.66497E-10 5.73816E-10 2.14163E-09 1.022E-09 1.404E-09 Niacin -9.9348E-11 -8.33465E-11 -5.75076E-11 -1.17436E-10 -8.941E-11 -8.941E-11 Thoephylline -0.030213424 -0.07271264 0.032756062 -2.339E-02 1.271E-03 Valproic Acid -8.48772E-10 2.05807E-09 2.88601E-08 1.002E-08 1.546E-08

The Combo: Side bi Side Diffusion Cell & Partition Studies Calculated Diffusivity Values [P=DK] Cell 1 Cell 2 Cell 3 Cell 4 Average Average Caffeine 5.33087E-10 2.82831E-10 4.63211E-10 5.79282E-10 4.646E-10 4.646E-10 Carbamazepine 2.74367E-10 2.9072E-10 6.1587E-11 2.39336E-10 2.165E-10 2.681E-10 Naproxen 3.23858E-09 3.73118E-10 2.5368E-09 6.25521E-10 1.693E-09 4.993E-10 Niacin -8.57832E-11 -5.90314E-11 -6.759E-11 -8.39125E-11 -7.408E-11 -7.408E-11 Thoephylline -2.86276E-09 -1.62092E-09 -2.59134E-09 -2.358E-09 -2.727E-09 Valproic Acid 1.0808E-07 6.36755E-08 9.938E-08 9.038E-08 8.588E-08

Calculated Diffusivity Coefficient Values [Non-Steady State Equation] 16.67 hours 6.8 hours 3 hours Caffeine 3.53E-11 7.37E-11 1.53E-10 Carbamazepine 5.82E-11 1.17E-10 2.31E-10 Naproxen 6.46E-11 1.15E-10 1.63E-10 Niacin 8.19E-11 1.94E-10 4.29E-10 Thoephylline 3.66E-11 8.03E-11 1.64E-10 Valproic Acid 4.96E-10 7.35E-10 1.12E-09

Table 12: A comparison of the % released profiles for Paracetamol

Comparison of Literature and AP-CAD Results Time (in hours) Squared Absolute (rounded) Literature AP-CAD Result Residual Residual Residual 0 0.00 0.00 0.00 0.00 0.00 0.5 0.70 2.71 2.01 4.03 2.01 1 1.74 5.75 4.01 16.05 4.01 1.5 3.14 8.45 5.32 28.28 5.32 2 5.79 10.99 5.20 27.06 5.20 2.5 8.69 14.20 5.51 30.36 5.51 3 11.57 16.57 5.00 25.00 5.00 3.5 14.06 19.50 5.44 29.65 5.44 4 16.68 21.98 5.30 28.09 5.30 4.5 20.21 24.69 4.48 20.04 4.48 5 22.65 27.39 4.74 22.50 4.74 5.5 25.78 29.76 3.97 15.80 3.97 6 28.22 32.13 3.90 15.23 3.90 6.5 30.66 34.83 4.17 17.38 4.17 7 33.70 36.69 2.99 8.92 2.99 7.5 36.24 38.55 2.32 5.36 2.32 8 38.34 41.09 2.75 7.57 2.75 8.5 40.93 43.29 2.36 5.57 2.36 9 43.58 44.98 1.40 1.96 1.40 9.5 45.99 47.00 1.01 1.02 1.01 10 48.43 49.71 1.28 1.63 1.28 10.5 50.41 51.40 0.99 0.97 0.99 11 52.39 53.09 0.70 0.49 0.70 11.5 54.62 54.78 0.17 0.03 0.17 12 56.45 56.81 0.36 0.13 0.36 12.5 58.54 58.67 0.13 0.02 0.13 13 59.93 60.19 0.26 0.07 0.26 13.5 61.99 61.88 -0.11 0.01 0.11 14 63.55 63.24 -0.32 0.10 0.32 14.5 65.34 65.27 -0.08 0.01 0.08 15 66.77 66.96 0.18 0.03 0.18 15.5 68.29 68.65 0.36 0.13 0.36 16 69.34 69.66 0.32 0.10 0.32 16.5 71.17 71.01 -0.16 0.03 0.16 17 72.50 72.37 -0.13 0.02 0.13

Total (Squared Residual) 313.65 Mean of Squared Errors 8.96 Root Mean Squared Error (RMSE) 2.99 F2 Comparison 84.97

F1 Comparison 5.74

Table 13: Summary of calculated partition coefficient values for Metoprolol

Partition Coefficient Correlation: x=Δδ y=23.383*(exp(-0.247*x)) AP-CAD Result Paracetamol 7.41 3.75 1.01 Metoprolol 4.51 7.68 2.07 Correction Factor: 0.27

Correlation: x=Δδ y=1/(x-3.5) AP-CAD Result Paracetamol 7.41 0.26 0.93 Metoprolol 4.51 0.99 3.62 Correction Factor: 3.65

Correlation: Aqueous Sol. y=22.54*(x^(-0.428)) AP-CAD Result Paracetamol 1.7E-02 128.92 0.93 Metoprolol 3.6E+00 12.98 0.09 Correction Factor: 0.01

Table 14: Summary of calculated drug diffusivity values for Metoprolol

Permeability Coefficient (Drug Diffusivity in the matrix) Correlation: x=Δδ y=7E-8x^(-2) AP-CAD Result Paracetamol 7.41 3.84E-06 3.50E-08 Metoprolol 4.51 1.42E-06 1.30E-08 Correction Factor: 9.11E-03

Correlation: x=MV y=1E-11e^(0.0198x) AP-CAD Result Paracetamol 130.20 1.32E-10 3.50E-08 Metoprolol 280.40 2.58E-09 6.85E-07 Correction Factor: 265.75

Permeability Coefficient (Drug Diffusivity in the coating) Correlation: x=Δδ y=7E-8x^(-2) AP-CAD Result Paracetamol 7.41 3.84E-06 5.00E-09 Metoprolol 4.51 1.42E-06 1.85E-09 Correction Factor: 0.0013

Correlation: x=MV y=1E-11e^(0.0198x) AP-CAD Result Paracetamol 130.2 1.32E-10 5.00E-09 Metoprolol 280.4 2.58E-09 9.79E-08 Correction Factor: 37.97

Table 15: Summary of calculated drug dissolution rate for Metoprolol

Drug dissolution Rate is inversely proportional to Aqueous Solubility Correlation: Aqueous Sol. Aqueous Sol. AP-CAD Result Paracetamol 1.7E-02 1.50E-02 Metoprolol 3.6E+00 7.02E-05 Correction Factor: 0.88

Table 16: A comparison of the % released profiles for Metoprolol

Comparison of Literature and AP-CAD Results Time (in hours) AP-CAD Squared Absolute (rounded) Literature Result Residual Residual Residual 0 0 0 0 0 0 0.5 12.5848 22.21 9.6278667 92.695817 9.6278667 1 26.38965 43.94 17.54787 307.92774 17.54787 1.5 41.77305 57.86 16.08383 258.68959 16.08383 2 57.4036 68.36 10.95926 120.10538 10.95926 2.5 70.8424 75.76 4.915625 24.163369 4.915625 3 80.4222 81.69 1.26815 1.6082044 1.26815 3.5 86.234 85.81 -0.4211667 0.1773814 0.4211667 4 89.9928 89.29 -0.70725 0.5002026 0.70725

Total (Squared Residual) 805.86768 Mean of Squared Errors 89.540854 Root Mean Squared Error (RMSE) 9.4626029 F2 Comparison 74.51

F1 Comparison 13.21