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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

by

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

© Copyright by Stephanie Kwan 2016

ii

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.

iii

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

v

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

vi

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

vii

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

viii

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

ix

Figure 15: The relationship between the experimentally determined partition coefficient and the


database (DrugBank, n.d.)), excluding values for niacin and theophylline. ................................. 37



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


octanol-water partition coefficient results of the drug substance (obtained from the drug bank

database (DrugBank, n.d.)). .......................................................................................................... 38


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


molecular weight of the drug substance. ....................................................................................... 40


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


molar volume of the drug substance. ............................................................................................ 41


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

x

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


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


method) and the aqueous solubility of the drug substance ........................................................... 51


method) and the drug substance’s octanol water partition coefficient ......................................... 52


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

xi

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

1

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.

3

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

4

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 = −D∂C

∂x

(1)

F=Flux

D=Diffusion Coefficient

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.

∂C

∂t= D

𝜕2C

∂x2

(2)


C=Concentration

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.

5

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.

Q = Dt(2C0 − Cs)CS (3)


Co=Concentration of drug loaded in the matrix

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.

7

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).

(4)

q = the amount of penetrant in the receptor cell t = time

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).

tVh

PA2)

C

C21ln(

0

r (6)

Vd=Volume

h-polymer thickness Cr=Concentration in the Receptor Cell

A=Surface Area

CD=Concentration in the Donor Cell Co=Initial Concentration in the Receptor Cell

t=time

P= permeability of drug through the membrane Q=total amount of permeate passing through the membrane

(7)

8

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.

(8)

C - concentration

t - time x - distance

(9)

C - concentration

C0 - Initial Reservoir Concentration D - diffusion coefficient

t - time

x - distance

(10)

C - concentration

C0 - Initial Reservoir Concentration

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 = D · K (11)

P - permeability of drug through the membrane

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).

(12)

K - partition coefficient C0 - Initial Reservoir Concentration

Cf - Final Reservoir Concentration

Cp - Polymer Concentration Vs - Reservoir Volume

Vp - Polymer Volume

9

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:

(13)

Cm - drug solubility in the polymer (g/cm3) Ρ - the density of the drug (g/cm3)=molar weight/molar volume

- V(δd- δp)2/RT; where V=molar volume δd - the total solubility parameter of the drug substance 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.

10

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

12

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,

13

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.

;

(14)

δd=Solubility parameter from dispersion forces

δp=Solubility parameter from polar forces

δd=Solubility parameter from hydrogen bonding

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.

15

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).

(15)

= Compatibility term

δd,d= dispersion forces from the polymer

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

(16)

χ= Flory-Huggins interaction parameter

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).

16

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).

17

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:

(17)

t = solubility parameter

Ecoh = cohesive energy density V = molar volume

18

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.

20

(18)

Cw - Water drug concentration

Cd - dissolved drug concentration

Csd - dispersed drug concentrations.

Cs - drug solubility

Dw - water diffusivity

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.

(19)

F1=Difference Factor

R=Reference dissolution value

T=Test dissolution value

n=no. of dissolution time points

21

(20)

F2=Similarity Factor

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.)

23

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.

24

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.

25

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.

28

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.

Insoluble MCC Core

Polymeric Coating-Eudragit NE®

Drug Layer:Paracetamol

ParacetamolDissolution

Curve (Mota, J., 2010)

Empirical Correlations

Determine Model Values (pellet)Drug dissolution rate, drug

diffusivity in the matrix/coating, partition coefficient (Trial & Error)

Determine Model Values (lab)Drug diffusivity in the

matrix/coating, partition coefficient (via Δδ, aq. solubility, molar volume)

Correction Factor

(Pellet & Lab)

Drug-Binder Solution (Mota, J., 2010)

Ingredients %

Paracetamol 15.0

HPMC E5 3.8

Isopropanol 71.5

Water 9.8

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).

Insoluble MCC Core

Polymeric Coating-Eudragit NE®

Drug Layer:Metoprolol

Tartrate

Correction Factor

(Pellet + Lab)

Empirical Correlations

Result: Model Values (pellet)

Drug dissolution rate, drug diffusivity

in the matrix/coating,

partition coefficient

Determine Model Values (lab):

Drug diffusivity in the matrix/coating, partition coefficient

(via Δδ, aq. solubility, molar

volume)

Compare with Metoprolol Tartrate Dissolution curve

(Mota, J., 2010)F1/F2 Sim/Diff.

Drug-Binder Solution (Mota, J., 2010)

Ingredients %

Metoprolol Tartrate 15.0

HPMC E5 3.8

Isopropanol 71.5

Water 9.8

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).

30

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

31

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.

33

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

Drug Substance Average Partition 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.

34

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.


and Δδ, excluding values for niacin and theophylline.


and Δδ, excluding values for niacin and theophylline; but showing calculated partition

coefficient data and its relationship with Δδ.

36

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.

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.)).

37


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.


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.

38

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.


and the octanol-water partition coefficient results of the drug substance (obtained from the

drug bank database (DrugBank, n.d.)).

39


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.

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.


and the molecular weight of the drug substance.


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.

41

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.


and the molar volume of the drug substance.

42


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.

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.

10000.001000.0010.000.10

25

20

15

10

5

0

Aqueous Solubility (Grouped)

Me

an

0-5

5-10

Δδ (Grouped)

Interaction Plot for Theoretical Partition ValuesData Means

Figure 24: The interaction plot for theoretical partition coefficient values, excluding

pseudoephedrine and verapamil.

44

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.

45

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)

46

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.

47

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.

48

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

Drug Substance Average Permeability (cm2/s)-Mass

Balance Method Average Permeability

(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

Drug Substance Diffusion Coefficient (cm2/s) (via

the time lag method) Diffusion Coefficient (cm2/s)

(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.

49

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.

50


method) and the calculated Δδ term.


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.


lag method) and the aqueous solubility of the drug substance

52


lag method) and the drug substance’s octanol water partition coefficient


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.

54

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.

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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

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

57

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

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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 pre-

determined 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

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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.

60

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.

66

5.3 Drug release kinetics AP-CAD© model

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).

67

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.

71

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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

80

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

Molecule

δd δp δh δt (Krevelen) δt (Fedor) Δδ (E. NE/NM)

Molecular Weight Molar Volume Density (Krevelen) (Fedor)

Tm (DrugBank,

in K) No. of Cs ΔS Fusion (Walden) Last Term Cm (Krevelen) Cm (Fedor)

AQ SOL (EXP,

in g/cm3)

Theoretical

Partition

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

81

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


Permeability Results: Time Lag Method


Caffeine 1.65612E-10 8.78684E-11 1.4385E-10 1.79922E-10 1.443E-10 1.443E-10


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


82

Table 11: The calculated diffusion coefficient values using the time lag and

Permeability/Partition Values


Diffusion Coefficient Results: Time Lag Method


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]


Caffeine 5.33087E-10 2.82831E-10 4.63211E-10 5.79282E-10 4.646E-10 4.646E-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


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

83

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

Comparison of Literature and AP-CAD Results

Time (in

hours)

(rounded) Literature AP-CAD Result Residual

Squared

Residual

Absolute

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

84

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


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


85

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


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


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


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


86

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

Comparison of Literature and AP-CAD Results

Time (in

hours)

(rounded) Literature

AP-CAD

Result Residual

Squared

Residual

Absolute

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

application of chemical structure-based parameters of drug … · 2017-12-15 · application of...

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