# Theoretical prediction of induction period from transient pore evolvement in polyester-based microparticles.

**ABSTRACT** A model was developed and compared to experimental results for prediction of the induction period during drug delivery from various compositions of biodegradable copolymer PLGA microparticles. The uniqueness of this model is that it considers transient pore evolvement and uses the kinetic parameters of polymer degradation, which are independent of experimental measurements of microparticle erosion, in its analysis. Delivery data from PLGA microparticles (50:50, 75:25, and 85:15) releasing ovalbumin (OVA, 46 kDa) and bovine serum albumin (BSA, 66 kDa) were determined and used as the model systems. Experimental measurements were carried out from 85 to 150 days depending on the PLGA characteristics. The predicted induction periods were approximately 45, 70, and 105 days for the release of both OVA and BSA from 50:50, 75:25, and 85:15 PLGA microparticles, respectively. Overall, these values were in very good agreement with experimentally estimated results.

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**ABSTRACT:**Recently, we reported the synthesis and biocompatibility of alkoxylphenacyl-based polycarbonates (APP); a promising new class of polymers that undergo photo-induced chain scission. In the current study, nanoparticles (NPs) were prepared from the APP polymer (APP-NPs) and loaded with doxorubicin (DOX) (DOX-APP-NPs) in order to identify and evaluate formulation and photoirradiation parameters that influence photoresponsive efficacy. Stable and spherical APP-NPs were prepared with diameters between 70-180 nm depending on APP concentration (10-40 mg/mL). There was a direct relationship between APP concentration and resultant particle size. Drug release studies indicated that exposure to the photo-trigger was capable of altering the rate and extent of DOX released. Photoresponsive DOX release was markedly influenced by the frequency of photoirradiation while the effect of APP concentration was most likely propagated through NP size. DOX released by photoactivation retained its efficacy as assessed by cytotoxicity studies in human lung adenocarcinoma (A549) cells. Studies in BALB/c mice indicated that DOX-APP-NPs induce less cardiotoxicity than DOX alone and that DOX-APP-NPs are not susceptible to dose dumping after photoirradiation.European Journal of Pharmaceutics and Biopharmaceutics 07/2014; · 4.25 Impact Factor - SourceAvailable from: Jacques LuxMathieu L Viger, Wangzhong Sheng, Kim Doré, Ali H Alhasan, Carl-Johan Carling, Jacques Lux, Caroline de Gracia Lux, Madeleine Grossman, Roberto Malinow, Adah Almutairi[Show abstract] [Hide abstract]

**ABSTRACT:**Near-infrared (NIR) light-triggered release from polymeric capsules could make a major impact on biological research by enabling remote and spatiotemporal control over the release of encapsulated cargo. The few existing mechanisms for NIR-triggered release have not been widely applied because they require custom synthesis of designer polymers, high-powered lasers to drive inefficient two-photon processes, and/or coencapsulation of bulky inorganic particles. In search of a simpler mechanism, we found that exposure to laser light resonant with the vibrational absorption of water (980 nm) in the NIR region can induce release of payloads encapsulated in particles made from inherently non-photo-responsive polymers. We hypothesize that confined water pockets present in hydrated polymer particles absorb electromagnetic energy and transfer it to the polymer matrix, inducing a thermal phase change. In this study, we show that this simple and highly universal strategy enables instantaneous and controlled release of payloads in aqueous environments as well as in living cells using both pulsed and continuous wavelength lasers without significant heating of the surrounding aqueous solution.ACS Nano 04/2014; · 12.03 Impact Factor - Industrial & Engineering Chemistry Research 10/2014; 53(40):15374-15382. · 2.24 Impact Factor

Page 1

Theoretical Prediction of Induction Period from Transient Pore

Evolvement in Polyester-Based Microparticles

AIYING ZHAO,1S.K. HUNTER,2V.G.J. RODGERS3

1Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, Iowa 52242

2Department of Obstetrics and Gynecology, Carver College of Medicine, The University of Iowa, Iowa City, Iowa 52241

3B2K Group (Biotransport & Bioreaction Kinetics Group), Department of Bioengineering, University of California,

A237 Bourns Hall, Riverside, California

Received 6 May 2009; revised 25 February 2010; accepted 2 March 2010

Published online 13 May 2010 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.22167

ABSTRACT:

induction period during drug delivery from various compositions of biodegradable copolymer

PLGA microparticles. The uniqueness of this model is that it considers transient pore evolve-

ment and uses the kinetic parameters of polymer degradation, which are independent of

experimental measurements of microparticle erosion, in its analysis. Delivery data from PLGA

microparticles (50:50, 75:25, and 85:15) releasing ovalbumin (OVA, 46kDa) and bovine serum

albumin (BSA, 66kDa) were determined and used as the model systems. Experimental mea-

surements were carried out from 85 to 150 days depending on the PLGA characteristics. The

predicted induction periods were approximately 45, 70, and 105 days for the release of both OVA

and BSA from 50:50, 75:25, and 85:15 PLGA microparticles, respectively. Overall, these values

wereinvery good agreementwith experimentally estimatedresults. ?2010Wiley-Liss,Inc.andthe

American Pharmacists Association J Pharm Sci 99:4477–4487, 2010

Keywords:

mathematical modeling; induction time; polymer degradation; transient pore

evolvement; bulk erosion kinetics; hindered transport; polyesters; microparticles; probabilistic

model

A model was developed and compared to experimental results for prediction of the

INTRODUCTION

Polyester-based microparticles undergoing bulk ero-

sion, especially poly lactic-co-glycolic acid (PLGA)-

based microparticles are potential delivery vehicles

for pulsatile release.1–3A number of factors influence

the overall release profiles including water intrusion

into the device, polymer degradation, diffusion of

protein molecules and polymer degradation products,

microenvironmental pH changes, osmotic effects,

adsorption/desorption process,4,5and protein decom-

position/denaturation.6,7Understanding the governing

mechanisms can provide the foundation for predict-

ability of long-term release profiles during controlled

drug delivery. This can have particular significance for

scenarios requiring rapid protocol adjustments for

administration of a variety of vaccines.

As systems such as PLGA microparticles undergo

bulk erosion, hydration is imminent and polymer

chains are simultaneously cleaved throughout the

microparticles. Thus, polymer degradation and trans-

port processes are two major interacting factors in

determining drug release profiles.1,8,9The inner morp-

hologiesofthemicroparticlesunderbulkerosion,which

is related to polymer degradation and significantly

influence various transport processes, have been found

to be very complex and usually heterogeneous.10–12In

addition, the spontaneous pore opening, closing and

coalescence during erosion make it difficult to predict

thetransientporestructureofthemicroparticles.13The

morphological limiting effect of polymer erosion is the

main cause to the induction period (or dead time),

which is defined as the time interval between two

pulses in drug delivery. The induction period is one of

the most important parameters in controlled drug

release which largely determines the overall release

profile. In addition to polymer erosion, other factors

affect the induction period including geometric proper-

ties of the polymeric systems, such as particle size, size

distribution and internal structure properties; physi-

cochemical properties and molecular weight of the

entrapped drug/protein. Geometric factors directly

influence the availability of particle contact points,

porosity, viscosity, and tortuosity of matrices, which of

all determines the effective surface area. Effective

Correspondence to: V.G.J. Rodgers (Telephone: 951-827-6241;

Fax: 951-827-6416; E-mail: victor.rodgers@ucr.edu)

Journal of Pharmaceutical Sciences, Vol. 99, 4477–4487 (2010)

? 2010 Wiley-Liss, Inc. and the American Pharmacists Association

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 11, NOVEMBER 2010

4477

Page 2

surface area of the particles, including external surface

area and internal surface area, plays an important role

in the variation of induction period for a fixed

formulation composition. Physicochemical properties

and molecular weight of the entrapped drug/protein

also affects polymer dissolution and pore evolvement,

consequently influence the induction period. Large

entrapped molecules tend to be associated with long

induction period.

Recognizing this, characterization of the micro-

particle morphology was approached early on in drug

delivery and a series of methods have been devel-

oped.14–17The hydrolysis kinetics of polyesters under

various conditions has also been investigated. The

molecular loss rate of copolymers was found to adhere

well to pseudo-first-order kinetics.3,18This hydrolytic

rate constants of polymers was found to be approxi-

mated using experimental results from gel permea-

tion chromatography.19

The resulting transport of entrained solutes, such

as proteins, in the microparticles under bulk erosion

has also been studied through various approaches

including hindered transport.20–22In particular, for

drug delivery from polyester-based microparticles,

the progress of hydrolysis and bulk mass loss have

beencorrelatedtothegrowthofexistingporesandthe

generation of new pores.10Batycky first directly

related pore growth to pore coalescence rate (kcoal),

RaveðtÞ / kcoalt(1)

where kcoaldepends on polymer erosion and its value

can be estimated through experimental observa-

tions.23Lemaire et al. followed this model and

describes the transient pore size as a function of

time by the approximation:

RpðtÞ ¼ kt þ R0

(2)

in which k is a constant representing the erosion

velocity and R0 is the initial pore radius.24In

addition, computational algorithms have also been

developed to couple drug release with polymer

degradation based on Monte Carlo techniques.1,3,25

However, in previous models, the erosion coefficient,

either kcoal or k, were determined directly from

experimentallyobservedpolymererosionbehavior.23,24

Nevertheless, theoretical prediction of drug deliv-

ery, particularly for the induction period for polye-

sters undergoing bulk erosion has not been, to our

knowledge,directlyrelatedtotheerosionkineticsand

transient pore evolvement information that are

independent of directmeasurements

degrading microparticle. Therefore, in this study, a

mathematical model is developed to directly predict

the induction period from molecular properties of

original polymer and erosion kinetics data that are

independent of the microparticle empirical degrada-

tion data.

fromthe

Here predictability of induction period is empha-

sized for potential vaccine applications. The pore

evolvement over time and the transport properties of

protein molecules in pores with increasing pore

diameter is addressed using hindered transport

theory.21,22The model results are compared to

experimental release result of ovalbumin (OVA,

46kDa) and bovine serum albumin (BSA, 66kDa)

from PLGA of ratios, 50:50, 75:25, and 85:15.

GENERAL MODEL DEVELOPMENT

Pore Generation and Growth in the Degrading

Microparticles

As a first approximation, the model begins by

assuming that the solute release process from PLGA

microparticles can be modeled as a constant–activity

cylindrical reservoir system. This approximation is

reasonable when addressing primarily the induction

period where overall pore distribution in the micro-

particle is relatively constant and, by nature of the

spherical particle shape,the massofthe encapsulated

material resides primarily near the outer particle

radius. In addition, since water intrusion is relatively

fast for PLGA particles that undergo bulk erosion, a

major factor that influences polymer degradation

kinetics is the solubility of the entrapped drug. In the

case of water-soluble proteins, many factors deter-

mine its solubility.26,27In addition, the released

protein molecules and polymer degradation products

willaffecttheporemicroenvironment,suchaspHand

viscosity of the medium, which will affect the polymer

degradation kinetics. The autocatalysis phenomenon

has been acknowledged by many researchers for

polyester-based microparticles as well; that is, the

degradation products of PLGA decrease the pH of

microenvironment and catalyze the degradation of

polymer. In the general model development, the

effect of drug/protein to the induction period will be

described by hindered transport through water-

filled pores; the effect of PLGA autocatalysis can be

coupled in the first-order coefficient of polymer

degradation kinetics. Thus the PLGA microparticles

can be modeled as a constant–activity cylindrical

reservoir system. We consider only pore evolvement,

and reduce our model to a straight pore in a

spherical particle with pore size growing at the

degradation time t (Fig. 1). For an arbitrary erodible

polymer, the degradation products include mono-

mers and oligomers. Therefore, to quantify the

transientporesize,the

require specification:

followingparameters

(a) The size of monomers and oligomers;

(b) The generation rate of monomers and oligomers;

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 11, NOVEMBER 2010DOI 10.1002/jps

4478

ZHAO, HUNTER, AND RODGERS

Page 3

(c) The diffusion rate of monomers and oligomers;

(d) The initial pore distribution.

The monomer and oligomer sizes can be estimated

by the analysis of molecular structure, and the

diffusion rate of monomers and oligomers through

porestructurescanbecalculatedbyvarioustransport

models.1–3,28Therefore the polymer degradation rate

remains the critical factor in predicting the transient

pore size. However, as is well known, polymer

degradation includes numerous spatially dependent

chemical reactions that follow a random process.10,29–

31In Batycky’s theoretical work, polymer erosion was

modeled as a process governed by both random chain

scission and end scission.23To minimize complexity

and still obtain reasonable predictability, we ana-

lyzed the transient pore evolvement using probabil-

istic methods.

Considering the polymer degradation mechanism,

once a bond is broken in a linear polymer chain, end

scissions, together with random chain scissions,

become important in future degradation. Therefore,

it is reasonable to assume that the generation of new

pores is induced by random chain scissions, while the

growth of an existing pore is attributed to both end

chain scissions and random chain scissions. As we

only consider the generation and growth of a single

new pore, the pore coalescence will be neglected. The

transient probability for end scissions (Xe) and the

probability for internal chain scissions (Xi) are

definedas polymerdegradation variables

degradation time t. In the case of end scissions, only

a specific u-mer is generated in unit time for cleavage.

Here u represents the number of repeat units in a

soluble oligomer or a monomer, which is also equal to

the number of bonds to be cleaved from the polymer

chain. However, for internal chain scissions, account-

ing for the growth of a certain pore, this cleavage

over

must occur close to the pore, and, subsequently, at

least two small molecules are generated in a given

unit cleavage time. These small molecules are very

likely to be different in size. In fact, the internal

random chain scissions positioned far from apore also

affect the pore evolvement when the moving front of

the pore gets closer to those points previouslycleaved.

It is also well known that the rate of end scission

development is much faster than the rate of random

chain scission development due to autocatalytic

action. Consequently, end scissions dominate the

degradation process close to an existed pore over a

short time. With the ongoing degradation process, the

influence of accumulated internal cleavages becomes

more and more important for the pore evolvement.

Thus, combining end scission and internal chain

scission, the transient probability or rate of generat-

ing a specific u-mer attributed to the pore growth at

time point t can be expressed as f(u):

fðuÞ ¼ Xeð1 ? XeÞu?1

þ XeXið1 ? XiÞu?1X

whereumaxisthemaximum number ofrepeat units in

a soluble oligomer cleaved from the polymer chain. In

Eq. (3), the term Xeð1 ? XeÞu?1

transient probability of end scissions only; the term

XeXið1 ? XiÞu?1P

the cases that include one end scission plus an

internal scission. Other internal scissions indirectly

contributing to the pore growth are denoted by the

suspension points.

As we know, pore growth is governed by numerous

bond cleavages simultaneously along the axial direc-

tion of the pore; consequently the moving front of the

pore would be irregular at different positions due to

umax

i¼1

ð1 ? XeÞi?1þ ???(3)

represents the

umax

i¼1

ð1 ? XeÞi?1is a summation of all

Figure 1.

Illustration of the process of polymer erosion and pore growth.

DOI 10.1002/jpsJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 11, NOVEMBER 2010

PREDICTING THE INDUCTION PERIOD FOR MICROPARTICLE DRUG DELIVERY

4479

Page 4

the size variation of dissolved small molecules over

time. Thus, the growing pore is expected to be

asymmetric and there is a pore size distribution at

various axial positions.14In order to characterize

the average pore size, the parameter _ uaveis defined as

the average number of bonds for all the dissolvable

monomers and oligomers generated per unit time.

Then,

_ uave¼

X

umax

u¼1

ufðuÞ (4)

Now we consider the size distribution of the polymer

degradation products. We begin by defining the

composition ratio of monomer A to monomer B in

the copolymer as l. The size of monomer A is denoted

as lAand the size of monomer B as lB. The size of a

monomer can be estimated by the composite bond

lengths. Then the representative average length of

the monomers, lave, is defined as:

lave¼

l

l þ 1lAþ

1

l þ 1lB

(5)

giving the linear length of the soluble u-mer as ulave.

For constant lave, the pore size change can be

described as

dRpðtÞ

dt

¼ lave_ uave

(6)

where Rp(t) represents the transient radius of a

growing pore.

Therefore, we obtain

dRpðtÞ

dt

¼ lave

X

umax

u¼1

ufðuÞðt > 0Þ(7)

Upon integration,

RpðtÞ ¼ lave

Zt

0

X

umax

u¼1

ufðuÞdt þ Rpð0Þ(8)

For simplification we can define Df(t) as the

combined distribution term that captures the effects

of bond cleavages and degradation products:

DfðtÞ ¼

Zt

0

X

umax

u¼1

ufðuÞdt(9)

Then the transient pore radius can be expressed as a

function of this distribution term,

RpðtÞ ¼ DfðtÞlaveþ Rpð0Þ(10)

Therefore, the transient pore radius can be simulated

by the above model. Moreover, the significance of this

work is the coupling of erosion kinetics to the pore

radius as a function of time to subsequently predict

the release rate, and the induction period for the

microparticle payload release.

Assumptions Leading to Coupling Rate of (uR1)-mer

Generation to Degradation Kinetics

The model outlined above can be used to predict

general pore evolvement provided additional infor-

mation, such as the specific rate of generation of

(uþ1)-mers, is provided or determined experimen-

tally. In this work, we couple the rate of generating of

oligomers and monomers to specific degradation

kinetics. We do this by first relating the probability

parameter f(u) to polymer erosion kinetics. Here, we

circumvent the kinetics complexity by invoking a

number of appropriate assumptions.

Previous researchers have shown that, for a linear

copolymer (-A-B-A-B-A-) or [-(A)i-(B)j-] such as PLGA-

based copolymers, the apparent degradation kinetics

follows the first-order expression:

?dMn

dt

¼ kdt(11)

where Mnis the number-average molecular weight of

the polymer at degradation time, t, and kdis the

degradationconstantdetermined

experiments.30,32The transient profile of Mn over

time can be obtained from Eq. (11). The number of

chain cleavages per initial number average molecule,

denoted by x, is:

directlyfrom

Mt

M0

n

n

¼

1

1 þ x

(12)

Here, Mt

molecular weight of the polymer at time t and zero,

respectively.29,33The apparent probability of the

random bond cleavage, which may be viewed as the

accumulated probability (Xt) of bond cleavages can be

calculated by relating the accumulated probability to

the initial number-average degree of polymerization

(N). Then,

Xt¼x

nand M0

nrefer to the number-average

N

(13)

Now for every differential time element, it is assumed

that the transient probability for bond cleavages

contributes to the accumulated probability without

probability transfer. Under this assumption, Xt is

related directly to the independent transient prob-

ability X(t) by

Xt¼

Zt

0

XðtÞdt (14)

Notethattheindependenttransientprobabilityofthe

random bond cleavage X(t) is a function of time t. It is

wellknownthatthedegradationratevarieswithtime

due to a number of local factors such as transient

proton concentrations and other transport phenom-

ena. Consequently, the transient probability of bond

cleavage, X(t), is clearly time varying. In the general

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 11, NOVEMBER 2010DOI 10.1002/jps

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ZHAO, HUNTER, AND RODGERS

Page 5

model

generating a u-mer at time point t is defined as

f(u). Since, X(t) is a transient parameter which

combines the total effects of degradation product

distribution with bond cleavages, we assume that X(t)

can be used to approximate f(u), or,

development,atransient probability of

fðuÞ ? XðtÞ (15)

Here, assuming the equal probability of u-mer

generation, we now relate the rate of generation of

average number of bonds for all the dissolvable

monomers and oligomers (Eq. 4), to obtain

_ uave¼umaxþ 1

2

XðtÞ (16)

Approximating Pore Growing Rate to Degradation

Kinetics

Substitute Eq. (16) into Eq. (6), we obtain

dRpðtÞ

dt

¼ðumaxþ 1Þlave

2

XðtÞ(17)

Therefore, we have

RpðtÞ ¼ðumaxþ 1Þlave

2

Zt

0

XðtÞdt þ Rpð0Þ(18)

and,

RpðtÞ ¼ðumaxþ 1Þlave

2N

M0

Mtn

n

? 1

??

þ Rpð0Þ(19)

Thus the profile of Rp(t) can be obtained theoretically

when the above assumptions are valid. In Eq. (19),

only Mt

nis a time dependent variable so we would

expect an exponential growth behavior of the pore

radius.

Relationship of Proposed Pore Growing Model to

Previous Efforts

It is instructional to note that this model above

correlates to previously obtained models if one

assumes the transient probability X(t) is time

independent. Denotedby X,then wehave thefamiliar

expression:23,24

RpðtÞ ¼ðumaxþ 1Þlave

2

Xtþ Rpð0Þ:

(20)

Use Hindered Transport to Model Protein Release from

Degrading Microparticles

The above model emphasizes the pore size evolve-

mentandappliestoanygeneraldrugdeliverycarrier.

To capture the rapid transition for protein delivery

after an induction phase, we elect to use hindered

transport theory to calculate an effective diffusion

coefficient. With the transient pore radius Rp(t), the

hindered diffusion coefficient D(t) is then calculated

and related to diffusive protein release. Other

hindrance models could also be used in this develop-

ment. In this model, the point for sudden rapid

increase in diffusion would be synonymous with an

induction time where pore opening became suffi-

ciently large to freely release previously encapsulated

macromolecules.

For this model we use polyester-based microparti-

cles that can undergo bulk erosion as the transport

vehicle. Generally, this is a spherical particle

characterized with a heterogeneous distribution of

protein and pore structures.12

Based on the morphological features of the micro-

particles, we have the following assumptions for this

system:

(1) Cylindrical pores in different size and tortuos-

ity distribute heterogeneously in a microsphere

with some interconnection. Protein molecules

only distribute in the pore structures.

(2) During bulk erosion the average pore size

begins to increase. At some position, inner

pores develop into a protein reservoir.

(3) Initially, very few pores interconnect to the

microparticle surface.

(4) During subsequent erosion, pores connecting to

the exterior of the particle develop and enlarge

over time. This is represented by Rp(t) and is a

function of polyester hydrolysis.

(5) The resulting protein molecules transport

through the pores to the media via diffusion.

(6) Protein concentration variation caused by

denaturation is neglected.

With the above assumptions, we further assume

radial diffusion only. Therefore Fick’s second law of

diffusion in spherical geometry can be used to

describe this system:

?

with BCs:

@C

@t¼ DeffðtÞ

@2C

@r2þ2

r

@C

@r

?

(21)

r ¼ 0;

@C

@r¼ 0(22)

r ¼ R;

C ¼ 0(23)

and IC:

t ¼ 0;

C ¼ C0

(24)

where Deff(t) is the effective diffusion coefficient

calculated through hindered transport theory, C is

transient protein concentration, C0 is the initial

protein concentration, r is the radius, and R is the

particle size. Thus in this model, the initial pore is

‘‘loaded’’ with protein but transport is constricted due

to hindrance until erosion increases the effective

DOI 10.1002/jpsJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 11, NOVEMBER 2010

PREDICTING THE INDUCTION PERIOD FOR MICROPARTICLE DRUG DELIVERY

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Page 6

diffusion to a point of transport. The induction time is

estimated as the time required to reach this point.

To include the effects of protein transport through

the serpentine channel, the tortuosity factor, t, is

introduced. The tortuosity factor is defined as unity

when the polymer matrix collapses and generally

ranges between 1 and 10.34,35However, it has been

shown that, for PLGA or PLA microparticles, the

tortuosity factor can be higher than 100.36In any

case, combining the effect of tortuosity factor, the

effective transient diffusion coefficient Deff(t) can be

corrected by the following expression:

DðtÞeff¼DðtÞ

t

(25)

where D(t) is the hindered diffusion coefficient. For

hindered transport in a growing pore, we now assume

D(t) varies with time due only to H(t) and

DðtÞ ¼ HðtÞD1

(26)

where H(t) is the well-known centerline approxima-

tion hindrance factor

HðtÞ

¼

6pð1 ? lÞ2

2

9=4p2

ffiffiffi

2

p

ð1?lÞ?5=21 þP

n¼1

anð1 ? lÞn

??

þP

4

n¼0

anþ3ln

ð0 <l< 1Þ

(27)

l ¼

Rd

RpðtÞ

(28)

and D1refers to the diffusivity at infinite dilution.22

The limiting effect of evolving pore size on drug

transport is described by the variable l, which is

defined as the ratio of drug size Rdto the pore size

Rp(t) in Eq. (28). Thus the most significant factor in

effecting the application of ahindered diffusion model

in this study is determining the transient pore radius

Rp(t). Here, Rp(t) can be obtained from the probabil-

istic model established above.

EXPERIMENTS AND METHODS

Materials

Poly (lactide-co-glycolide) (PLGA) 50:50, 75:25, and

85:15 (Resomer RG503, 755 and 858, Boehinger

Ingelheim, Ingelheim, Germany) were obtained.

The average molecular weights were 34k, 68k, and

220k, respectively. Ovalbumin (OVA) (Grade V,

MW¼44k),

(Fraction V, MW¼64k), bicinchoninic acid (BCA)

protein assay, and poly (vinyl alcohol) (PVA) (MW

30,000–70,000) were purchased from Sigma (St.

bovineserumalbumin(BSA)

Louis, MO). Methylene chloride (MC) was obtained

from Fisher Scientific (Pittsburgh, PA).

Preparation of PLGA Microparticles

The microencapsulation procedure was based on

double-emulsion (w/o/w) method.12PLGA was used

as the wall polymer, protein as the encapsulating

agents, MC as the organic solvent, and PVA as the

emulsion stabilizer. The general experimental details

are described elsewhere.12The microparticles were

first frozen in liquid nitrogen and then freeze-dried

(Freeze Dryer 4.5, Labconco, MO) at ?508C and

10mmHg overnight.

Characterization of PLGA Microparticles

After microencapsulation, the surface properties and

general particle sizes were examined by scanning

electron microscopy (SEM) (Hitachi S-4000, Tokyo,

Japan). The particle size distribution was further

analyzed by the software of Image J (Rasband, NIH,

US Government) based on the images from SEM

investigations. Total protein loadings and surface

protein loadings of the microparticles were examined

by standard methods.37The experimental details are

described elsewhere.12

In Vitro Polymer Degradation and Protein Release

Themicroparticlesweremixed withPBS buffer (pH7.4,

containing0.02%sodiumazideasabacteriostaticagent)

andincubatedinanorbitalshaker(Model4520,Thermo

Forma, Marietta, OH) under 378C and 250rpm. The

vessels were carefully sealed to prevent water evapora-

tion over a long period. For sampling, a small amount of

supernatant after centrifuge was taken out of the

incubation mixture. The protein release in the medium

was measured by BCA protein assay at various time

points. The incubation medium was frequently replaced

by fresh PBS buffer to ensure a dilute solution for

proteinsandpolymerdegradationproducts.Inaddition,

parallel experiments were performed to determine the

effects of protein denaturation by incubating blank

PLGA 50:50, 75:25, and 85:15 microparticles together

with BSA solutions in a series of concentrations under

exactly the same conditions. Protein release profiles

were obtained by normalizing theapparent release data

by the protein degradation results. Induction periods

were estimated for each protein-polymer combination

from the cumulative release curves. Each experiment

was performed in triplicate.

RESULTS AND DISCUSSION

Experimental Protein Release Profiles and the Estimated

Induction Periods

SEM analysis showed that the microparticles were

spherical and smooth. The size distribution was

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ZHAO, HUNTER, AND RODGERS

Page 7

uniform in the range of 1–10mm. Average particle

sizes and size distribution with standard deviations

are listed in Table 1. High protein surface loadings

(>50%) were found with regard to total protein

loadings (Tab. 2).

The in vitro protein release profiles of OVA-loaded

and BSA-loaded PLGA microparticles are shown in

Figures 2 and 3, respectively. As in the mathematical

model, the influence of protein denaturation is not

considered; therefore the effects of protein denatura-

tion were eliminated by normalizing the apparent

release data with the protein denaturation results.

OVA release profiles for PLGA 50:50 and PLGA

85:15 demonstrate a burst release (24.4% and 38.8%)

in 1 day; while for PLGA 75:25, a small burst release

(5.9%) was observed within the first day (Fig. 2). After

1 day of incubation, the release rate was dramatically

reduced indicating that the prior rate was due to the

transport of surface proteins. Although the micro-

particles formulated with PLGA 50:50 and PLGA

75:25 continued to demonstrate a slight but still

continuous positive rate of protein release, we could

still estimate an induction period for each type of

microparticles. Assuming the induction period was

between the burst release and the next significant

positive change in release rate (the significant

increaseof releasecurve slope) for cumulative protein

release,theinductionperiodswereestimatedtobe45,

70, and 105 days, respectively for the release of OVA

from PLGA 50:50, 75:25, and 85:15 formulations.

The release profiles of BSA through the PLGA

microparticles were slightly different than OVA

release profiles (Fig. 3). A high burst release was

observed within 1 day for all the three polymers

(57.4%, 37.1%, and 43.7% for PLGA 50:50, 75:25, and

85:15, respectively). These values are higher than

the corresponding cases using OVA but this is

consistent with the higher BSA surface loadings

relative to that of OVA surface loadings. Using the

method to estimate the induction period described

above in OVA release, the induction period for the

release of BSA from PLGA 50:50, 75:25, and 85:15

microparticles were estimated to also be 45, 70, and

105, respectively. Protein release from different

PLGA-formulated microparticles demonstrated a

variation of release characteristics, such as the ratio

of burst release, the occurrence and length of

induction period, the occurrence and ratio of second

pulse. These differences were caused not only by

different monomer ratios in each wall polymer that

Table 2. Protein Loadings of the Microparticles for Various PLGA Formulations

Protein

Protein Loaded/Particle

Weights (w/w) (%), PLGA

Ratio

Protein Loaded/Total

Protein Used (%), PLGA

Ratio

Surface Protein Loading

(%) (mg protein/mg

microparticles), PLGA

Ratio

Surface Loading/Total

Loading (%), PLGA

Ratio

50:5075:2585:1550:5075:2585:1550:5075:2585:1550:5075:2585:15

OVA

BSA

5.6

4.8

5.2

5.0

5.0

5.3

65.4

55.8

60.6

57.8

58.7

61.5

3.28

3.34

3.15

3.95

3.29

4.41

58.5

69.7

60.7

79.6

65.4

83.5

Figure 2.

ferent monomer ratios (50:50, 75:25, and 85:15). The par-

ticles were fabricated using a double-emulsion method and

incubated at 378C at 250rpm. Using the time between

significant rate changes the induction periods for the PLGA

50:50, 75:25, and 85:15 microparticles are estimated to be

45, 70, and 105 days, respectively. The vertical colored lines

are used to indicate the end of the induction period for each

formulation.

OVA release from PLGA microparticles in dif-

Table 1. Average Particle Sizes of PLGA Microparticles

in Different Monomer Ratios

Wall Polymers

Encapsulated

Materials

Average Particle

Size (mm)

PLGA 50:50 DI water

OVA

BSA

DI water

OVA

BSA

DI water

OVA

BSA

3.47?1.39

3.77?1.37

4.16?1.49

3.93?1.44

5.08?1.97

3.16?0.70

2.48?0.52

4.33?1.41

4.78?1.72

PLGA 75:25

PLGA 85:15

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PREDICTING THE INDUCTION PERIOD FOR MICROPARTICLE DRUG DELIVERY

4483

Page 8

led to different erosion kinetics, but also by the

variation of initial and subsequent protein distribu-

tion profiles resulted from multiple microencapsula-

tion processes.14

Theoretical Predictions of the Induction Periods

Here we apply our mathematical model to PLGA

microparticles for prediction of the induction period.

PLGA is a well-documented polyester undergoing

bulk erosion. Lactic acid (LA) and glycolic acid (GA)

are two monomer components for this copolymer. The

sizes ofLA and GAmolecules aredenoted bylAand lB,

respectively. These values were estimated from the

composite bond lengths and bond angles to give

lA¼3.517A˚, lB¼3.510A˚. Using these values and

Eq. (5), and the composition ratio of monomer A to

monomer B, l, (e.g., l¼3 for PLGA 75:25), lavewas

calculated. Using the initial number-average mole-

cular weight (M0

n) of the polymer and the monomer

molecular weight, the initial number-average of

polymerization (N) was calculated. The degradation

kinetics for all three PLGA ratios investigated was

obtained from the literature. Table 3 summarizes the

parameters used in the subsequent estimate of the

pore evolution. The number of chain cleavages per

initial number average molecule, x, was calculated

and the accumulated probability, Xt, of bond clea-

vagesovertimet,Xt?t,wasobtainedfromt¼1dayto

t¼90, 120, 160 days depending on the time of

complete degradation for each of the specific PLGA

polymers.ForPLGApolymers,themaximumnumber

of bonds in a soluble oligomer (umax) was documented

as 9.23The tortuosity factor, t, was assumed to be 3.

Finally, the effective diffusion coefficient, D(t) was

determined using hindered transport theory.

Figure 4 shows the predicted effective diffusion

coefficients for the PLGA microparticles for the

release of simulated OVA and BSA. The induction

period of protein release from PLGA microparticles

obtained here is correlated to the point of rapid

change in theeffective diffusion coefficient. As a burst

release was observed in the experiments due to

surface protein release, in order to describe the

induction period for the experimental results, we

followed the convention and used the time duration

between the initial burst and the most significant

rapid change in release during the overall period. For

themodelprediction, theinductionperiodwas elected

to be the time required for rapid change in the

effective diffusion coefficient. From the theoretical

calculations, the induction periods for OVA-loaded

microparticles were estimated to be 45, 70, and

105 days for PLGA 50:50, 75:25, and 85:15 formula-

tions, respectively; BSA-loaded microparticles had

detectable induction periods as 50, 75, and 110 days

for PLGA 50:50, 75:25, and 85:15 formulations,

respectively. As can be seen, the induction periods

estimated from theoretical simulations (summarized

in Tab. 4) are in very good agreement with the values

estimated from experiments.

The consistency of the theoretical simulations with

experimental results demonstrates that the transient

pore evolvement combined with hindered diffusion

model works well to predict hindered protein release

from PLGA microparticles undergoing bulk erosion.

Given the simplicity of the model with respect to the

complex erosion process and the particle size dis-

Figure 3.

ferent monomer ratios (50:50, 75:25, and 85:15). The par-

ticles were fabricated using a double-emulsion method and

incubated at 378C at 250rpm. Using the time between

significant rate changes the induction periods for the PLGA

50:50, 75:25, and 85:15 microparticles are estimated to be

45, 70 and 105 days, respectively. The vertical colored lines

are used to indicate the end of the induction period for each

formulation.

BSA release from PLGA microparticles in dif-

Table 3.

Critical Parameters in Induction Period Prediction Model for PLGA Microparticles

PolymerMn

Initial Number of Bonds

Per Polymer Molecule N

Average Monomer

Size, lave(A˚)

Degradation Rate

Constant, kd(day?1)

PLGA 50:50

PLGA 75:25

PLGA 85:15

20,462

40,366

108,647

314

588

1553

3.514

3.515

3.517

?0.0773a

?0.0622a,b,c

?0.0522a,b,c

The average monomer sizes were estimated from bond lengths and bond angles.

The available degradation rate constants for PLGAs varied between 0.02 and 0.1day?1. The values used in this calculation were obtained from:aRef. 9,

bRef. 15 andcRef. 30.

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ZHAO, HUNTER, AND RODGERS

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tributions,

well, albeit, the error may still on the order of days.

This implies that the polymer degradation kinetics is

the dominant contribution and can be correlated to

the release rate for PLGA microparticles. It is

reasonable that this theoretical simulation method

can be extended to other polyester-based micropar-

ticles as well. In the time scale of an induction period,

the effects of other phenomena, such as spontaneous

pore coalescence and pore closing on pore evolvement

are not significant, thus were ignored from this

mathematical model. Pore coalescence can accelerate

pore growth, while pore closing decelerate the

apparent pore growth rate. The interactions of

these two factors cause dissipation of both effects.

these resultscorrelatesurprisingly

As a matter of fact, pore coalescence rate/closing rates

largely depend on the initial pore distribution profile

and the followed pore growth rate. For the initial

stage of bulk erosion, pore coalescence is not

significant because the existed pores are insufficient

for a large number of coalescence. In addition,

polymer degradation and the subsequent pore growth

dominate the induction period in bulk erosion; thus

pore closing is negligible in this case. When degrada-

tion proceeds after the induction period, pore

coalescence will become a significant factor which

leads to fast drugreleaseand particle matrixcollapse.

As our work is focused on pore evolvement in the

induction period, this phenomenon is beyond our

discussion.

Particle size (R) is also an important control

parameter for drug release patterns not only through

changesindiffusion rates

secondary effects including drug distribution in the

particle, polymer degradation rate, and erosion rate of

the particles.36Generally speaking, the reduced

particle size will result in an increase of the surface

area to volume ratio, which will speed up the buffer

penetrationintotheparticlesandtheescapeofpolymer

degradation products. However, a more complex

relationship was acknowledged between the particle

size and protein release. First, a liner relationship

betweenthepolymerdegradationrateandparticlesize

was observed, with the larger particles degrading

faster.37Later research shows that the degradation

behavior of polymer matrix may not be significantly

affectedbythedevicesizeandtheabsolutereleaserate

of the drug may increase with the increasing particle

radius because large microparticles can become more

porous during drug release than small microparticles,

leading to higher apparent diffusivities and drug

transport rates.38In our work, the effect of particle

size (R) on induction time was investigated by this

dynamic hindered diffusion model coupled with pore

evolvement by variation of boundary condition in

Eq. (23). A more complete evaluation requires a

systematic study that combines both experimental

evidence and a broad theoretical analysis.

In drug delivery system designs, the induction

period is a crucial parameter that determines when

the actual release starts. Especially for pulsatile

release, such as the desirable single-shot vaccine for

Hepatitis B, the induction period tells the length of

waiting time between two pulses, which is vital

with regard to the timeliness and effectiveness of

boosting shot (releases). The mathematical modeling

of induction period will provide meaningful informa-

tion not only in selection of polymers, but also in

designing the geometric structure of the particles to

achieve the desirable drug release profile. Using this

model, we can modulate important parameters for

certain polyester-based protein delivery formulations

butalsothrough

Figure 4.

sion coefficients of protein molecules in the growing pores of

PLGA matrices calculated by hindered model. For OVA,

D1¼7.2?10?7cm2/s; for BSA, D1¼5.9?10?7cm2/s. The

point of onset for rapid change in the effective diffusion

coefficient is used to indicate the end of the induction period

for the modeled system.

Model results for the transient effective diffu-

Table 4. Comparison of Estimated Induction Periods

from Experiment (Figs. 2 and 3) and Model (Fig. 4)

Wall Polymer

Encapsulated

Protein

Estimated Induction

Period (Days)

ExperimentallyTheoretically

PLGA 50:50 OVA

BSA

OVA

BSA

OVA

BSA

45

45

70

70

105

105

45

50

70

75

105

110

PLGA 75:25

PLGA 85:15

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PREDICTING THE INDUCTION PERIOD FOR MICROPARTICLE DRUG DELIVERY

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to optimize the drug release. More importantly, this

model allows the prediction of the microparticle drug

delivery induction time without direct experimental

observations of the microparticle erosion.

CONCLUSIONS

A theoretical model for transient pore evolvement in

biodegradable copolymer matrix based on polymer

degradation kinetics and probability theory was

developed.Thetransientporeevolvement,ascaptured

by the effective diffusion coefficient of the protein in

the copolymer matrix, is related to the distribution

function of bond cleavages and degradation products.

The effective diffusion coefficient in PLGA micropar-

ticles was modeled using hindered transport theory.

The results showed that the theoretical estimates of

theinductionperiodwereinverygoodagreementwith

experimental release studies of OVA and BSA from

PLGA-formulatedmicroparticles.Themodelisunique

in that it can provide predictions of microparticle

induction times without direct experimental micro-

particle erosion data. For systems in which the

induction time may be on the order of months, this

couldprovideaconsiderablebenefit.Inparticular,this

modeling approach can provide a substantial benefit

for estimating booster times for single-shot vaccine

devices.

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