prediction of kinetics of doxorubicin release from sulfopropyl dextran ion-exchange microspheres...

European Journal of Pharmaceutical Sciences 24 (2005) 401–410

Prediction of kinetics of doxorubicin release from sulfopropyl dextranion-exchange microspheres using artificial neural networks

Yongqiang Lia, Andrew M. Rauthb, Xiao Yu Wua,∗a Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto, ON, Canada M5S 2S2b Experimental Therapeutics, Ontario Cancer Institute, Toronto, ON, Canada M5G 2M9

Received 17 November 2004; accepted 9 December 2004Available online 1 February 2005

Abstract

The purpose of this work was to develop artificial neural networks (ANN) models to predict in vitro release kinetics of doxorubicin (Dox)delivered by sulfopropyl dextran ion-exchange microspheres. Four ANN models for responses at different time points were developed todescribe the release profiles of Dox. Model selection was performed using the Akaike information criterion (AIC). Sixteen data sets were usedt cted releasep ndt dict releasek ss rospheres.©

K

1

lspradtD

nDDDb

core-3;edthe

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ethesedelf the

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o train the ANN models and two data sets for the validation. Good correlations were obtained between the observed and predirofiles for the two randomly selected validation data sets. The difference factor (f1) and similarity factor (f2) between the ANN predicted a

he observed release profiles indicated good performance of the ANN models. The established models were then applied to preinetics of Dox from the microspheres of various initial loadings in media of different ionic strengths and NaCl/CaCl2 ratios. The resultuggested that ANN offered a flexible and effective approach to predicting the kinetics of Dox release from the ion-exchange mic2005 Elsevier B.V. All rights reserved.

eywords:Artificial neural networks; Prediction; Release kinetics; Doxorubicin; Ion exchange microspheres

. Introduction

A good controlled release (CR) dosage form should de-iver therapeutic agents at a precisely controlled rate for theake of safety and therapeutic efficacy. This requirement isarticularly critical for delivering potent drugs that have nar-ow therapeutic indices such as doxorubicin (Dox). Dox is

widely used anticancer drug that causes irreversible car-iac toxicity following repeated administration at effective

herapeutic levels (Moore and Erlichman, 1998; Singal andiskovic, 1998). To eliminate the severe adverse effect, our

Abbreviations:AIC, Akaike information criteria; ANN, artificial neuraletworks; DDI, distilled deionized water; Dox, doxorubicin HCl; Dox-MS,ox loaded microspheres; Dox-MS-0.30, microsphere with a weight ratio ofox to MS of 0.30 (w/w); Dox-MS-45, microsphere with a weight ratio ofox to MS of 0.45 (w/w); MS, microspheres; SP-MS, sulfopropyl dextran-ased microspheres∗ Corresponding author. Tel.: +1 416 978 5272; fax: +1 416 978 8511.E-mail address:[email protected] (X.Y. Wu).

group has developed a microsphere system for the logional delivery of Dox (Liu et al., 1999, 2000, 2001, 200Cheung et al., 2004). Reduced systemic toxicity and delaytumor growth in tumor-bearing mice were observed withtreatment of intratumoral injection of the Dox-loadedfopropyl dexran microspheres (SP-MS) (Liu et al., 2003).To optimize the MS formulation and predict bioavailabliof Dox, in vitro–in vivo correlation (IVIVC) of Dox releaskinetics was studied (Cheung et al., 2004) and mathematcal modeling of Dox loading was attempted (Abdekhodaieand Wu, unpublished data). Although the in vivo releasprofile of Dox can be predicted from in vitro data byIVIVC established previously, prediction of in vitro releaprofile of a given MS formulation by a mathematical mois not possible at this stage because of the complexity osystem.

Previous work showed that the rate of Dox releasethe SP-MS increased with increasing salt concentrationdecreased with increasing initial drug loading; Dox rele

928-0987/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.ejps.2004.12.005

402 Y. Li et al. / European Journal of Pharmaceutical Sciences 24 (2005) 401–410

was resumed as the medium was replaced by a fresh one(Liu et al., 2003; Cheung et al., 2004). These results sug-gest that Dox release from the MS is not only dominated bythe ion-exchange mechanism, but is also influenced by someunknown mechanisms and external conditions. Although nu-merical methods, such as the finite element method, can beemployed to investigate drug release kinetics of complex sys-tems (Zhou and Wu, 1997, 2003; Zhou et al., 2004; Wu andZhou, 1998a, 1999; Wu et al., 1998b), a mechanistic model isrequired for the computation. In case that an explicit physicalmodel cannot be built owing to unclear correlations betweencausal factors and responses, other mathematical methods,such as artificial neural networks (ANNs), may offer a usefultool.

ANNs, like the response surface method, do not requiremechanistic models for building correlations between depen-dent and independent variables (Hinton, 1989; Cartwright,1993; Carpenter and Hoffman, 1995; Bourquin et al., 1997).ANNs are an intelligent non-linear mapping system builtloosely to simulate the functions of human brains. An ANNmodel consists of many nodes and their connections. Itscapacity is characterized by the structure, transfer functionand learning algorithms (Hinton, 1989). Transfer functions,such as sigmoid function, introduce non-linearity to the net-works and the learning rate, momentum and weight decaya ft su-p edi pastd 995;B eta 000;I hida,2 a-c adigm( rs

asep ingva eh eta n-s aceut 98;B Nsi itedd na-t uldb ernalm be owm emi pro-d .,2 timep

In a standard ANN method, all input nodes, hidden nodesand output nodes are incorporated in one model; the samehidden nodes serve different responses at the same time andthe relationships between each output property and inputvariables are explored simultaneously during the trainingprocess. Use of this method requires the ANN model bepowerful enough to search a complex, multi-dimensionalweight space and find the weight vectors to satisfy all trainingcases. However, because the size of training data is limited,ANN cannot map the design space thoroughly, which,together with a single stop criterion (i.e., the minimizationof the sum of squared error) of the ANN model for allresponses, would result in variant performance of prediction.For example, some responses are predicted accurately, yetothers poorly. To solve such problems,Takayama et al.(1999a,b, 2000)proposed a partitioned ANN structure.

On the basis of Takayama et al. suggestions and the prac-tice of response surface methodology where dependent vari-ables are modeled individually, we attempted to model thefractional release of Dox-MS at each time point individuallyusing ANNs. With this new ANN modeling method, the ki-netics of Dox release from SP-MS was modeled and predictedbased on a time point by time point estimation. The effectsof Dox loading level and composition of the release mediumon the release kinetics of Dox were investigated using ANNm

2

2

thepb icalC pyld fromP withv S)( s oft .g.,2 oxr S ina als,PC tionsa res teda oxr eter( h of5

ndentv con-c reda m the

re applied to train the ANNs (Plaut et al., 1986). Because oheir model-independence, non-linearity, flexibility, anderior data-fitting and prediction ability, ANNs have gain

ncreasing interests in the pharmaceutical field in theecade (Hussian et al., 1991; Erb, 1993; Achanta et al., 1ourquin et al., 1997, 1998;Bozic et al., 1997; Takayamal., 1999a,b, 2000; Agatonovic-Kustrin and Beresford, 2

chikawa, 2003; Sun et al., 2003; Yamashita and Has003). Most ANN models developed so far for pharmeutical research are based on back-propagation parRumelhart et al., 1986) or its variations with a multiple layetructure.

Among various applications, prediction of drug relerofiles and optimization of formulation and or processariables using ANN modeling have been reported (Bozic etl., 1997; Ebube et al., 1997; Chen et al., 1999, 2002; Pl., 2000; Ibric et al., 2002). Previous studies have demotrated the advantages and usefulness of ANNs in pharmical research (Bozic et al., 1997; Rowe and Roberts, 19ourquin et al., 1998). Nevertheless, the application of AN

n practice confronts several challenges. One is the limata set available for training and validation. The learning

ure of ANN determines that its generalization ability woe better with a large training data set and extensive intapping of the design space (Reed and Marks, 1998; Plumt al., 2002), though there is no definite rule to regulate hany data are sufficient for ANN training. Another probl

s that the ANN with general structure may occasionallyuce poor estimation of some responses (Takayama et al003). This will lead to unreasonable results at someoints in the case of predicting drug release kinetics.

-

odels after the training and validation.

. Methodology

.1. Data sets

The experimental data used for this study came fromaper published by our group (Liu et al., 2001). Doxoru-icin hydrochloride was purchased from Sigma Chemompany, St. Louis, MO and the cross-linked sulfoproextran-based microspheres (Sephadex SP C-25) wereharmacia, Peapack, NJ. The microspheres loadedarious levels of Dox (0.05–0.45, w/w ratio of Dox/MDox-MS) were prepared by addition of known amounthe MS to a Dox solution with a fixed concentration, e.5 ml of 0.22 mg/ml Dox in DDI water. The kinetics of Delease from Dox-MS was measured by placing Dox-Mcuvette containing a solution of NaCl (Fisher Chemicittsburge, PA) or a mixture of NaCl and CaCl2 (ACPhemicals, Saint-Leonard, Quebec). The concentrand ratio of NaCl to CaCl2 in the release medium aummarized inTable 1. The release tests were conduct 37◦C under a well-stirred condition. The amount of Deleased was monitored by a UV–vis spectrophotomHewlett-Packard 8452A, Palo Alto, CA) at a wavelengt00 nm.

The experimental data sets comprised three indepeariables: drug loading level, concentration of NaCl andentration of CaCl2. The ionic strength was not consides an independent variable since it can be calculated fro

Y. Li et al. / European Journal of Pharmaceutical Sciences 24 (2005) 401–410 403

Table 1Experimental data sets for ANN training and validation which include initial Dox loading, salt concentration, and fractional release of Doxa

Training orvalidation

Initial Dox loading in MS(Dox/MS weight ratio)

NaCl(%, w/w)

CaCl2(%, w/w)

Ionicstrength (M)

Fractional release atvarious times (h)

0.5 1 2 4

T 0.05 2.5 0 0.43 0.70 0.87 0.98 1.00T 0.05 0.5 0 0.09 0.54 0.61 0.66 0.71T 0.05 0.25 0 0.04 0.36 0.39 0.40 0.40T 0.05 2.5 0.4 0.52 0.99 1.00 1.00 1.00T 0.05 0.5 0.08 0.10 0.94 1.00 1.00 1.00T 0.05 0.25 0.04 0.05 0.89 0.95 1.00 1.00

T 0.15 2.5 0 0.43 0.82 0.96 0.99 0.99T 0.15 0.5 0 0.09 0.25 0.36 0.42 0.43T 0.15 0.25 0 0.04 0.15 0.25 0.33 0.39T 0.15 2.5 0.4 0.52 0.86 1.00 1.00 1.00V1 0.15 0.5 0.08 0.10 0.73 0.94 1.00 1.00T 0.15 0.25 0.04 0.05 0.52 0.76 0.92 0.97

T 0.45 2.5 0 0.43 0.50 0.64 0.81 0.89T 0.45 0.5 0 0.09 0.11 0.20 0.31 0.43T 0.45 0.25 0 0.04 0.05 0.08 0.14 0.22T 0.45 2.5 0.4 0.52 0.49 0.69 0.89 1.00V2 0.45 0.5 0.08 0.10 0.33 0.55 0.79 0.97T 0.45 0.25 0.04 0.05 0.22 0.39 0.64 0.88

T, the data were used for training in this study; V, the data were used for validation in this study.a The data were adapted from the reference published byLiu et al. (2001).

concentrations of NaCl and CaCl2. The dependent responseswere the fractional release of Dox at four different time points(i.e., 0.5 h, 1 h, 2 h and 4 h), respectively. The weight concen-tration of NaCl ranged from 0.25 to 2.5 and CaCl2 from 0 to0.4% (w/w). Detailed information about the data is shown inTable 1.

2.2. Artificial neural network modeling

Four independent ANN models were developed and eachserved one response. This approach not only simplifies thestructure of networks, but also improves the prediction accu-racy and stability of every response. The preliminary resultsshowed better predictions using this approach than using thestandard method that includes all responses in one model.However, the independent model approach has the disadvan-tage that the information included in such models is less thanthat in the standard model. Thus, the predictive ability andaccuracy of these models were analyzed as presented later.

The neural network simulator, based on the back-propagation algorithm, was developed in this work. Threeindependent variables, i.e., drug loading level, concentrationof NaCl and CaCl2 in the release medium were used as theANN inputs and the fractional release of Dox-MS at four dif-ferent time points as the outputs, i.e., responses (seeTable 1a tea l re-s fours oughd Nm eachr

The number of hidden nodes was estimated according tothe equation introduced byCarpenter and Hoffman (1995).

Nhidden= Nsample/β − Noutput

Ninput + Noutput+ 1(1)

Fig. 1. Structure of hierarchical ANN (a) regular ANN structure for theentire time course and (b) downsized ANN structure for one time point.

ndFig. 1). Four ANN models with adaptive learning rand momentum were developed separately for individuaponses. In this way, a complex network was split intoimple networks, which ensured that each net has enata for training and validation. The stop criterion of ANodels became the minimization of the squared error of

esponse.


whereNhiddenis the number of hidden nodes,Nsamplethe num-ber of training data sets,Ninput the number of input nodes andNoutput is the number of output nodes. The constantβ deter-mines the degree of over-determination. It has three values:β < 1, under-determinated;β = 1, determined andβ > 1, over-determined. In brief,β ≥ 1 is preferred.

Of 18 experimental data sets listed inTable 1, tworepresentative data sets, without being the slowest andthe fastest release, were randomly chosen as the valida-tion data, while the remaining 16 data sets were usedas the initial training data for the ANN model develop-ment. In this study,Nsample= 16, Ninput = 3, Noutput= 1 fordownsized ANN structure, thusNhiddenwas calculated fromEq. (1) to be 3 for β = 1 and 2 forβ = 1.45. The opti-mality of ANNs with Nhidden values was evaluated usingAkaike’s information criterion (AIC) (Akaike, 1974; Fogel,1991):

AIC = ns × ln(SS)+ 2 × nw (2)

wherens is the number of data sets,nw the number of weightsin the ANN, and SS is the residual sum of squares betweenobserved and predicted response variables.

Simulations using variousNhiddenvalues indicated that anANN model with a structure ofNhidden= 3 had the smallestvalues of AIC:−16.39,−17.20,−20.54 and−27.84 for fourr simu-l ith

good generalization ability. Hence,Nhidden= 3 was used inthe subsequent analyses.

3. Results and discussion

Four ANN models, each with three hidden nodes, weretrained with 16 experimental data sets (labeled “T” inTable 1)consisting of six different release media, three different drugloading levels, and corresponding release profiles. The gen-eralization ability of ANN model was validated using anothertwo data sets (labeled “V1” and “V2” in Table 1) that were notexposed to the model before. The performance of the trainedANN models was then evaluated using difference and simi-larity factors.

3.1. Measurement of ANN prediction performance

3.1.1. Performance measurement using training datasets

Fig. 2 shows a reasonably good correlation between thepredicted and the observed fractional Dox released from MSfor 16 training experimental data sets and four release timepoints (total 64 data points). The correlation coefficients,r2,ranges from 0.955 to 0.973 and the slopes are very closeto 1.00. The residuals of predicted versus observed releasep atedi

Fa

esponses, respectively, and was powerful enough toate every property of the release kinetics of Dox-MS w

ig. 2. Correlation between ANN predicted responses and observed 16 trainnd (d) 4 h. The solid lines show the linear regression between the predictio

rofiles at each time point distribute randomly, as illustrn Fig. 3.

ing data sets (labeled “T” inTable 1) at four time points: (a) 0.5 h; (b) 1 h; (c) 2 hns and the observations.


Fig. 3. Residual distribution of predicted response around observed fractional release for 16 training data sets (labeled “T” inTable 1) for responses at fourtime points: (a) 0.5 h; (b) 1 h; (c) 2 h and (d) 4 h.

3.1.2. Performance measurement using difference andsimilarity factors

Recently, difference factor (f1) and similarity factor (f2)have been proposed to assess the similarity of two in vitrodissolution profiles (US FDA, 1997), or one dissolution pro-file predicted by an ANN model and the other obtained fromphysical experiments (Peh et al., 2000; Costa et al., 2003) forcontrolled release formulations. Difference factor is a mea-sure of the percent difference in the fractional dissolution be-tween the two drug release curves over all time points (Moore

F ep

and Flanner, 1996):

f1 =∑n

t=1|Rt − Tt|∑Rt

× 100 (3)

whereRt andTt are the percent drug released from referenceformulation and from the test formulation, respectively, attime t andn is the number of sampling time-points.

Similarity factor is a function of the reciprocal of meansquare-root transformation of the sum of squared error. It is ameasure of the similarity in the fractional dissolution betweenthe curves over all time points:

f2 = 50× log

{[1 + 1

n

∑(Rt − Tt)

2]−0.5

× 100

}(4)

FDA considers two dissolution profiles to be similar iff1is between 0 and 15 andf2 is between 50 and 100.Fig. 4andTable 2depict that all thef1 values for the 16 observed andANN-predicted release profiles are below 0.25 andf2 valuesare well above 50 except one that is a little bit less than 50.These results indicate that the prediction performance of theANN models developed in this study is satisfactory.

3.2. ANN generalization ability

The generalization ability of the ANN models was testedb e-

TDp

82
ig. 4. Difference factor (f1) and similarity factor (f2) for each of 16 releas
rofiles.

y two validation data sets.Fig. 5portrays that a good corr

able 2ifference factor (f1) and similarity factor (f2) of all 16 in vitro dissolutionrofiles predicted using ANN

f1 f2

Mean 0.083 67.6S.D.a 0.066 13.9

a Standard deviation.


Fig. 5. Correlation between ANN predicted and the observed fractional re-lease for two validation experimental data sets (a) V1 and (b) V2 shown inTable 1.

lation between the predicted and the observed release profilesfor the validation data sets. Ther2 values range from 0.981to 0.994 and the slopes from 0.977 to 1.00.

3.3. Prediction of release kinetics of Dox-MS by ANNmodels

After successful training and validation, the ANN modelswere employed to predict Dox release kinetics influenced byvarious factors, which is difficult to investigate thoroughly byexperiments due to cost and time constraint. The followingexamples are presented to demonstrate the usefulness of theprediction in the analysis of a formulation factor (e.g., drugloading level) and environmental conditions.

3.3.1. Effect of drug loading levelsFig. 6illustrates the release profiles of Dox-MS of various

initial Dox loading levels (10%, 20%, 30%, 35% and 40%) ina medium of an ionic strength of 0.54 M consisting of 2.5%NaCl and 0.4% CaCl2 (i.e., NaCl/CaCl2 = 6.25). In the first2 h, the release rate increases as the initial loading decreaseswhich is in agreement with the experimental result reportedpreviously (Liu et al., 2001). After 2 h, the difference betweenthe five curves diminishes, reaching a complete release. Thestrong dependence of release rate on the initial drug loadingi Doxm ntra-t the

Fig. 6. The effect of drug loading level on the kinetics of Dox release fromDox-MS. The ionic strength was 0.54 M, and the concentration of NaCl andCaCl2 was 2.5 wt.% and 0.4 wt.%, respectively (i.e., NaCl/CaCl2 = 6.25).

drug-loaded MS and reducing the interaction between Doxand water (Liu et al., 2001). The merge of the curves at latetimes is attributable to the early completion of drug releaseof the Dox-MS with low initial loadings at such high con-centrations of NaCl and CaCl2. Figs. 7 and 8also evidencethat the negative impact of initial Dox loading on the releaserate occurs in release media of various ionic strengths andsalt ratios.

3.3.2. Effect of electrolyte composition andconcentration in the release medium

Four different scenarios of drug release kinetics in rela-tion to electrolyte composition and concentration have beeninvestigated using the ANN models: the release medium (1)with varied NaCl concentration but without CaCl2; (2) withvaried CaCl2 concentration but a fixed NaCl concentration(2.5 wt.%); (3) at a fixed NaCl/CaCl2 ratio and varied to-tal ionic strength and (4) with a fixed total ionic strength of0.15 M but varied NaCl/CaCl2 ratio. The results are presentedbelow, respectively, inFigs. 7–10.

(1) Effect of NaCl concentration: Fig. 7a–d are the surfaceplots of the release kinetics of Dox-MS of various drugloading levels as a function of NaCl concentration inthe release medium at four time points, respectively.

sedcen-in

x, itse

con-tent

( ClaseeCl.nClthe1 to

s a unique characteristic of Dox. It was interpreted thatolecules in the MS would self-associate at high conce

ions, blocking the pathway for water to penetrate into

,

These figures illustrate that the fraction of Dox releaat a given time decreases with decreasing NaCl contration at all initial Dox levels. Though the increasethe NaCl concentration promotes the release of Doeffect is limited. In the absence of CaCl2, the drug releasis incomplete even at 4 h in the studied range ofcentrations up to 2.5 wt.%. This prediction is consiswith the experimental observation (Liu et al., 2001).

2) Effect of CaCl2concentration at a constant level of Na:Fig. 8a–d shows the surface plots of fractional releversus Dox loading level and CaCl2 concentration in thmedium containing a fixed amount (2.5 wt.%) of NaThe presence of CaCl2 makes a significant contributioto the release of Dox from MS at early times. As Ca2concentration is increased from 0 wt.% to 0.4 wt.%,fraction of Dox released in 0.5 h increases from 0.5


Fig. 7. Predicted response surface of release kinetics of Dox-MS as a function of Dox loading level (weight ratio of Dox/MS: 0.05–0.45) and concentration ofNaCl (0.25–2.5 wt.%).

0.99. At later times, i.e., after 2 h, the effect of CaCl2 be-comes less profound, so does the initial Dox loading. Thisphenomenon may be explained as that the drug releaseapproaches equilibrium after 2 h in a medium compris-ing 2.5 wt.% NaCl. The insensitivity of fractional releaseto initial Dox loading at late times is also evident inFig. 6.

(3) Effect of ionic strength at a fixed NaCl/CaCl2: Fig. 9shows ANN predicted release curves for (a) Dox-MS-0.30 and (b) Dox-MS-0.45 in media of different ionicstrengths. It is seen that with the NaCl/CaCl2 ratio beingfixed at 6.25, the release rate increases significantly asthe ionic strength increases from 0.052 M to 0.52 M.

(4) Effect of NaCl/CaCl2ratio at a constant total ionicstrength: In examples (2) and (3) presented above,when the NaCl concentration or CaCl2 concentrationis altered, the total ionic strength is also changed.However, in a physiological fluid, the total ionic strengthis maintained at about 0.15 M. To mimic this condition,release profiles were computed using the ANN models

with a fixed ionic strength of 0.15 M but varied ratioof NaCl to CaCl2. Fig. 10 depicts that even thoughthe ionic strength is kept constant, a slight decrease inthe NaCl/CaCl2 ratio from 8 to 5, i.e., an increase inthe CaCl2 content, promotes Dox release noticeably,which is reflected by a higher release rate and a greaterfractional release at equilibrium. At a Dox loadinglevel of 0.45 (Dox-MS-0.45), the drug release does notapproach equilibrium yet at 4 h (Fig. 9b); while at aloading level of 0.30 (Dox-MS-0.30), all curves show aplateau after 2 h (Fig. 9a). Apparently, only in a mediumwith a NaCl/CaCl2 ratio of 5 does the Dox release reachcompletion. The rest two curves for NaCl/CaCl2 = 6.27and 8 reach only 0.90 and 0.82, respectively, at 4 h.

These results can be explained by a higher affinity to thepolymer and greater ion exchange capacity of Ca2+ than Na+.Although the bigger radius of Ca2+ would slow its diffusionrate, its higher binding capacity seems to play a more impor-tant role because one mole of Ca2+ can exchange with two


Fig. 8. Predicted response surface of release kinetics of Dox-MS as a function of Dox loading level (weight ratio of Dox/MS: 0.05–0.45) and concentration ofCaCl2 (0–0.4 wt.%). The concentration of NaCl was fixed at 2.5 wt.%.

Fig. 9. The effect of ionic strength of the release medium on the kineticsof Dox release from (a) Dox-MS-0.30 and (b) Dox-MS-0.45 with a fixedNaCl/CaCl2 weight ratio of 6.25.

Fig. 10. The effect of NaCl/CaCl2 weight ratio in the release medium of anionic strength of 0.15 M on the kinetics of Dox release from (a) Dox-MS-0.30and (b) Dox-MS-0.45.


moles of Dox+ as depicted by the following formulas (Liu etal., 2001):

MS-SO3−DOX+ + Na+Cl− � MS-SO3

−Na+

+ DOX+Cl− (5)

2MS-SO3−DOX+ + Ca2+Cl2

− � (MS-SO3−)2Ca2+

+ 2DOX+Cl− (6)

For Dox-MS with high drug loading, the fact that the ef-fect of CaCl2 on the release rate decreases after 2 h might beattributed to the ion exchange equilibrium described aboveat the current salt concentrations of NaCl and CaCl2. An-other possible contributor is the formation of strong cross-links constituted by Ca2+–polymer complex, which block thepathway for Ca2+ to attack other ionic binding sites on thepolymer (Liu et al., 2001).

4. Conclusion

The release kinetics of Dox-loaded sulfopropyl dextranMS was modeled by artificial neural networks. Satisfactoryresults were achieved for predicting the kinetics of Dox re-lease from SP-MS with different drug loadings in release me-d achr or hand en-a intsw tudys thep witht itlya

A

s ofH eof-f sityo n thisw ngL

R

A cro-ished

A uralInd.

A ficialtical

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C Com-ease

E ula-ork.

E put-

F ork

H 40,

H urals. 8,

I eeling

I aceu-

L nicosen-harm.

L char-s and807–

L uth,romlease

L liv-st sar-res.

ia of various compositions. The method of modeling eesponse separately seemed to be a feasible approach fling the problem of time-series data in this case, whichbled the prediction of fractional release at four time poith good agreement with the experimental data. This suggests that ANN is a useful tool for the prediction oferformance of drug delivery systems whose correlation

he formulation and environmental variables is not explicvailable.

cknowledgements

This work was supported by the Canadian Instituteealth Research. The authors would like to thank Dr. G

rey E. Hinton, Department of Computer Science, Univerf Toronto, for his valuable suggestions and comments oork. University of Toronto Ben Cohen Fund to Yongqiai is also acknowledged.

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prediction of kinetics of doxorubicin release from sulfopropyl dextran ion-exchange microspheres...

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