ORIGINAL PAPER

Identification of heparin samples that contain impuritiesor contaminants by chemometric pattern recognition analysisof proton NMR spectral data

Qingda Zang & David A. Keire & Lucinda F. Buhse & Richard D. Wood &

Dinesh P. Mital & Syed Haque & Shankar Srinivasan & Christine M. V. Moore &

Moheb Nasr & Ali Al-Hakim & Michael L. Trehy & William J. Welsh

Received: 18 April 2011 /Revised: 29 May 2011 /Accepted: 30 May 2011 /Published online: 17 June 2011# Springer-Verlag 2011

Abstract Chemometric analysis of a set of one-dimensional(1D) 1H nuclear magnetic resonance (NMR) spectral data forheparin sodium active pharmaceutical ingredient (API)samples was employed to distinguish USP-grade heparinsamples from those containing oversulfated chondroitinsulfate (OSCS) contaminant and/or unacceptable levels ofdermatan sulfate (DS) impurity. Three chemometric patternrecognition approaches were implemented: classification andregression tree (CART), artificial neural network (ANN), and

support vector machine (SVM). Heparin sodium samplesfrom various manufacturers were analyzed in 2008 and 2009by 1D 1H NMR, strong anion-exchange high-performanceliquid chromatography, and percent galactosamine in totalhexosamine tests. Based on these data, the samples weredivided into three groups: Heparin, DS≤1.0% and OSCS=0%; DS, DS>1.0% and OSCS=0%; and OSCS, OSCS>0%with any content of DS. Three data sets corresponding todifferent chemical shift regions (1.95–2.20, 3.10–5.70, and1.95–5.70 ppm) were evaluated. While all three chemo-metric approaches were able to effectively model the data inthe 1.95–2.20 ppm region, SVM was found to substantiallyoutperform CART and ANN for data in the 3.10–5.70 ppmregion in terms of classification success rate. A 100%prediction rate was frequently achieved for discriminationbetween heparin and OSCS samples. The majority of classifi-cation errors between heparin and DS involved cases where theDS content was close to the 1.0% DS borderline between thetwo classes. When these borderline samples were removed,nearly perfect classification results were attained. Satisfactoryresults were achieved when the resulting models werechallenged by test samples containing blends of heparin APIsspiked with non-, partially, or fully oversulfated chondroitinsulfate A, heparan sulfate, or DS at the 1.0%, 5.0%, and 10.0%(w/w) levels. This study demonstrated that the combination of1D 1H NMR spectroscopy with multivariate chemometricmethods is a nonsubjective, statistics-based approach forheparin quality control and purity assessment that, oncestandardized, minimizes the need for expert analysts.

Keywords Heparin . Proton nuclear magnetic resonance(1H NMR) . Pattern recognition . Classification andregression tree (CART) . Artificial neural network (ANN) .

Support vector machine (SVM)

FDA disclaimer The findings and conclusions in this article have notbeen formally disseminated by the Food and Drug Administration andshould not be construed to represent any Agency determination or policy.

Q. Zang :W. J. Welsh (*)Department of Pharmacology, Robert Wood Johnson MedicalSchool, University of Medicine and Dentistry of New Jersey,Piscataway, NJ 08854, USAe-mail: welshwj@umdnj.edu

Q. Zang : R. D. WoodSnowdon, Inc.,1 Deer Park Drive, Suite H-3,Monmouth Junction, NJ 08852, USA

Q. Zang :D. P. Mital : S. Haque : S. SrinivasanDepartment of Health Informatics, School of Health RelatedProfessions, University of Medicine and Dentistry of New Jersey,Newark, NJ 07107, USA

D. A. Keire : L. F. Buhse :M. L. TrehyDivision of Pharmaceutical Analysis,Food and Drug Administration, CDER,St. Louis, MO 63101, USA

C. M. V. Moore :M. Nasr :A. Al-HakimOffice of New Drug Quality Assessment,Food and Drug Administration, CDER,Silver Spring, MD 20993, USA

Anal Bioanal Chem (2011) 401:939–955DOI 10.1007/s00216-011-5155-4

Introduction

Heparin, a highly sulfated glycosaminoglycan (GAG), iswidely used as an anticoagulant in multiple settings,including: kidney dialysis, invasive surgical procedures,cure of acute coronary syndromes, and deep venousthrombosis treatment [1, 2]. Heparin sodium is among theoldest drugs still in widespread clinical use and one of thefirst polymeric carbohydrate drugs. Millions of doses ofheparin are dispensed every month and tons of heparin areused every year. Heparins are composed of repeatingdisaccharide units that contain a hexosamine and ahexuronic acid which may be N- or O-sulfated in differentpositions. Structurally, they are long, unbranched, negativelycharged, and polydisperse polysaccharides [3–5].

Heparin is usually extracted from animal tissues in crudeform, such as porcine intestinal mucosa or bovine lung,followed by further purification to active pharmaceuticalingredients (APIs) prior to formulation to drug product andadministration as an anticoagulant [6]. The productionprocess can involve proteolytic digestion, precipitation ofthe preparations as quaternary ammonium complexes orbarium salts, and eventually making sodium or calciumsalts [7, 8]. Heparin sodium and formulations made fromthese APIs may contain varying amounts (specified by theUS Pharmacopeia (USP) to be NMT 1%) of several naturalGAG impurities. The most common impurity found inheparin sodium is dermatan sulfate (DS) which, likeheparin, contains L-iduronic acid units. Due to the structuralsimilarity and chemical affinity between DS and heparin,complete removal of DS impurity in heparin is difficult toachieve [9, 10]. The content of DS in the heparin APIs is anindicator of the quality of the drug substance.

In 2008, heparin raw materials and finished drugproducts imported into the USA were found to containnonnative contaminants which were associated with anincrease in adverse events and numerous deaths [11, 12]. Inresponse to this crisis, the US Food and Drug Administra-tion (FDA) developed new analytical methods to identifyand quantify heparin contaminants [13–17]. Heparin lotscorrelated with adverse events were examined usingorthogonal high-resolution analytical techniques, includinghigh-field nuclear magnetic resonance (NMR) spectroscopy[10, 18–20]. After intense studies, oversulfated chondroitinsulfate (OSCS) was identified as a contaminant and as thelikely source of anaphylactic reactions in susceptiblepatients.

Due to its high sensitivity to even minor structuralvariations, 1H NMR spectroscopy represents an information-rich technique for characterizing the chemical compositionand providing characteristic fingerprints for heparin andother GAGs [9, 21–25]. As described in our previous reports[26–28], each spectrum of a collection of heparin samples

was preprocessed into a reduced set of discrete variableswhich served as input for clustering, classification, andquantitative prediction of the heparin samples using chemo-metric analysis. These studies, along with the present study,establish that the combination of 1D 1H NMR spectroscopyand chemometrics is extremely useful for the identificationof the presence of contaminants and impurities in heparinsamples and for the discrimination of contaminated orotherwise unacceptably impure heparin samples from USP-grade heparin samples.

Chemometrics has demonstrated its utility for purposesof quality control and safety assurance of a wide range ofmanufactured products, especially food, medicine, andconsumer-packaged goods [22, 29–33]. For pattern recog-nition, both “unsupervised” (clustering) and “supervised”(classification) techniques have been applied successfully[29, 34]. Unsupervised techniques explore the naturalstructure of the data without the requirement of informationabout class membership. The most common of thesemethods are principal components analysis and hierarchicalcluster analysis (HCA). By contrast, supervised techniquesdefine classification rules where the class membership ofeach sample in the training set is assigned prior toclassification. Examples of common classification methodsare partial least squares discriminant analysis (PLS-DA),linear discriminant analysis (LDA), and k-nearest neighbor(kNN). Selection of the most appropriate method dependson the specific nature of the data set being analyzed, suchas the number of classes, number of samples, number ofvariables, level of noise, and expected complexity requiredfor class separation. In typical cases that contain linearboundaries and a high ratio of samples to variables, manyalgorithms can achieve satisfactory results. In practice, theoptimal choice of algorithm is usually obtained by trial anderror.

In a previous study [27], we evaluated three classifica-tion methods, i.e., PLS-DA, LDA, and kNN, with respect totheir ability to discriminate among pure, impure, andcontaminated heparin samples based on analysis of their1H NMR spectral data. The performance of these models onexternal test sets, designated heparin, DS, and OSCS, was76–89% between heparin and DS samples and up to 100%between heparin and OSCS samples. In the present study,we extended the range of classification methods todetermine whether statistically more robust models wereattainable. Specifically, a relatively new machine learningalgorithm (i.e., support vector machine (SVM)) wascompared with two well-known pattern recognition meth-ods (i.e., classification and regression tree (CART) andartificial neural networks (ANNs)). CART derives simpleclassification rules from a reduced set of variables obtainedfrom the chemical shifts of heparin protons while ANNtrains the model to discern complex relationships between

940 Q. Zang et al.

input–output data that may be linear or nonlinear in nature[30]. SVM has already demonstrated superior performancein spectral classification studies and is particularly suitablein cases where there are more variables than samples in thedata sets [34].

The overall purpose of this study was to buildstatistically robust classification models useful for rapidscreening of new lots of bulk heparin APIs to distinguishUSP-grade heparin samples from those containing OSCScontaminant and unacceptable levels of DS impurity. Morebroadly, the chemometric methods implemented in thisstudy are intended for use as nonsubjective, statistics-basedtools for heparin quality control and purity assessment thatminimizes the need for expert analysts.

Materials and methods

HPLC analysis of heparin The weight percent of OSCScontent in heparin was measured by strong anion-exchangehigh-performance liquid chromatography (SAX-HPLC)method as described in previous works [13–16]. DS levelswere assessed by 1H NMR and SAX-HPLC as described inRef. [16]. The samples were further analyzed using HPLCwith a pulsed amperometric detector as described in theUSP monograph [35] to determine weight percent galac-tosamine (%Gal) content of the sample. This techniquemeasures total galactosamine content, regardless of theparticular source (e.g., DS, chondroitin sulfate A (CSA), orOSCS).

Proton NMR spectroscopy measurement All samples wereanalyzed using a Varian Inova 500 instrument at theWashington University (St. Louis, MO) Chemistry De-

partment NMR Facility operating at 499.893 MHz.Details on the NMR measurements of the heparinsamples can be found elsewhere [26]. Representative 1HNMR spectra of the three classes of heparin samples(heparin, DS, and OSCS) plotted in the range from 1.95 to6.00 ppm are shown in Fig. 1. The methyl protons of theN-acetyl methyl groups resonating at a chemical shift ofca. 2 ppm were well separated from the complex pattern ofoverlapping resonances from 3.0 to 6.0 ppm. Thespectrum of each contaminant or impurity spiked intoheparin revealed distinctive features, and their respectivesignal patterns were readily distinguished from oneanother in the 1.95–2.20 ppm region. A single peakappears at 2.05 ppm for the N-acetyl protons of heparin,for DS at 2.08 ppm, and for OSCS at 2.15 ppm.

Data processing More than 200 heparin sodium APIsamples obtained by the FDA for analysis in 2008–2009with various levels of OSCS and DS were analyzed by 1HNMR [16]. MestRe-C (version 5.3.0) was used to processthe 1H NMR spectral data. Phase and baseline correctionswere achieved through automated zero- and first-ordercorrection procedures. Each 1H NMR spectrum wasreduced and converted into a sequential array of 125regions of width 0.03 ppm spanning the interval from1.95 to 5.70 ppm, and peak integration of each spectralregion yielded 125 corresponding variables. During initialprocessing, heparin batches were found to containresidual processing solvents and reagents, including:methanol (at 3.35 ppm, singlet), ethanol (at 1.18, triplet,and at 3.66 ppm, quartet), and acetate (at 1.92 ppm,singlet) at varying levels [10]. In addition, each spectrumexhibited a residual water (HOD) resonance at 4.77 ppm.The spectral data at these frequencies was excluded from

3.23.43.63.84.04.24.44.65.15.35.55.75.9

f1 (ppm)

2.012.032.052.072.092.112.132.152.172.19

f1 (ppm)

Fig. 1 1H NMR spectra on authentic samples analyzed in 2008–2009of USP-grade heparin (green, 0.19% DS and 0% OSCS), heparincontaining high DS impurity levels (blue, 7.61% DS and 0% OSCS),

and heparin containing OSCS contaminant and high DS impuritylevels (brown, 5.60% DS and 17.20% OSCS)

Identification of heparin samples containing impurities 941

the analysis, yielding a final data set of 74 variables foreach spectrum. The area within the spectral regions wasintegrated, after which each of the 74 variables wasnormalized by the summed integral value to compensatefor differences in concentration among the heparinsamples. Prior to chemometric analysis, the spectra wereconverted into ASCII files where the data were repre-sented as a two-dimensional n×m array (n and m equal tothe number of samples and the number of variables,respectively), and the resulting data matrix was importedinto Microsoft Excel 2003. The data were preprocessed byautoscaling, also known as unit variance scaling (i.e., eachof the variables is mean-centered and then divided by itsstandard deviation).

Data sets Revisions proposed by the FDA to the stage 3heparin sodium USP monograph specify that the level ofgalactosamine in total hexosamine (%Gal) may not exceed1.0% (w/w). For this work, % (w/w) will be assumed toexpress heparin, DS, and OSCS content in samples.Acceptable heparin lots may not contain any detectableOSCS. DS is the primary chondroitin impurity observed inheparin APIs and, for the purpose of this study, the %Gal ispresumed to be the same as the %DS for samples notcontaining OSCS. For the classification studies, the heparinsamples were divided into three groups, viz., heparin, USP-grade heparin with DS≤1.0% and OSCS=0%; DS, impureheparin with DS>1.0% and OSCS=0%; and OSCS,contaminated heparin with OSCS>0% and with anycontent of DS. An additional fourth class (DS+OSCS)was included to characterize samples that contained DS>1.0%, OSCS>0%, or both. In these samples, the DScontent varied from 0% to 19% of the disaccharide mixture,and the OSCS content varied from 0% to 27%. The data setwas split into two subsets: a training set employed to buildthe model and a validation set employed to test thepredictive ability of the model. The data set of 178 heparinsamples was randomly split 2:1 into 118 samples fortraining (54 heparin, 33 DS, and 31 OSCS) and 60 samplesfor external validation and testing (28 heparin, 17 DS, and15 OSCS). Separate classification models were constructedfor the entire region (1.95–5.70 ppm) and two local regions(1.95–2.20 and 3.10–5.70 ppm), which correspond to 74, 9,and 65 variables, respectively.

A series of blends developed with contaminants otherthan DS or OSCS was used to challenge the classificationmodels. These blend samples were prepared by spiking“clean” heparin APIs with native impurities CSA, DS,heparan sulfate (HS), or synthetic contaminantsoversulfated-(OS)-CSA (i.e., OSCS), OS-DS, OS-HS, orOS-heparin at the 1.0%, 5.0%, and 10.0% weight percentlevels [15]. The detailed composition of the series of blendsis reported in the section of results and discussion.

Software All the data processing, multivariate analysis, andstatistical model building were implemented using the Rstatistical analysis software for Windows (Version 2.8.1)[36]. The packages rpart, nnet, e1071, and stats in R wereused for CART, ANN, SVM, and hierarchical clusteranalysis, respectively [34, 37]. R is a powerful, freesoftware environment for data analysis, statistical comput-ing, and graphical representation that provides a flexibletool accessible to users in academia and industry.

Results and discussion

Classification and regression tree CART is a nonparametricapproach that models a data set to a tree structure andmakes no assumption about the distribution of the data.This methodology applies decision trees to solve classifi-cation and regression problems for handling both categor-ical and continuous responses. A classification tree isproduced when the response variable is categorical whilethe final output is a regression tree when the responsevariable is continuous. In general, a CARTanalysis consistsof three steps [38–40]: in the first step, an over-large tree,called the maximal tree, is built by recursive partitioning ofthe original training data using a binary split procedure; inthe second step, the overgrown tree, which usually showsoverfitting, is pruned so that a series of less complex trees isderived; in the final step, the tree with the optimal size isselected by a cross-validation (CV) procedure.

The tree construction starts by dividing the root node,containing all objects in the training set, into exactly twosubgroups or child nodes, and then each child nodebecomes a parent node which is further split into twomutually exclusive child nodes. The splitting procedure isrepeated for each of the resulting nodes until the maximaltree is achieved. This is defined as the tree in which eachterminal node consists of either just one object, or containsa predefined number of objects, or all objects contained inthe node are as pure or homogeneous as possible, i.e., thesamples in a node share the same or similar values of theresponse variable. To find the most appropriate variable forsplitting and the best value of the variable to minimize theerror or to maximize the predictive power, CART scansthrough all possible split values over all explanatoryvariables. In the decision tree, the first branch is producedby the variable with the best split point, and each sequentialsplit is conducted by following some fit criteria or errormeasures with the purpose of minimizing the number ofmisclassifications. Among numerous splitting criteria thathave been proposed for choosing the best split point, theGini index represents a good balance between simplicityand interpretative power [37]. The Gini index is a statistical

942 Q. Zang et al.

measure of the frequency of one class relative to thefrequency of all other classes, and can be expressed as:

Gini ¼Xkj¼1

plj 1� plj� � ¼ Xk

j¼1

nljnl

1� nljnl

� �ð1Þ

where k denotes the number of possible classes; nl is thenumber of objects in node l, and nlj is the number of objectsfrom class j present in the node l. When the node is pure,i.e., contains only objects of the same group, the minimumGini index value is attained.

The tree built in the first step fits the training set almostperfectly but usually exhibits poor predictive ability fornew samples because the large number of terminal nodesproduces an overfitted model. Thus, it is necessary to findtrees with less complexity but better predictive accuracy. Insubsequent steps, the optimal tree size can be determinedby successively pruning the terminal branches of themaximal tree. During this pruning procedure, a series ofsmaller subtrees (T) is derived from the maximal tree, andthe optimal tree with the minimum classification error isobtained by calculating values of the cost-complexityparameter (CPα(T)), which is defined as a linear combina-tion of the tree cost (Ql(T)) and tree complexity (|T|) [34]:

Minimize : CPaðTÞ ¼XTj j

l¼1

nlQlðTÞ þ a Tj j ð2Þ

where |T| denotes the size of a tree or the number ofterminal nodes, and α is an adjustable tuning parameterbetween 0 and 1 that establishes the penalty for eachadditional terminal node and establishes the best compro-mise between classification error and tree size. For eachvalue of α, the optimal tree size is selected by minimizingCPα(T). By gradually increasing the value of α startingfrom 0 corresponding to the maximal tree, a nestedsequence of trees with decreasing size or complexity isthen derived. The last step involves selection of the optimaltree by generating and selecting a sequence of subtreeswhich are compared by evaluation of the cross-validatedprediction error.

In this study, classification trees were built using threeseparate regions of each 1H NMR spectrum (i.e., 1.95–2.20,3.10–5.70, and 1.95–5.70 ppm) corresponding to 9, 65, and74 input variables. In turn, the four designated classes(heparin, DS, OSCS, and (DS+OSCS)) corresponded to theresponse or output variables. The trees were grown andpruned using the Gini index as a splitting criterion. Theoptimal tree size was determined using 10-fold CV. Theclassification tree with three nodes for the heparin versusDS versus OSCS model in the 1.95–2.20 ppm region isshown in Fig. 2a. The values of the two splitting variables,2.08 ppm and 2.15 ppm, correspond respectively to the

characteristic chemical shifts of DS and OSCS. The firstsplit at 2.15 ppm divides the samples into the two groups(heparin+DS) and OSCS; the second split point at2.08 ppm divides the (heparin+DS) group into the classesheparin and DS. A plot of the 10-fold CV relative errorversus the CP and the tree size is shown in Fig. 2b. Eachterminal node represents the majority of the samples in aspecified class. The OSCS terminal node is called a purenode in that it contains only samples of the OSCS class,i.e., all of the 31 OSCS samples are correctly classifiedand no heparin or DS samples are located in this terminal. The(heparin+DS) group was split into the DS and heparin classessolely by the chemical shift 2.08 ppm. Both of these terminalnodes contain misclassifications. The DS node contains twoheparin samples while the heparin node contains six DSsamples. The classification rates, summarized in Table 1, were93.2% (110/118) for the training set (eight misclassifications)and 90.0% (54/60) for the test set (six misclassifications).

When modeling the data set for the 3.10–5.70 ppmregion, the resulting classification tree consisted of fiveterminal nodes (Fig. 2c). The split variables were 3.53,3.95, 4.48, and 5.67 ppm. Variable 4.48 ppm split off theOSCS class from the heparin and DS classes, and thenvariable 3.53, 3.95, and 5.67 ppm sequentially divided thesamples on the left-hand side into two separate classes:heparin and DS. A plot of the relative error (RE) versus theCP and tree size is displayed in Fig. 2d. The RE decreasesas the number of terminal nodes increases, having its lowestvalue for a tree with five terminal nodes. Based on thelowest cost-complexity measure, the optimal tree size=5nodes. To select a simpler tree than the one with theminimum CVerror, the rule of one standard deviation error(1-SE) was applied, by which the optimal tree is selected asthe simplest one among those that have a CVerror within(1-SE) of the minimal CVerror. Although the simpler tree size=4 (CP=0.058) was slightly less accurate than tree size=5 for thetraining set (86.4% vs 88.1%), the former tree yielded a betterprediction rate for the test set (85.0% vs 80.0%) (Table 1).Consequently, the pruned tree size=4 is more appropriate forprediction purposes. It should be noted that both results arepoorer than those obtained for the 1.95–2.20 ppm region.

With respect to heparin versus DS, the correspondingmodel has two terminal nodes by splitting the data using2.08 ppm for both the 1.95–2.20 ppm and 1.95–5.70 ppmregions. Success rates of 90.8% (79/87) and 88.9% (40/45)were achieved for the training and test sets, respectively.For the 3.10–5.70 ppm region, chemical shifts 3.53 and3.86 ppm were selected to divide the data, leading to asuccess rate of 83.9% (73/87) for the training set and 80.0%(36/45) for the test set. These trees have no pure nodes,meaning that perfect discrimination between heparin andDS was not achieved by CART. For the heparin versusOSCS model, the classification tree contained two terminal

Identification of heparin samples containing impurities 943

nodes when 2.15 ppm was used to split the data in the1.95–2.20 and 1.95–5.70 ppm regions. Both heparin andOSCS samples were classified into pure nodes in theclassification tree, giving perfect separation of the twogroups (100% discrimination). In contrast, the classificationrates for the 3.10–5.70 ppm region were 97.6% (83/85) forthe training set and 97.7% (42/43) for the test set by

selecting 4.48 ppm as a splitting variable. For heparinversus (DS+OSCS), a model with complexity or tree size=3 was built using splitting variables 2.08 and 2.15 ppm.This tree is equivalent to that for the heparin versus DSversus OSCS model using either the 1.95–2.20 ppm regionor 1.95–5.70 ppm region. The classification rates of thismodel were 91.5% (108/118) for the training set and 90.0%

Fig. 2 Classification trees and corresponding plots of the 10-foldcross-validated relative error versus the complexity parameter (bottomaxis) and tree size (top axis) for the heparin versus DS versus OSCS

model. (a, b) for the 1.95–2.20 ppm region; (c, d) for the 3.10–5.70 ppm region. The vertical bar for each point in (b) and (d)represents the standard error

944 Q. Zang et al.

(54/60) for the test set (Table 1). Using the 3.10–5.70 ppmregion, a classification tree with five terminal nodes wasobtained for the discrimination of heparin from (DS+OSCS) by selecting the four splitting variables 3.53, 3.95,4.48, and 5.67 ppm, resulting in a tree resembling that ofheparin versus DS versus OSCS, and the test set of 60samples was predicted with 83.3% (50/60) accuracy.

The above results reveal that the performance of theclassification trees improves considerably when built usingthe 1.95–2.20 or 1.95–5.70 ppm regions rather than the3.10–5.70 ppm region. In addition, the performance of theclassification trees is identical whether the entire 1.95–5.70 ppm region or only the local 1.95–2.20 ppm regionwas used for discrimination. Although the 1.95–5.70 ppmregion contains more variables (74) and many more details interms of chemical shifts, the CART model selected only 2.08and 2.15 ppm as the splitting variables and ignored the 3.10–5.70 ppm region entirely. This observation highlights thesingular importance played by the N-acetyl methyl protonchemical shifts (1.95–2.20 ppm) in discriminating heparinfrom its impurities and contaminants in the CART model.

Artificial neural network An ANN is a modeling tool usedfor solving problems such as classification, pattern recog-nition, regression and estimation [30, 31, 41–44]. ANN isparticularly suitable when the mathematical relationshipbetween the independent (input) and response (output)variables cannot be established. The typical feed-forwardback-propagation ANN is composed of a large number offully interconnected processing elements or neurons whichare organized into a sequence of layers. The first layer is theinput layer which contains as many neurons as the numberof independent variables and is used to receive the input

data. The last layer is the output layer which consists of thesame number of neurons as the number of dependentvariables and serves to provide the response of the ANNmodel to the input data. One or more hidden layers aretypically incorporated between the input and output layersthat are responsible for communicating with the neurons ofthe input and output layers. Of the various learningalgorithms available for training an ANN, the most widelyused approach for multilayer networks is the single hiddenlayer network with an appropriate number of neurons. ThisANN architecture can model virtually any linear ornonlinear relationship with any degree of accuracy. In afeed-forward ANN, signals are propagated sequentiallyonly in the forward direction, i.e., from the input layerthrough the hidden layer(s) to the output layer, where theoutput from a previous layer is employed as an input for thesuccessive layer.

The propagation of the signal through the network fromone neuron in a layer to another neuron in the next layergreatly depends on the strength of the connection. Theseinterconnections between neurons are represented by a setof adjustable parameters called weights that are calculatedby the ANN algorithm, which trains the neural network andmodifies the weights to an optimum set of values. Theback-propagation approach is a popular learning strategythat adjusts the weights in a layer to minimize the errorsbetween the network result and the expected result (i.e.,known class affiliation) in the training set. The errors arefed backwards through the network to adjust the weights.This process is repeated until the interconnections areoptimized to minimize the error, to achieve a specified levelof accuracy, or when a predefined number of iterations arereached.

Model Region(ppm)

Nodes Selected variables(ppm)

Training (%) Test (%)

Heparin versus DS 1.95–5.70 2 2.08 90.8 (79/87) 88.9 (40/45)

1.95–2.20 2 2.08 90.8 (79/87) 88.9 (40/45)

3.10–5.70 3 3.53, 3.86 83.9 (73/87) 80.0 (36/45)

Heparin versus OSCS 1.95–5.70 2 2.15 100 (85/85) 100 (43/43)

1.95–2.20 2 2.15 100 (85/85) 100 (43/43)

3.10–5.70 2 4.48 97.6 (83/85) 97.7 (42/43)

Heparin versus(DS+OSCS)

1.95–5.70 3 2.08, 2.15 91.5 (108/118) 90.0 (54/60)

1.95–2.20 3 2.08, 2.15 91.5 (108/118) 90.0 (54/60)

3.10–5.70 5 3.53, 3.95, 4.48, 5.67 89.8 (106/118) 78.3 (47/60)

3.10–5.70 4 3.53, 3.95, 4.48 88.1 (104/118) 83.3 (50/60)

Heparin versus DSversus OSCS

1.95–5.70 3 2.08, 2.15 93.2 (110/118) 90.0 (54/60)

1.95–2.20 3 2.08, 2.15 93.2 (110/118) 90.0 (54/60)

3.10–5.70 5 3.53, 3.95, 4.48, 5.67 88.1 (104/118) 80.0 (48/60)

3.10–5.70 4 3.53, 3.95, 4.48 86.4 (102/118) 85.0 (51/60)

Table 1 Model parametersand classification rates forCART

Identification of heparin samples containing impurities 945

The relationship between the input variable xi and theoutput variable y is defined by the following equation [41]:

y ¼ fX

jwjf

Xiwijxi þ bi

� �þ bj

h ið3Þ

where wij and wj represent the connection weights fromthe input layer to the hidden layer and from the hiddenlayer to the output layer, respectively, and bi and bj arebias constants. The transfer function f(x), which can belinear or nonlinear depending on the topology of thenetwork, determines the processing inside the neuron. Thelogistic sigmoid activation function is a widely used transferfunction:

f ðxÞ ¼ 1

1þ e�xð4Þ

In the present study, a three-layer feed-forward networktrained with a back-propagation algorithm was investigatedto build classification models for class identification anddiscrimination. ANN was performed where the input layercontained the same number of neurons as chemical shiftvariables in the data set, viz., nine for the 1.95–2.20 ppmregion, 65 for the 3.10–5.70 ppm region, and 74 for theentire 1.95–5.70 ppm region. The output layer containedfour nodes, corresponding to the four classes of heparin,DS, OSCS, and (DS+OSCS). The number of neurons in thehidden layer was varied to assess its influence on networkperformance. ANNs having too few hidden neurons canproduce unstable models while having too many hiddenneurons can cause overfitted models with poor predictiveability on test sets. The sigmoid transfer function wasemployed for activation of both the hidden and outputlayers.

The output from the ANN is a prediction of the classmembership of the samples in each class, consisting of amatrix Ŷ with the same dimensions as the dependentvariable Y that contains the binary values of 1 or 0 foreach class and comprises as many columns as there areclasses. The numeric value of element ŷij in Ŷ lies between0 and 1, which can be regarded as an estimate of theprobability for assigning the ith sample to the jth class. Inpractice, the test sample was ascribed to the modeled classfor which the output value was 0.7 or above. This criterionensured that the sum of the other output nodes not selectedwas 0.3 or lower.

A commonly used error function for ANNs is the crossentropy or deviance defined in Eq. 5 [34]:

Minimize : �Xni¼1

Xkj¼1

byij logbyij ð5Þ

Since ANN is very sensitive to overfitting, a regulariza-tion term, called weight decay, is introduced. The modified

criterion is given by Eq. 6:

Minimize : �Xni¼1

Xkj¼1

byij logbyij þ lX

parametersð Þ2 ð6Þ

where “parameters” represent the values of all parametersthat are used in the ANN training. The second term of Eq. 6accounts for the magnitude of these parameters, and thevalue of the adjustable parameter 1, which can vary from 0to 1, controls their relative contribution. When 1=0 (i.e.,zero weight decay) or is small, the boundary or edgebetween classes is rough or nonsmooth, leading to over-fitting of the model and poor predictive ability. As the valueof 1 increases, the boundary between classes adopts asmoother profile.

The number of hidden neurons and the value of 1 wereoptimized by cross validation. The dependence of themisclassification rate for variable values of 1 and thenumber of hidden neurons for heparin versus DS versusOSCS in the 1.95–5.70 ppm range are shown in Fig. 3 forthe training set, test set and 10-fold CV process. ANNs withhidden neurons ranging from three to 30 were developedwith the weight decay 1=0.1. The predicted results, plottedas a function of the size of hidden layer in Fig. 3a, showthat nine neurons in the hidden layer are optimal. Thedependence of the error rate on the weight decay 1 whenthe number of hidden neurons is set at nine is depicted inFig. 3b.

The results of the ANN analysis, together with theoptimal values of these parameters, are presented in Table 2.For heparin versus DS versus OSCS, with the optimalsettings of 1=0.075 and hidden neurons=6, the classifica-tion rates of the ANN model were 96.6% (114/118) for thetraining set and 91.7% (55/60) for the test set using the1.95–2.20 ppm region. The corresponding classificationrates for the training and test sets were 95.8% (113/118) and88.3% (53/60) for the 1.95–5.70 ppm region and, similarly,93.2% (110/118) and 86.7% (52/60) for the 3.10–5.70 ppmregion. For heparin versus OSCS, the ANN modelclassified all members of the training and tests setscorrectly with 100% prediction accuracy. The classifica-tion rates for the heparin versus DS model for the threeregions are very close with 95.4–97.7% for the trainingset and 84.4–88.9% for the test set. For the heparinversus (DS+OSCS) model, the classification rates of thevarious networks were quite similar at 90.0–91.7% forthe three regions (Table 2). In general, the performance ofthe ANN models was slightly better for those built fromthe 1.95–2.20 ppm region than from either the 3.10–5.70 ppmor 1.95–5.70 ppm regions.

Support vector machine SVM is a recently developedmodeling technique that has demonstrated its utility for a

946 Q. Zang et al.

broad range of classification and regression problems [45–48]. SVM performs pattern recognition by finding anoptimal hyperplane as the decision boundary for separatingtwo classes of patterns, which can maximize the marginbetween the closest data points of each class. The SVMalgorithm derives the classification rule using only afraction of the training samples, known as support vectors(SVs), that are typically situated nearby the margin borders.In general, the number of SVs is much lower than thenumber of training samples. For the linear case, the classboundary is determined in the space of the originalvariables by defining an optimal hyperplane which divides

the data space into two regions with opposite sign andmaximizes the margin between them [45, 46]:

wTxþ b ¼ 0 ð7Þ

where w is a weight vector normal to the hyperplane, b is afree threshold parameter, b/||w|| is the perpendicular distanceto the origin, and ||w|| is the Euclidean norm (i.e., unsignedscalar value) of w.

In nonlinear cases, the complex class boundaries aremodeled by using adequate kernel functions that map theoriginal vectors from input space to higher dimensional

Fig. 3 Misclassification error rate from ANN for the heparin versus DS versus OSCS model for the data set in the 1.95–5.70 ppm range; (a) withvariable number of hidden neurons; weight decay set at λ=0.1; (b) with variable values of weight decay λ; number of hidden neurons set at 9

Model Region(ppm)

Number ofhidden neurons

Weightdecay (1)

Training (%) Test (%)

Heparin versus DS 1.95–5.70 9 5.0×10−1 95.4 (83/87) 86.7 (39/45)

1.95–2.20 6 5.0×10−2 97.7 (85/87) 88.9 (40/45)

3.10–5.70 9 3.0×10−1 96.6 (84/87) 84.4 (38/45)

Heparin versus OSCS 1.95–5.70 9 1.0×10−1 100 (85/85) 100 (43/43)

1.95–2.20 6 2.0×10−2 100 (85/85) 100 (43/43)

3.10–5.70 9 1.0×10−1 100 (85/85) 100 (43/43)

Heparin versus(DS+OSCS)

1.95–5.70 9 2.5×10−1 94.9 (112/118) 91.7 (55/60)

1.95–2.20 6 3.0×10−2 99.2 (117/118) 91.7 (55/60)

3.10–5.70 9 2.0×10−1 99.2 (117/118) 90.0 (54/60)

Heparin versus DSversus OSCS

1.95–5.70 9 1.0×10−1 95.8 (113/118) 88.3 (53/60)

1.95–2.20 6 7.5×10−2 96.6 (114/118) 91.7 (55/60)

3.10–5.70 9 8.0×10−1 93.2 (110/118) 86.7 (52/60)

Table 2 Model parameters andclassification rates for ANN

Identification of heparin samples containing impurities 947

feature space where the nonlinear relationship is expressedin linear form and a linear separation operation can beperformed. In the presence of noisy data, the resultingmodel may fit the noise and force zero training error thusleading to model overfitting and poor prediction ability. Toallow violation of the margin constraints of the hyperplane,a set of nonnegative error variables ξi>0 (i=1, … , n) areintroduced, where ξi is the distance of sample xi from themargin of the corresponding class. Given the sum of theallowed errors ∑ξi, the optimization requires simultaneous-ly maximizing the margin 1/2||w||2 and minimizing thenumber of errors or misclassifications. Accordingly, theobjective function that is designed to balance the classifi-cation error with model complexity can be expressed asfollows [47]:

1

2wk k2 þ C

Xni¼1

xi ð8Þ

The immediate goal is to determine a soft margin for thehyperplane that minimizes the dual form of the aboveexpression, where the regularization parameter C controlsthe trade-off between the first term embodying modelcomplexity and ∑ξi in the second term tallying the numberof allowed misclassifications in the training set. If C is toosmall, large training errors are permitted which can lead tounstable or underfitted SVM models. If C is too large, smalltraining errors are imposed which can lead to over-complexand overfitted models with poor predictive ability.

The results of the SVM approach depend highly on thechoice of the kernel function, which decides the sampledistribution in the mapping space and may influence theperformance of the final model. The four kernel functionscommonly used in SVM include the linear, polynomial,sigmoid, and radial basis function (RBF). The RBF, orGaussian function, is formulated as [48]:

K xi; xj� � ¼ exp �g xi � xj

�� ��2� �ð9Þ

where xi and xj are two independent variables; γ is a tuningparameter that controls the amplitude of the kernel functionand, therefore, controls the generalization performance ofthe SVM. A very large γ value can produce overfittedmodels because most of the training samples are used as thesupport vectors while a very small γ value can lead to poorpredictive ability as all data points are regarded as oneobject.

Using the same training and test sets as for CART andANN, the SVM algorithm with the nonlinear soft marginwas employed to build classification models. Using theRBF kernel, the optimization requires the specification oftwo parameters, viz., the amplitude of the kernel function γ,and the regularization parameter C. Their combination

determines the boundary complexity and, thus, greatlyinfluences the classification performance or predictionability of the model. CV is widely used to determine theparameters for evaluating the performance of the model andminimizing the risk of overfitting. The parameters C and γare optimized by the user, and the optimal values areobtained by performing an exhaustive grid search with 10-fold CVon the training set using their various combinations.The set of C and γ values giving the highest percentageaccuracy or the lowest error rate is selected for furtheranalysis. In this study, a wide range of γ and C values weretuned simultaneously in a 9×9 grid of 81 possiblecombinations for C from 1 to 108 and γ from 10−8 to 1.After all the combinations had been searched, a contourplot was created in decimal logarithmic scales, indicatingthe prediction accuracy or classification error. The optimi-zation grids, plotted as the CV classification rate for themodels heparin versus DS versus OSCS and heparin versusOSCS, are presented in Fig. 4. The two coarse grid plotsof γ and C values delineate regions that locate the optimalparameter settings. The two deep red “islands” in Fig. 4acorrespond to combination of the γ and C values thatproduce the lowest prediction error for the heparin versusDS versus OSCS model. The size and bimodal character inthis case reflects the difficulty encountered sometimes intuning the γ and C values to achieve optimal discrimination.In the case of heparin versus OSCS, the optimal setting of γand C is contained in a single red band (Fig. 4b), indicatingthat parameter optimization here is relatively straightforward.To increase resolution, this range of γ and C values wasfurther explored over a finer grid to achieve the final SVMmodel. For heparin versus DS versus OSCS, the SVM modelwith optimum values C=6.0×104 and γ=1.0×10−3 for the1.95–5.70 ppm region gave the best classification perfor-mance. For heparin versus OSCS, the optimal parametersettings C=1.0×103 and γ=1.0×10−4 led to perfect (100%)discrimination.

Using the optimal paired values of γ and C, the resultsfrom SVM are summarized in Table 3. The predictionaccuracy was >90% in all cases considered for both thetraining and test sets. A large proportion of the sampleswere classified correctly, with few (≤3–5) misclassifica-tions. Notably, SVM achieved nearly identical results forthe 1.95–2.20 ppm and 3.10–5.70 ppm regions, highlight-ing its ability to differentiate even subtle differences in theheparin, DS, and OSCS spectra. This exceptional perfor-mance of the SVM model is appreciated by visualinspection of the heparin, DS, and OSCS spectra (Fig. 1),where distinctions are clearly discernible in the 1.95–2.20 ppm region but not in the 3.10–5.70 ppm region.

Analysis of misclassifications As shown in Tables 1, 2, and3, the predictive abilities of the classification models built

948 Q. Zang et al.

from CART, ANN and SVM were outstanding in differen-tiating heparin from DS and OSCS with few errors. Allthree pattern recognition methods were able to discriminatebetween heparin and OSCS with classification rates of100% under optimal conditions. As can be seen by crosscomparison of Tables 1, 2, and 3, however, the modelgenerated from SVM consistently outperformed ANN,which in turn marginally outperformed CART using thesame input variables. When the entire chemical shift regionwas divided into two subsets (1.95–2.20 and 3.10–5.70 ppm), better results were achieved for the former thanthe latter region. The sole exception was SVM, whichachieved nearly identical results from both regions. SVM

performed better in every aspect, as can be appreciated bycomparing the misclassification rates in Tables 1, 2, and 3.Taking the heparin versus DS versus OSCS model for the3.10–5.70 ppm region as an example, the success rates ofthe training and test sets were appreciably higher for SVM(98.3% and 95.0%) than for CART (86.4% and 85.0%) andANN (93.2% and 86.7%).

The results of the classification matrices evaluated forboth training and test sets in the 1.95–5.70 ppm region aresummarized in Tables 4, 5, and 6. All of the misclassifiedsamples were contained in heparin and DS: several samplesbelonging to heparin were predicted as DS, and vice versa.Using SVM, two misclassifications were observed for the

Fig. 4 Contour plots in decimal logarithmic scales obtained from 9×9 grid search of the optimal values of γ and C for the SVM model. (a) Heparinversus DS versus OSCS for the 1.95–5.70 ppm region; (b) Heparin versus OSCS for the 1.95–5.70 ppm region

Model Region(ppm)

C γ Training (%) Test (%)

Heparin versus DS 1.95–5.70 2.0×103 1.0×10−4 97.7 (85/87) 91.1 (41/45)

1.95–2.20 1.0×104 1.0×10−3 96.6 (84/87) 93.3 (42/45)

3.10–5.70 1.8×104 1.0×10−4 97.7 (85/87) 93.3 (42/45)

Heparin versus OSCS 1.95–5.70 1.0×103 1.0×10−4 100 (85/85) 100 (43/43)

1.95–2.20 1.0×103 1.0×10−4 100 (85/85) 100 (43/43)

3.10–5.70 1.0×103 1.0×10−4 100 (85/85) 100 (43/43)

Heparin versus (DS+OSCS) 1.95–5.70 8.0×104 1.0×10−5 98.3 (116/118) 95.0 (57/60)

1.95–2.20 1.0×107 2.0×10−4 97.5 (115/118) 95.0 (57/60)

3.10–5.70 1.0×105 1.8×10−5 98.3 (116/118) 95.0 (57/60)

Heparin versus DS versus OSCS 1.95–5.70 6.0×104 1.0×10−3 97.5 (115/118) 95.0 (57/60)

1.95–2.20 2.0×105 1.0×10−3 99.2 (117/118) 95.0 (57/60)

3.10–5.70 1.5×105 1.0×10−5 98.3 (116/118) 95.0 (57/60)

Table 3 Model parameters andclassification rates for SVM

Identification of heparin samples containing impurities 949

heparin versus DS model in the training set, and only oneheparin sample and three DS samples were misclassified inthe test set (Table 4). Misclassification of heparin as DSoccurred only once, and DS as heparin twice, for theheparin versus (DS+OSCS) model (Table 5). The sameresult occurred for the threefold heparin versus DS versusOSCS model, where SVM produced a total of only threemisclassifications (Table 6).

When examining the misclassified samples it was notedthat, in most cases, these misclassifications occurred when theDS content of the sample ranged from 0.90% to 1.20%, i.e.,they straddled the DS=1.0% impurity borderline defining theheparin and DS classes. These cases are difficult to distinguishfrom each other due to the similarity in their 1H NMR spectralpatterns. When these borderline samples were removed fromthe data set, the overall performance of the CART, ANN, andSVM models improved considerably with very few mis-

classifications. This was especially the case for SVM, whereonly one sample was misclassified in the test set and none inthe training set (Tables 4, 5, and 6).

Classification analysis of heparin samples spiked withother GAGs Heparin APIs may contain GAG impuritiesother than DS, such as CSA, HS, and other possible syntheticoversulfated contaminants that can mimic the functions ofheparin. To assess the capability of the classificationmodels todiscriminate and detect a wide range of potential GAG-likeimpurities and contaminants previously unseen in the heparinsamples, a series of blends was prepared by spiking heparinAPIs with native impurities CSA, DS, and HS, as well as theirpartially oversulfated (PS)- or fully OS versions OS-CSA (i.e.,PS-CSA or OSCS, respectively), OS-DS, OS-HS, and OS-heparin at the 1.0%, 5.0% and 10.0% (w/w) levels [15]. Theseblend samples were then analyzed to assign them to one of

All samples After removing borderline samples

Training set Test set Training set Test set

Heparin DS Heparin DS Heparin DS Heparin DS

CART

Heparin 52 6 25 2 48 3 23 0

DS 2 27 3 15 2 23 2 13

ANN

Heparin 52 2 27 5 50 0 25 2

DS 2 31 1 12 0 26 0 11

SVM

Heparin 53 1 27 3 50 0 25 1

DS 1 32 1 14 0 26 0 12

Table 4 Classification matricesfor the heparin versus DS modelin the 1.95–5.70 ppm region

Table 5 Classification matrices for the heparin versus (DS+OSCS) model in the 1.95–5.70 ppm region

All samples After removing borderline samples

Training set Test set Training set Test set

Heparin (DS+OSCS) Heparin (DS+OSCS) Heparin (DS+OSCS) Heparin (DS+OSCS)

CART

Heparin 49 5 24 2 46 3 23 0

(DS+OSCS) 5 59 4 30 4 54 2 28

ANN

Heparin 52 4 27 4 50 0 24 2

(DS+OSCS) 2 60 1 28 0 57 1 26

SVM

Heparin 52 1 27 2 50 0 25 1

(DS+OSCS) 2 63 1 30 0 57 0 27

950 Q. Zang et al.

the three classes: heparin, DS, or OSCS. These adulteratedsamples (“blend samples”) are highly diverse in compositionwhen compared with the clearly defined heparin, DS andOSCS classes, since they contain multiple components withvarying degrees of sulfation and concentration from 1% to10% as shown in Table 7.

For exploratory purposes, agglomerative HCA wasperformed on the 30 blend samples. As an unsupervisedtechnique, HCA describes the nearness between objects,identifies specific differences, and discovers natural group-ings of the data set without knowledge of class affiliation.Visually, HCA displays the relationships between objects inthe form of a dendrogram [34, 39]. The procedure starts bysetting each object in its own cluster, and then two objectsclosest together are joined, followed by the next step inwhich either a third object joins the just formed cluster, ortwo clusters join together into a new cluster. Each stepyields clusters with a number less than the previous step.The iterative procedure is repeated until all objects aremerged into a single cluster. HCAwas implemented usingthe Euclidean distance for measuring the similarity amongblend samples with average linkage for merging theclusters. Figure 5 depicts the hierarchical clustering of theblend samples in the 1.95–5.70 ppm region. This dendro-gram displays two distinct clusters which were formedaccording to the content of GAGs. The cluster on the leftincluded samples with low content of GAGs (1%), whilethe cluster on the right comprised two subclusters with highcontent of GAGs (i.e., 5% and 10%). One of thesesubclusters contains the native GAGs, i.e., CSA (B1 andB2), DS (B4 and B5), and HS (B7 and B8); the othersubcluster contains oversulfated GAGs where the samples

with the same GAG composition lay close to each other andclustered in pairs.

The test results obtained in the identification of the blendsamples using the resulting models from CART, ANN, andSVM are summarized in Table 7. Unlike class modelingwhere a blend sample can be assigned to a single class, tomore than one class, or to none of the specified classes [28],for pure classification, the training samples are partitionedinto the data space where there are as many regions as thenumber of classes, and the classification rule constructs aborder separating these classes. A test sample can be onlyassigned to a specific region or class to which it mostprobably belongs. Blend samples B28-30 (blank or controlsamples), B4-6 (DS), and B10-12 (OS-CSA) correspond tothe classes heparin, DS and OSCS, respectively. Asexpected, all of them were correctly classified to theirrespective classes. None of the remaining blends belong toany one of the designated classes, but they must be assignedto a class. Some blends containing low levels (1%) of GAGswere assigned to heparin, most of those with nativeimpurities (CSA and HS) were assigned as DS, and blendswith oversulfated synthetic compounds were assigned toOSCS except those with low GAGs content (1%). Overall,the models were highly successful in distinguishing betweenUSP-grade heparin samples and unacceptable samples.

Conclusions

To develop robust and highly predictive classificationmodels for rapid screening of heparin samples with varying

Table 6 Classification matrices for the heparin versus DS versus OSCS model in the 1.95–5.70 ppm region

All samples After removing borderline samples

Training set Test set Training set Test set

Heparin DS OSCS Heparin DS OSCS Heparin DS OSCS Heparin DS OSCS

CART

Heparin 52 6 0 25 2 0 48 3 0 23 1 0

DS 2 27 0 3 14 0 2 23 0 2 12 0

OSCS 0 0 31 0 1 15 0 0 31 0 0 15

ANN

Heparin 52 3 0 25 5 0 50 0 0 25 2 0

DS 2 30 0 3 12 0 0 26 0 0 11 0

OSCS 0 0 31 0 0 15 0 0 31 0 0 15

SVM

Heparin 53 0 0 27 2 0 50 1 0 25 1 0

DS 1 33 0 1 15 0 0 25 0 0 12 0

OSCS 0 0 31 0 0 15 0 0 31 0 0 15

Identification of heparin samples containing impurities 951

amounts of DS impurity and OSCS contaminant, threechemometric approaches, i.e., CART, ANN, and SVM,were assessed. In combination with 1H NMR spectroscopy,the classification performance of ANN, CART, and SVMwas compared using three data sets based on differentchemical shift regions (1.95–2.20, 3.10–5.70, and 1.95–5.70 ppm). The results show that these pattern recognitionapproaches are useful tools for the generation of classifica-tion models with outstanding performance attributes. Thedegree of success depended on the specific chemometricprocedures as well as the particular data sets.

CART is a simple but powerful technique for classdiscrimination. This method is able to select the mostrelevant explanatory variables from the data set and deriveclassification rules on the basis of the reduced set ofvariables, so the tree-structured models are easy to interpretand understand. For heparin and its derivatives, the

characteristic N-acetyl methyl proton chemical shifts arelocated in the 1.95–2.20 ppm region. Specifically 2.08 and2.15 ppm, the characteristic chemical shifts of DS andOSCS, respectively, were found to possess the greatestdiscriminating power for heparin versus DS and heparinversus OSCS, respectively. After excluding the N-acetylregion, we observed that the classification and predictionrates in the local region 3.10–5.70 ppm were evidently poordue to the lack of distinguishable characteristic peaks,implying that the 2.0–2.2 ppm subregion plays an importantrole in discriminating heparin from its impurities andcontaminants in the classification tree. Therefore, thevariables or chemical shifts selected in the CART analysiswere interpretable and the resulting trees were physicallyreasonable.

As a widely accepted computational modeling andpattern learning approach, ANN is able to model input–

ID GAGs Content (%) SVM CART ANN

Classified as Heparin (H), DS (D) or OSCS (O)

B1 CSA 10 D D D

B2 CSA 5 D D D

B3 CSA 1 D D D

B4 DS 10 D D D

B5 DS 5 D D D

B6 DS 1 D D D

B7 HS 10 D D D

B8 HS 5 D D D

B9 HS 1 H H H

B10 FS-CSA 10 O O O

B11 FS-CSA 5 O O O

B12 FS-CSA 1 O D D

B13 FS-DS 10 O O O

B14 FS-DS 5 O O O

B15 FS-DS 1 D D D

B16 OS-HS 10 O O O

B17 OS-HS 5 O O O

B18 OS-HS 1 H H H

B19 OS-Hep 10 O O O

B20 OS-Hep 5 O O O

B21 OS-Hep 1 H H H

B22 PS-CSA#1 10 O O O

B23 PS-CSA#1 5 O O D

B24 PS-CSA#1 1 D H H

B25 PS-CSA#2 10 O O O

B26 PS-CSA#2 5 O O D

B27 PS-CSA#2 1 D H H

B28 Blank – H H H

B29 Blank – H H H

B30 Blank – H H H

Table 7 Compositions of theseries of blends of heparinspiked with other GAGs and testresults for classification fromSVM, CART, and ANN in the1.95–5.70 ppm region

CSA chondroitin sulfate A, DSdermatan sulfate, HS heparansulfate, FS fully sulfated, OSoversulfated, PS partiallysulfated, Blank control (pureheparin sample). The weightpercent sulfur content forPS-CSA#1 and PS-CSA#2 is11.01% and 11.14%,respectively

952 Q. Zang et al.

output data with highly complex relationships that arelinear or nonlinear in nature. Despite its popularity andutility, ANNs are prone to model overfitting and poorpredictive ability due to the large number of adjustableparameters to be optimized. By introducing the notion ofweight decay in our study, the risk of model overfitting wasminimized. While the predictive performance of ANNmodels on the test set is comparable to that of CARTmodels for the 1.95–2.20 ppm region, ANN was slightlysuperior to CART in the 3.10–5.70 ppm region.

Although still a relatively new machine learning method,SVM has attracted considerable attention and has demon-strated utility in a broad range of statistical learningproblems. SVM can model complex nonlinear boundariesby using adapted kernel functions. The problem of over-fitting can be effectively solved and remarkable generaliza-tion performance can be achieved due to the high mappingpower of the kernel, resulting in a more highly predictivemodel. SVM can deal with high-dimensional data withrelatively few samples in the training set and, as aconsequence, no prior step of variable reduction is requiredas with many other methods [27]. Model learning with theSVM algorithm requires optimization of the kernel param-eter γ and the regularization parameter C. Parameter tuningis a critical step, and the optimal values are typicallyacquired by an exhaustive searching procedure. In thisstudy, it was quite easy to tune the parameters for heparinversus OSCS. By contrast, discrimination of heparin andDS was more difficult due to the similarity of samples nearthe 1.0% DS borderline between the two classes. SVMoutperformed CART and ANN, and gave the best classifi-

cation results in all cases. In addition, the predictive ratesby SVM for both the 1.95–2.20 and 3.10–5.70 ppm regionswere nearly identical, indicating that even minor structuraldifferences between heparin and DS can be discerned andproduce remarkable discrimination.

The validated heparin versus DS versus OSCS modelwas challenged by the blend samples for classification inwhich the heparin APIs were spiked with native orpartially/fully oversulfated CSA, DS, and HS at the 1.0%,5.0%, or 10.0% (w/w) levels. Overall, the results obtainedfrom classification assignment of the blends were excellenteven though the three chemometric approaches are not classmodeling techniques [28], which means that any object,even a clear outlier, will be assigned to one of thedesignated classes. The blend samples containing partiallyor fully oversulfated components, and the potential GAGimpurities, were readily distinguished from USP-gradeheparin by the classification models.

The present study shows that SVM, ANN, and CARTcan be employed to build classification models fordiscriminating heparin from impurities and contaminantsby combination with proton NMR spectral data with bettergeneralization capabilities than commonly used linearclassification methods, such as PLS-DA, LDA, and kNNwhich usually require a prior step of variable reduction[27]. The choice of the statistical analysis software R wasdriven in part by our long-range plan to develop a freelyavailable, customized computational tool for chemometricanalysis of APIs and related commercial products forpurposes of quality control, quality assurance, and moni-toring of impurities and contaminants.

Fig. 5 Dendrogram on theseries of blends of heparinspiked with other GAGs,generated based on theirEuclidean distances andaverage linkage

Identification of heparin samples containing impurities 953

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