INTRAUTERINE GROWTH RESTRICTION (IUGR) RISK DECISION BASED ON SUPPORT VECTOR MACHINES

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1 Mathematcal and Computatonal Applcatons, Vol. 15, No. 3, pp , Assocaton for Scentfc Research INTRAUTERINE GROWTH RESTRICTION (IUGR) RISK DECISION BASED ON SUPPORT VECTOR MACHINES Zeynep Zengn 1, Fkret Gürgen 1*, Füsun Varol 2 1 Boğazç Unversty, Dept. of Computer Eng. Bebek, Istanbul/Turkey 2 Trakya Unversty, Ob/Gyn Dept, Edrne/Turkey { zeynep.zengn@okan.edu.tr, gurgen@boun.edu.tr, fvarol@yahoo.com.tr} Abstract- Ths paper studes the rsk of ntrauterne growth restrcton (IUGR) usng support vector machnes (SVM). A structured and globally optmzed SVM system may be preferable procedure n the dentfcaton of IUGR fetus at rsk. The IUGR rsk s estmated n two stages: n the frst stage, nonnvasve Doppler pulsatlty ndex (PI) and resstance ndex (RI) of umblcal artery (UA), mddle cerebral artery (MCA) and ductus venosus (DV) and amnotc flud ndex (AFI) are retrospectvely analyzed and the Doppler ndces are appled to the SVM system to make a dagnoss decson on the fetal wellbeng as reactve or nonreactve and/or acute fetal dstress (AFD) on the nonstress test (NST) (tranng data). In the second stage (testng data), the decson s valdated by the NST (target value). Experments are performed on prevously collected data. Fortyfour preterm wth IUGR and wthout IUGR pregnances before 34 weeks gestaton are consdered.the nonparametrc Bayes-rsk decson rule, k-nearest neghbor (k-nn), s used for comparson. It s observed that the SVM system s proven to be useful n predctng the expected rsk n IUGR cases n ths small populaton study. The PI and RI values of UA, MCA and DV are also effectve n dstngushng IUGR at rsk. Key words- Intrauterne growth restrcton (IUGR), Doppler ndces PI and RI, support vector machnes (SVM), k-nn. 1.INTRODUCTION Intrautern growth restrcton (IUGR) s a fetal growth dsorder whch s assocated wth fetal hypoxa and ncreased pernatal morbdty / mortalty [1-5]. The comparson of absolute measurements wth reference ranges allows the detecton of devatons between expected and actual growth. The classfcaton of fetuses by brth weght percentle has also a sgnfcant advantage for detecton of IUGR who are at rsk for adverse health events. The relatonshp between fetoplacental hemodynamc characterstcs, fetal behavor, amnotc flud producton and fetal heart rate has been greatly extended by advanced ultrasound technology. Placental hemodynamc problems cause fetal growth delay and adaptve organ responses n uterus. Adaptve responses are ntended to enhance fetal survval n hypoxc envronment. Exhauston of placental and fetal adaptve potental leads to decompensaton of fetoplacental unt. Severe dsturbances of fetal growth s a challenge to the many researchers. The ultmate severe condtons n IUGR are accepted as absent end dastolc flow or reverse flow n umblcal artery (UA) and hgh values of UA PI values, decreased PI n

2 Z. Zengn, F. Gürgen and F. Varol 473 fetal mddle cerebral artery (MCA), appearance of retrograde flow pattern n ductus venosus (DV), severe olgohydramnos (AFI<5), non-reactvty n nonstress test (NST). These typcal features may be employed to montor the IUGR fetuses at rsk. Support vector machnes (SVM) has been one of the most promsng statstcal decson technques [6-14]. Ths s proven n varous applcatons [9-13]. SVM offers some advantages n the rsk estmaton of IUGR fetuses snce t uses support vectors to optmze the decson regon along the class boundares. Ths gves an opportunty to fnd the rsky IUGR cases. The process of rsk estmaton has two stages: The frst stage s feature extracton for rsk estmaton. Nonnvasve UA, MCA and DV Doppler ndces (PI and RI) and amnotc flud ndex (AFI) are retrospectvely analyzed n actual cases and are labeled as reactve and nonreactve and/or acute fetal dstress (AFD) fetuses. Reactve class corresponds to fetuses n normal condtons and nonreactve and/or AFD class corresponds to IUGR fetuses at rsk assocated wth hypoxa. So these features are employed n the SVM system to obtan a two-class decson. In the second stage the fast rsk decson s supported by a NST tool. As a result the overall system conssts of Doppler readngs, SVM based decson and NST tests at cascaded levels for screenng the rsk n IUGR. Moreover we compare the SVM decson to that of k-nearest neghbor (k-nn) as a nonparametrc Bayes-rsk estmator. Ths paper s organzed as follows: Secton 2 summarzes the rsk analyss wth SVM classfer. The expermental evaluaton and the decson results are gven and are compared to the results of k-nn n Secton 3. Secton 4 provdes a bref dscusson on results and concluson. 2. SVM-BASED RISK ANALYSIS 2.1. Expected and Emprcal Classfcaton Rsk In the deal two-class classfcaton problem, the expected rsk R(f) s estmated and mnmzed under the dstrbuton P(x,y) whch s assumed to be known by the choce of a functon f : X { ± 1} from the avalable set of functons F based on expected rsk mnmzaton prncple [6-8]. In practcal applcatons, the dstrbuton should be estmated from the lmted number of tranng data pars (x, y ), =1,,m (an ll-posed problem) by mplementng the emprrcal rsk mnmzaton (R emp (f)). The R emp (f) s the average value of loss over the tranng set, whle R(f) s the expected value of loss under the true probablty measure. We can not mnmze expected rsk drectly snce the dstrbuton P(x,y) s unknown. However, t s possble to estmate Vapnk-Chervonenks (VC) bound [3] that holds wth the probablty(1-η) R(f) Remp(f) + φ(h / m,ln( η)/ m) (1) The bound of the test error depends on the emprcal rsk and the VC dmenson, h, defned as the largest number of samples that can be separated usng the class of functons f(x). The VC dmenson represents the complexty of the functon class related to the amount of avalable tranng data and the confdence term φ s referred to as over fttng. In summary, usng the structural rsk mnmzaton prncple, we

3 474 Intrauterne Growth Restrcton (IUGR) Rsk Decson conclude that the mnmum expected rsk s obtaned by usng a SVM model wth the mnmum sum of emprcal rsk and by selectng a VC confdence. 2.2.Lnear and non-lnear SVMs In the lnear separable vector space case, we fnd the optmal hyper-plane wth the maxmum margn between the classes by the soluton of a global maxmum or optmum for the quadratc optmzaton problem. The hyper-plane decson functon can be wrtten as m f ( x) = sgn y = 1 ( x x ) + b. (2) α Here the tranng samples wth nonzero α s are called support vectors (SV) and the decson functon s constructed by only these vectors. The fewer number of SVs ndcates better generalzaton capablty. In the non-separable case, the soluton s to allow errors of the SVM by ntroducng postve slack varablesξ, = 1,..., m, then: y ( w x + b) (1 ξ ) 0, = 1,..., m. If an error occurs, ξ becomes an upper bound on the number of tranng errors. The decson boundary s then determned by mnmzng 2 ( ) k, where C s a w / 2 + C ξ user-defned parameter ndcatng the degree of penalty to errors. Now, the only dfference from the lnear separable case s that the α have an upper bound of C, and the support vectors can le on the margn or nsde the margn. The common approach for separaton n ths case s to map the orgnal nput space to a hgher dmensonal feature space usng kernel functons. As the key dea of non-lnear SVMs, kernel functons, K ( x, x j ) = Φ( x ) Φ( x j ), descrbe the nner products between vectors x and x j. Then the optmzaton follows the same procedure as the lnear SVM ndependent from the feature space dmenson. Includng the kernel nner products, the decson boundary s: m f ( x) = sgn α y K ( x, x ) + b (3) = 1 The choce of the kernel functon s crtcal for the success of the SVM classfer IUGR Rsk Decson based on SVM The Doppler ndces of placental fetal vessels (PI, RI s of UA, MCA, DV vessels) and amnotc flud ndex (AFI) are nputted to the supportve system based on SVM to predct preterm IUGR cases at a mnmum expected rsk ( Fgure 1). The SVM dstngushes reactvty and nonreactvty and/or fetal dstress fndngs as an ndcaton of placental functon/dysfuncton at the frst stage. In the second stage, SVM fndngs are valdated by NST value (reactvty,nonreactvty and/or fetal dstress).

4 Z. Zengn, F. Gürgen and F. Varol 475 Small? IUGR suspcon Absent end Dastolc flow n UA, Decreased PI n MCA, AFI < 5 Bweekly Examnatons AC measurement Ultrasound UA, MCA and DV, and AFI, NST dagnoss IUGR at rsk IUGR Fgure 1: A Flowchart for IUGR fetuses at rsk The advantageous propertes of the SVM model n the IUGR applcaton are to gve a sngle soluton characterzed by global mnmum optmzed functons and not to rely so heavly on heurstcs. Fnally t s flexble structure obtans a mnmum expected rsk by VC bound. So the rsk lmts n IUGR may be adjusted by a C parameter choce. Once the related support vectors are derved from IUGR nput space, a sngle clear decson on rsky cases can be made. Clncal stage 1 Clncal stage 2 IUGR suspcon UA, MCA, Doppler values and AFI Test Vector Tranng Vector SVM Decson + Reactve, Nonreactve and/or AFD IUGR Decson Rsky IUGR cases NST and AFD values Fgure 2: IUGR Decson at Mnmum Expected Rsk Nonnvasve measurements of PI, RI s and AFI s to make dependable decson n a short tme nterval s a necessty and an nstant mnmum expected rsk estmaton s also vtal pont n IUGR management. In ths aspect, a fast nonnvasvely obtaned feature set and globally mnmzed flexble SVM system appears to be good choce.

5 476 Intrauterne Growth Restrcton (IUGR) Rsk Decson 3. RESULTS Fortyfour preterm pregnances (<34weeks) wth IUGR and wthout IUGR were analyzed retrospectvely [2]. Ths study has been approved by ethcal commtte (Trakya Unversty Medcal School Ethcs Commttee - protocol no: TUTFEK-2004/057, protocol date: 13/05/2004. Group 1 ncludes 18 pregnances wth IUGR (%40.1) and group 2 has 26 pregnances wthout IUGR (%59.9) (Table 1). Two classes defned as reactve and nonreactve and/or AFD. Table 1: Features of 44 pregnances wth IUGR and wthout IUGR Group 1 wth IUGR (n=18) Group 2 wthout IUGR (n=26) overall (n=44) Age 25,67 ± 4,3 27,35 ± 5,9 26,7 ±5,3 UA PI 1,41 ±0,08 1,08 ±0,08 1,60 ±0,35 UA RI 0,77 ±0,35 0,70 ±0,28 0,80 ±0,08 MCA PI 1,49 ±0,38 1,67 ±0,5 1,22 ±0,32 MCA RI 0,78 ±0,34 0,82 ±0,35 0,73 ±0,12 DV PI 0,77 ±0,13 0,63 ±0,12 0,69 ±0,24 DV RI 0,58 ±0,28 0,50 ±0,17 0,53 ±0,14 AFI 4,56 ±0,76 6,62 ±0,51 5,77 ±3,8 Doppler PIs and RIs of UA, MCA, DV and AFI values were the data chosen to demonstrate an ablty for SVM to extract nformaton. The SVMs, besdes ther Lagrangan formulaton, can dffer n two aspects : () coeffcent C controlled capactes () the ansotropc radal bass n the Gaussan kernel transformaton controlled classfer functons. All data from 44 preterm pregnances are dvded nto two halves: tranng and test data. Thrtyfour values are reserved for tranng and the rest (a total of 10 values s constructed by a combnaton of 6 reactve and 4 nonreactve and/or AFD cases at each experment) s used for testng. The experments are repeated 10 tmes for unseen test values and the average performance s computed. Dfferent cases are consdered: Locally lnear classfer functons wth capacty fxed at C value s employed. A lnear combnaton of predctors weghted wth varous coeffcents approxmates the dscrmnatng rule n ths case. A more detaled pcture s seen wth the ncreasng capacty of classfer functons. Normal and rsky areas become localzed. By decreasng the radal bass the SVM wll try each case and the complexty wll also be ncreased. For large C values the SVM only localzed to one cluster of nonreactve cases. The area outsde ths cluster s assocated wth approxmately equally hgh score values. The area outsde ths clusters assocated wth approxmately equally hgh score values. The SVM manages to learn non-reactve cases n even a small sze populaton. Ths result s obtaned by tranng (Fgure 3). Fgure 4 demonstrates sample dstrbuton and the support vectors n PI- UA and PI-MCA space. The reactve and non-reactve classes are descrbed wth star and crcle. The squared star and crcle show the support vectors computed by tranng samples. The dark star and crcle show reactve and non-reactve samples of the experments.

6 Z. Zengn, F. Gürgen and F. Varol 477 Fgure 3: The relatonshp between performance and C value Fgure 4: The dstrbuton of samples and support vectors of PI-UA and PI-MCA space. The reactve and non-reactve classes are denoted by star and crcle. The squared star and squared crcle show the support vectors. The dark star and dark crcle show reactve and non-reactve test samples. The SVM decson results wth parameters (C=13000, γ=0.03) n small populaton experments are represented n Table 2. Varous combnatons of nput features ( y:yes and n:no) n the classfcaton task and accuraces are examned: Frst,t s observed that SVM becomes an effectve tool n management of the IUGR. Second, PI feature s effectve n SVM experment and UA-PI, MCA-PI and RI measurements gves the best accuracy of the system. Non-metrc,b-valued AFI s also supportng evdence of

7 478 Intrauterne Growth Restrcton (IUGR) Rsk Decson IUGR. Fnally The PI values obtaned from all vessels have separatng ablty IUGR at rsk. Table 2: Classfcaton performances for varous combnatons of PIs and RI s of UA, MCA and DV. Experment UA MCA PI RI PI RI y y y Y y y y y y N n n y y n Y y n y y n N n n PI y n DV n Y n n RI y n n N n n Accuracy (%) The accuracy,senstvty,specfcty and postve predctve value (PPV) for selected features n SVM system are shown n Table 3. It s observed that PI values n UA,MCA and DV ntroduce a good and balanced senstvty and specfcty results n the experments. Addton of RI to the PI UA and MCA has postve effect on accuracy, specfcty and PPV value however senstvty drops. Table 3: The accuracy, senstvty, specfcty and PPV values for the selected features n SVM system SVM results Accuracy (%) Senstvty(%) Specfcty (%) PPV (%) PI, RI n UA and MCA PI n UA, MCA and DV PI n UA and MCA PI,RI n UA, MCA, DV Furthermore Bayes-rsk estmaton was employed for comparson purposes. Because of lmted number of samples nonparametrc k-nn decson rule becomes a proper choce. In the clncal stuaton of 44 pregnances, k-nn experments for k=1 to k=7 are performed wth best performance (Table 4). Although k-nn classfer gves comparable performance to SVM system the balanced senstvty and specfcty values are only obtaned wth the SVM system. Table 4: The accuracy, senstvty, specfcty and PPV values for the selected features n Bayes-rsk estmate through k-nn decson rule. Specfcty (%) PPV (%) k k-nn decson rule Accuracy (%) Senstvty(%) PI, RI n UA and MCA PI n UA, MCA and DV PI n UA and MCA PI,RI n UA, MCA, DV

8 Z. Zengn, F. Gürgen and F. Varol DISCUSSION AND CONCLUSION Prognostc role of fetal Doppler velocmetry n growth-restrcted fetuses can not be overlooked. The proposed SVM based decson n IUGR s presented. In the frst stage Doppler ndces of UA, MCA and DV, AFIs and fetal responses n NST are retrospectvely analyzed. In the second stage valdaton of results are done usng NST tool. So SVM system s employed for a fast and mnmum expected rsk estmaton of each case. Although the data gven s extracted from a small populaton, SVM s are stll capable of extractng nformaton wth 70% of a senstvty, 81.7% of specfcty wth PI ndces of UA, MCA and DVs. The effectveness of the system s supported by 71.8 % PPV on dagnoss of hypoxa suspcon. However the ncluson of UA and MCA RIs drops the senstvty to 62.5%. Ths causes an ncrease on the false negatvtes and dagnoss of more non-reactvtes as reactve. The ncluson of RIs causes unbalancng effect. In such hgh rsk pregnances these supportve computaton methods may draw obstetrcan s attenton to evdences of unexpected hypoxc events and further analyss nto IUGR It s observed that the ncluson of RI mproves the accuracy 81% on dagnoss of IUGR cases. Both ndces,pi and RI employ nformaton on systolc-end-dastolc peak velocty n common, but ther usage of the data on tme-averaged maxmum velocty and systolc peak velocty dffer. Whle systolc peak velocty may properly classfy rsky pregnances but does not contrbute to a balanced mprovement of both senstvtes and specfctes. The detecton of AFI as beng <5 makes the most mportant contrbuton to these fuzzy Doppler ndces. Ths b-valued non-metrc feature commonly occurs wth the dsturbance n UA PI ( and PIs n MCA and DV later on) and fnally nonreactvtes and fetal dstress are seen on NST recordngs. The proposed SVM system s compared wth k-nn as a nonparametrc Bayes-rsk estmator. It s found that k-nn also performs reasonably well nterms of accuracy, specfcty and PPV. However SVM does much better n senstvty and gves a balanced par of senstvty and specfcty. It s also observed that SVM system s superor to the other neural structures. As a concluson, SVMs gve an opportunty to obtan the results not very obvous at frst glance and to easly tune wth only a few parameters such as rsk estmaton n IUGR. SVMs n IUGR management are based on very few restrctve assumptons and can reveal some mportant features overlooked by many other methods. Therefore they may become an opton of choce at rsk decson of IUGR. Although a very lmted data n IUGR are retrospectvely analyzed, the results are meanngful. On emay extend ths study wth new and large sets of data and alternatve formulatons of SVMs better suted for processng large data sets. Authors Contrbutons FV supervsed the data collecton and dscussons n Ob/Gyn. Area. FG supervsed and prepared the manuscrpt. ZZ carred out the numercal experments.

9 480 Intrauterne Growth Restrcton (IUGR) Rsk Decson Acknowledgement The work presented n ths paper has been supported by Boğazç Unversty Research Fund (BAP 09A102P project). 5. REFERENCES 1. James D.K., Steer P.J., Wener C.P., Gonk B., Hgh Rsk Pregnancy Management Optons, Thrd Edton, Fetal Growth Dsorders, Chapter 12 by Ahmet Alexander Baschat, Thrd Edton, Saunders Elsever, , Balık G. (Supervsor Füsun Varol), Relatonshp Between Veous Doppler and Pernatal Outcomes n Fetal Growth Restrcton, Gynecology and Obstetrcs Specalty Thess, Trakya Unversty, Campbell S., Warsof S. L., Lttle D., et al., Routne Ultrasound Screenng for the predcton of Gestatonal Age, Obstet Gynecol, 65, , Gürgen Fkret, Önal Emrah, Varol Füsun, IUGR Detecton by Ultrasonographc examnatons usng neural networks, IEEE Eng Med Bol Mag, 16, No 3, 55-58, May/june, Gürgen Fkret, Güler Nlgün, Varol Füsun, Antenatal Fetal Rsk Assessment Usng a NeuroFuzzy Technque, 20, No 6, , Moguerza, J. M., Munoz, A. Support Vector Machnes wth Applcatons. Statstcal Scence. 21, , Vapnk V., The Nature of Statstcal Learnng Theory, Sprnger Verlag, NewYork, NY, Bartlett P. L., Jordan M. I. and McAulffe J. D., Convexty, Classfcaton, and Rsk Bounds, Journal of the Amercan Statstcal Assocaton, 101, , Dng C., and Dubchak I., Mult-class proten fold recognton usng support vector machnes and neural networks. Bonformatcs , Furey T. S., Crstann, N., Duffy, N., Bednarsk, D., Schummer, M. and Haussler, D. Support vector machne classfcaton and valdaton of cancer tssue samples usng mcroarray expresson data. Bonformatcs , Hardle W., Moro R. A., Schafer D., Predctng Bankruptcy wth Support Vector Machnes, SFB , Humboldt-Unverstät zu Berln, Germany, Flz Güneş, Nurhan Türker, Fkret Gürgen, "Sgnal-Nose Support Vector Model of a Mcrowave Transstor," Intl. Journal of RF and Mcrowave Computer Aded- Engneerng, , July Lungh F., Magenes G., Pedrnazz L. And Sgnorn M. G., Detecton of Fetal Dstress through a Support Vector Machne based on Fetal Heart Rate Parameters, Computers n Cardology, 25, Issue 25-28, , Hsu, C. W., Chang C. C., Ln C. J., A Practcal Gude to Support Vector Classfcaton, Dept. Of CS and IE, Natonal Tawan Unversty, Tape, 2001.