Automatic Analysis of Archimedes' Spiral for Characterization of Genetic Essential Tremor Based

15 Pages·2017·3.78 MB·English

entropy
Article
Automatic Analysis of Archimedes’ Spiral for
Characterization of Genetic Essential Tremor Based
on Shannon’s Entropy and Fractal Dimension
KarmeleLopez-de-Ipina1,* ID,JordiSolé-Casals2 ID,MarcosFaúndez-Zanuy3 ID,
PilarM.Calvo1,EnricSesa3,JosepRoure3,UnaiMartinez-de-Lizarduy4,BlancaBeitia5,
ElsaFernández1,JonIradi6,JosebaGarcia-Melero7andAlbertoBergareche8
1 SystemsEngineeringandAutomationDepartment,EleKinResearchGroup,UniversityoftheBasque
CountryUPV/EHU,20018Donostia,Spain;[email protected](P.M.C.);
[email protected](E.F.)
2 DataandSignalProcessingResearchGroup,UniversityofVic—CentralUniversityofCatalonia,
08500Barcelona,Spain;[email protected]
3 EscolaSuperiorPolitècnicaTecnocampus,UniversitatPompeuFabra,08002Barcelona,Spain;
[email protected](M.F.-Z.);[email protected](E.S.);[email protected](J.R.)
4 DepartmentofElectronicTechnology,EleKinResearchGroup,UniversityoftheBasqueCountryUPV/EHU,
20018Donostia,Spain;[email protected]
5 DepartmentofMathematics,EleKinResearchGroup,UniversityoftheBasqueCountryUPV/EHU,
1006Gasteiz,Spain;[email protected]
6 DepartmentofEnterprisesOrganization,EleKinResearchGroup,UniversityoftheBasqueCountry
UPV/EHU,20018Donostia,Spain;[email protected]
7 DepartmentofMechanicalEngineering,EleKinResearchGroup,UniversityoftheBasqueCountry
UPV/EHU,1006Gasteiz,Spain;[email protected]
8 DepartmentofNeuroscience,BioDonostiaHealthInstitute,20014Donostia,Spain;
[email protected]
* Correspondence:[email protected];Tel.:[phone];Fax:[phone]
(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:1)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Received:20May2018;Accepted:11July2018;Published:16July2018
Abstract: Amongneuraldisordersrelatedtomovement,essentialtremorhasthehighestprevalence;
infact,itistwentytimesmorecommonthanParkinson’sdisease. ThedrawingoftheArchimedes’
spiralisthegoldstandardtesttodistinguishbetweenbothpathologies. Theaimofthispaperisto
selectnon-linearbiomarkersbasedontheanalysisofdigitaldrawings. Itbelongstoalargercross
studyforearlydiagnosisofessentialtremorthatalsoincludesgeneticinformation. Theproposed
automaticanalysissystemconsistsinahybridsolution: MachineLearningparadigmsandautomatic
selectionoffeaturesbasedonstatisticaltestsusingmedicalcriteria.Moreover,theselectedbiomarkers
comprisenotonlycommonlyusedlinearfeatures(staticanddynamic),butalsoothernon-linear
ones: ShannonentropyandFractalDimension. Theresultsarehopeful,andthedevelopedtoolcan
easilybeadaptedtousers;andtakingintoaccountsocialandeconomicpointsofview,itcouldbe
veryhelpfulinrealcomplexenvironments.
Keywords: essentialtremor;automaticanalysisofdrawing;spiralofArchimedes;entropy;fractal
dimension;automaticselectionoffeatures
1. Introduction
Essentialtremor(ET)isaworldwidediseasethatistwentytimesmorecommonthanParkinson’s
disease(PD)[1]. Inthewesternworld,theprevalenceofthismotordisorderisabout0.3%to4.0%.
Itsincidenceis23.7per100,000individualsperyear,andbothmenandwomenof40yearsoldare
Entropy2018,20,531;doi:10.3390/e20070531 www.mdpi.com/journal/entropy
Entropy2018,20,531 2of15
affectedmoreorlessinthesameproportion;therearenodifferenceswithregardtogender. Studies
pointoutthat50–70%ofETcasesareestimatedtobegenetic[1]. ETisarhythmictremor(4to12Hz)
whichonlymanifestswhenthemuscleisexerting,andthetremor’samplitudevariesasthepatient
becomesolder. ETischaracterizedbybothkineticandposturaltremor,andmostofthetimesitaffects
thehands. Almosteveryothertremoroccurscombinedwithhandtremor[2].
Theclinicaldiagnosisofthefirstmanifestationsofthediseaseiscrucialtopalliateandmanage
thesymptoms,sincetheyproduceproblemsintheperformanceindailyactivities. Inrecentyears
wehavewitnessednotoriousadvancesinearlydiagnosistechniquesandinthecreationofusable
clinical markers. The differential diagnosis between PD and ET is clinical. When the diagnosis is
doubtful, a SPECT-DAT scan can be performed, which consists in evaluating the striatal uptake
of 123I-2b-carbomethoxy-3b-(4-iodophenyl)-N-(3-fluoropropyl)-nortropane using a SPECT (Single
PhotonEmissionComputedTomography),atestthatisextremelyexpensive,andthereforenoteasily
accessibleinhabitualclinicalpractice[3]. Inspiteoftheusefulnessofthesebiomarkers,theexpenses
andrequirementsoftheneededtechnologymakeitunfeasibletousethesetestswitheverypatientthat
hasmotorconditions. Inthiscontext,intelligenttechniquesthatarenon-invasiveforthediagnosiscan
beveryusefultoolsforearlydiagnosisofneurodegenerativedisorders. Staffwhoarenon-technical
intheenvironmentofthepatientcouldbeabletousethesetechniquesandotherbiosignalswithout
interferingwiththepatient’sdailylife,asanalysisofspeech,analysisofhandwritingoranalysisof
drawingsarenotconsideredstressfulbymostpatients. Furthermore,thecostofthesetechniquesis
lowandtheirrequirementsregardinginfrastructureormedicalequipmentarenotextensive,whereas
theyprovideinformationinaneasy,quickly,andinexpensiveway[4–8]. Medicalstaffcommonlyuse
handwritingtasksfordiagnosingessentialtremor. Nowadays,Archimedes’spiralisthegoldstandard
testinclinicaldiagnosis[9].
The analysis of handwriting has traditionally been performed off-line, as only the strokes on
the paper were available for the analysis. Nowadays, new devices, such as digitizing tablets and
pens (with ink or without), can collect both written data and their temporal information (on-line
handwritinganalysis). Newdigitizingtabletsgathernotonlythexandycoordinatesofthemovement
of the device of writing, but they also gather other data, for example: the pressure on the surface
of the writing device, the azimuth (angle between the pen and the horizontal plane), the altitude
(anglebetweenthepenandtheverticalaxis),oreventhein-airmovementwhenthereisnocontact
betweenthepenandthewritingsurface. Allthesecapabilitiesmakeit. possibletoanalyzebothstatic
anddynamicfeatures[10,11].
Inthefieldofmedicine,theanalysisofhandwritinghasfoundtobeusefultomakeadiagnosisand
trackneurodegenerativediseases. Forexample,thedegradationofhandwritingskillsandAlzheimer’s
Disease(AD)seemtobecloselyrelated[12,13],andseveralhandwriting-relatedaspectscanbeusedas
indicatorsfordiagnosingit[12],orcoulddifferentiatemildADfrommildcognitiveimpairment[12,13].
Handwritinganalysishasalsobeenshowntobehelpfultostudyhowsubstancessuchasalcohol[14],
marijuana[15],orcaffeine[16]affectpatients. Psychologyhasbenefited,aswell,fromtheanalysis
ofhandwritingthankstonewdevicesofacquisition. Forexample,Rosenblumetal.[17]reportthe
relationbetweentheabilityofthewritersandthedurationofthein-airtrajectoriesofthehandwriting.
Theprogressivedegreeofimpairmentcanbenoticedbyvisuallyinspectingthepen-downimage,
whenthedrawingismoredisorganized,andtheeffectinthreedimensionsisonlynoticedformild
casesofETandPDpatients. TherearecurrentlyreferencesthatanalyzethedetectionofETbymeans
ofdigitalplatforms. In[18],newnumericaltechniquesareproposedinordertoevaluatethemwith
regardtotheagreementwithvisualratingandreproducibility. Forexample,[19]analyzestheincrease
inthevariabilityofthedrawingofthespiralinpatientswithfunctional(psychogenic)tremor. Louise
presentsaninterestingstudyoverfourcohortsofET[20]. Ontheotherhand,recentreferences[21–24]
presentadvancesinPDanalysisbymeansofdigitaldevicesaswell. Thevisualinformationfromthe
in-airtrajectoriesofthedrawingsofunhealthypeoplealsoshowsdisorganizationandaprogressive
impairmentwhenthosepeopletrytoplantheirdrawings.Itisworthnoticingthatifpen-upimagesare
Entropy2018,20,531 3of15
comparedbetweenunhealthyindividualsandsubjectsinthecontrolgroup,italsorevealsimportant
differenEcnetrsop.yI 2n01a8d, 2d0,i xt io ntoalongerin-airtime,therearemorehand-movementsbeforethey3p ouf 1t5t he
penbackonthesurface. Therefore,thesemeasuresofgraph-motortypecanbeusefulwhenapplied
unhealthy individuals and subjects in the control group, it also reveals important differences. In
totheanalysisofwritinganddrawinginordertoanalyzetheprecisenatureandprogressionofthe
addition to a longer in-air time, there are more hand-movements before they put the pen back on the
writingsaunrfdacder. aTwheirnegfodreis, othredseer msreealsautreeds otof gnreauphro-mdeogtoern teyrpaet icvaen dbeis uesaesfeusl. when applied to the analysis of
Thwerwitinogrk anpdr edseranwteindg inin tohridserp atop earnailsyzpea trhteo pfraecilsaer gneartucrreo asnsds tpurdogyreasismioend ofa tthdei awgrnitoinsgin agnda nd
charactderraizwiningg edsissoerndteiarsl rtreelamteodr .toT nheiusrroedseegaerncehraitsivceo dnidseuacsteesd. attheBiodonostiaHealthInstitute,and
it analyzesTfahme iwlioersk wpirtehseindteedn tiinfi etdhisg epnapeteirc ilso pciar[t2 5o,f2 6a ].larNgeerv cerrothsse lsetussd,yt haeimsetdu dayt dpiraegsneonsitnegd ainndt he
characterizing essential tremor. This research is conducted at the Biodonostia Health Institute, and it
manuscript is aimed at the characterization of essential tremor, and its objectives are focused on
analyzes families with identified genetic loci [25,26]. Nevertheless, the study presented in the
establishing the limits related to the natural variability of ET and the ability to discriminate ET
manuscript is aimed at the characterization of essential tremor, and its objectives are focused on
from physiological tremor. Therefore, the subject of study is not the ability to make a differential
establishing the limits related to the natural variability of ET and the ability to discriminate ET from
diagnosiswithPD.Regardingthegatheringofnon-linearbiomarkersfromhandwritinganddrawings,
physiological tremor. Therefore, the subject of study is not the ability to make a differential
Archimedes’spiralisthetesttobeexplored. Thistestisalsoabletodetectotherdiseasessuchasstress,
diagnosis with PD. Regarding the gathering of non-linear biomarkers from handwriting and
whichcdoruawldinagpsp, Aearrchinimceodnetsr’o slpiinradl iivs itdhue atelss.t Iton bthe eexnpelxotreSde.c Ttihoisn ste,swt ies walsilol aabnlae ltyoz deenteoctt oonthleyr cdoimseamseosn ly
used dysuncahm aisc satrnesds,s wtahtiicchl icnoeualdr afepapteuarre isn, cbounttrootl hinedrinviodnu-allisn. eIanr thoen nesexat sSewcteiolln,si,. ew.,e fwrailclt aanladlyimzee nnosti on
and entornolpy yc.omPmotoennltyi aulsebdio dmynaarmkeicr sanwdi slltabtiec liidneeanrt iffieaetdurbesy, bmuet aonthsero nfosne-vlienreaalr aounetos masa wtiecll,c il.aes.,s firfiaccatatli on
techniqduiems.enLsaisotnly ,atnhde eqnutaroliptyy.o Pfothteenstiealle cbtieodmfaerakteurrse swwilli lbleb eidaeunttoifmieadt ibcayl lmyeaannasl yozfe dsebveyrauls ianugtoMmaactihci ne
classification techniques. Lastly, the quality of the selected features will be automatically analyzed
Learningparadigms.
by using Machine Learning paradigms.
2. Materials
2. Materials
2.1. SystemofAcquisition
2.1. System of Acquisition
The acquisition is performed with an Intuos Wacom 4 digitizing tablet. Figure 1 shows the
The acquisition is performed with an Intuos Wacom 4 digitizing tablet. Figure 1 shows the
information, which is captured by the USB pen. The tablet gathers 200 samples/second: spatial
information, which is captured by the USB pen. The tablet gathers 200 samples/second: spatial
coordinates (x, y), the applied pressure of the pen, and a pair of angles, which are the azimuth
coordinates (x, y), the applied pressure of the pen, and a pair of angles, which are the azimuth (angle
(anglebbeettwweeeenn ththee ppene nanadn tdhet hheorhizoorniztaoln ptlaalnpe)l,a anned) ,tahne dalttihtuedael t(iatnugdlee b(eatnwgeleenb tehtew peeenn anthde thpee nveartnicdalt he
verticalaaxixsi)s [)1[01,101,1].1 C].olCleocltliencgt ionnglyo tnhleyset hdyesneamdiycn faeamtuicrefse, aatfuterrewsa,radfst,e mrwoarer dinsf,omrmoarteioinn fcoarnm bae tiinofnercreadn. be
inferredF.oFr oerxaemxapmlep, lvee,lvoeciltoyc, itayc,caelcecrealteiorant, iotann,gteanntgiaeln atciacellaecracetiloenr,a tcieonnt,ricpeentatrl ipacectealleraactcioenle, raantigolne ,oafn tghlee of
theinstiannsttaannteaoneuosutsr tarjaejcetcotorryy,,i innssttaannttaanneeoouus sddisipslpaclaemceemnte, nrat,driuasd oiuf scuorfvactuurrve,a etutcr. e[2,6e]t.c I.n[ F2i6g]u.rIen 1F, tihgeurree 1,
is a modern digitizing tablet, and the graphic representation of the angles of the azimuth and
thereisamoderndigitizingtablet,andthegraphicrepresentationoftheanglesoftheazimuthand
altitude. It also represents the capture of a handwritten text (the Spanish word
altitude. Italsorepresentsthecaptureofahandwrittentext(theSpanishword“biodegradable”—
“biodegradable”—i.e., biodegradable in English but with a different pronunciation), and two captures
i.e.,biodegradableinEnglishbutwithadifferentpronunciation),andtwocapturesofthedrawingof
of the drawing of a house. Please note that every capture comprises both on-surface and in-air
ahouse. Pleasenotethateverycapturecomprisesbothon-surfaceandin-airtrajectories.
trajectories.

Figure 1. Information from the digitizing tablet.
Figure1.Informationfromthedigitizingtablet.
Entropy2018,20,531 4of15
2.2. DatabaseofIndividuals
ThispaperisbasedonadatabasenamedBIODARW,whichcontainssamplesfrombothhands
of50people: 21controlindividuals(CR)and29ETpatientswithidentifiedgeneticloci. Thedataset
belongstoalargerresearchstudyonthediagnosisofETconductedbytheBiodonostiaHealthInstitute
aimedatcharacterizingthisimpairment. Theparticipantsarefamilieswithidentifiedgeneticsloci.
SubjectswereselectedamongpatientsofapreviousstudythatcomprisesfamiliarandsporadicET
cases,whereascontrolindividualswererecruitedintheMovementDisordersUnitoftheDonostia
UniversityHospital(inSanSebastian,Spain).Anewinformedconsentwassignedbyeveryparticipant
inourstudy,whichwasapprovedbytheethicscommitteeoftheDonostiaUniversityHospital[25,26].
Foreachindividual,anelectrophysiologicaltest(EPT)andfMRIareavailable. Inthetest,individuals
draw a line, the Archimedes’ spiral, and do some handwriting both with the dominant and the
non-dominanthand[25,26].Inthisstudy,weuseonlythespiralofArchimedes(Figure2).Thedatabase
presentsvariabilityregardingtheamplitude,frequency,andpatternofthetremor;scaleofdiagnosis;
anddemographicdata(genderandage). Asfarastheindividualsselectedforthestudyareconcerned,
asubsetofsamplesofthespiralofArchimedesispickedupfromtheoriginaldatabaseanalyzing
geneticandclinicalassessment. Withregardtothesamplesofthespiralsstudied,thesesamples(or
spiraldrawings)comefromsubjectsdiagnosedwithETaccordingtoclinicalandelectrophysiological
criteria[27]. Tremorratingscalesprovidecrude,non-linearandsubjectiveassessmentsoftheseverity
oftremor. Amongthemostcommonlyusedscales,theFahn-Tolosa-Maríntremorratingscale(FTM)
usesagradingof0–4toevaluatetremorinArchimedes’spiraldrawings. ThescaleofBainandFindley
uses a grading of 0–10. Both scales have a strong logarithmic relationship with the amplitude of
thetremormeasuredbymeansofadigitaltablet(consistentwiththeWeber-Fechnerlaw). Actually,
thedigitizingtabletsaremuchmoreaccuratethantheclinicalclassifications,butthisadvantageis
mitigatedbythenaturalvariabilityofthetremor,andhence,thisiswhythestudythatwepresent
makessense[28]. WithinthegroupofindividualswithET,onlythesamplesofthehandaffectedby
essentialtremorareused,butfivepatientsarenottakenintoconsiderationduetothepoorqualityof
theirsamples. Forthecontrolindividuals,thebestsampleisselected(mostlythedominanthand),and
forsomeindividualsthenon-dominanthandisalsoused. Therefore,thissub-databaseBIODARWOis
madeof51samplesselectedfromtheoriginaldataset:27samplesselectedfromthecontrolindividuals,
and24samples(thehandaffectedbytremor)fromtheETindividuals. Ahigherdatabasewouldbe
very useful. Unfortunately, as often happens, the study has a limited number of samples. This is
aclassicalBiomedicalEngineeringproblem. Inthebibliography,wecanfindmanyrealexamplesin
thesamescenario. Oneofthetypicalcasesisthemodellingandexploringofthegenesthatcaused
aspecifictypeofcancer. Inthiscase,therearemorethan4000genes-features,soafewofthemare
selectedtobeusedasfeaturestofeedaclassifier. Additionally,underHospitals’EthicalCommittees’
advisors,thisisastandardstudy,andworkingwithothersubsetsofthedatainapreviousphase,
wealreadyobtainedresultsusingasmallersamplesize,butalsoasmallersetoffeatures,reaching
similarnumericalaccuracies. ThecomplexityoftheproblemliesinthedifficultyinobtainingfMRI
samplesinthesepatientsthatcanonlybegatheredaspartofaresearchstudy,notinhabitualclinical
practice. Forthisreason,thesampleislimited. Thestudycanbeconsideredafeasibilitystudy,whichis
notthesameasapilotstudy[29].
Entropy 2018, 20, x 5 of 15
EEnnttrrooppyy 22001188,, 2200,, 5x3 1 55 ooff 1155

Figure 2. Example of (X, Y) and pressure (P) o f the Archimedes’ spiral carried out by two individuals
wFFiiiggthuu rrEeeT 22:.. lEEoxxwaa mmleppvlleeel oo(flfe ((fXXt ,, iYYm)) aaagnnedd); p parrneedssss uuhrirgeeh ((P Pl)e) vooeff ltt hh(reei gAAhrrtcc hhimiimmaeegddeee).ss ’’T ssipmpiireraa lel vccaoarrlruriiteeidodn oo uuistt sbbhyyo ttwwwnoo iiinnn dddiivivfifiddeurueaanllsts
wcwoiilttohhu ErEsTT (::b lloeogwwin llneeivvneegll (i(nllee bfftltu iimem aaanggdee) )e;;n aadnniddn ghh iiigngh hr elledevv).ee ll ((rriigghhtt iimmaaggee)).. TTiimmee eevvoolluuttiioonn iiss sshhoowwnn iinn ddiiffffeerreenntt
ccoolloouurrss ((bbeeggiinnnniinngg iinn bblluuee aanndd eennddiinngg iinn rreedd))..
3. Methodology
33.. MMeetthhooddoollooggyy
3.1. Derived Measures
33..11.. DDeerriivveedd MMeeaassuurreess
Thanks to on-line drawing it is possible to evaluate the time spent and the pressure exerted
whileTT hhwaarnniktkisns tgto,o o fronon-ml-ilni neae dq rduarawanwitniitgnagtiti viitse pipso opsisnoitbs sloeibft love ieetvowa e.l uvFaaotleru atihntees tttaihnmec eet,is mpitee ni sst pwaenendltl tahknendop wrtehnses tuphrraeetse AsxueDrrte e pdeaxtweierhntietldes
wswprheintiliden gmw,rofirrtoeinm tgim,a ferq oaumnadn a tpi trqaoutdiavunectiept asotiiminvtep olpefrov ianinetwd o .sfo Fvfotieerrw isn.t srFtoaoknre csien [,s1it2ta]ni,s cwewh, eiiltlel ipks newoopewlllen kwtnhiotahwt EAnT Dt hapnatda t AiPeaDnrt kspinastpsioeennn’tdss
Dmspiosereneadst iemm poerraoend tdiumcpeer o aldensudsc epsrtsaoimbdlupec leper rseaimsnsdpulrseeor f ptaenartdtse tsrroonfkste e[sr1 [s21t,r23o]0,k,w3e1sh] [.i1 leI2n]p, e[w2o9hp]il,le etw hpeiet ohapbElieTl iwtayni tdohf PE atThr kea innidnsod Pniav’rsikdDiuniassleosan si’ess
prDerlioasdeteaudsce e tploer sospdsrutecasebs ulleeresps r easstnasdub lreei npp-araeitrts esrutnrrasej e[p1ca2tot,3tre0ier,3ns1 s] (.[t1hI2ne,i3r[0 2,93l]e1,n].tg hItehn) a [b2[i93l]i2t, –yt3ho5ef] . tahbAeilniitnoydt hiovefri d thuneae lwsin idsiinvretiedlarueteasdtlsin tigos
pcrherelaasrtsaeucdrt eeratiosnt dicpi nroe-fas sirmutroread jeeacrnntod ro ienisn-l(-itanhiere irhtlareannjdegcwtthor)irt[ii3en2sg – 3(a5thn].eaAilry nsoilset hniegsr thtnh)e awt[ 3ii2nt –te3cra5en]s. tibnAegancro htihanre armc teninreidwst i icniofnoftremmreoasdtteiionrnng
cocohnla-lleriacntceetdehr awinsthdiciwl eor tifth ienm gpoeadnne adrlnoy esosis nni-oslitnt heexa ethriatt npcdarnewsbrsiuetairnerg ion nam nthainely dssuiisnr ffaioscr emt. hFaaitgti ouinrt ecc o3al nrlee cpbtreeedasrew nihntsi ltmehteihn dedr paiewnnfiondrgom eoasf tntihooent
secpxoeilrlreatclp toerfed s Awsurhcrhielieom nthetedh epese sncua rdrfroaieceesd .n Fooiutg teu xbreeyr 3tt hprrerepeesr esiusnerdnei tvosindth utehaelds sr: auawr fciaoncnget.o rFofilgt hiunerdesi p3vi irrdaeulpaorlef,s Aaennrc thEs iTtmh ieen ddderisvawicdaiurnragile odaft o tahunet
ebsapyritlryha rls eoteafg inAed,r ciavhniiddmu aeandls eE:sTa c cainornrditiervdoid loiunuadtl ibavyti d atuhnar ael,dea vinnaEndTciveiidnd dustiaavlgisd:e u a[a 2cl6oa]n.t tParenonle -iadnrodlywivsnitd a(ugoaenl,-,as aunnrd fEaacTne EitnrTdaijienvcditdiovuriaidelsu a)a tal araent
saehnaoralwyd nvs taianng cbee,ld uaens,t daw gahenil [eE2 6Tp] e.innP-deuinpv- id(dionuw-aalni ra (tto rananj-e sacutdrovfraaicenesc)et ardar ejse tscahtgooerw i[e2ns6 )i]na. r Preeesdnh.- odFwoigwnunrien ( o4b nlru-esepu,rrewfsahecnielt estr ptahejeenc -wtuoprriite(iisnn)g -aa orierf
ttshrhaeoj ewwctnoo rriidne sbB)lIauOree,D swEhhGoiwRlenA piDennAr-eBudLp.E F( iinfgr-uoarmier t4rtharejeep crCteoRsre inegstrs)o atuhrpee wsthoro itbwienntgt eionrf ritelhldue.sw Ftroiagrtuder Beth I4Oe rDepEpeGrne-RsueApnD tasA ntBdhLe pEwefnrrio-tdimnogwt honef
iCtnhRfeo grwrmooaurtpdio tnBo.I bOTehDtteeE riGnilR-lauAisrDt rinaAtfBeoLrtmhEe afptrieoonmn-,u opthr aepn eCdnRp-u egpnr,- odisuo pwsh ntooiw nbfnoe ritntme rra etiidlol,nu a.sntTrdha tetehi net -hoaein r-pisneufnrof-raumcpea atiinnofdno ,rpomreanpt-iedonon-wu opnr,
piisnesfnoh-rodmwoawntinion nisr. esTdhh,oeaw ninnd -iatnhi reb ilonunfeo-.s rumrafaticoeni,n oforr pmeant-iuonp,o irs psehno-wdnow inn riesds,h aonwdn tihneb olune-s.urface information or
pen-down is shown in blue.

Figure 3. Sketching of the spiral of Archimedes carried out by (from left to right): a CR individual, an
Figure3. SketchingofthespiralofArchimedescarriedoutby(fromlefttoright): aCRindividual,
EFTig uinrde i3v.i dSkueatlc ahti nagn o ef atrhley ssptairgael ,o af nAdr cahni mEeTd einsd ciavrirdieuda lo autt bany (afdrovman lceefdt t ost raiggeh.t )B: oat hC Rp einnd-divoiwduna (lt, oapn
an ET individual at an early stage, and an ET individual at an advanced stage. Both pen-down
iEmTa gined iinv ibdluuea)l aant da np eena-rulyp (sbtaogtteo, man idm aagne E inT riendd)i vairde usahlo awt na sni maduvltaannceeodu ssltya.g e. Both pen-down (top
(topimageinblue)andpen-up(bottomimageinred)areshownsimultaneously.
image in blue) and pen-up (bottom image in red) are shown simultaneously.
Entropy2018,20,531 6of15
Entropy 2018, 20, x 6 of 15

FFiigguurree 44.. PPeenn--ddoowwnn ((ttoopp iimmaaggeess)) aanndd ppeenn--uupp ((bboottttoomm iimmaaggeess)) ttrraajjeeccttoorriieess ooff ddiiffffeerreenntt ccaappttuurreess ooff
bbiiooddeeggrraaddaabbllee ffoorr tthhee ccoonnttrrooll ggrroouupp..
Therefore, the movements of the hand when drawing or writing some text can be divided into
Therefore,themovementsofthehandwhendrawingorwritingsometextcanbedividedinto
two categories: on-surface trajectories (pen-down), and in-air trajectories (pen-up) [35]. The
twocategories: on-surfacetrajectories(pen-down),andin-airtrajectories(pen-up)[35]. Thepen-down
pen-down corresponds to the movements of the writing device when it touches the writing surface.
corresponds to the movements of the writing device when it touches the writing surface. Each of
Each of these on-surface trajectories is a visible stroke. The pen-up corresponds to the movements of
theseon-surfacetrajectoriesisavisiblestroke. Thepen-upcorrespondstothemovementsofthehand
the hand when changing from one stroke to the next, that is, there is no pressure at all on the writing
whenchangingfromonestroketothenext,thatis,thereisnopressureatallonthewritingsurface.
surface. Our past studies on recognition of people based on biometry showed that these two kinds of
Ourpaststudiesonrecognitionofpeoplebasedonbiometryshowedthatthesetwokindsofdata
data are complementary [10], and their discrimination capability is similar, even when using a
arecomplementary[10],andtheirdiscriminationcapabilityissimilar,evenwhenusingadatabaseof
database of 370 individuals [11,34].
370individuals[11,34].
33..22.. EExxttrraaccttiioonn ooff FFeeaattuurreess
IInn tthhiiss ssttuuddyy,, wwee pprreesseenntt aa pprreelliimmiinnaarryy eexxppeerriimmeenntt wwhhoossee mmaaiinn ggooaall iiss ttoo eessttaabblliisshh tthhrreesshhoollddss
ffoorr ssoommee hhaannddwwrriittiinngg rreellaatteedd bbiioommaarrkkeerrss.. AAss mmeennttiioonneedd aabboovvee,, iitt bbeelloonnggss ttoo aa bbrrooaaddeerr rreesseeaarrcchh
ssttuuddyy aaiimmeedda taet aeralyrldyi adginaogsniossoisf EoTf. TEhTe. reTfhoerere,ftohrees, etahrec hsoefarfecaht uorfe sfeinatouurerss tuind youairm sstuadtpy reacilminsi caatl
pevreacluliantiicoanl oervieanlutaatteiodnt oworaierdntsattheed dteofiwnaitridons otfheef fedcetfiivneittieosnts ofof redfifaegcntiovsei ntgesEtTs [f9o,1r2 ,d20ia,2g5n,o26si]n.g ET
[9,12,20,25,26].
3.2.1. LinearFeatures
3.2.1. Linear Features
TheaimistoautomaticallydifferentiatebetweenETindividualsandhealthypeoplefromthe
analyTshise oafimse vise rtaol aliunteoamrafetiactaulrlyes d(iLffFe)r,ewnthiaicthe abreetwateternib uEtTe sinodrivvaidriuaabllse sanlidn ehaeralylthdye ppeenodpelen tfroonmd athtae,
aannadlyvsairsi aonf tsse(vmerinal, mlinaexa,rm feeadtiuarne,sa (nLdF)m, weahni)c,he xatrrea cattetrdibfurotems tohre virarhiaanbdlews rliintienagrsl:y dependent on data,
and variants (min, max, median, and mean), extracted from their handwritings:
1. Time-relatedmeasures: timeon-surface,timein-air,andtotaltime(on-surfaceplusin-airtimes).
12.. TSipmatei-arleclaotmedp omneenatssuarnesd: vtaimriaen tosn:-csouorrfdaicnea, tetismXea nind-aYi,ra, ltaintudd etoatnagl letimO,ea z(oimn-ustuhrfaancgel epAlu,sa nignl-eaiZr
taimndesm). odulusRpolarcomponentsandtheirprojectionsforbothin-airandon-surfacesignals
2. S(Fpiagtuiarle c5omshpoownse,nints tahnedd vraawriainngtso: fcothoerdinindaitveisd Xua alnwdi tYh, EalTt,itaundiel launsgtrlaet Oio,n aozfimthuethd iasntogrltei oAn, oafntghlee
Zp oalnadr cmomodpuolnuesn Rts p).olar components and their projections for both in-air and on-surface signals
(Figure 5 shows, in the drawing of the individual with ET, an illustration of the distortion of the
3. Pressureandvariants(min,max,mean,median,std).
polar components).
4. Features of dynamic nature and variants: speed and acceleration for both in-air and
3. Pressure and variants (min, max, mean, median, std).
on-surfacesignals.
4. Features of dynamic nature and variants: speed and acceleration for both in-air and on-surface
5. Zerocrossingrate.
signals.
6. Frequency related features: spectral components for both in-air and on-surface signals
5. Zero crossing rate.
(Figure6)[26].
6. Frequency related features: spectral components for both in-air and on-surface signals (Figure
6) [26].
Entropy2018,20,531 7of15
Entropy 2018, 20, x 7 of 15
Entropy 2018, 20, x 7 of 15

Figure 5. Projections of the polar components of the drawing of the spiral of Archimedes carried out
Figure5.ProjectionsofthepolarcomponentsofthedrawingofthespiralofArchimedescarriedout
Figure 5. Projections of the polar components of the drawing of the spiral of Archimedes carried out
by a control person (left image) and a patient with ET (right image).
byacontrolperson(leftimage)andapatientwithET(rightimage).
by a control person (left image) and a patient with ET (right image).

Figure 6. Spectrum of the coordinate X of the pen-down signal for a individual of the control group
Figure 6. Spectrum of the coordinate X of the pen-down signal for a individual of the control group
Fig(ulerfet 6im.Sapgeec)t raunmd aonf itnhdeicvoidorudailn watiethX EoTf (trhigehpte inm-daogwe)n. signalforaindividualofthecontrolgroup
(left image) and an individual with ET (right image).
(leftimage)andanindividualwithET(rightimage).
3.2.2. Non-Linear Features
3.2.2. Non-Linear Features
3.2.2. Non-LinearFeatures
The objective is to use the analysis of non-linear features (NLF) extracted from the subjects’
The objective is to use the analysis of non-linear features (NLF) extracted from the subjects’
samThpeleos bojfe chtaivnedwisrtiotinugs eint hoerdaenra tloy sdisisotifnnguonis-hli naeuatormfeaattiucarellsy (bNeLtwF)eeenx thraecatlethdyf rinodmivtihdeuaslusb ajencdts E’T
samples of handwriting in order to distinguish automatically between healthy individuals and ET
samsupffleesreorfs.h Tahned wNrLiFtisn gunindeorr dcoenrstiodedriasttiionng uairseh: faruatcotaml adtiimcaellnysiboentsw (eFeDn) haenadlt hthyeiinr dviavriidanutasl s(manind, EmTax,
sufferers. The NLFs under consideration are: fractal dimensions (FD) and their variants (min, max,
sufmfeeraenrs a.nTdh emNedLiFasnu) nfodre rthceo npsriedsesurartei oanndar teh:ef rsapcatatiladl icmomenpsoionnesn(tFs Dx,) ya,n cdotmhepiurtveadr iuasnintsg( mthien ,Hmigauxc,hi
mean and median) for the pressure and the spatial components x, y, computed using the Higuchi
meaalgnoarnitdhmm e(HdiFaDn)) faonrdt htheep Creassstuigrelioannid atlhgeorsipthamtia (lCcFoDm)p; othnee netnstrxo,pyy, c(oEm) apnudte idtsu vsainriganthtse (Hmiignu, cmhiax,
algorithm (HFD) and the Castiglioni algorithm (CFD); the entropy (E) and its variants (min, max,
algmoreiatnh man(dH FmDe)daiannd) thfoer Cthaset ipgrlieosnsuiraelg aonridth tmhe( CspFDat)ia;lt hceomenptroonpeynt(sE )x,a nyd; aitnsdv asrigiannatls d(mistinor,tmioanx ,by
mean and median) for the pressure and the spatial components x, y; and signal distortion by
meaannaalynzdinmge ldoicaanl )pfeoarktsh.e pressureandthespatialcomponentsx,y;andsignaldistortionbyanalyzing
analyzing local peaks.
localpeTahkes .fractal dimension of an object is a measure of its self-similarity. A self-similar object is
The fractal dimension of an object is a measure of its self-similarity. A self-similar object is
apTphroexfimraacttaellyd siimmeinlasri oton ao pfaarnt oofb ijtescetlfi,s thaamt iesa, sifu wree oefxaitmsisneelf i-ts icmloislearr,i twy.e Awislle flifn-sdim smilaarlleorb vjeecrtsiiosns
approximately similar to a part of itself, that is, if we examine it closer, we will find smaller versions
apopfr oitx. iImn aotredlyers tiom qiluaarntotifayp saerlft-osifmitislealrfi,tyth, awteis c,aifnw meeeaxsuamrei ntheei tnculmosbeer,r wofe bwuiillldfiinngd-bslmocakllse rthvaetr asrioen psart
of it. In order to quantify self-similarity, we can measure the number of building-blocks that are part
ofoitf. aIn poartdteerrnt;o thqius amnteiafysusreel fi-ss itmheil asroi-tcya,lwleed cfarnacmtael adsiumreenthsieonnu (mFDb)e.r Foofrb au gilidvienng -wblaovcekfsorthma,t tahreerep aisr tno
of a pattern; this measure is the so-called fractal dimension (FD). For a given waveform, there is no
ofraepfeartetnercne ;otfh tihsem FeDas vuarleuies itth sehsoou-lcda lhleadvefr. aAcdtadlidtiiomnaenllysi,o ans (sFigDn)a.lFso arrae gniovte unswuaalvlye fsotarmtio,nthareyre, iins nmoost
reference of the FD value it should have. Additionally, as signals are not usually stationary, in most
refteercehnnciequofesth, eshFoDrtv sailguneailt ssehcotuiolndsh aarvee .uAseddd iitnio onradlleyr, atos sciaglncaullsataer efenaottuuressu afrlloyms tathtieo nwaarvy,eifnormmo. sFtor
techniques, short signal sections are used in order to calculate features from the waveform. For
tecehxnaimqupelse,, sthhoer tssigignnaall csaecnt iboen ssaprleitu isnetdo inshoorrdte priteocceasl ciunl aotredfeera ttuor ecsaflrcoumlatteh ethwea vfeeafoturmre.s Foofr eeaxcahm ppilee,ce,
example, the signal can be split into short pieces in order to calculate the features of each piece,
thewshigicnha lisc atnheb etescphlnitiqinuteo tshhaot rwtpei ehcaevsei ntaokredne rintotoc aaclccuoluantet. tIhne ofetahteurr ewsoorfdes,a cwhep cieocme,pwuthei cthhei sftrhacetal
which is the technique that we have taken into account. In other words, we compute the fractal
tecdhinmiqeunseiothna otfw sheohrat vseegtmakeenntsi notfo thaec csoigunnat.l, Ianndo tohbesrewrvoer dthse, weveocluotmiopnu otef tthhee rfersauctltasl adliomngen tshieo nwohfole
dimension of short segments of the signal, and observe the evolution of the results along the whole
shosirgtnsaelg, mtryenintsg otof tdhiescsoigvnera lf,raanctdalo cbhsaerravcetetrhiesteicvso tlhuatito cnouolfdt hbee rheesluplftusla tloo nidgetnhteifwy hdoiflfeerseignnt aell,emtryeinntgs of
signal, trying to discover fractal characteristics that could be helpful to identify different elements of
totdhiastc osivgenraflr. aTchtaelrec haarera scetvereirsatli caslgthoraitthcmousl dthbaet chaenlp bfeu ultsoedid teon mtifeyasduirfefe trheen tFeDle. mIne onutsr ostfutdhya,t tshieg nfoacl.us
that signal. There are several algorithms that can be used to measure the FD. In our study, the focus
Thiesr eona rtehes eovpetriaolnasl gesoprietchimallsyt shuaittacbalne bfoeru tsheed atnoamlyseiass uofr etitmhee sFeDri.eIsn wohuirchst uddo yn,otht enefoedcu asniys opnretvhioeus
is on the options especially suitable for the analysis of time series which do not need any previous
opmtioondseleisnpge coifa ltlyhes usiytastbelmef.o Srothmeea noaf lythseisseo fmtiemtheosdesri eisncwluhdiceh tdhoe nHoitgnuecehdi aanlgyoprirtehvmio u[s36m],o tdheel inKgatz
modeling of the system. Some of these methods include the Higuchi algorithm [36], the Katz
ofathlgeosryitshtmem [.3S7]o manedo fththee Cseasmtiegtlhioondis ainlgcoluridthemth e[3H8]i.g uHcihgiuaclhgio arinthdm C[a3s6ti]g,ltihoeniK watezrea lgsoelreitchtemd, [3a7s] in
algorithm [37] and the Castiglioni algorithm [38]. Higuchi and Castiglioni were selected, as in
previous works in under-resourced conditions, this approach has proven to be more accurate
previous works in under-resourced conditions, this approach has proven to be more accurate
[7,8,39–41].
[7,8,39–41].
Entropy2018,20,531 8of15
andtheCastiglionialgorithm[38]. HiguchiandCastiglioniwereselected,asinpreviousworksin
under-resourcedconditions,thisapproachhasproventobemoreaccurate[7,8,39–41].
Ontheotherhand,physicalsystemsentropyisadisordermeasure. Forasinglediscreterandom
variableX,theentropyHmeasuresitsaverageuncertainty. Shannonentropy[42]iscomputedas:
∑
H(X) = − p(x )logp(x ) (1)
i i
xi
3.3. SetsofFeatures
Next,wepresentthesetsoffeaturesusedintheexperimentation:
1. SetofLinearFeatures(LF),thissetwillbedescribedin3.3.1.
2. SetofNon-LinearFeatures(NLF),whichconsistsofLFandthesetthatwillbedescribedin3.3.2.
(Higuchi(HFD),Castiglioni(CFD),entropy(E),andfractaldimension(F)):LFHFD,LFCFD,LFE,
LFHFDEandLFCFDE.
3. TheresultingsetoffeaturesafterselectionbymeansofANOVA:SLF(SelectionofLinearFeatures),
SLFHFD,SLFCFD,SLFE,SLFHFDEandSLFCFDE.
Table1showsthecompletelistofacronymsandtheirmeanings.
Table1.Completelistofacronymsandtheirmeanings.
Acronym Description
ET EssentialTremor
PD Parkinson’sdisease
FD FractalDimension
HFD HiguchiFractalDimension
CFD CastiglioniFractalDimension
E Shannon’sEntropy
LF LinearFeatures
NLF Non-linearFeatures
LFXFD LinearFeaturesandFractalDimension
LinearFeaturesandFractalDimensionand
LFXFDE
Shannon’sEntropy
SLF SelectionofLinearFeatures
SLFXFD SelectionofLinearFeaturesandFractalDimension
SelectionofLinearFeaturesandFractalDimension
SLFXFDE
andShannon’sEntropy
SVM SupportVectorMachine
MLP MultiLayerPerceptron
NNHL Neuronnumberinthehiddenlayer
k-NN K-NearestNeighbor
NF NumberofFeatures
TS TrainingStep
CER ClassificationErrorRate
Acc Accuracy
ACCER AccumulativeClassificationErrorRate
3.4. AutomaticSelectionofFeatures
The automatic feature selection is based on statistical tests (ANOVA). The MatLab one-way
balancedanalysisofvariancefunction(anova1)isused[43].
Two or more columns of data that represent independent samples that contain mutually
independentobservationsarecomparedwithregardtotheirmeans. Thetestcomputestheprobability
(p-value)underthenullhypothesisthateverysampleisdrawnfrompopulationswiththesamemean.
Ifpisneartozero,wecansaythatthenullhypothesisisveryunlikely,sowecanassumethatthe
Entropy2018,20,531 9of15
mean of at least one of the samples is significantly different from the means of the other samples.
Commonlyusedsignificancelevelsare0.05or0.01;inourcaseitis0.05. ThestandardANOVAtest
differentiatesthevariabilityofthedataintotwotypes: ontheonehand,thevariabilityduetothe
discrepancybetweenthesamplemeans,orvariabilitybetweengroups;andontheotherhand,the
variabilityduetothedifferencesbetweenthedataineachsampleandthesamplemean,orvariability
inside the groups. The size of the F-statistic and the p-value are derived from the box plot of the
samples. SignificantdifferencesbetweenthecenterlinesoftheboxesleadtolargevaluesofF,and
thereforesmallvaluesofp.
3.5. AutomaticClassification
Theprincipalaimofthisstudyistheselectionofpotentiallyusefulhandwritingfeaturesuseful
forpreclinicalevaluationtodefinetestsinordertodiagnoseET.Suchfeaturesshoulddifferentiate
betweenthegroupofcontrolindividuals(CR)andthegroupofindividualswithessentialtremor
(ET).Asthesetechniqueshavetobeusefulinrealenvironmentsforreal-timeapplications,asecond
objectiveistooptimizethecomputationalcost. Therefore,themodelofautomaticclassificationwill
beperformedbearinginmindthesetwogoals. ThreedifferentclassifiersimplementedintheWEKA
softwaresuite[44]wereused. Allconfigurationswereorientedtorealtime:
1. ASupportVectorMachine(SVM)usingpolynomialkernel(e=1.0).
2. AMultiLayerPerceptron(MLP)usingneuronnumberinthe(unique)hiddenlayer(NNHL)=
max(Attribute/Number+Classes/Number)andtrainingstep(TS)=NNHL×10.
3. K-NearestNeighborAlgorithmork-NN(usingk=1).
Inordertoevaluatetheresults,weusedAccuracy(Accin%),ClassificationErrorRate(CERin%)
and Accumulative Classification Error Rate (ACCER in %) for every model [5,24]. In the steps of
trainingandvalidationweusedk-foldcross-validation(k=10). Cross-validationisarobusttechnique
fortheselectionofvariables[45]. Thankstorepeatedcross-validation(ascomputedbyWEKA),robust
statisticaltestsarepossible. Weusedthemeasurementprovidedbythefunction“Coverageofcases”
ofWEKA(confidenceintervalat95%level)aswell.
4. ResultsandDiscussion
The experiments were performed using the balanced subset BIODARWO. The aim of the
experimentwastoassessthepotentialofselectedfeaturestoautomaticallymeasurethedegradation
oftheArchimedes’spiraldrawnbysubjectsthatsufferET.Therefore,thepreviouslydefinedsetsof
featureshavebeenassessedtodifferentiateproperlybetweencontrolandessentialtremorgroups.
ExtractionofLinearandNon-LinearFeatures
Inafirstphase,linearandnon-linearfeatureswereextractedusingthetechniquesofSection3.4
(seeTable2),andanautomaticclassificationwasperformedbymeansoftheclassifiersenumeratedin
Section3.5. Figure7summarizestheresultingCERs(%)forthedifferentclassifiers,withlinearand
non-linearfeaturesets. Intheseresultswecanobservethat:
• Thesetsofnon-linearfeaturesprovidebetterresultsforeveryclassifier.
• MLPandSVMhavethebestresultsinmostofthecases.
• BothFDfeaturesareabletoprovidebetterresultsforeveryclassifier.
• ShannonentropyhasthebestperformanceforMLPwheniscombinedwithCFD.
• ThebestoptionisLFCFDEwithCastiglioniFD,entropyandMLP,wheretheCERis13.73%with
225features.
EntEronptyro2p0y1 280,1280,, 2503,1 x 10o1f01 o5f 15

Figure7.CER(%)forthethreeclassifiersconsideredwithlinearandnon-linearsetsoffeatures.
Figure 7. CER (%) for the three classifiers considered with linear and non-linear sets of features.
Table 2. Sets of features and number of features (NF).
Table2.Setsoffeaturesandnumberoffeatures(NF).
LF LFHFD LFCFD LFE LFHFDE LFCFDE SLF SLFHFD SLFCFD SLFE SLFHFDE SLFCFDE
NF 186 2L1F3 LFH2F13D LFCF19D8 LFE 225L FHFDELF22C5F DESL7F0 SLFH7F3D SLFCFDS7L7F E SLF7H6 FDE SL7F9C FDE 86
NF 186 213 213 198 225 225 70 73 77 76 79 86
In a second stage, an automatic selection of features is performed by applying the ANOVA test
described in Section 3.5. Figure 8 shows the details for the selected feature time-up (in-air), which
Inasecondstage,anautomaticselectionoffeaturesisperformedbyapplyingtheANOVAtest
represents the time that the pen is not on the writing surface. In Table 2, we can see that the number
describedinSection3.5. Figure8showsthedetailsfortheselectedfeaturetime-up(in-air),which
of features (NF) for linear and non-linear cases is reduced by about 65% after the selection process.
representsthetimethatthepenisnotonthewritingsurface. InTable2,wecanseethatthenumber
Finally, an automatic classification process was applied to the entire database using the previously
offeatures(NF)forlinearandnon-linearcasesisreducedbyabout65%aftertheselectionprocess.
described classification algorithms. Figures 9 and 10 graphically summarize the CERs (%) yielded by
Finally,anautomaticclassificationprocesswasappliedtotheentiredatabaseusingthepreviously
each algorithm when considering linear and non-linear sets of features. In these results, we can
describedclassificationalgorithms. Figures9and10graphicallysummarizetheCERs(%)yielded
observe that:
byeachalgorithmwhenconsideringlinearandnon-linearsetsoffeatures. Intheseresults,wecan
observethat:
• The automatic selection of features improves the results for most of the algorithms when
linearfeaturesareconsidered(Figure9). Withtheselectedfeatures,MLPisthealgorithmthat
performsworst.
• Whenthenon-linearselectedfeaturesareincluded,theresultsarebetterinmostcaseswithregard
totheLFs.
• Both non-linear features (FD and entropy) improve the results regardless of the applied
classificationalgorithm.
• ShannonentropyperformsbetterwithSVM,andwhencombinedwithFD.
• ThebestoptionwithregardtofeaturesetsisSLFCFDwithCastiglioniFDandMLPwithNF=77
features(CER=5.89%). ThesamefeaturesetprovidesthebestresultsforSVMwhenapplying
theHiguchialgorithmforFD.
• Goodresultsarealsoobtainedwithk-NN,requiringalowercomputationalcostwiththesetsthat

includefeatureselectionbyANOVAandFD.
Figure 8. Example of ANOVA analysis: time-up for the CR group in blue and the ET group in red.