Heart pacemaker wear life model based on frequent properties and life distribution*

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1 J. Boedcl Scece d Egeerg,, 3, JBSE do:.436/jse..345 Pulshed Ole Aprl (hp:// Her pceer wer lfe odel sed o freque properes d lfe dsruo* Qo-Lg Tog, Xue-Cheg Zou, J Tg, Heg-Qg Tog Depre of Elecroc Scece & Techology, Huzhog Uversy of Scece & Techology, Wuh, Ch; Depre of Mhecs, Wuh Uversy of Techology, Wuh, Ch. El: qlog@gl.co Receved 4 Jury ; revsed Jury ; cceped 5 Jury. ABSTRACT The lfee of her pceer s por for pe d resercher. To forecs he lfee of her pceers we us deere s dsruo regulry. I hs pper, her pceer wer lfe odel s roduced y usg frequecy propery, d lfe dsruo s preseed. The prerc properes of he desy re suded. The oe esor wh egve order s used, whch s jus he xu lelhood esor. A ew ehod of preer ese, ese of preer, s proposed. Ths ehod s sule o oh ruced sples d coplee sples, wheher or o he dsruo c e rsfored o sdrd dsruo whou y preers. Keywords: Her Pceer Lfe Dsruo; requecy; Negve Order Moe Esor; Mxu Lelhood Ese; Ese. INTRODUCTION The her pceers (HPM) hve ore d ore exesve clcl pplcos. Alos ll users of HPM worry he lfee of HPM. If soe e hs HPM sops wor ou of he lue, h wll e serous roule. Pospog or dvcg o replce or o repr HPM s o sule. So forecsg he lfee of her pceer s por for pe d resercher. Exedg HPM lfee s he sgfc o reduce he cos of crdc pcg []. The fcors whch pc HPM Lfe coe: e fcors d cqured fcors (such s elecrogec felds, drugs, ec.) [], u he forer s ore por. The e fcors clude y specs whch wll e roduced s follows. The ery cpcy s decded y ery eergy d ery cuge. or he se fucol crcu, cresg ery cpcy wll ehce s cpcy, *The reserch ws suppored y he Nol Nurl Scece oudo of Ch (3576, 6773). decrese pcg power d prolog he HPM lfe. Ierl frdc curre s sgfc, depede fcors reled o ery lfe. Low erl frdc curre s por role o sve ery lfe [,3]. Alhough here s lle lerure o roduce he relvy ewee erl frdc curre d ery lfe, soe scholrs for hs sudy h h erl frdc curre hs jor pc o HPM lfe d ye s greer h he ery cpcy d oupu eergy. Mrewz, ec. [3] foud h decresg he erl frdc curre cosupo eles o reduce overll curre cosupo of HPM d g loger lfe, whch pproves h he erl frdc curre s foreos fcor of fluecg HPM lfe. Pcg frequecy lso hs red fluece o HPM lfe, d s level of eergy cosupo s proporol o he HPM. HPM elecrode fuco s he wees l he syse, whch s lso he os por fcors o deere he secury d lfe of HPM syse [4]. Afer he HPM pulse geeror (Pulse geeror, PG) ws desged, he ery cpcy d curre cosupo hs ee defed d re cos. Iprovg he wre elecrode fuco s he oly wy o prolog HPM lfee. Elecrodes hve y fcors whch wll ffec he HPM lfe. Accordg o Oh s lw, he hgh pedce (> oh) c reduce he loss curre, cresg he HPM lfe. Led s lso ecessry. The fuco of elecrode led s rsg elecrcy, u s echs cply s por for ssurg he lfe of pceer. The cply osly les o he erl of sulg surfce. Slc gel y e he es choce, whch hs ee used over ps 3 yers. The ressce of led res wh s legh. The legh of elecrode wh doule pole s wo es copred wh upolr oe. I he heory, elecrode wh doule pole uses ore eergy. Iducve crcu d pcg wh ul-cvy or doule cvy wses ore eergy h sgle cvy d ducve crcu. I hs pper, ew her pceer lfe dsruo s preseed ccordg o relve fluece fcors. The Pulshed Ole Aprl ScRes. hp://

2 376 Q. L. Tog e l. / J. Boedcl Scece d Egeerg 3 () her pceer y e wor or dged fer worg for log e, herefore, s vro d frequecy y e chged. The frequecy of her pceer c e recorded y frequecy record eer. The her pceer lfe d s relly c e vesged y he lyss of he her pceer frequecy. Le A,, e he plude vlues of he frequecy of orl her pceer, A,, e h of he dged her pceer. We defe he frequecy preer : A () A Experes hve show h we c deduce he level of he wer or he dge of her pceer ccordg o he lyss of he frequecy preer. Whe x, he her pceer c o wor orlly. The vlue of he frequecy preer creses s he wor e of her pceer creses. I geerl, we suppose r, he, we wll ge, where r r deoes he chge re of. I y e ffeced y y depede lle fcors such s cply of ery, he fuco of elecrode, led, erl d so o. We suppose h r s rdo vrle wh orl dsruo wh defo r : r r C fr r, r ro fr rdr (), we ow C, where r s he dsruo fuco of sdrd orl. Le e he her pceer wer lfe, T r, he s lso rdo vrle. The desy fuco of her pceer wer lfe dsruo s r C f r r Whe, s dsruo fuco s x x, r (3) r (4) r Now, we prculrly vesge sscl propery of her pceer wer lfe dsruo. rs, we see he grph of f. Pu, he f, ecuse, pu, f. Dfferee f, he r f f f s The soluo of equo r r 8 4 Secod, we see he chge of flure re. f Le r r (5) (6) r r r (7) r r g r he c g d (8), where c s cos. Becuse l g (9) r r r l g l r r l We hve l l. The grph of s lso loced o he frs qudre. Is lef l s org d s rgh sypoc le s xs.. MOMENT ESTIMATE WITH NEGATIVE ORDER OR COMPLETE SAMPLE Whe we vesge he preer ese of he desy fuco f of her pceer wer lfe dsruo, we oce h hs wo depede preers oly. Le, r, he he desy fuco of her pceer wer lfe dsruo s f, () I Eq.3, f hs hree preers,, r. They re depede he physcl process, u hey re depede he desy fuco. We c ese, Copyrgh ScRes. JBSE

3 Q. L. Tog e l. / J. Boedcl Scece d Egeerg 3 () fro Eq.. We eed o ese ddo, he we c ese,r. rs, we cosder oe esor. or coo j oe esor E ( ), j,,, we c o clcule s egro. If we e use of oe esor j wh egve order E ( ), j,,, he egro c e clculed esly. ET 3 d y y dy () y ET 4 d 3 y y dy () Le,, e..d. sple d of he her pceer wer lfe. We e use of he sple oe o ese he populo oe. The dfferece s he sg of he order of oe. ro he syse of equos (3) we hve s (4) Moreover we c o he soluo d fro Eq.4. They re he oe ese of d. Secod, we cosder he xu lelhood esor of preers. The lelhood fuco s L, Copyrgh ScRes. (5) Tg dervo of L,, we hve L (6) d L (7) Splfyg Eq.6 d Eq.7, we hve s s e s s (8) Nog h Eq.8 s jus Eq.9, we ow h he oe esor wh egve order of her pceer wer lfe dsruo s jus s xu lelhood esor. I s ore resole o e he oe esor wh egve order for her pceer wer lfe dsruo. 3. PARAMETER ESTIMATE OR TRUNCATED TESTING Lfe esg s ofe ruced y he gve sze of sples, ecuse he e d he cos of esg re led. Suppose producs re e s lfe esg. We hve oserved producs whch hve ee flures. re precedg order sscs of producs lfe. or oel dsruo, Weull dsruo, orl d logorl dsruo, we c gve preer esor ruced esg. These dsruos c e rsfored o sdrd dsruos whou y preer. Accordg o he order ssc of he sdrd dsruo, we c copue s eco, vrce d covrce. The, we c o he Bes Ler Used Eso y he les squre ehod. Bu we c o do hs wy for her pceer wer lfe dsruo. The reso s c o e rsfored o y sdrd dsruo whou y preer. The xu lelhood es- JBSE

4 378 Q. L. Tog e l. / J. Boedcl Scece d Egeerg 3 () e of her pceer wer lfe dsruo fro he order sscs of he ruced sples s o cer o coverge, ecuse s desy fuco does o ssfy soe of he covergecy codos. I hs pper, ew sscl ehod, ese of preer, s proposed. I s sule o y dsruo wheher or o c e rsfored o sdrd dsruo. Wh s ore, hs o defo of sple sze. We c cosder he prole hs wy. or he lves of producs lfe esg, we hve oserved precedg lves of producs. We hve o oserved le lves of producs u hey re exse. or he eprcl dsruo fuco of lfe, we hve oserved,,. We hve o oserved he le vlues, u hey lso exs. ro Glveo-Cell Theore, we ow h eprcl dsruo fuco of rdo vrle wh proly oe coverges o s dsruo fuco uforly. Th s, P l sup (9) Therefore we c o pproxe equos,.e.,,,, () The preers o e esed re coed he syse of Eq.. The prole s chged o solvg oler regresso odel. Solvg he odel y he les squre ehod, we c o he preers o e esed. We cll ese of preer. Ovously, hs ehod s relle heory, sple copuo d exesve pplco. ro [5], we ow h her pceer wer lfe dsruo s The regresso equos re (),,, () Mg use of he les squre ehod, we eed o see he u y chgg preers :, Q, (3) Or we solve he followg syse of equos: Of course, hs ehod s lso sule o coplee sples, h s. 4. COMPUTATION EXAMPLE AND COMPARISON O PRECISION I order o vesge he properes of her pceer wer lfe dsruo crefully, d es he ew sscl ehod, ese of preer, we copue les o copuer. The preers, re gve d rdo uers re geered d re sequeced ers of Eq.. Usg hese d, frs we copue he oe esors wh egve order (d lso he xu lelhood esors) ˆ, ˆ sed o Eq.4 or Eq.8. Secod, we copue he esors of preers ˆ, ˆ usg Eq.3. Thrd, we e precedg d d copue he esors of preers ˆ ˆ, ccordg o Eq.3 lso. Copred he repeedly y chgg sple sze, preers, d ruced uer. ro he resuls of coprso, we ow h s rous o e solue vlue Eq.3. Q, (4) We e he Powell lgorh proved y Srge o Copyrgh ScRes. JBSE

5 Q. L. Tog e l. / J. Boedcl Scece d Egeerg 3 () copue Eq.4 d he seco ehod o copue Eq.4. Whe d re sll sples, we e sple sze, ruced uer, l preers.9, 3.. The copued resuls re Tle. The rdo d re geered 5 es d copuos re repeed 5 es. Whe he rdo d re geered, her seeds re dffere. rs of ll, hese seeds re geered s rdo d depedely. If s ecessry o clcule gre uer of rdo d, we c chge he odules of pseudordo d ye. Usg hs ehod, he repeed uer c e very lrge. We c clcule he eprcl dsruo fuco of he sscs,, d. Therefore, we c drw up he dsruo fuco les of he sscs for gve precso ccordg o Glveo- Cell Theore. I y cse, we re ssfed wh he copued resuls Tle, ecuse he sple sze s so sll. Whe d re coo sples, we e sple sze, ruced uer 5, l preers lso use 9., 3.. Copued resuls re Tle. Of course, hey re ore ccure d lso e us ssfed. 5. CONCLUSIONS More d ore fucos re ghered her pceer. I s used ore frequely log wh he develope ofoedcl egeerg. Exedg d forecsg he lfee of her pceer s very por o user. I hs pper, we roduced her pceer wer lfe odel y g use of he frequecy propery, d deduced s lfe dsruo. The prerc properes of he dsruo desy re eresg ecuse s oe Tle. Copued resuls wh =, =, =.9, = Tle. Copued resuls wh =, = 5, = 9., = esor wh egve order s jus s xu lelhood esor. We lso propose ese of preer h s sule o oh ruced sples d coplee sples. Through copuo le d coprso of precso, we c ge ssfyg resuls. Th es wheher or o he dsruo c e rsfored o sdrd dsruo whou y preers, we c ese he preers ruced d sple. 6. ACKNOWLEDGEMENTS We would le o h he ers who e her e o chec, pprove hs pper d gve us vlule suggesos. REERENCES [] Oh, O.J. d Dlovc, D. (997) Iprovees pceer eergy cosupo d fucol cply: our decdes of progress. Pcg d Clcl Elecrophysology,, -9. [] Kder, M., Schw, B., Berg, M. d röhlg, G. () Logevy of dul cher pceer: Devce d pe reled deers. Pcg d Clcl Elecrophysology, 4(5), [3] Mrewz, A., Kros, D., Keyer, A., Kulch, H., Wehold, C., Doerg, W. d Rechr, B. (995) Deers of dul cher pulse geerors logevy. Pcg d Clcl Elecrophysology, 8(), 6-. [4] Crossley, G.H., Jeffrey, A.B., Reyolds, D., Wll, S., Johso, W.B., Howrd, H. d Ls, T. (995) Serod eluo proves he sulo hreshold cvefxo rl pere pcg led. Crculo, 9(), [5] Ro, C.R. (997) Ler sscl ferece d s pplcos. Wley & Sos, New Yor. Copyrgh ScRes. JBSE