2
3KcnPECC-AHAJlH13 CEPACEqHO-COCYJl1CTOI'I Cl4CTEMbi C FIOMOLLIbFO 4HJAYKTHBHO-EMKOCTHOMI MOCEJ1i4 CEPJ,LIA 5eperoBaq H. B., KopeHoBcKaq 0. Ji. )NUmoMUpCKUU eocydapcmeeHHblu mexHonoouLlecKuu- yHueepcumem yn. 4epHRxoecKoeo, 103, )KumoMup, 10005, YKpaUHa Ten.: (0412) 22-14-10, e-mail: [email protected] AHHoma4uR - nlpeAnoeeHa MeTOA/LKa npMmeHeHI*1 napa- meTpa 3neKTpmqecKoU go6pOTHOCTH cepAja nR npoBegeHMP 3Kcnpecc-aHanIm3a HaceneHHl c nOMOU.4blO MHgYKTHBHO- eMKOCTHOA Mogens cepgL4a. 1. BBeAeHu4e B nocnegHee BpeMq npu npOBegeHHH Kapgmonorm4e- CKUX mccnegOBaHU HMmeiouLXC5q napamerpOB AnS Onll- caHHR pa6OTbl cepgiLa CTaHOB4TCS HegoCTaTO4HO. no- 3TOMy npOBOJJ;TCA pa6OTbi no OTKpbIThIO 14 BHegpeHUHH HOBbIX Bc)KHbIX napamerpOB gJSn gmarHOCTfKI4. Mccnego- BaHHR B 3TOU o6iacTm npOBOpgJ1H MHOrme y'eHbie. Bay- HbIl BKnag BHeC Bono6yeB A. H., KOTOpbIU npeAnOKUn B KaqeCTBe MogeJ¶4, onlUCblBatueA pa6oTy cepg4La, MC- nOn1b3OBaTb HgYKTUHBHO - eMKOCTHyIO Mogenb [1]. gao cMx nop C'MTanOCb, 4TO 6monorM4eCKaS TKaHb o6nagaeT TOnbKO eMKOCTHbIMH CBOACTBaMm, HO Ha npaKTUKe 6blnO goKa3aHO, 4TO OHa xapaKTepU3yeTcq cyuLecTBeHHO 14 HgyKTHBHOCTbIO. I4enbIo gaHHOu cTa- TbU RBnSAeTCI paccmoTpeHUe 3neKTpOreHe3a cepgia C nOMOLLAbIO 14HgyKT4BHO-eMKOCTHOA Mogenf, noKa3aTb Ba)KHOCTb napameTpa 3neKTpwiecKoA Ao6pOTHOCTM cepgL,a JnJ npoBegeH4R mccnegOBaHMFI u garHOCTUKM Cepge4HO-COCygHCTOA CUCTeMbI. ILOCHOBHas 4aCTb CornacHo HHyKTUMBHO-eMKOCTHoU MogenJ cepgeq- HYIO TKaHb MO)KHO OXapaKTepM3OBaTb TpeMl napaMeTpa- Mm: ConpoTIBJ1eH4eM, 4HgykT4BHOCThlO H eMKOCThIO. MC- CJ1egOBaHH. [1, 2, 3] B gaHHOM HanpaBMeHMM nlOKa3an4, 'TO HHgyKTMBHOCTb U COnpOThBneHHe MO)KHO C'MTaTb nO4Tm nOCTOqHHbIMH BenJ IHaMm. B npoi4ecce Kapguo- L4Ktna npOmCXOgmT L43MeHeHUe eMKOCTm C, 4TO CB93aHHO c L4HKnH4ecKoA 4aCTOTOU BpauLeHHSF 4HTerpanbHoro 3neK- Tpm4ecKorO BeKTopa cepgLa (I.I3BC). IMeHHo Bono6yeB A. H. npegno)Kwn, B Ka4ecTBBe gononHMTenbHoro napa- meTpa npm npOBseeHHH uccnegOBaHuu HCcnoJlb3OBaTb 3.neKTpMeCKO go6pOTHoCTb cepgi4a. MbI Ke CwMTaeM, 4TO 3TOT napameTp MO)KHO OCTaB4Tb B OgHH PsA C gpy- rtMM BeJ1MqHHaMm, KOTOpblMU onepMPMIT npu M3y'eHMH 1 gmarHocThKe cepgLia. Ba)KHOCTb aToro napameTpa noKa- 3bIBaeT KnfHHHeCKaq npaKTmKa: gawe npfH HepKO Bbipa- )KeHHOU naTonorMm, Korga 13MeHeHH$ napameTpoB 3Kr nOqTM He 3aMeTHbI, npOHCXOgMT H3MeHeHHe go6poTHo- CTh. flo3TOMY, KOHTPOJ14pyq TeHgeHLA4MI H3MeHeH S4 jgo6- pOTHOCTU cepALa B TeBeHHM HeKOTOpOrO BpeMeHM MO)KHO cge.naTb BbIBOg 0 pa3BMTum naTonorndecKoro npoLAecca, ga)Ke ecnm OCTaJbHbie KOHTPOJ1MpyeMbie napameTpbl 3Kr HaXOg,TCS B npegenax HOpMbI. CnegOBaTenbHO, gnr 6o- nee rny6oKoro Hcc1egOBsaH MA Ba)KeH pacqeT go6poTHo- CTH cepgL4a. B npo4jecce Kapg4oLmKvna go6poTHoCTb 13MmeHqeTCq no 3KcnOHeHH4HanbHOMY 3aKoHy: Q=Qoexp(-R(t-to)/L) (1) rge QO = /oRIL - go6pOTHOCTb 3KBtBaneHTHorO KOHTy- pa B MOMeHT BpeMeHM to., R, L - aKTHBHOe COnpOTHBneHme H HHgyKTHBHOCTb, CO- OTBeTCTBeHHO. 6onee TO4HO OnpegentMTb 3TOT nOKa3aTenb MO)HO MaTeMaTHMeCKH, gn3 3TorO Heo6XogmMO BbIBeCTM cXop- Mylny paC'eTa Q0. Jo6pOTHOCTb MO)KHO OnpegeWJ1Tb 13 OTHOwIeHWS 3neKTpOKapgmorpaXu44ecKMX MHTepBarJOB AtQT l AtQS . 06a 3TU MHTepBana He 3aB4CRT OT nonoKe- HMFl 3fleKTpM4eCKOk OCm cepgLa. 03 [1] 1 + 2arctgvfR7- LR= 1 R 12arctgv&~fRf AQ 1+!2arctgv&RJY 2, QTR 1 + 2arctg[R _ 27r , Qo Qo (3) rge AtQRS - gllUTenbHOCTb KOMnnJ1eKCa QRS, AtQT - gnJTenBHOCTb 3fleKTpMLeCKOA CMCTOnbl QT, R, T- mnlnlTygbI 3y6LAOB 3Kr. Wcnonb3ysl CBOUCTBa COnpUKOCHOBeHMR CPyHKL4MU HyneBoro U4 nepBOro nlopgKa, M3 3TOrO COOTHOWeHHR BbIBegeM 4opMyny gns pacqeTa Qo: 2arctgRJI r+2ir -2r atrctgJFR'TJ QO .(4) ir + 2 -4 artgjR77I LkQRS KaK BHgHO U3 4OpMynbl (4), BCe BeJ1UMUHbi Heo6Xo- gNMbie npu nogcqeTe MO)KHO onpegeJNTb no 3neKTpo- KapgMorpaMMe. HaMM pa3pa6oTaHa nporpaMMa, KOTOpa5 nO3BoJnieT aBTOMaT"qeCKH onpegenqTb 3neKTpMLIeCKyi io 6poT- HOCTb cepgL4a, BbiqLMCJ1Tb yron HanpaBneHHq 3neKTpu- qeCKOU OCM, OTHOweHme LIR H CTpOUTb OCHOBHbie rpaC4MKM 3aBHC4MOCTeM. 3KCnepHMeHTarlbHO, nyTeM CHFTMI4 3KF naI4HeHTOB, 6blJio yCTaHoBJ1eHO, 1TO 3JneKTpMqeCKaq go6pOTHOCTb cepgLAa yMeHbwaeTcS npm nmTnorJO eCKHX npoI4eccax, B CpaBHeHHH C HOpManbHOA pa6oTOA Cepg14a. 3To no- 3BOnJeT HaxogMTb pa3HMLy A Q H no HeA CygHTb 0 pa3BMTHM naTonorLm. Ha cnegyiou.teM 3Tane npOBOgMT- c.q pa6oTa no Ha6opy cTaTHCTHKH H cocTaBneHHO 6a3b1 gaHHbIX, KOTOpa5 nO3BOJ1MT 6onee WHpOKO npHMmeHSTb 3TOT napameTp B KnMHMqeCKOi npaKTHKe. J,rn 6onee 6bIcTporo H HarnqgHoro onpegeneHH5 nocTpoeHa HOMOrpaMMa Am1H onpegeneHL4sq 3neKTpLlqe- CKOA go6pOTHOCTM cepgAa (rpa4MK 3aBHCIMOCTH OTHO- wleHMq HHTepBanOB AtQT /AtQR OT OTHOWeHHF aMnni4- Tyg 3y614oB RIT ), np4BegeHHaq Ha PHCYHKe 1. CnegoBaTenbHo, Ben"ql4HHY 3neKTpjqeCKOA go6poT- HOCTU cepgLAa MO)KHO onpegen4Tb no rpa4oHKy (pHCyHoK 1) Mum 6onee TOqHO COrnaCHO copMyne (4). 2005 15th Int. CIimean Conference "Microwave & Telecommunication Technology" (CnMiCo'2005). 12-16 September, Sevastopol, Crimea, Ukraine © 2005: CriMiCo'2005 Organizing Comunittee; Weber Co. IEEE Catalog Number: 05EX1089 863

[IEEE 2005 15th International Crimean Conference Microwave and Telecommunication Technology - Sevastopol, Crimea, Ukraine (2005.9.12-2005.9.16)] 2005 15th International Crimean Conference

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3KcnPECC-AHAJlH13 CEPACEqHO-COCYJl1CTOI'I Cl4CTEMbiC FIOMOLLIbFO 4HJAYKTHBHO-EMKOCTHOMI MOCEJ1i4 CEPJ,LIA

5eperoBaq H. B., KopeHoBcKaq 0. Ji.

)NUmoMUpCKUU eocydapcmeeHHblu mexHonoouLlecKuu- yHueepcumemyn. 4epHRxoecKoeo, 103, )KumoMup, 10005, YKpaUHa

Ten.: (0412) 22-14-10, e-mail: [email protected]

AHHoma4uR - nlpeAnoeeHa MeTOA/LKa npMmeHeHI*1 napa-meTpa 3neKTpmqecKoU go6pOTHOCTH cepAja nR npoBegeHMP3Kcnpecc-aHanIm3a HaceneHHl c nOMOU.4blO MHgYKTHBHO-eMKOCTHOA Mogens cepgL4a.

1. BBeAeHu4eB nocnegHee BpeMq npu npOBegeHHH Kapgmonorm4e-

CKUX mccnegOBaHU HMmeiouLXC5q napamerpOB AnS Onll-caHHR pa6OTbl cepgiLa CTaHOB4TCS HegoCTaTO4HO. no-3TOMy npOBOJJ;TCA pa6OTbi no OTKpbIThIO 14 BHegpeHUHHHOBbIX Bc)KHbIX napamerpOB gJSn gmarHOCTfKI4. Mccnego-BaHHR B 3TOU o6iacTm npOBOpgJ1H MHOrme y'eHbie. Bay-HbIl BKnag BHeC Bono6yeB A. H., KOTOpbIU npeAnOKUn BKaqeCTBe MogeJ¶4, onlUCblBatueA pa6oTy cepg4La, MC-nOn1b3OBaTb HgYKTUHBHO - eMKOCTHyIO Mogenb [1].

gao cMx nop C'MTanOCb, 4TO 6monorM4eCKaS TKaHbo6nagaeT TOnbKO eMKOCTHbIMH CBOACTBaMm, HO HanpaKTUKe 6blnO goKa3aHO, 4TO OHa xapaKTepU3yeTcqcyuLecTBeHHO 14 HgyKTHBHOCTbIO. I4enbIo gaHHOu cTa-TbU RBnSAeTCI paccmoTpeHUe 3neKTpOreHe3a cepgia CnOMOLLAbIO 14HgyKT4BHO-eMKOCTHOA Mogenf, noKa3aTbBa)KHOCTb napameTpa 3neKTpwiecKoA Ao6pOTHOCTMcepgL,a JnJ npoBegeH4R mccnegOBaHMFI u garHOCTUKMCepge4HO-COCygHCTOA CUCTeMbI.

ILOCHOBHas 4aCTbCornacHo HHyKTUMBHO-eMKOCTHoU MogenJ cepgeq-

HYIO TKaHb MO)KHO OXapaKTepM3OBaTb TpeMl napaMeTpa-Mm: ConpoTIBJ1eH4eM, 4HgykT4BHOCThlO H eMKOCThIO. MC-CJ1egOBaHH. [1, 2, 3] B gaHHOM HanpaBMeHMM nlOKa3an4,'TO HHgyKTMBHOCTb U COnpOThBneHHe MO)KHO C'MTaTbnO4Tm nOCTOqHHbIMH BenJ IHaMm. B npoi4ecce Kapguo-L4Ktna npOmCXOgmT L43MeHeHUe eMKOCTm C, 4TO CB93aHHOc L4HKnH4ecKoA 4aCTOTOU BpauLeHHSF 4HTerpanbHoro 3neK-Tpm4ecKorO BeKTopa cepgLa (I.I3BC). IMeHHo Bono6yeBA. H. npegno)Kwn, B Ka4ecTBBe gononHMTenbHoro napa-meTpa npm npOBseeHHH uccnegOBaHuu HCcnoJlb3OBaTb3.neKTpMeCKO go6pOTHoCTb cepgi4a. MbI Ke CwMTaeM,4TO 3TOT napameTp MO)KHO OCTaB4Tb B OgHH PsA C gpy-rtMM BeJ1MqHHaMm, KOTOpblMU onepMPMIT npu M3y'eHMH 1gmarHocThKe cepgLia. Ba)KHOCTb aToro napameTpa noKa-3bIBaeT KnfHHHeCKaq npaKTmKa: gawe npfH HepKO Bbipa-)KeHHOU naTonorMm, Korga 13MeHeHH$ napameTpoB 3KrnOqTM He 3aMeTHbI, npOHCXOgMT H3MeHeHHe go6poTHo-CTh. flo3TOMY, KOHTPOJ14pyq TeHgeHLA4MI H3MeHeH S4 jgo6-pOTHOCTU cepALa B TeBeHHM HeKOTOpOrO BpeMeHM MO)KHOcge.naTb BbIBOg 0 pa3BMTum naTonorndecKoro npoLAecca,ga)Ke ecnm OCTaJbHbie KOHTPOJ1MpyeMbie napameTpbl 3KrHaXOg,TCS B npegenax HOpMbI. CnegOBaTenbHO, gnr 6o-nee rny6oKoro Hcc1egOBsaHMA Ba)KeH pacqeT go6poTHo-CTH cepgL4a.

B npo4jecce Kapg4oLmKvna go6poTHoCTb 13MmeHqeTCqno 3KcnOHeHH4HanbHOMY 3aKoHy:

Q=Qoexp(-R(t-to)/L) (1)

rge QO = /oRIL - go6pOTHOCTb 3KBtBaneHTHorO KOHTy-pa B MOMeHT BpeMeHM to.,

R, L - aKTHBHOe COnpOTHBneHme H HHgyKTHBHOCTb, CO-

OTBeTCTBeHHO.

6onee TO4HO OnpegentMTb 3TOT nOKa3aTenb MO)HOMaTeMaTHMeCKH, gn3 3TorO Heo6XogmMO BbIBeCTM cXop-Mylny paC'eTa Q0. Jo6pOTHOCTb MO)KHO OnpegeWJ1Tb 13OTHOwIeHWS 3neKTpOKapgmorpaXu44ecKMX MHTepBarJOBAtQT lAtQS . 06a 3TU MHTepBana He 3aB4CRT OT nonoKe-HMFl 3fleKTpM4eCKOk OCm cepgLa. 03 [1]

1 + 2arctgvfR7-LR=1R 12arctgv&~fRf

AQ 1+!2arctgv&RJY 2,QTR 1 + 2arctg[R _ 27r ,

Qo Qo(3)

rge AtQRS - gllUTenbHOCTb KOMnnJ1eKCa QRS,AtQT - gnJTenBHOCTb 3fleKTpMLeCKOA CMCTOnbl QT,R, T- mnlnlTygbI 3y6LAOB 3Kr.Wcnonb3ysl CBOUCTBa COnpUKOCHOBeHMR CPyHKL4MU

HyneBoro U4 nepBOro nlopgKa, M3 3TOrO COOTHOWeHHRBbIBegeM 4opMyny gns pacqeTa Qo:

2arctgRJI r+2ir -2r atrctgJFR'TJQO .(4)

ir+2-4 artgjR77ILkQRS

KaK BHgHO U3 4OpMynbl (4), BCe BeJ1UMUHbi Heo6Xo-gNMbie npu nogcqeTe MO)KHO onpegeJNTb no 3neKTpo-KapgMorpaMMe.

HaMM pa3pa6oTaHa nporpaMMa, KOTOpa5 nO3BoJnieTaBTOMaT"qeCKH onpegenqTb 3neKTpMLIeCKyi io 6poT-HOCTb cepgL4a, BbiqLMCJ1Tb yron HanpaBneHHq 3neKTpu-qeCKOU OCM, OTHOweHme LIR H CTpOUTb OCHOBHbierpaC4MKM 3aBHC4MOCTeM.

3KCnepHMeHTarlbHO, nyTeM CHFTMI4 3KF naI4HeHTOB,6blJio yCTaHoBJ1eHO, 1TO 3JneKTpMqeCKaq go6pOTHOCTbcepgLAa yMeHbwaeTcS npm nmTnorJO eCKHX npoI4eccax,B CpaBHeHHH C HOpManbHOA pa6oTOA Cepg14a. 3To no-3BOnJeT HaxogMTb pa3HMLy A Q H no HeA CygHTb 0

pa3BMTHM naTonorLm. Ha cnegyiou.teM 3Tane npOBOgMT-c.q pa6oTa no Ha6opy cTaTHCTHKH H cocTaBneHHO 6a3b1gaHHbIX, KOTOpa5 nO3BOJ1MT 6onee WHpOKO npHMmeHSTb3TOT napameTp B KnMHMqeCKOi npaKTHKe.

J,rn 6onee 6bIcTporo H HarnqgHoro onpegeneHH5nocTpoeHa HOMOrpaMMa Am1H onpegeneHL4sq 3neKTpLlqe-CKOA go6pOTHOCTM cepgAa (rpa4MK 3aBHCIMOCTH OTHO-wleHMq HHTepBanOB AtQT /AtQR OT OTHOWeHHF aMnni4-

Tyg 3y614oB RIT ), np4BegeHHaq Ha PHCYHKe 1.CnegoBaTenbHo, Ben"ql4HHY 3neKTpjqeCKOA go6poT-

HOCTU cepgLAa MO)KHO onpegen4Tb no rpa4oHKy (pHCyHoK1) Mum 6onee TOqHO COrnaCHO copMyne (4).

2005 15th Int. CIimean Conference "Microwave & Telecommunication Technology" (CnMiCo'2005). 12-16 September, Sevastopol, Crimea, Ukraine© 2005: CriMiCo'2005 Organizing Comunittee; Weber Co. IEEE Catalog Number: 05EX1089 863

Puc. 1. HoMoapaMMa dnm onpedeneHuR3fleKmpuYecKou do6pomMHocmu cepdtua Q

3HaYeHUw 3ieKmpuYecKou do6pOmHOCMU, KOmOpbiecoomeemcmeyiom KpU8blM:

1-4.6, 2-4,5,3-4,4, 4-4,3, 5-4,2, 6-4,74 8-3,9, 9-3,85,10 -38, 11-3,75

12- 3,7, 13- 3,65Fig. 1. Nomogram for electric Q ofhuman heart

Q values:1- 4,6, 2- 4,5, 3- 4 44 4,3, 5- 4,2, 6- 4, 177-4, 8-3,9 9-3,85, 10 -3,8, 11-3,75,

12-3,7, 13-3,65

III. 3aKnIuoeHmeTaK14M o6pa3oM, nony4eHHbie pe3ynbTaTbi nO3BO-

nMOT 4cnOnb3OBsaT pa3pa6oTaHHyo Mogenb u npo-rpammy WIls npoBegeHMS 3Kcnpecc-aHanM3a COCTORHASHaceneHMS.

J,ns npf4MeHeHAF mogenr Ha npaKTHKe Heo6xopgMococTaBneHme 3Kr aTnacoB (6a3bi gaHHbix), Hag YeM inpOBOpUTCFI janbHe1asw pa6oTa. 3To nO3BOnYT aBTO-MaTW3t4pOBaTb 3neKTpoKapgworpaO4f4ecKLe LccJlego-BaHMS U gUarHOCTHw, a TaioKe cyu4eCTBeHHO y8en4qMlTMX B03MO)KHOCTV4

IV. CnucoK nITepaTypbl[11 Bono6yee A. H. Kypc MeAWlLtHcKoiA u 6wonoriqecKo M4rn3M-

KM. CaMapa.: CaMapCKiA /OM neiaTH, 2002.- 432c[2] PawMep P. jQwHaMtrKa cepgeYHO-COCygWCTO4 CV4CTeMbi.

lep. c aHrJl. M.: Me,uwLJi,Ha, -1981. -346c.[3] XoawKUH A. HepBHbiH mmnynbc. nep. c aHrn. M.: Mp,

1965.- 128c.

864

SNAP ANALYSIS OF CARDIOVASCULARSYSTEM BASED ON INDUCTANCE-CAPACITANCE HEART MODEL

Beregovaya N. V., Korenovskaya 0. LZhytomyr State Technological University

103 Chemyakhovskogo Str., Zhytomyr, Ukraine 10005phone/fax +380 (412) 221410

e-mail: [email protected]

Abstract - A technique is proposed of using electric Q ofhuman heart in order to conduct snap analysis based on induc-tance-capacitance heart model.

I. IntroductionCurrently available parameters that describe cardiac per

formance are becoming increasingly inadequate during cardiol-ogy examinations. Research is underway to discover and im-plement new significant diagnostics parameters.

The goal of this paper is to discuss cardiac electrogenesisby means of inductance-capacitance model and to show theimportance of electric Q cardiac parameters in the studies anddiagnostics of cardiovascular system.

IL. Main PartElectric Q of the heart is suggested as another diagnostics

parameter whose importance is proven by clinical practice:even for inconspicuous pathologies, when variations in ECG pa-rameters are almost imperceptible, a change in Q occurs. Thus,by monitoring tendencies in cardiac Q variations over a periodof time a pathologic process may be registered, even if othermonitored ECG parameters are within the normal range. An in-depth analysis would consequently require calculations of car-diac Q.

Within a single cardiac cycle the cardiac Q changes expo-nentially:

Q=Q exp(-Ry(t -to) iL)A more exact formula to calculate cardiac Q has been de

rived using mathematical techniques.

2m~__IF7r+2g "T-2-~ arctg\lvR1T~\ QRS AtfQRS g

+2 arctgv'RT

It has been established experimentally through ECGs thatthe value of cardiac Q decreases during pathologic processescompared to normal cardiac performance, which allows for thedifference in Q to be found and used to monitor the develop-ment of pathology. The next stage in the research would involvegathering statistics and developing a database to make this pa-rameter more widely available in clinical practice.

In order to define cardiac Q in a fast and pictorial manner, anomogram shown in Fig. I has been developed.

Ill. ConclusionBased on the obtained results, the developed model along

with ECGs may be used for snap analyses of the population'shealth condition.

To implement this model in actual practice, ECG atlases(databases) should be developed, which is the subject of theprospective research. This would allow for ECG examinationsand diagnostics to be automated and their potential to be sig-nificantly increased.

2005 15th Int. Crimean Conference "Microwave & Telecommunicatior %echnology" (CriMiCo'2005). 12-16 September, Sevastopol, Cfnmea, Ulkaine© 2005: CriMiCo'2005 Organizing Committee; Weber Co. IEEE Catalog Number: 05EX1089