A Mathematical Model for the Effect of Magnetic, Body Acceleration and Time Dependence on Blood Flow in Stenosed Artery

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Coral Gordon
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1 sli Jol of Bsic d pplied Scieces 6: ISSN Mheicl Model fo he Effec of Mgeic Body cceleio d Tie Depedece o Blood Flow i Seosed ey hd ez ghighi d Nsi sghi Depe of Mheics Ui Uivesiy of TechologyUi I Depe of Mheics Islic zd Uivesiy Cel Teh BchTeh I bsc: Blood flow i seosed be hs bee odeled i he pese ivesigio The odel is ied sdyig he effec of seosis o flow e d she sess disibio o ie depede plsile flow of blood i he eies The odel hs bee coped wih he ie idepede odel d show h he ie depede hs sigific effec o he flow siio The odel ccos fo he olies of blood flow sch s; bled velociy pofile d Fhes Lidqis effec FLE The odel lso hs bee sdied fo vios of peic effecs sch s geic body cceleio size of Blood cells Cople Sessfeqecy plide phse diffeece pecege seosiscosicio d legh of seosis Oe of he os ipo spec of he pese odel is h he odel hs bee sdied fo diffee blood diseses d coped wih he cse of ol blood Key wods: Seosed ey Flow es of blood She Sess INTODUCTION Oe of he os pedicble ps of h life is geig ffeced by he ck I is le by sisicl svey h oe o evey is geig ffeced by he ck od he globe By d lge we kow ow cses ssocied wih he he ck hogh exc cse of he se is sill f wy fo he kow spec Oe of he cses ibed de o he ck is hiig of he pssge cosicio of blood flow The eso gi fo cosicio is ibed de o cclio of fy sbsce choleseol d blood clos o he ieio p of be lethe expeiel sdy sgges h p o 7% cosicio he pie do o feel cofoble ll d he/she c cope p wih he eqiee of blood spply o vios ohe ps oweve fo he cosicio i he ge of 8% d bove docos geelly eso o sgey fo he pies pese hee e o gidelies whe is he igh ie o go fo he sgey Sgeos eed o hve gide lie wh effecs cosicio hs o segh of he eies d how esisive e he eies wih vied degee of cosicio I view of he ipoce of blood flow sdies i Cdiovscl syse he pese sdied hve bee oieed wih is pplicio o blood diseses lso he odel hs bee ied o iclde effecs of ie depedecy Sivsv LM d Sivsv VP 98;Mdl PK Mdl d in 7 plsile e olies of blood flow Fhes Lidqis effec FLE Diefss L 967 ild geic effecs o blood flow Bohy MF969; Vdy V973; Deshikch KS chd o 985 blood cells sspeded i pls Bgliello G d Sevill J97 viscosiy of blood fo diffee blood diseses Plhd N d Schlz D;Sk DSd K elh7 d feqecy eled effecs ghighi d N Plhd8;Msph N d Mdl PK; Woesley J955 o he flow The blood is ssed o be epeseed by ico-coi cople sess flid poposed by Sokes 966 I his ppe he sdies hve bee bsiclly focsig oo ccoig of plsile e of blood geic d body cceleio i he seosic ey wih view o cco i fo diffee blood diseses Mheicl ee of he sdies hs bee oped fo kel sfoio ppoch ised of coveiol eihe eicl o epiicl ppoch Deiled spec of flow pees d is viios wih he plsile geic body cceleio d blood cells hs bee exploed i his ppe lysis: I is ssed h he flow is plsile d li d blece effecs i he body e egleced p ρ η z Eqio i cylidicl pol co-odies de he peiodic body cceleio i he pesece of geic field is give by Coespodig ho: hd ez ghighi Depe of Mheics Ui Uivesiy of Techology Ui I E-il: hhghighi@gilco 359

2 s J Bsic & ppl Sci 6: G z p B ρ σ η ρ Whee is he velociy i he xil diecio e he desiy d viscosiy of blood is he cople sess pee is he elecicl codciviy is he exel geic filed d is he dil coodie 3 The flow geoey of blood flow hs bee show i Fige Fig : Blood flow i seosedbe The elio bewee be geoey d xis is give by he followig elio Ikbl Md S Chkvy S d Mdl PK 9 cos L d z L z π δ ohewise L d z d Fo he iiil clclio of velociy flow e Q pesse gdie d body cceleio e ssed o be of he fo Tvee S 5 cos z p ω 5 cos G ω 6 Whee he sedy-se p of pesse gdie is he plide of he oscilloy p f ω π d is he he plse feqecy is he plide of body cceleio f π ω d f is body cceleio feqecy is he phse diffeece z is he xil disce d is ieflow vibles hve bee olized by sig followig elios: ω ω ρ ω ω ω z z 7 Eqio siplifies o fe doppig ss b cos cos 8 Whee cople sess pee Woesley pee is he be d is he dis of he pipe

3 s J Bsic & ppl Sci 6: ω ω ωρ σ η b B 9 The iiil d body codiios fo his poble e ghighi d N Plhd8: cos J J fiie e d Tvee 5 hve lyzed he odel fo velociy copio d fo he sigh be his expessio fo velociy hs bee ke fo fhe ivesigios i he pese sdies wih ppopie chges fo he cosiced seosed be } cos } si cos } { } } si }cos } si }cos b b e b b b b J J h 3 Whee h d J d J e hebessel fcios of ode zeo d oe especively d e he oos of eqio J Used of sfo echiqes SeddoN98 hve bee de se i solvig eqio 8 She Sess: She sess z τ which is oe of he physiologicl ipoce pees hs bee coped by sig followig elio ez τ 5 Usig Eqio 3 She sess siplifies o

4 s J Bsic & ppl Sci 6: } cos } si cos } { } } si }cos } si }cos b b e b b b b J J h τ 6 Whee is he viscosiy of pls which is ke s cpi he pese odel d ω τ τ z odiesiolshe sess Flow e: Flow e Q hs bee coped by sig followig elio d Q π 7 } cos } bsi }cos } { } } bsib }cos } si }cos b e b b Q h π 9 ESULTS ND DISCUSSION Oe of he i objecives of he odel is o sdy exhsively he effecs of she sess d esisce o flow o blood flow ece copios e ily focsed oo she sess d esisce o flow fo vios peic effecs She sess d esisce o flow hve bee coped fo he cse of Nol Blood d fo he disesed blood Polycyhei Pls Cell Dyscsis d fo bss The d eqied fo he copio hs bee ke fo TveeS5;Plhd N d D Schlz d show i Tble Use of Mlb d Mple sofwe Yg WY Co W Chg TS d Mois J ;sel CD hs bee de se while copig fo she sess d esisce o flow Tble : Viscosiy D Plhd N d D Schlz Diseses cp cp Nol Blood 38 Polycyhei 675 Pls cell Dyscsis 99 bss 39 She sess hs bee coped fo he cse of Nol Blood d ohe blood diseses Polycyhei Pls cell Dyscsis d bss Effec of peic viio hve lso bee obseved i he lysis The esls hve bee show i Fige -9The obsevios e highlighed below

s J Bsic & ppl Sci 6: 359-37 Fig : She Sess fo seosed diffee s Fig 3: She Sess fo seosed diffee s Viio of she sess wih Fige -9 d Fige 9 shows h he vles of she sess iceses wih he especive icese i peic

5 s J Bsic & ppl Sci 6: Fig : She Sess fo seosed diffee s Fig 3: She Sess fo seosed diffee s Viio of she sess wih Fige -9 d Fige 9 shows h he vles of she sess iceses wih he especive icese i peic vles oweve wih Fige 9-3 d ie Fige 6-7 i is obseved h she sess decese wih icese i peic vles These obsevios e fod o be i geee wih he physics of flow d defoio Fo isce icese i es decese i blood cells cos which i e shold icese velociy gdie d hece i sheig sess vle which is bee obseved by he fidigs of he pese lysis Siilly iceses i geic effec body 363

6 s J Bsic & ppl Sci 6: cceleio d ie obsevio shold decese he she sess sice geic effec d body cceleio ehce body fcioig d ie will sbside ll iiil pebios I is lso oed h disic behvio of ie depedecy wih h of ie idepedecy hs bee obseved if we obseve he she sess vle 5 d 5Fige -5Oe of he os sigific obsevio i sess disibio fod is whe coped wih he viio of pecege icese of seosis heighcosicio Fige -5 Fig : She Sess fo seosed diffee s Fig 5: She Sess fo seosed diffee s 36

s J Bsic & ppl Sci 6: 359-37 I is obseved h she sess iceses wih iceses of seosis heigh fo o 6 howeve whe coped fo 8 we fod h he sess vles sddely dops off This sge behvio c be ibed de o sdde chokig of

7 s J Bsic & ppl Sci 6: I is obseved h she sess iceses wih iceses of seosis heigh fo o 6 howeve whe coped fo 8 we fod h he sess vles sddely dops off This sge behvio c be ibed de o sdde chokig of he le d his sge he evese flow y s of d h cold be he eso fo sdde decesig i sess vle This obsevio is i geee wih h of Yog 979 whose expeiel obsevio fod h he flow behves bolly fe 7-8% of cosicio Fig 6: She Sess fo seosed diffee s Fig 7: She Sess fo seosed diffee s 365

8 s J Bsic & ppl Sci 6: Fig 8: She Sess fo seosed diffee s Fig 9: She Sess fo seosed diffee s 366

s J Bsic & ppl Sci 6: 359-37 Fig : She Sess fo

9 s J Bsic & ppl Sci 6: Fig : She Sess fo seosed diffee s Fig : She Sess fo seosed diffee s 367

10 s J Bsic & ppl Sci 6: Fig : She Sess fo seosed diffee s Fig 3: She Sess fo seosed diffee s 368

11 s J Bsic & ppl Sci 6: Fig : She Sess fo seosed diffee Fig 5: She Sess fo seosed diffee 369

12 s J Bsic & ppl Sci 6: Fig 6: She Sess fo seosed diffee Fig 7: She Sess fo seosed diffee 37

13 s J Bsic & ppl Sci 6: Fig 8: She Sess fo seosed diffee Fig 9: She Sess fo seosed diffee 37

14 s J Bsic & ppl Sci 6: Coclsios: Blood flow i seosed cosiciobe hs bee sdied i he pese ivesigio de o is ipoce i Cdio-vscl d bioedicl sciece Fg YC98986 The flow of blood is ssed is be epeseed by cople sess flid Effec of geic Body cceleio ogehe wih ie depedecy plsile e of blood flow hs bee cosideed i he odel The sdy lso cco fo diffee blood diseses Polycyhei Pls Cell dyscsis d b ss d coped wih he cse of ol blood The esls idice h he effecs of ie depedecy o flow pees sch s sheig sess hve sigific effec o he flow i copiso o sedy spec lso Effec of geic body cceleio hs sigific effecs wih ie depedecy The size effecs hve fod o ggve flow siio i Nol blood d wose i cse of disesed cse de o he pesece of oe blood cells Oe of he os sigific specs of he pese ivesigio is h he odel cofis wih he fidigs of Yog 979 beyod cosicio of 8% he flow becoes ciicl d exhibi qie bol behvio EFEENCES Sivsv LM d VP Sivsv 98 Peislic spo of blood: Csso odel II J Bioechics 7: 8-89 Bohy MF96969 Biologicl effecs of geic fields: Vol d Ple Pess New Yok Bgliello G d J Sevill97 Velociy disibio d ohe chceisics of sedy d plsile blood flow i fie glsses bes Bioheology 7: 85-7 Deshikch KS d chd o985 Effec of geic field o he flow d blood oxygeio i chels of vible coss-secio I J Egg Sci 3: -39 Diefss L 967 Ivesio of he Fhes-Lidqvis pheoeo i blood flow hogh cpillies of diiishig dis Ne 555: 99 Fg YC 98 Bio-echics Spige-Velg Fg YC986 Bio-dyics Spige-Velg ghighi d N Plhd 8 Effec of Low Pesses o he Physiologicl spec of h body fo vied eeoologicl d ebolic codiios Ieiol Jol of Mheicl Scieces d Egieeig pplicios IJMSE 3: 5-9 sel CD Mseig Mlb7 Lodo Ikbl Md S Chkvy KL Kelvi Wog J Mzdb d PK Mdl 9 Usedy espose of o-newoi blood flow hogh seosed ey i geic field Jol of copiol d pplied Mheics 3: 3-59 Mdl PK S Chkvy Mdl d N i 7 Effec of body cceleio o sedy plsile flow of o-newoi flid hogh seosed ey ppl Mh Cop 89: Msph N PK Mdl P Johso d N i eicl silio of sedy blood flow hogh li-iegl eil seoses pplied Mheicl Modellig 3: Plhd N d D Schlz Modelig of eil seosis d is pplicios o blood diseses J Mheicl Bioscieces 3- Sk DS K elh 7 o-newoi flid flow odel fo blood flow hogh cheeized ey-sedy flow pplied Mheicl Modelig 3: Seddo N 98 Specil fcio of heicl physiscs d cheisy Log Sokes VK 966 Cople sesses i flid The Phy Of Flids 9: Tvee S 5 Blood flow hogh ow bes wih peiodic body cceleio i pesece of geic field d is pplicio o cdiovscl diseses PhD Thesis Glbg Uivesiy Idi Vdy V973 Effec of geic field o blood flow Biofizik 83: 9-96 Yg WY W Co TS Chg d J Mois pplied Neicl Mehods Usig Mlb Wiley- Iesciece New Jesey Yog DF 979 Flid echics of eil seoses J of Bioechicl Eg Ts SME : Woesley J955 Mehod Fo The Clclio of Velociy e of Flow d Viscos dg i eies whe he Pesse Gdie is Kow J Phsiol

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of

One of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo