Mucus Transport in the Larger Airway Due to Prolonged Mild Cough: Effect of Serous Fluid and Cilia Beating

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1 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 Mc npo in he Lge Aiwy De o olonged Mild Cogh: Effec of Seo Flid nd Cili Being Ai Sxen * A.. ygi.depen of Mheic,FE, Mnv chn Inenionl Univeiy,Fidbd,, Hyn, Indi.Depen of Mheic,Fcly of Science, D.E. I.,Dylbgh, Ag, 85, U.., Indi *ixen.fe@i.ed.in Abc Since c podcion nd npo i n ipon defene echni of he lowe iwy, hi dy foce on hi pec. In hi ppe i i ed h he co-xil flow of c nd i i king plce in cicl be epeening lge iwy. In he cenl coe, i i ed o flow nde qi edy e blen condiion nd he c lye onding hi cenl coe i ed o flow nde nedy lin condiion. he polonged ild cogh i epeened by ie dependen pee gdien fncion. o conide he effec of eo flid, i h been ed h he cili bed i ppoxied by poo ix wihin which eo flid flow following Dcy lw. Fhe, he effec of cili being h been conideed by ing h conn en velociy which i e of effecive nd ecovey oke i iped on he eo flid nd hi velociy i peipoed on he Dcy flow. Fo conn pooiy of cili bed nd c vicoiy, i i hown h i nd c flow e decee wih incee in eo flid vicoiy. he effec of pooiy of cili bed nd cili being h been fond o incee he i nd c flow e. Keywod Cili Being; oo Mix; Mc npo; Cicl Model; olonged Mild Cogh. MSC () No.:76Z5. Inodcion Ne h povided highly coplex ye in hn body nd he hn lng i no excepion (Gobeg ). he lng, he lowe p of epioy c known bonchil ee, coplex ye of bnching of be, ing fo che dividing ino wo bonchi nd conining p o he lveoli, whee he g exchnge occ in cdiovcl ye. Ding nol behing, he iwy npo i ino he lng nd wih i, lo d, oxic ge, nd icoogni e inhled, ny of which e depoied in he lowe iwy. Mc podcion nd conino c npo fo he lowe iwy o he oophynx i n effecive defene echni o cle he iwy of lien eil nd keep he lng eile. he iwy c i copoed of inly long chin glycopoein nd l in penion of we (Silbebeg 8, Sleigh 8). he c vicoiy y nge fo oie o oie low he e ( ec - ) nd i gnide i bo. oie high he e ( ec - )( King e l., chelle e l. 8). Ye in 8 conideed c Newonin flid while oe ohe eeche eed i Mxwell flid. he cili e pced nifoly long he cell fce in elxed hexgonl lice nd he cili pcing i bo.-. icoee (Sleigh e l. 88). he cili pefo wvy oveen o eove d nd bcei long wih c fo he iwy owd he ho nd h pevening iwy of he lng fo infecion. Cili be in coodined wve like oion hogh he ol lye (Sndeon e l. 8) h c npo i govened by he echnicl foce of ciliy being nd iflow. he wok done ding he effecive oke i evel ie he on of wok done pefoed ding he ecovey oke (Geon ). he dion of effecive oke i. econd. he ecovey oke l nely wice long he effecive oke. h, he cili e ble o npo he c lye. he goble cell podce c while eo cell podce eo flid, we like bnce. he eo flid behve like Newonin flid. I vicoiy vie fo.-. oie. A ixe of lipopoein clled fcn i eceed by pecil fcn cell h e p of he lveol epiheli nd bonchiole, efl in c npo by cing lip he inne wll of ech lng. (Sleigh e l. 88) In he liee, ny eeche wok on cociliy npo. ecenly, Sih e l. 7 hve developed heicl odel of he npo of c nd CL in he iwy. Soe eeche died he cociliy npo nlyiclly by conideing wo lye flid odel, c being vicoelic Mxwell flid nd eo lye low vicoiy Newonin liqid (e.g. o nd Coin 7, Sphi 8). Once he gloi i eopened, bi-phic b of i -5 /ec pid pek, wih high flow e nd polonged lowe flow e phe vel hogh he pilly collped che nd ohe iwy, he flow becoing blen (Sleigh e l. 88). he heing foce ce cceleion of c lye leding o i npo nd he e conined wihin i. A died by Vnde Schn e l. c clence w conidebly le in pien wih chonic iflow obcion nd nol elic ecoil pee hn in pien wih chonic iflow obcion nd deceed elic ecoil pee. Foced iion wee le effecive in eing eenion of c in pien wih low hn wih nol elic ecoil pee. Sih e l. 8 6

2 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 ecenly diced heicl odelling of he flid echnic of cociliy clence nd inodced he ophology of he bonchil nd chel iwy fce liqid (ASL) nd cilied epiheli.. Govening Eqion wih Bondy nd Mching Condiion In view of he bove conideion nd ing ndl ixing lengh heoy, he en of qi edy e eqion in he blen lye nd he nedy e eqion of c in he lin lye cn be wien in cylindicl coodine follow (Schliching,6) Fig. Mc npo in cicl be: : egion I: Qi edy blen flow of i p z ( ) τ ; egion II: Unedy lin flow of c ( ) p z ; ( τ ) 6 τ l l () : τ () In eqion () nd (), i he ie, z i he coodine long he xi of he be in he flow diecion, i he coodine in he dil diecion nd pependicl o flid flow, i he hickne p o i-c inefce, i he di of he be, p i he en pee which i conn co wo lye,, e he en velociy coponen of i (nde blen flow) nd c (nde lin flow) in he z diecion epecively, τ i he en he e in he i nd τ i he en he e in he lin c lye, nd e he deniie of i nd c epecively nd i vicoiy of c. he ixing lengh l l (-), whee l i conn nd deeined eienlly. Ce. o dy he effec of eo flid, i h been ed h he cili bed i ppoxied by poo ix wihin which eo flid flow following Dcy lw. Bondy condiion () p () z In he egion of cili bed ( ) we hve ed h eo flid i flowing following Dcy lw cili bed i ed o behve like poo ix. Hee i he coefficien of pooiy. Ce. o dy he effec of cili being i i popoed h he poo ix foed by cili bed i live nd cive de o cili being nd hi bed ove wih en velociy in he diecion of flow. hi pec cn be ken ino ccon by chnging he bondy condiion. Bondy condiion (5) z p U (6) C In hi ce, in he egion of cili bed ( ) o ee he effec of cili being on c npo ding polonged ild cogh, he cili e ed o be being in coodined nne in ch wy o h he en velociy (e of effecive oke nd ecovey oke) U c i iped on c in ddiion o he velociy in he poo bed ced by pee gdien. Mching condiion τ τ (7) ; Eqion (7) epeen he coniniy of he velociy nd e coponen he wo inefce. p f (8) z Whee i he engh of he polonged ild cogh, he gnide of which depend pon he ineniy of blence ced by polonged ild cogh nd hi incee flow e lo incee. If hee i no polonged ild cogh hen i zeo eveywhee. B ill c npo ke plce bece of he en

Cheicl nd oce Engineeing eech www.iie.og ISSN -767 (pe) ISSN 5- (Online) Vol., 5 6 velociy of cili being [Fig.]. Fig. Mc npo in cicl be Fig.

Anlyi of odel Ce. o ee he effec of eo flid vicoiy we olve he odel ()-() ing he bondy condiion (), (), ching condiion e given by (7).

3 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 6 velociy of cili being [Fig.]. Fig. Mc npo in cicl be Fig. Fncion epeening olonged Mild Cogh he fncion f() in (8) i ed o be given by, α α f () Whee i he dion of cogh nd α i he conn which i. nd. ec. hi fncion epeen he polonged Mild Cogh (Leih 77). Anlyi of odel Ce. o ee he effec of eo flid vicoiy we olve he odel ()-() ing he bondy condiion (), (), ching condiion e given by (7). o olve he nedy eqion in lin lye we e he ehod of veging done by Sek nd Chle in 68.he velociy coponen in ech lye cn be fond follow: l (.) (.) he voleic flow e in ech lye cn be defined d Q d Q π π, (.) hi fe ing eqion (.) nd (.) cn be wien 5 8 l Q π (.) Q 8 6 π (.5) Ce. o ee he effec of cili being we olve he odel ()-() ing bondy condiion (5), (6) nd he ching condiion e given by (7). o olve he nedy eqion in lin blye we gin e he ehod of veging done by Sek nd Chle in 68. In hi ce he velociy coponen in ech lye cn be fond follow: x - in econd f() in econd

4 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 65 l c U (.6) c U (.7) he voleic flow e given by (.) fe ing eqion (.6) nd (.7) cn be wien 5 8 c U l Q π (.8) c U Q 8 6 π (.) o olve he nedy eqion in lin lye we e he ehod of veging done by Sek nd Chle in 68. h,by biing he cceleion e on he igh hnd ide of eqion () by i en vle co he fil hickne i.e. Ψ d (.) hen eqion () edce o Ψ τ (.) Whee Ψ i fncion of ie only, nd given in eqion (8). Now by diffeeniing Eqion (.) o (.7) wih epec o nd ing eqion (.) f (.) Whee, f denoe he deivive of fncion fwih epec o. And 6 Now on olving (.) ing (8) nd (), we ge

5 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 66 α α p (.). Dicion nd el We now dy he i nd c flow e wih epec o vio pee. We pply he odel nlyi o he lge iwy nd conide he ce whee.5 - c. o dy he effec of vio pee on i flow e nd c npo qniively he eion fo Q nd Q hve been clcled nd ploed by ing he following e of pee (Shkl e l. )..ec, -.5 ec, l l..5 - c,.-. poie. - g c -. g c - -. g - c ec.-. poie g c - ec c U c.-.5 c ec - Fige. ille he effec of ie on i nd c flow e fo 5 poie,.5 g - c ec nd vio vle of nd fo hee fige i i obeved h i nd c flow e incee eo flid vicoiy decee. I i obeved fo Fige. h fo fixed c nd eo flid vicoiie, he coefficien of pooiy incee i nd c flow e incee. In fige. pee gdien i conideed o be zeo o ee he effec of cili being nd hence i cn be een eily h i nd c flow e incee he en velociy of cili being incee.

6 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 Fig..: Viion ofq nd Q wih fo diffeen (.5 g - c ec, 5 poie) Uppe denoe. poie Middle denoe.5 poie Lowe denoe. poie Fig..: Viion of Q, Q wih fo diffeen Uppe denoe Middle denoe. g- c ec.5 g - c ec Lowe denoe g- c ec ( 5 poie,.5 poie) 67

7 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 Fig..: Viion ofq nd Q wih fo diffeen U c (.5 g - c ec,.5 poie, 5 poie, ) Uppe denoe U c.c ec - Middle denoe U c.5 c ec - Lowe denoe U c c ec - 5. Conclion Fo he nlyi of he odel he following el hve been obined.. Ai nd c flow e follow he e pen he ie dependen pee gdien fncion epeening olonged Mild Cogh.. Ai nd c flow e decee wih incee in eo flid vicoiy.. he effec of pooiy of cili bed nd cili being h been fond o incee he i nd c flow e. I i poined o hee h hee el e in geeen qliively wih eienl el of vio eeche pblihed in liee. We hope h hi dy will how oe ligh on he ole of cili being nd eo flid in c npo in he lge iwy de o polonged ild cogh. efeence Gobeg, J. B. (), epioy flid echnic nd npo pocee, Annl eview of Bioedicl Engineeing,, -57. Geon, S., Levi-Gevich, K. (), Enegeic conideion of ciliy being nd he dvnge of echonl coodinion, oc Nl Acd Sci USA, 6, 5. King, M., Agwl, M. nd Shkl, J. B. (), A p odel fo cociliy npo: Effec of c vicoeliciy, Bioheol., -6. chelle, E., Zh, J. M. nd Dvivie, C. (8), Spinnbiliy of bonchil c: elionhip wih vicoeliciy nd c npo popeie, Bioheology,, -. o, S. M. nd Coin, S. (7), el of n nlyicl odel of cociliy pping, J. Appl. hyiol. 7, -. Sndeon, M. J., Sleigh, M. A. (8), Ciliy civiy of cled bbi chel epiheli, Be pen nd echony, J Cell Sci, 7,. Sphi, D. K. (8), Mheicl Modelling of c npo in he lng nde phologicl nd nol condiion, h. D. hei, Dep. of Mheic, Indin Inie of echnology, Knp. Schliching, H. (6), Bondy Lye heoy, McGw-Hill Book Copny, Inc., New Yok. Sek, J. nd Chle, M. E. (68), An ppoxie olion fo he -p flow of powe-lw flid in be, J. Che. Engg. Sci., 7-7. Shkl, J. B., Chnd,., Sphi, D. K. nd King, M. (), Soe Mheicl odel fo c npo in lng de o foced iion o cogh, oc. Inenionl Confeence on Fonie of Bioechnic, Bngloe, Indi, Decebe, -6. Silbebeg, A. (8), Bioheologicl ching: Mcociliy inecion nd epihelil clence, Bioheol., 5-. Sleigh, M. A. (8), Ciliy fncion in c npo, Che 8, Decebe, Sleigh, M. A., Blke, J.. nd Lion, N. (88), he poplion of c by cili, A. ev. epi. Di. 7, Sih, D. J., Gffney, E. A., Blke, J.. (8), epioy hyiology & Neobiology, vol. 6, Ie, Novebe,

8 Cheicl nd oce Engineeing eech ISSN -767 (pe) ISSN 5- (Online) Vol., 5 Sih, D. J., Gffney, E. A., Blke, J.. (7), A vicoelic cion lye odel of co-ciliy npo, Bll Mh Biol, 6, 8 7. Vn de Schn, C.., ie, D. A., Beekhi, H., Koee, G. H., Vn de k, h. W., o, D. S., hoex (), Effec of foced iion on c clence in pien wih chonic iflow obcion: effec of lng ecoil pee. 5, Ye, G.., W,. Y., Johnon,. E., Cheng, A.. W. nd Fnd, C. L. (8), A heoeicl nd eienl dy on chel cociliy npo, Bioheol. 7, 5-6. Leih, D. E. (77), Cogh: in epioy defence echni, J. D. Bin, D. F. oco nd L. N. eid, ed, p II, Mcel Dekk, Inc. New Yok,

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Solvability of nonlinear Klein-Gordon equation by Laplace Decomposition Method Vol. 84 pp. 37-4 Jly 5 DOI:.5897/JMCSR4.57 icle Nbe: 63F95459 ISSN 6-973 Copyigh 5 hos ein he copyigh of his icle hp://www.cdeicjonls.og/jmcsr ficn Jonl of Mheics nd Cope Science Resech Fll Lengh Resech