Vestibular apparatus: dynamic model of the semicircular canals

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1 Modelling in Mediine nd Biology VIII Vetibl ppt: dyni odel of te eiil nl L. Gtldi, S. Ptoelli & M. Soli Diptiento di Meni Politenio di Toino, Itly btt Te etibl ppt ply fndentl ole in eqilibioeption. It i loted in te inne e nd it btntilly opie otolit, wi indite line eletion, nd eiil nl, wi detet ottionl eletion. In ti ppe odel of diffeent oplexity of te eiil nl e epoted nd died: ononl ydo-elti odel nd tee-nl odel, in wi intetion between nl e onideed. Diffeent tend e obtined by ipleenting te two odel in Mtlb enionent. Te neil elt of te ononl odel e oped wit te lil toion-pendl odel nd wit litete dt; wile, fo te tee-nl odel, epone to ngl eloity dieted pllel to te pyiologil xe e epoted. Keywod: eiil nl, ydoelti odel, tee-nl odel, eno-tndtion. Intodtion Te etibl yte i te ppt tt detet infotion bot ptil poition nd oeent of te ed nd of te body. Ti infotion i fndentl inpt to ontol te pote, te pigt poition nd to oodinte eye nd ed oeent. Te etibl i qite oplex yte nd not ll of te enil-neo tndtion eni e opletely known; ti i lo de to te ipoibility of dietly eing n neo ignl. Mo et l. deeloped odel of te etibl ppt to be ed fo te otion eing lgoit of oeent ilto [], bt it n be lo effetiely eployed to bette ndetnd te fntioning of te yte itelf o wit dignoti i to elte ptologie of te blne yte. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) doi:0.95/bio WIT Pe

2 Modelling in Mediine nd Biology VIII In ti ppe odel of te eiil nl, wi detet only ottionl oeent, i peented. Sine it dioey t te end of te XIX enty, te tndtion biopyi of te etibl ppt beoe n objet of inteet nd in litete tee e oe odel tt deibe te eni of te eiil nl wit diffeent ppoxition leel: -ping-dping lped pete odel [, ] tt deibe te o-eni of te penoenon nd ononl [] o tee-nl [5] flidodyni odel. Te i of te deelopent of new odel i to obtin igoo tetil deiption tt n be ed to lidte iple o lineied foltion o oponent in oe oplete odel tt ont fo te etibl-ol eflex o te enil-eleti tntion peli to te eiil nl. egding te geoetil nd pyiologil dt of te eiil nl, de to te intini diffilty of diet eeent, te to efeed to litete, onideing nd oping, wenee poible, diffeent oe nd ege le wee tken. Pyiology of te eiil nl Peipel ppt of te etibl yte opie diffeent ogn tt pefo ditint enoil fntion nd peeie tti nd/o dyni oeent oding to te ix d.o.f. tt teie body tt oe in tee-dienionl pe. To egite ed oeent, o oe peiely ed oeent nge, te etibl ppt opie two diffeent enoil tte, bot pled in te lbyint of te inne e: otolit to detet line eletion; eiil nl to detet ngl eletion. Bot enoil ogn ontin te e eepto, te i ell, bt tey e teied by two diffeent peli ntoil tte tt deteine te peifiity in deteting line o ngl oeent. Te eiil nl (fig. ) e tee tee-qte il dt tt inteonite in te tile nd tey e filled wit flid lled endolyp. oding to tei poition, nl e deignted oizontl, poteio nd nteio. Tey e ligned ppoxitely otogonlly to one note nd te oizontl nl fo 0 ngle wit te pyiologil tnee plne, wile te peio nd poteio nl e ligned ogly t 5 ngle to te gittl plne. E nl n expnded end, te pll, wi open into te tile nd te peio nd poteio nl join togete t one exteity. In te intenl epiteli of te pll, next to te tile, geltino tte ned te pl i peent; it intode diontinity in te nl nd te i ell ili e ibedded inide. Te ili ell opete te tndtion of enil defotion de to eletion into neo iple tt will be elboted by te entl neo yte. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

3 Modelling in Mediine nd Biology VIII 5 oizontl nl poteio nl nteio nl pll pl tile Fige : Pyiology of te eiil nl. Te pyil piniple i te following: wen twiting te ed, te bone tte of te eiil nl tt e integl to it elete wit te e lw, wile te endolyp, de to inetil effet, oe wit lg, ing eltie dipleent between te dt nd te endolypti flid. Ti flow e pl defotion nd ition of te et poition of te i ell nd ene nge of te nee iple dige te ied by te etibl nee fibe to te bin te. Toion-pendl odel Te fit tetil deiption of te pyiology of ngl otion detetion i epeented by te toion-pendl odel fit intoded by Steinen [6]. Te ingle eiil nl i deibed ing dped -ping odel bjet to n inetil foe popotionl to te. Tog te ye eel integtion e been de to ti foltion, eeent on etibl odel pointed ot tt ention deteted ding ottionl oeent e oe oplex tn toe pedited by te toion-pendl odel. Yong nd On [7] intoded n dpttion opeto in de to eole te diffeene between te peeied epone expeientlly eed nd te one pedited by te toion-pendl odel. Zi [8] ggeted te intodtion of fte te to lo onide nel tndtion dyni. Let onide te nl etition of fig.. k e Fige : Toion-pendl odel of eiil nl. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

4 6 Modelling in Mediine nd Biology VIII Te tnfe fntion of te eni of te eiil nl n be deied fo te blne of te foe ting on te yte, wi, ing te Lple tnfo, y be witten : e () k wee: ngl eloity of te nl ngl dipleent of te eiil nl dt, onideed integl wit te ed nd efeed to te inetil yte; e ngl dipleent of te endolyp, efeed to te inetil yte; k elti ontnt oeffiient of kineti ioity of te endolyp; De to te io teiti of te endolyp, ti i n oe-dped yte nd eqn. () beoe: e () intoding: / k long tie ontnt / ot tie ontnt Te ot tie ontnt i doinnt fo ig feqenie nd i defined by te tio of te nd te io dping. On te onty te long tie ontnt, defined te tio of te io dping te nd te tiffne te, inflene te yte beio fo te low feqeny nge. Te neil le of te ot tie ontnt n be deied by te eiil nl pyiology nd tee i btntil geeent in ing fo n =0.005 [9], wile fo te le of te long tie ontnt dt epoted in bibliogpy e diodnt. Vn Egond et l. [0], oding to ebl epone of n bjeted to io otion inpt, ed long tie ontnt of 0 ; Myne [] ed te diogyl illion nd etited le between 8 nd, wile Goen [], ing nytg eod, obtined 6. Te etition of te long tie ontnt bed on bjetie epone i qite diffilt, it to be pged of te effet of nel poee. ing tt no nel poe tke ple fo etibl-ol nytg, Sidt et l. [] llted =8 ; ti elt i onitent wit te onidetion of ote to [,, ] we ed ti le to etite te feqeny epone of te toion-pendl odel. Een if te pete of ti lped pete odel e not eily identifible, ti tetil deiption ein te ot popl tool in nlying te beio of te eiil nl. Howee, te toionpendl odel i nble to deibe te dipleent of te pl nd it intetion wit te endolyp. To elte te el dipleent tt deibe te i ell odel, flid eni e needed. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

5 Hydoelti-flidodyni ononl odel detiled nlyi of te flid eni in tooidl dt bjeted to pee gdient w peented by Vn Bkik nd Gnt []. note detiled odel w obtined by bbitt nd Dino [5], ing pefet tooid nd ppoxiting te pl line elti plte. In te peent tdy, in ode to deelop te ononl odel, te to tted te tetent fo tigt dt wit il etion bjeted to n xil otion lw. ing tt te flid otion in te dt i lin nd tt te endolyp i newtonin nd inopeible flid, te Nie-Stoke eqtion fo te flid xil oponent i: P t z () wee: dt eletion dt-endolyp eltie eloity endolyp denity endolyp dyni ioity P flid pee z xil oodinte t dil oodinte tie Te oltion of te diffeentil eqtion, expeed in te Lple doini i: P J 0, () z J 0 t wee t i te dt di, J 0 i zeo ode Beel fntion nd /. Te eiil nl n be onideed, t let on fit ppoxition, plne tooid; te nl nd te tile e epeented wit two diffeent etion, btended epetiely by te ngle nd, nd wit intenl di nd, epeented in fig.. i te di of te te of te tooid, onideed ontnt, wile z i te iline oodinte long te dt xi wit te oigin in te pl. te flid eloitie in te nl e eltiely low nd ppoing lin flow, foe nd eletion of te flid tt e not xilly dieted y be negleted. Hene we n iilte te tooidl lengt to etiline dt wit eloity eql to te peipel eloity of te dt itelf. Wen onideing n ngl eloity of te eiil nl ond te xi pependil to te tooid nd ping in te te ente, te eloity of te flid eltie to te nl i: P J 0, (5) z J 0 wee P z i te xil pee gdient in te nl. Modelling in Mediine nd Biology VIII 7 WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

6 8 Modelling in Mediine nd Biology VIII nl Fige : tile z pl Dietiztion of te eiil nl fo te ononl odel. In eqn. (5) te dt di i negleted, being», nd te iline oodinte ie in te nge 0 z. Siilly, fo te tile lengt, wee te dt di nnot be negleted nyoe if oped to te tooid di, eqn. () beoe:, P J 0 z J0 P wee i te xil pee gdient in te tile nd te iline z oodinte ie in te nge z. Obeing tt te eiil nl i loed iit, te following eltion between te ition of pee P in te nl lengt, te ition of pee P in te tile nd te pee diffeene P on te pl ebne n be witten: (6) P P P (7) Fo te tile, te pee ition P n be deied fo eqn. (6) nd, onideing te onetion of flow, it n be expeed fntion of te flid eloity eltie to te nl eloity, being / te tio of te nl nd tile o etion: J 0 J P 0 (8) J 0 J0 To elte te pee dop on te pl, ti d been odelled n elti il ebne lped t te plly wll long it entie peiete nd bjeted to ditibted lod P in te xil dietion. ing tt pl nd endolyp e te e denity [, 5], te ebne defletion n be expeed in te Lple doin /, epeenting wit te ebne tikne, wit te extenl di of te ebne, wit E nd Yong nd Poion odl, te diffeene of pee P i: WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

7 6E P (9) Sbtitting fntion (8) nd (9) in eqn. (7) n expeion of P n be deied. By intoding it in eqn. (5), te tnfe fntion of / n be pointed ot nd ene te tnfe fntion between te ngl dipleent oeponding to te ebne defletion nd te nl ngl eloity i: K C M G, (0) wee oeffiient G, M, C nd K e epetiely: 6 G M 8 C 56 E K Coping expeion () nd (0), it n be notied tt te tnfe fntion of te peented ydoelti flidodyni odel tte nlogo to te one deied wit te oe iple toion-pendl odel, bt wit te dntge tt te teiti tie ontnt K C, C M nd te gin K G n be expeed fntion of te yte pyiologil pete. In fig. te gp of te feqeny epone / fo te toion-pendl odel deibed by eqn. () nd fo te ydoelti flidodyni odel e own. Fo te ltte, te en ngl dipleent of te pl i epoted. Te le of te pyiologil pete ed fo te nei iltion nd lited in tb. e been extted fo litete [, 5, 5]. Fo fte opion in fig. te feqeny epone of te Vn Bkik nd Gnt [] odel i lo epoted. Te feqeny epone e onitent, lo onideing te netinty of te pyiologil pete. Te peeption bnd of te eiil nl i in te nge of 0. Hz nd 00 Hz, wit n ttention t lowe nd ige feqenie. In te peeption bnd te pl defletion nd te eloity e in onte pe, wile fo lowe nd ige feqenie te yte peent epetiely lg of - 90 nd Modelling in Mediine nd Biology VIII WIT Pe WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line)

8 0 Modelling in Mediine nd Biology VIII Fige : Tble : Feqeny epone of te en defletion nd ngl eloity. ntoil nd pyiologil dt ed in te neil odel. nl te di intenl di of te nl intenl di of te tile ngle btended by te nl ngle btended by te tile ebne di ebne tikne ebne Yong odl ebne Poion odl dyni ioity of te endolyp denity of te endolyp E d 0. d N/ P 000 kg/ 5 Hydoelti-flidodyni tee-nl odel Te oienttion of te tee eiil nl deteine te etibl ppt enibility to ngl eletion dieted in ny dietion [6]. In genel, gien til, e nl nwe in diffeent nne. To elte te epone it i neey to indiidte te eletion oponent dieted t te nl tooid xe nd ten to tdy te yte flid-dyni beio. depited in fig. 5, te etil nl, nteio nd poteio, join in oon egent, wit o etion tt i bot twie te etion of te ingle nl, befoe oneging in te tile nd tey e ot of it t oppoite end. We wnt to onide, fo lltion eon, iplified geoety tt i till loe to te ntoil one, nlogoly to wt d been done fo te ononl odel; te nl d been deibed tooid wit il pln etion, wit e being otogonl. Tee plne e oiented in epet of te WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

9 Modelling in Mediine nd Biology VIII pyiologil xe, own in fig 5. Te tile i odelled egent of te oizontl nl wit n enlged etion; te nteio nd poteio nl e te etil egent wit te doble etion nd e e lf tile wit te oizontl nl. nt. nl po. plne z etil egent y x nt. plne o. plne po. nl o. nl tile Fige 5: Dietiztion of te etibl ntoil geoety. Bed on te etition epoted in fig. 5, it i poible to wite te eltion between pee in te diffeent egent of te eiil nl: oizontl nl poteio nl nteio nl () () P / P P / P / p P P P / p P / P P P / () wee P i te pee ition t te tile end, P te pee dop on te pl, P te pee ition in te etil egent ed by te nteio nd poteio nl nd P te pee ition long te nl. Sbipt / /p nd / indite gnitde eltie epetiely to oizontl, poteio nd nteio nl. nlogoly to te ononl odel, te endolyp i ed to be newtonin inopeible flid goened by te Nie-Stoke eqtion. Uing ontinity of pee nd onetion of flow, fte oe lgeb, te eltion () between te ebne dipleent eto of te tee nl [ p ] nd te ngl eloity eto pojeted in te dietion pependil to te nl plne [ p ] beoe: p b B b p C () wee te tix oeffiient, llted fo te pl xi deflexion, wi i in oepondene to te nl xi, e: WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

10 E 6 E B p 8 E C 8 p b p b p p Te noenlte ed in te oeffiient expeion te e ignifine it d in te ononl odel, wit te ddition of bipt p nd to indite epetiely te oizontl, poteio nd nteio nl nd te etil ed egent; te ngle i te btended by te oon etil egent. Te feqeny epone /, / p nd / of te ple en defletion fo tee e of ed ottion long te pyiologil xe: oll (xi x), yw (xi y) nd pit (xi z) e own in fig. 6. ntopoetil nd pyiologil dt e ed eql fo te tee nl nd e te e lited in tb., wit te ddition of = 0. d. Modelling in Mediine nd Biology VIII 009 WIT Pe WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line)

11 Modelling in Mediine nd Biology VIII b Fige 6: Feqeny epone of te tee nl ege pl defletion nd ngl eloity fo: ) oll; b) pit nd ) yw otion. Te p bnd i till te e te ononl odel, bt gin le nge oding to te dietion of te otion. In ptil te oizontl nl gin i pelent fo te yw otion, wile fo te oll otion it i lowe tn 00 db. Vetil nl peent beio ey iil in ll tee otion lw teted. 6 Conlion In ti ppe te flidodyni nlyi of te eiil nl bed on iplified geoety i peented. Bot ononl odel nd tee-nl odel d been deibed. Fo te fit odel elt of te feqeny epone between te pl defletion nd te otion lw e onitent wit te tend of te iple toionl-pendl odel nd wit ote flidodyni odel peented in litete. Fo te tee-nl odel in litete expeientl elt e not peent, o it wold be neey to ollet oe dt nd ti i llenging gol. In ft, diet expeientl ee e not poible nd fo te indiet ee, exploiting te nytg eltion, it i neey to lo tke into ont te nel nwe dyni. Te olletion of expeientl dt i till n open qetion in ee bot te etibl yte. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe

12 Modelling in Mediine nd Biology VIII efeene [] Mo S., Mttizzo G., Ptoelli S., Soli M., Deelopent of fligt ilto: otion eing lgoit, XVII Congeo IMET, Fienze, Itly, pp. -5, 005. [] Oby C., Model of Hn Dyni Oienttion, P.D. Tei, Mett Intitte of Tenology, Cbidge, M, 97 [] Yong, L.., Dyni ontol odel of te eiil nl, Dyni epone of Bioenil Syte, pp.-5, 970. [] Vn Bkik W. C., Gnt J. W., Vetibl Meni, Te Bioedil Engineeing Hndbook, Seond Edition, pp , 000 [5] bbitt. D., Dino E.., Hydoelti Model of Moeni in te Endolypti Vetibl Cnl, Jonl of Flid Meni, 8, pp. 7-69, 99 [6] Steinen W. Übe die beobtngen de pl in de bognegngpllen de lbyinte de libenden et. Pflege, pp.500 5, 9. [7] L.. Yong, C. M. On, Model fo Vetibl dpttion to Hoizontl ottion, eope Mediine, 0, pp , 969 [8] Zi, G.L., Motion Sention Dependene on Vil nd Vetibl Ce, 977, P.D. Tei, Mett Intitte of Tenology, Cbidge, M. [9] Stee,.W., Te inflene of ngl nd line eletion nd tel tiltion on te n eiil nl, Tei, M.I.T. [0] Vn Egond,.., Goen, J. J., nd Jongkee, L. B. W., Te Meni of te Seiil Cnl. Jonl of Pyiology. 0, pp. -7, 99 [] Myne,.., Syte Conept of te Vetibl Ogn, Hndbook of Senoy Pyiology, Vetibl Syte, Spinge-Velg: New Yok, pp , 97. [] Goen J.J., Te eni of te eiil nl, J. Pyiol. Lond., 0, pp.-7, 957 [] Sid,.M., Stefnelli, M., Mi, E., Mtetil odelling. t Otolyngol. 7, pp. 9-0, 97. [] Goldbeg, J.M., nd Fenndez, C., Pyiology of Peipel Neon Inneting Seiil Cnl of te Sqiel Monkey. II. epone to Sinoidl Stiltion nd Dyni of Peipel Vetibl Syte. Jonl of Neopyiology, (): p , 97. [5] Sto H., Sndo I., Tki H., Copte-ided tee-dienionl eeent of te n etibl ppt, Otolyngology - Hed nd Nek Sgey, 07(), pp , 99. [6] bbitt.d., Dietionl Coding of Tee-Dienionl Moeent by te Vetibl Seiil Cnl, Biologil Cybeneti, 80, pp. 7-, 999. WIT Tntion on Bioediine nd Helt, Vol, ISSN 7-55 (on-line) 009 WIT Pe