NUMERICAL AND EXPERIMENTAL INVESTIGATION OF FLOW FIELD INSIDE ARTERIES AND VEINS

Transcription

1 Nmbe Volme 3 ne 7 onal of Engineeing NUMERICAL AND EPERIMENTAL INVESTIGATION OF FLOW FIELD INSIDE ARTERIES AND VEINS ABSTRACT PofD Najdat Nashat Abdlla AsstPof Hssain Yosif Mahmood Gadate Stdent Sadiq Elias Abdllah Depatment of Mechanical Engineeing Uniesity of Baghdad Nmeical and epeimental inestigation of blood flow thogh stenotic and tapeed ateies nde plsation condition ae stdied Blood is consideed as non-newtonian flid Atey is consideed as a igid wall tapeed essel with diffeent tapeing angles 5 o, o,5 o, as well as, staight essel fo compaison The goening eqations hae been witten in steam- oticity method and ae tansfomed into genealized coodinate system The time maching has been employed to sole the eslting patial diffeential eqations The epeimental wok caied ot to eamine pesse in essel and pesse dop acoss the stenosis nde plsation condition Diffeential pesse tansdce copled to the data acqision cad type PCI-9DG, which is bilt in compte was sed to ecod pesse data The eslts showed that, as a tapeing angle inceases 5 o, o, 5 o both wall shea stess and pesse dop inceasing, also as stenosis inceases 5%, 6%, 75% both wall shea stess and pesse dop inceasing These behaios ae fond in liteate, pesse dop is sed to compae epeimental data and nmeical eslts, which indicates ageement As the distance into tape section inceased both wall shea stess and pesse dop ae inceased, as well as, both wall shea stesses and pesse dop inceased with inlet flow ate inceased, while deceased with inlet diamete incease الخلاصة 5,, 5 -

2 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah PCI- Tansdce 5,, 5 9DG, 75%, 6%, 5%, INTRODUCTION, Consideable attention was paid to stdy elated ciclatoy flow in blood essels towad the beginning of the last centy A lage nmbe of theoetical and epeimental Inestigations eleant to this biomechanical aspect hae been caied ot in ecent yeas Hadly need mention that, abot thee qate of all death occing these days ae mainly cased by ciclatoy diseases associated with distbed flow condition in the blood essels which lead to the malfnction of the cadioascla Chen 3 The pesence of stenosis inceases flow esistance in ateies which foces the body to aise the blood pesse to maintain the necessay blood spply Both the high blood pesse and naowing blood essel case high flow elocity, high shea stess and low o negatie pesse at the thoat of the stenosis In addition to low shea stess, flow sepaation and wall compession o een collapse at the distal side of stenosis This may elated to the thombs fomation, atheoscleosis gowth and plaqe cap pte which lead diectly to stoke and heat attack Seeal stdies of flid dynamics thogh stenosis hae been caied ot to ealate the flow patten and the shea stess at walls at steady and plsate flow conditions Some attempts to stdy epeimentally,walbn and Stein 98 meased elocity with Lase Dopple anemomete in pleiglass tbe with tapeed of 5 o, 5 o and 5 o, meased fom centeline to the wall ding steady flow These angles wee compaable to the angles of tape obseed in abdominal aota of nomal sbject 5 o ± o "ange o to 3 o " as epoted They calclated tansition ynolds nmbe which based on diamete of tbe at point of measement The eslts show inceasing of tansition ynolds nmbe with inceasing angle of tapeing, also with inceasing distance into tapeed section fo constant angle of tape These obseations sggested that, tapeing of abdominal aota tends to pomote lamina flowojha, et al 989, sed a photochomic tace method to ecod plsatile flow elocity pofiles simltaneosly at thee aial locations along a flow channel Theeby enabling the time and spatial distibtion of the wall shea stess to be stdied, as well as isalizing of the flow In addition, they stdied the tansition to tblence tiggeed by the modeate stenosis Asymmetic and aisymmetic stenosis models wee sed Shape of stenosis wee based on clinic obseations, pecent of aea edction wee 45%,65% and 75% fo aisymmetic,while 38% "of total aea coss section " fo asymmetic stenosis The wok was done fo ynolds nmbe in the anges of and Womesley nmbe of 75 Othe nmeical stdies deal blood as non Newtonian flid, Pontelli 999 inestigated steady aisymmetic flow in a consticted igid tbe A shea- thinning flid which modeling the defomation dependent iscosity of blood The goening eqation was witten in oticity steam fnction and soled nmeically by finite diffeence method The constiction was descibed by eponential fnction The eslts demonstate that, the non-newtonian chaacte of the blood in some typical egimes modify the flow patten een beyond the consticted egion, edce the pesse dop and shea stess at the wall acoss the stenosiskimmel and Dinna 983, modeled blood flow thogh a segment of lage ateies between bifcations as plsate flow of Newtonian flid in tapeed coneging tbes of small angle of coneging p to degee In this stdy, flow ate consideed as a

3 Nmbe Volme 3 ne 7 onal of Engineeing focing fnction athe than nifom pesse gadient Integal method was sed in soltion of Naie Stokes eqations The eslt showed that, change in flow condition de to tapeing of blood essel ae significant een fo small tapeing angle and cannot be ignoed Also as tapeing angle inceases, peak shea stess at wall also inceases, bt still below the citical ange which lead to damage of endothelial Poenta et al 985, sed a finite element method to model plsating flow in ateies segment inclding tape, banch, and obstctions In banch model,they assmed that the pesse diffeent acoss location whee banch diete fom the main steam was small and can be neglected, while in obstctions model,they calclate pesse diffeence acoss stenosis The eslts indicate that, the pesse wae wee taeling along atey shows an amplification in distal diection,and they conclde that each nonlinea tem contibtes to the effect noticed in the nonlinea case While the inflence of the conectie acceleation tem in momentm eqation was stonge,also the combined effect of both nonlineaities was lage than the added effect of each indiidal tem The effect of stenosis on pesse shows that the distal pesse fo 5% stenosis only slightly edced, and distal flows wee slightly damped,while fo high stenosis 75% and 9 % had lage effect Wall shea stess is an impotant facto in the stdy of blood flow,and an accate pedication of the distibtion of wall shea stess ae paticlaly sefl fo ndestanding the effect of blood on endothelial cells Go-Tao et al 4 inestigated distibtion of wall shea stess by simlation of plsating blood flow thogh stenotic tapeed atey The incompessible Naie-stokes eqations wee soled nmeically by a finite diffeence method The eslts indicated that, the height of stenosis was moe impotant facto inflencing blood flow than wall tapeing Tapeing fond to hae no effect on flow patten, bt only change the ale On the othe hand, it becomes bigge ale than withot tapeing; also the peak ale of shea stess of tapeed atey was bigge than that withot tape In paallel wok, Hn ng et al, 4 sed a finite olme method to sole thee dimensional, flly deeloped flows and blood taken as a non Newtonian flid which obeys to Caea-Yasda They compaed the eslts with Ojha et al 989 fo case of 45% stenosis tapezoidal pofile, and a good ageement was shown Fo cosine pofile stenosis, a nmeical comptational was condcted fo 5 %and 75% stenosis, and the eslt showed that, the seeity of the stenosis had significant effect on the geneal flow feates sch as sepaation ynolds nmbe and size of the sepaation egion, while the shape of stenosis had less effect Also, it showed that, the peak ales of wall shea wee eeted at the stenosis and negatie shea stess wee obseed in the egion whee a ote eists Smmay of the past stdies indicated that, the flow of non-newtonian flid thogh consticted tape atey nde plsation condition was not consideed As a conclsion, Go-Tao et al4, consideed Newtonian flid thogh consticted tape pipe, bt only fo small angle 5 o, while the pesent stdy etended to inole o, and 5 o Also noted that, Hn-jg et al 4, consideed flow of non-newtonian flid thogh consticted tbe nde plsating condition, bt they ignoed effect of tapeing and esticted the stdy to small pecent of stenosis5%,33%,5%,which its effect was small on pesse dop acoss stenosis Poenta et al 985 The pesent wok will conside the flow of non-newtonian flid thogh consticted atey nde plsation condition fo tapeing angles p to 5 o and pecent of stenosis p to 75%Nmeical and epeimentally inestigations of blood flow thogh consticted tape atey ae caied at plsation condition fo essels with 5%, 6% and 75% stenosis Blood consideed as a non- Newtonian flid obeying the shea thinning model MATHEMATICAL MODEL AND NUMERICAL CALCULATION The goening eqations of blood flow thogh stenosis atey at plsation condition ae fomlated and stated in pola coodinate The woking flid is consideed as a Non-Newtonian flid and incompessible

4 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah A schematic of the stenosis tbe geomety consideed in this stdy is shown in Fig, which consists of two main pats, tbe and the stenosis, stenosis geomety is shown in Fig Let s now conside a cylindical coodinate system,,θ haing the -ais coincident with the pipe ais since we seek an aisymmetic D soltion,all aiable ae assmed independent of θ and the azimthal component of anishes,eqation of motion can be witten as follows: p t µ µ µ ρ p t µ µ µ ρ Whee, ae the components of V in the and diections espectiely Comple heological behaio of blood is appoimated sing a shea thinning model, whee the appaent iscosity is epessed as a fnction of the shea ate Pontelli 999 and Hn ng et al 4 log µ e o 3 Whee o and ae asymptotic iscosities as and espectiely is a mateiel constant with dimension of time epesenting the degee of shea thinning shea ate which epesents a scala mease of the ate of defomation is gien by Pontelli 999 and Hn ng et al 4 ji ij j i e e 4 To non-dimensionalized the goening eqations, a set of aiables ae intodced Pontelli 999 R, R, f t t, V, V, 5 V p p ρ, R ΛV Λ, δ Whee: R essel inlet adis and V aeage elocity at inlet eq can be witten in following fom ] p t λ 5 and eq can be witten in following fom ] p t λ 6 Whee: υ λ f R Womesley nmbe, µ ρr ynolds nmbe; ƒ Feqency of plsation

5 onal of Engineeing Volme 3 ne 7 Nmbe Non dimensional iscosity which is gien below ] log δ e 7 Steam oticity appoach By coss diffeentiating and by sbtacting the contepats of eqs5 and 6, we obtain the oticity steam fnction fomlation : * t λ ] 8 and shea ate can be witten as follows ] 4 9 Voticity and steam fnction ae elated by poisson eqation: Steam oticity appoach obtained by eliminating the pesse tems fom the momentm eqations Since its impotant to know pesse dop to sed to compae nmeical eslts and epeimental data, the pesse dop along - ais deied fom momentm eqation fo steady incompessible, and non Newtonian flid eq5, Nallasamy 986pesse dop calclated fom following eqation: ] d dp Also, shea stess at wall is impotant facto which has diect effects on intenal laye of essel, whee a high ale of shea stess leads to damage in essel wall, shea stess at wall calclated fom eqation: wall wall τ Initial and bonday conditions To sole oticity tanspot eqation eq8 and Poisson eqation eq, it eqied that, the appopiate epessions fo steam fnction and oticity be specified at the bonday Andeson et al 984 The specification of these bonday conditions is etemely impotant since it diectly affects the stability and accacy of the soltion It is impotant and cae mst be taken to ense that the physics of the poblem is coectly modeled, on how to teat these geometies o models Hence the bonday conditions ae smmaized as follows:- - At tbe cente line: Voticity and steam fnction sets eqal zeo,,

6 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah - At tbe wall: Since no-slip condition at wall, elocity component eqal zeo, steam fnction set wall q/ 3 Whee q is flow ate fo eal sitation Taylo et al 998, the flow changes as shown in Fig3 While oticity at wall deied fom Poisson eq, with no slip condition, fo that eq can be witten as Agawal and Sengpta 989 and Cheng et al 974 R wall 4 3- At tbe inlet: Since the flow at inlet nifom, the oticity ale will set eqal zeo, while steam fnction at inlet aied fom zeo at cente line to ale of eq 3 4- At tbe eit: At eit, the aiation in oticity and steam fnction is negligible 5 5-Initial condition: Assme no flow, then steam fnction and oticity set eqal to zeo Since the stenosis atey is a comple domain, theefoe, the goening eqations ae tansfomed fom pola coodinate to genealized coodinate TRANSFORMATIONS OF GOVERNING EQUATIONS Tansfomation steam- oticity eqation:- β α 6 α : : β 7 Tansfomation oticity tanspot eqation:- t W * / ] ] λ α * / * β α β β α / ]*

7 onal of Engineeing Volme 3 ne 7 Nmbe ] * 8 Tansfomation of pesse dop eqation:- * / / d dp * β α 9 Tansfomation of shea ate eqation:- ] β α 4 ] * Tansfomation of bonday eqation:- wall Gid Geneation The most common patial diffeential eqation ses fo gid geneation in two dimensional is a Poisson eqation in the fom Fletche 987 and Andeson 984 ]/,, Q P β α ] /,, Q P β α 3 Whee α,, β and all gids sed in this inestigation ae geneated with P, Q, Bamley and Sloan 987 and Ali The non linea diffeence eqations ae soled iteatiely sing a point SOR method and, at each cycle of iteation, the coefficients β α, and ae ealated sing peios appoimations Fig4a and Fig4b show the physical and comptational domains which ae sed in the pesent stdy

8 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah Time Maching The basic pinciple of time maching is to stat fom an initial gess of the flow patten, then the method soles the nsteady continity, momentm eqations fo the eoltion of the flow in time ntil eqilibim is established Basically, the flow egion is diided in to a gid netwok so that diffeent tems in the goening eqations ae defined at each gid point The flow field is then soled fom the goening eqations in finite diffeence fom sbjected to the imposed bonday conditions With the flow eqations applied to each gid point in tn, the soltion becomes close to the nsteady state soltion fo each time step Iatidis 987 Epeimental Wok The ig was designed to simlate the blood flow thogh consticted atey, which mst satisfy nmbe of eqiements: plsation flow, non-newtonian flid, tape essel, stenosis essel, deeloping flow and Lamina flow as shown in Fig5 Dosing pmp type ALLDOS Model EN634 with flow ate 5 L/h, 3 bas, powe 9Kw, 88-9 Ampee and 7 RPM is sed, which its opeation is based on sing diaphagm moement by ode connected eccentic disc, to geneate plsating flow In ode to mease a pesse dop in the test section nde plsation condition, the diffeential pesse tansdce type FOPRO with ange of mba is sed Its opeation is based on diaphagm moement and coneting the pesse dop to electical signal Switch flow mete with ange of 3L / h which gies indication fo the nmbe of plses in sec and feqency Flow mete is connected with inteface cad and accessed to compte The amont of flow ate was meased by collecting woking flid in containe and time was acconted by stop watch To simlate the flid dynamic behaio of blood, a soltion of :3 glycein-wate with density of g/cm 3 and iscosity 35-4 CP was sed Rose et al 998, Cebal et al Density and iscosity wee meased eey day befoe stating to ecod data To simlate the atey Acylic tbe with inlet diamete 6,8 and mm Co et al 979 and Wellbon and Stein 98,with tape angle fo each size 5, and 5 degee wee sed Walbn and Stein 98,Kimmel and Dinna 983The length of test section was 75 mm Walbn and Stein 98 and mm theaded added in entance to se in connection with Acylic block The tape of inside diamete of tbe match tape angle of ot side diamete of stenosis to fi the stenosis in fist thid length of tbe Small tap was sed psteam of joins block to peent bbbles to inte test section Stenosis model is made fom Acylic with tapezoidal shape Ojha et al 989 and Vaghese and Fankel 3 as shown in Fig Fie taps with sizes accoding to ISO standad 567 Mille 983 wee dilled in test section and locations of taps ae shown in Fig6 A coppe tbe with 4mm ot diamete was fied on taps,, 4, and 5 by epoy, as shown in section A, while bolt M4 was sed fo tap 3, which eqied a special connection, as shown in section B Data acqisition cad type PCI-9 is sed, this data acqisition cad is based on the 3-bit PCI bs achitecte High pefomance design and the state-of-the-at technology make this cad ideal fo data logging and signal analysis application in aeas like medicine and pocess contol, Aimen 5 In ode to ead the signal fom the Pesse Tansdce and Swatch flow mete senso a pogam is eqied to ecod signal Befoe witing this pogam it is necessay to ense that the MATLAB defines the DAC in its tools slts and Discssion

9 Nmbe Volme 3 ne 7 onal of Engineeing To stdy the inflence of stenosis and tape on blood "Non Newtonian flid" flow thogh atey, the comptations wee condcted fo aios stenosis seeity 5%, 6% and 75% and diffeent ales of tapeing essel angles, 5 o, o, and 5 o To pefom a caefl paamete analysis, the instantaneos steamlines ae calclated and shown ding cycle of plsation flow at inteals of sec The non dimensional Womesley and ynolds nmbes ae consideed as 7 and 5 espectiely The stdy was caied ot nde constant flow ate Nmeical eslts As a fist step in the analysis, a check fo alidation pogam is pefomed thogh the compaison of nmeical eslts with eslts of Pontelli 999, fo steady flow, Newtonian and non- Newtonian flid at a ynolds nmbe of The stenosis pofile sed in this compaison is descibed as eponential fnction The steam at wall "maimm steam fnction" is 5 Pontelli 999 Compaison shown in the Fig7 and Fig8 which indicated that,the pesent eslt has highe ales than eslts in Pontelli 999, fo both cases Newtonian flid and Non Newtonian flid The diffeence in eslts is de to method of calclation, the sed eqation in calclation of wall shea stess and inpt paamete of Pontelli 999 The nmeical stdy is caied ot nde plsation condition, No 5 and Womesley No 7Blood is consideed as a non- Newtonian flid with paamete Λ 5 which epesents the degee of shea thinning and fo atio of asymptotic iscosities at zeo and infinity eqal to δ 4 Pontelli 999 The nmbe of gid points along the ais in, is 76, 6, the time step has been selected as small T -7 compaed to T -6 fo steady case Pontelli 999] in ode to gaantee the conectie and diffsie stability condition in all cases Fletche 987,]Diffeent angles of essel tapeing,5 o, o,5 o with diffeent degee of stenosis,5%,6%,75% ae consideed Steamline, wall shea stess and pesse dop eslts ae plotted and stdied Steamline distibtions inside blood essel at each time step ae plotted fo diffeent stenosis pesent and diffeent essel tapes The eslts indicate that, the steam line changes as inlet flow ate change as shown in Fig9, the sepaation egion is noted clealy at time step 4 sec and gows as time adanced Also it can be noted that, the sepaation egion psteam of stenosis showed to be stated at time step 8 sec The WSS distibtion fo tapeed essel 5 o, with 75% stenosis is shown in Fig De to tape angle, the WSS inceases as distance inceased into tapeed section, the peak ale of WSS is shown at stenosis pat While the WSS ales at time step 4 sec, 5 sec, 7 sec and 8 sec ae not inceased de to low inlet flow ate at these time steps At time step 7 sec and 8 sec negatie ales of WSS ae indicated The WSS distibtion indicated same behaio as seen when stenosis 6% bt a lowe edction is obseed with negatie ale of WSS at time step 8 sec, also this effect become lowe at 5% stenosis Compaison WSS of distibtions at some instantaneos times eeals that, the highest of stenosis has a significant inflence on the WSS at the thoat, the downsteam of thoat, and the length of sepaation egion Since high WSS is not only damage the essel wall and cases intimal thickening, bt also it acties platelets which cases' aggegation, and finally eslts in the fomation of a thombs, the wall shea stess at thoat desees to be noticed Go-Tao et al 4 Pesse dops along the aial length of essel ae plotted, which indicated that, the pesse dops at stenosis pat and this dop in pesse edces at distal stenosis Also, pesse dop changes as the inlet flow ate changes at each time step Fthe, the dops change accoding to the stenosis pecent changes Fig shows pesse dop along the aial length and the pesse dop changes as inlet flow ate changes A high edction in pesse is obseed at time step sec and 3 sec fo high flow ate Pesse at distal stenosis was highe than pesse at poimal stenosis de to the back flow at distal stenosis Epeimental slts

10 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah Epeimental wok was condcted at No 58, Womesley No 63, and feqency Hz The density of the woking flid was taken as g/cm 3 and the iscosity in ang of 35-4 Posie Test was caied ot at an aeage flow ate of 5 ml/sec and the data ecoded at ate of 8 samples fo dation of 5secAs the stenosis is inceased the pesse diffeence inceased As the stenosis incease the coss sectional aea deceases and flow acceleates, conseqently, the pesse enegy is coneted to the kinetic enegy The edction in pesse can be calclated fom Benolli's eqation and it can be witten as follows Walbn and Stein 98: D 4 p 5ρ V 4 d m Whee d m is diamete of cente stenosis: D is diamete psteam stenosis It is clea that, diamete of stenosis had a diect effect on ale of pesse dop ale, and powe inde "fo" eplain the diffeence in pesse dop fo diffeent pecent stenosis 5%, 6% and 75% as shown in FigThis eslts ae in ageement with the eslts of Poenta et al 985, Bapat 5, and consistence with the geneal obseation of the effect stenosis of less than 5% hae little effect on pesse and flow This is one of the eason why stenosis ae difficlt to diagnose at an ealy stage The pesse diffeence in all measements ae non dimensionalzed with ρ V fo all the cases In tape section, the flow is acceleated and enegy is coneted fom pesse enegy to kinetic enegy This edction in pesse enegy can be calclated by sbstitting the continity eqation into the Benolli eqation, with some maniplation, yields Walbn and Stein 98 D 4 p 5ρV ] 5 D l tanθ eq5 indicate that, as tapeing angle inceases the pesse dop incease as shown in Fig3, also the pesse dop inceases as distance of tape section inceases Compaisons To check the alidity of the nmeical techniqe, seeal compaisons of nmeical eslts fo diffeent cases ae pefomed at time step sec, whee the discepancy is clea and this is de to the maimm flow ate Epeimental eslts fo pesse dop ae compaed with nmeical eslts and with aailable liteate fo same cases The effect of diffeent pecent stenosis on the WSS fo 5 o tape essels ae shown in Fig4, which indicates that, as stenosis degee inceases WSS inceases and the same tend is by Hn ng et al 4 Pesse dop plots ae sed fo compaison of nmeical eslts with epeimental data fo the pesent stdy to inestigate the effects of stenosis pecent fo diffeent tape essels Fig5 indicates that, the pesse dop inceases as degee of stenosis inceases in staight essel and a high pesse diffeence is fond at 75% stenosis compaed with 5% and 6% stenosis This behaio was in ageement with Bapat 5 as shown in Fig6It indicates that, pesent epeimental data has a highe ale, this de to constant iscosity and shape of stenosis sed by Bapat 5, also it is coincident with the conclsion of the sey inestigated by Yong 979 On the othe hand, the effects of tapeing angle ae inestigated with and withot stenosis Fo case of withot stenosis, compaison of epeimental data with Walbn and Stein 98 is pefomed as shown in Fig7 It is clea that, pesent data hae highe ales than Walbn and Stein 98 data,this is de to the iscosity 3 Poise compaed with a mite flid with iscosity in ange 35 to 4 Poise in pesent stdy Also as tapeing angle inceases WSS inceases, and this is cleae at the end of the essel This is in ageement with Kimmel and Dinna 983 as shown in Fig8It shows that, the ales of WSS in the pesent stdy ae highe than

11 Nmbe Volme 3 ne 7 onal of Engineeing Kimmel and Dinna 983 ales, becase they ae assmed Newtonian flid, diffeent inpt flow ate and one dimension flow In ode to compae the nmeical eslts with epeimental data in the pesent stdy, calclations ae pefomed with sine wae pofile inlet flow ate to confim the epeimental wok with No 58 and Womesley No 63 as shown in Fig9 This indicate that, the nmeical eslts hae same behaios as epeimental eslts, bt with highe ales Conclsions Comptational and epeimental simlations fo blood flow thogh stenosis atey nde plsation condition wee caied ot in this stdy A shea thinning model was sed to epess Blood, which is consideed as non-newtonian flid Attention was focsed on the effect of stenosis on pesse dop and wall shea stess The following ae the main conclsions dawn fom the pesent inestigation wok,both pesse dop and wall shea stess wee inceased as tape angle of essel incease 5 o, o, 5 o, de to incease in kinetic enegy, also inceased as stenosis incease 5%, 6% and 75%, and a lage effect seen fo 75% stenosis Wall shea stess had negatie ales whee ote eists, ote egion may be the oigin of ed cell damage and thombs fomation and the stenosis will pogess fthe, and the high stess is eeted nea the stenosis thoat of blood essel de to fast flow and will geneate seios physical damages Tapeing of the atey did not change flow pattens, bt only changed ales, amplified the ales of wall shea stess and pesse dop As the distance into tape section inceased both pesse dop and wall shea stess wee inceased Both pesse dop and wall shea stess wee inceased as the distance into tape section inceased Fo the stenosis pecent less than 5% a little effect on pesse and flow was seen This is a eason fo why the stenosis pecent ae difficlt to diagnosis at an ealy stage As a elated to the pesent wok, following sggestions can be pt fowad Vessel wall will be conside as a distensible, ced atey will be conside, whee ced is moe eality, and Bifcation will be conside REFERENCES Agawal, AK and Sengpta S, 989 "Lamina flow and heat tansfe in blocked annli", Nmeical Heat Tansfe, Pat A, Vol5, PP Aimen, M A B, 5,"Wea monitoing tning pocesses sing ibation and stain measements", MScThesis, Uniesity of Baghdad Ali, L Kaeed,"Nmeical stdy of foced conection oe bank of tbes by sing body fitted coodinates system "M Sc Thesis, Uniesity of Technology Andeson,D" Comptional Flid Dynamics: the Basics with Applications" Mc Gaw Hill,Inc Andeson, D A, Pletche, RH and Tannihill, C 984 "Comptational Flid Mechanics and Heat Tansfe",Hemisphee Pblishing Copoation Bapat, A5 " Pedicting stenosis in blood essels " on web Site Bamley, S, and Sloan, DM, 987,"Nmeical soltion fo two dimensional flow in a banching channel sing bonday fitted coodinates", Comptes and Flids, ol 5, No3, pp 97 3

12 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah Cebal, R, Yim, P, Lohne, R, Soto, O, and Choyke, PL,, " Blood flow modeling in caotid ateies with comptational flid dynamics and MR Imaging", Academic diology, Vol 9 No, pp Chen, May 3, "A nonlinea iscoelastic Mooney-Rilin thin wall model fo nsteady flow in stenotic ateies", M Sc Thesis, Woceste Polytechnic Institte Cheng, LC, Robetson, M, and Clak, ME, 974,"Calclation of plane plsatile flow past wall obstacles", Comptes and Flids, Vol, pp Co, T, Hoften, DA, and Hwang, HC, 979,"Inestigation of a plsatile flow field downsteam fom a model stenosis", Biomechanical Engineeing, ol, pp 4 5 Fletche, CA, 987,"ComptationalTechniqesfo Flid Dynamics ", Spinge Velag seies Fletche,CA, 987,"Comptational Techniqes fo Flid Dynamics ", Spinge Velag seies Go Tao li, Wang,, Ai B Q, and Li, L G, 4, "Nmeical stdy of plsating flow thogh a tapeed atey with stenosis", Chinese of Physics, Vol 4, No 4 I Hn ng, Choi, W, and Pak, C G, 4,"Asymmetic flows of non-newtonian flids in symmetic stenosed atey", Koea Astalia jonal, Vol 6, No, pp -8 IATRIDIS, MI, 987,"A theoetical stdy of boyancy dien ciclation in a liqid dop ", MSc Thesis, Uniesity of Liepool Kimmel, E and Dinna, V, 983,"Plsatile flow in tapeed tbes: a model of blood flow with lage distbances", Biomechanical Engineeing, Vol5, pp 9 Mille, RW, 983,"Flow Measement Engineeing Hand Book", Mc Gaw Hill Book Company Nallasamy, M986,"Nmeical soltion of the sepaating flow de to an obstction" Comptes Flids, Vol4, No, PP59-68 Ojha, m, Cobbold, C, ohnston, K W, and Hmmel, RL, 989"Plsatile flow thogh consticted tbes: An epeimental inestigation sing photo chomic tace methods", Flid Mech, Vol3, pp73-97 Pontelli, G, 999,"Blood flow thogh an aisymmetic stenosis", Institto pe le applicazioni Del Calcolo CNR Viale Del Policlinico,37, 6 Roma, Italy Poenta, G, Yong, DF, and Rogge,TR, 985," A finite element model blood flow in ateies inclding tape, banches, and obstctions", Biomechanical Engineeing Rose, ML, Febay 998,"Deelopment of a mscle poweed blood pmp: flid mechanic consideations", Ph D Thesis Uniesity of Glasgow, Depatment of Cadiac Sgey, Faclty of Medicine Taylo, C A, Hghes, T R, and Zains, CK, 998, "Finite element modeling of thee dimensional plsatile flow in the abdominal aota: leance to atheoscleosis" Annals of Biomedical Engineeing Vol 6, pp

13 Nmbe Volme 3 ne 7 onal of Engineeing Vaghese, SS, and Fankel, S H, 3,"Nmeical modeling of plsatile tblent flow in stenotic essels ', of Biomechanical Engineeing, Vol 5, pp Walbn, F, and Stein, PD, 98, "Effect of essel tapeing on the tansition to tblent flow: Implications in the cadioascla system", Biomechanical Engineeing, Vol 3, pp6 - Yong, DF, 979,"Flid mechanics of ateial stenosis", Biomechanical Engineeing, Vol,pp Fig : Schematic of geomety Fig : Geomety of stenosis

14 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah Flow ate q ml Time sec Fig3: Physiological flow ate in atey Taylo et al 998 Fig 4a: Physical domain Fig4b: Comptational domain Fig4: Physical and comptational domain

15 Nmbe Volme 3 ne 7 onal of Engineeing F e e d L in e C o n s ta n t H e a d R e s e o i 5 3 O e F lo w L in e V a l e 6 C o lla c tin g T a n k 9 P o w e S p p ly W ie C o n n e c tio n H o s e C o n n e c tio n Fig5: Epeimental ig Fig6: Location of pesse tapes

16 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah 5 Wall shea stess dyne/cm Pesent stdy Pontelli ] Aial length / R Fig7: Compaison of nmeical eslts of wall shea stess Newtonian flid with Pontelli 999 Mesh fo tapeessel,5 deg,with 75% stenosis Wall shea stess dyne/cm Wall shea stess dyne/cm Aial length / R T 6 sec Pesent stdy Pontelli ] Fig8: Compaison of nmeical eslts of wall shea 5 stess Non Newtonian flid with Pontelli 999 Pesent stdy Pontelli ] Steam Aial length / R Steam T sec Steam T 7 sec Steam T sec Steam T 8 sec T 3 sec T 4 sec Steam Steam Fig9: Instantaneos steamline patten at diffeent time steps in plsate flow, fo 5 o tape essel with 75% stenosis T 5 sec Steam

17 Nmbe Volme 3 ne 7 onal of Engineeing Wallshea stess dyne/cm Tape essel, 5 deg with 75% stenosis T sec T sec T 3 sec T 4 sec T 5 sec T 6 sec T 7 sec T 8 sec 5 5 Aial distance / R Fig: Wall shea stess at diffeent time steps,fo 5 o tape essel with 75% stenosis pesse dop dyne/cm Tape essel,5 deg with 75% stenosis T sec T sec T 3 sec T 4 sec T 5 sec T 6 sec T 7 sec T 8 sec 5 5 Fig: Pesse dop at diffeent time steps, fo 5 o tape essel with 75% stenosis Nondimensional pesse dop DP Dia6 mm ; Staight essel Nmbe of sampling Fig: effect of stenosis pecent on pesse dop in essel at flow ate 5ml/s S75% S6% S5% Non dimensional pesse diffeence with atmosphee Dia6 mm ; Withot Stenosis Nmbe of sampling Fig3: Effect of tapeing angles on pesse in essel at flow ate 5 ml/sec 5 deg deg 5 deg deg Tape essel, 5 deg Wall shea stess dyne/cm Withot stenosis 5 %Stenosis 6% Stenosis 75 % Stenosis 5 5 Aial distance / R Fig4: Effect of stenosis pecent on wall shea stess at time step sec Pesse D op dyne /cm Tape essel,5 deg Withot stenosis 5% Stenosis 6%Stenosis 75% Stenosis 5 5 Aial distance / R Fig5: Effect of stenosis pecent on pesse dop at time step sec 5 o tape essel

18 N N Abdlla Nmeical and Epeimental Inestigation of Flow HYMahmood Field Inside Ateies and Veins S EAbdllah Tape, deg N on dim ensional pesse dop Tape, 5 deg Staight Tape,5 deg Bapat 56] Nondimensional pesse dop Pesent stdy Walbn 8] Stenosis % Tape angle degee Fig6: Compaison of epeimental eslts fo diffeent stenosis pecent with epeimental eslts of Bapat 5 Fig7: Compaison of epeimental eslts fo tapeing angles with epeimental eslts of Walbn and Stein 98 5 N o n d im e n s io n a l p e s s e d o p -5-5 *-3 4] *-4 4] *-5 4] Tape,5 deg Tape, deg Tape,5 deg Non dimensional pesse dop DP 4 3 Nmeical Epeimental 5 5 Aial distance / R Stenosis % Fig8: Compaison of nmeical eslts fo tapeing angles with nmeical eslts of Kimmel and Dinna 983 Fig9: Compaison of nmeical eslts fo diffeent stenosis pecent with epeimental eslts fo tape essel 5 degee

19 Nmbe Volme 3 ne 7 onal of Engineeing NOMENCLATURES symbol Meaning Units D Diamete m e Stain ate /s L length m P Pesse N/m q Flow ate ml/s -coodinate R Radis m ynolds nmbe ρvr /µ Velocity component in -diection m/s Velocity component in -diection m/s V Velocity ecto m/s -coodinate α Tansfomation paamete in gid geneation β Tansfomation paamete in gid geneation Tansfomation paamete in gid geneation Shea ate /s δ δ atio of asymptotic iscosities at zeo to infinity Coodinate in the tansfomed domain Coodinate in the tansfomed domain Shea iscosity N/m θ Tape angle deg λ Weomsly NoR ν f atio of tansient inetia foce to iscose foce Λ Mateial constant s µ Dynamic iscosity kg/ms ν Kinematics iscosity m /s ρ Flid density kg/m 3 τ Shea stess N/m Geneal dependent fnction φ Non-dimensional iscosity Steam fnction m /s Voticity /s Gid step distance in -diection Gid step distance in -diection