Simulation study of the Hemopump as a cardiac assist device

Transcription

1 Simultion study of the Hemopump s crdic ssist device X. Li 1 J. Bi 1 P. He 2 1 Institute of Biomedicl Engineering, Deprtment of Electricl Engineering, Tsinghu University, Beijing, Chin 2 Wright Stte University, Dyton, Ohio, USA Astrct A dynmic model ws developed for Hemopump tht withdrws lood from the left ventricle nd dischrges it to the ort through miniture xil-flow pump. Incorportion of the Hemopump model in previously estlished model for the cnine circultory system enled the effects of the Hemopump on vrious hemodynmic vriles of the circultory system to e studied, nd the enefit of the Hemopump to the filing hert ws investigted. In ddition, the influence of the physiologicl sttus of the right ventricle on the Hemopump performnces ws exmined, nd the synchronous nd non-synchronous opertions of the Hemopump were compred. Results verified tht the Hemopump ssists the filing hert y incresing the oxygen supply, while reducing the oxygen consumption of the hert through reduction in the worklod of the left ventricle. These eneficil effects were enhnced when the pump s rottion speed ws incresed. When pump speed ws incresed from 17 to 23 revolutions min 1, the oxygen supply incresed 11%, nd the oxygen consumption decresed 6%. However, when the pump rottion speed ws too high, the inflow to the pump could e impired nd the pump performnce could e negtively ffected. Predictions from the model were in good greement with the results previously otined in niml experiments nd in vitro mesurements. Keywords Crdic ssist device, Computer simultion, Hemopump, Ischemi Med. Biol. Eng. Comput., 2,, Introduction MECHANICAL HEART ssistnce hs een used s ridge to hert trnsplnt. It cn lso e used temporrily for ptients ffected y severe hert filure nd drug resistnce, with the gol of recovering the filing hert nd preventing multi-orgn filure. Mny types of ssist device, including the intr-ortic lloon pump nd domen left-ventriculr ssist device (FREED et l., 1988, NORMAN et l., 1977; 1981), hve een put into clinicl use since DeBkey first inserted mechnicl crdic ssist pump in n open chest opertion in 1964 (DEBAKEY, 1971). In 1988, new kind of crdic ssist device, the Hemopump, ws introduced y BULTER et l. (199), nd its first humn tril ws reported y FRAZIER et l. (199). The Hemopump consists of disposle pump ssemly, high-speed motor nd control console. The miniture xilflow pump itself is situted in the ort. The inlet flow cnnul of the pump psses retrogressively through the ortic vlve, with its tip locted in the left ventricle. Power to drive the pump is trnsmitted from n externl electric motor y flexile cle threded through sheth. When the device is ctivted, the pump impellers rotte, nd lood is drwn through the inlet cnnul into the pump nd then dischrged into the ort. In this process, the left ventricle is relieved of its mjor worklod. Correspondence should e ddressed to Dr Jing Bi; emil: dej@tsinghu.edu.cn Pper received 26 Novemer 1 nd in finl form 6 Mrch 2 MBEC online numer: # IFMBE: 2 The cpility to e inserted into the circultory system without mjor surgery mkes the pump s sfe nd convenient s the intr-ortic lloon pump (IABP). On the other hnd, the pump my e more effective thn the IABP in ssisting the left ventricle, owing to its ility to pump the lood ctively nd djust the flow rte with no restrints from the function of the nturl hert. All these dvntges mke this device promising lterntive to trnsplnttion in the future. Although it hs een more thn ten yers since its first introduction, the enefits nd opertion of the Hemopump re still under investigtion, nd its clinicl pplictions hve een limited (DREYFUS, 1996). Assessment of the performnce of the Hemopump in clinicl setting is difficult, owing to the lck of sophisticted pump mngement system (SIESS et l., 1996). The vriility of the humn physiologicl system nd possile dministrtion of vrious medicines further complicte the ssessment of the ssistnt effects of the Hemopump. In this pper, we propose mthemticl model for the Hemopump, sed on pulished experimentl dt, nd incorporte it into cnine circultory system model tht ws developed previously y our group (ZHOU et l., 1998; BAI nd ZHAO, ). Using this model, the opertion mode of the Hemopump nd the prmeters of the circultory system cn e djusted esily, nd the hemodynmic prmeters cn e oserved conveniently, so tht the performnce nd ssistnt effects of the Hemopump cn e ssessed under different conditions. 2 Model description 2.1 Stedy model of Hemopump Assuming tht the inflow of the pump is not hmpered, the flow produced y the Hemopump is function of the rottion 344 Medicl & Biologicl Engineering & Computing 2, Vol.

2 speed of the pump nd the pressure difference etween the outlet nd inlet of the pump (MEYNS et l., 1996). In typicl clinicl ppliction, the pressure difference is the ortic pressure minus the left-ventriculr pressure. The idelised reltionship etween the stedy pump flow Q stedy nd the pump pressure hed Dh cn e descried y the following eqution (IONEL, 1986): Dh ¼ DP stt rg ¼ u2 g u g cot pd Q stedy where DP stt is the sttic pressure difference, r is the density of the fluid, g is the grvity ccelertion, u is the liner velocity of the liquid (e.g. lood), is the ngle of the impeller outlet, d is the dimeter t the impeller output, nd is the width of the pump impeller. If we express u s function of the rottion speed n in revolutions min 1 u ¼ pdn ð2þ 6 (1) cn e trnsformed to Q stedy ¼ A n B n DP stt ð3þ ð1þ Fig Results of lest squres fit to reported dt otined from in vitro mesurements of Hemopump operted t seven rottion speeds: ( þ) 1;(u) 2;(n) 3;(s) 4;() 5;(6) 6;(,) 7 where A n ¼ np2 d 2 6 cot nd B n ¼ 6 nr cot (3) shows liner reltionship etween the pump flow nd the pressure difference for fixed rottion speed n. Given the vlues of A n nd B n t certin rottion speed, the stedy pump flow under vrious pressure differences cn e determined. In our present study, we chose to model the Hemopump type HP31 (Medtronic, Minnepolis, Minnesot, USA). This pump cn e operted t seven different rottion speeds rnging from 17 (speed 1) to 26 revolutions min 1 (speed 7), with n intervl of 15 revolutions min 1. MEYNS et l. (1996) performed in vitro mesurements of the stedy flow pressure difference reltionships of the pump t the ove seven speeds under pressure differences of up to 23 mmhg. Their dt (Fig. 2 in MEYNS et l. (1996)) showed nerly liner reltionship etween the flow nd pressure difference in the region of lowpressure difference. In the region of high-pressure difference, this liner reltionship ws roken down owing to flow seprtion within the rotor. In our present study, we only consider the pressure difference up to 1 mmhg nd deliertely do not investigte the effects of flow seprtion. Consequently, we otin the vlues of the two coefficients A n nd B n, in the liner eqution (3) y fitting lest squres line to the corresponding dt of MEYNS et l. (1996) in the rnge of 1 mmhg. Figure 1 shows the seven fitted stright lines, nd Tle 1 lists the vlues of A n nd B n for ech of the seven pump rottion speeds. A stedy model of the pump sed on (3), is shown in Fig. 2; it consists of constnt flow source Q n nd resistnce R n. The model gives the following reltionship etween the pump flow Q stedy nd the pressure difference DP stt : ð4þ By compring (5) with (3), we otin Q n ¼ A n nd R n ¼ 1=B n ð6þ nd they oth depend upon the rottion speed of the pump, s shown in Tle 1. In (3), the idelised reltionship etween Q stedy nd DP stt is descried. Considering the viscous property of the lood, the viscous resistnce R n to the pump flow should e investigted. The vlue of R n cn e given pproximtely y the Poiseuille stedy-stte formul (RIDEOUT, 1991): R n ¼ 8ZL pr 4 ð7þ where Z is the lood viscosity, nd L nd r re, respectively, the length nd internl rdius of the pump cnnul. Using the dt from MEYNS et l. (1995; 1996): Z ¼ 3.48 mp s, L ¼ 8.5 cm, r ¼ d/2 ¼ 4.5 mm, we otin the vlue of R n : R n ¼ 2: P sm 3 ¼ 2:161 2 mmhg sml 1 Compring the vlue of R n with the vlues of R n in Tle 1, we found tht R n is out 1 times smller thn R n. This indictes tht, when the pump works t speeds 1 7, the lood viscosity hs little effect on the pump flow. In fct, in Tle 1, the vlues of the two coefficients A n nd B n were not otined directly from (4) ut were clculted sed on liner fit to the experimentl dt from MEYNES et l. (1996). As, in their mesurements, glycerol-in-wter solution hving the sme viscosity s lood ws used, R n in Tle 1 hs incorported the resistnce to the pump flow due to the lood viscosity. 2.2 Dynmic model of Hemopump ð8þ Q stedy ¼ Q n 1 R n DP stt ð5þ Eqution (3) is for stedy flow under constnt pressure difference. When the pump works in living circultory Tle 1 Vlues of prmeters of liner model shown in (3) for pump operted t seven rottion speeds Speed level A n,mls B n,ml=ðsmmhgþ R n, ðmmhg sþ=ml Medicl & Biologicl Engineering & Computing 2, Vol. 345

3 P in P out P in (t) Q stt P stt = P out P in Qt () R n R n Q n system, the pressure t the inlet (P in ¼ pressure in left ventricle), the pressure t the outlet (P out ¼ pressure in ort) nd the pump flow ll chnge with time during crdic cycle, nd the inertil property of the liquid needs to e considered. To include the effects of the inertil property of the lood in the pump, we modified the stedy model of the Hemopump y including n inerti H in the dynmic model of the Hemopump, s shown in Fig. 2. To determine the vlue of H in terms of the mechnicl property of the lood, we strted from the fct tht the inertil property of the lood mnifests itself s force tht opposes ny chnge in the flow velocity (SIESS et l., 1996): F ¼ d ðm nþ ¼@m m ð9þ (for incompressile fluid), where F is the force, nd n nd m re, respectively, the velocity nd mss of the fluid within the cnnul of the pump. Equivlently, the inertil property of the lood cn e modelled y pressure difference DP tht is induced y the chnge in flow rte. Numericlly, DP is equl to the force F divided y the cross-sectionl re A of the cnnul of the pump DP ¼ F A ¼ 1 A dv dt m ¼ L r A dq H ð1þ dt Fig. 2 P out (t) DP()=P t out P in H () Stedy model nd () dynmic model for Hemopump Q H Q n where L is the length of the cnnul, r is the fluid density, nd Q H is the volumetric flow rte. Bsed on (1), the inerti H in Fig. 2 cn e determined s H ¼ L r ð11þ A Using the dt from MEYNES et l. (1995) nd REUL (1994), L ¼ 8.5 cm, A pr 2 ¼ mm 2, r ¼ kg m 3, we otin the vlue of H for our model H ¼ 1:749 P s 2 ml 1 ð12þ HP LVH LVI AV AR LA A 1 Cor A 2 B 1 Pul RV A 3 P 2 RA P 1 V P 3 B 2 A 4 P 8 P 7 P 6 P 5 P 4 A 5 A 11 A 1 A 9 A 8 A 7 A 6 Fig. 3 Block digrm of model for cnine circultory system. LA ¼ left trium; LVH ¼ helthy portion of left ventricle; LVI ¼ ischemic portion of left ventricle; AV ¼ortic vlve; AR ¼ ortic root; HP ¼ Hemopump; Cor ¼ coronry circultion; RA ¼ right trium; RV ¼ right ventricle; Pul ¼ pulmonry circultion; A n ¼ ortic segment; B n ¼ rnch of ort; P n ¼ periphery segment; V ¼ lumped venous system 346 Medicl & Biologicl Engineering & Computing 2, Vol.

4 2.3 Complete cnine crdiovsculr model including pump A cnine crdiovsculr model ws developed previously tht cn simulte the dynmic reltionship etween the crdic function nd the vsculr function, s well s e used s tool to investigte the mechnism of hert filure nd the effects of crdic ssist device system (JARON et l., 1985; ZHOU et l., 1998; BAI nd ZHAO, ). As shown in Fig. 3, the model consists of four hert chmers, pulmonry circultion, 11 ortic segments nd lumped venous nd peripherl vsculr systems. The detiled structure nd opertion of ech lock of the model cn e found in BAI nd ZHAO () nd ZHOU et l. (1998). Here, we just give rief description of the model for the left ventricle with regionl ischemi. The left ventricle is functionlly divided into two non-physiologicl comprtments, one consisting of ll the norml myocrdium, nd the other consisting of ll the ischemic myocrdium. We use R m to denote the rtio of the ischemic myocrdil mss to the totl myocrdil mss. In this study, vlue of 3% is used for R m, which models the typicl ischemic condition of cnine hert 15 min fter its left nterior descending coronry rtery hs een ligted (MOHL et l., 1984). During ech crdic cycle, ech comprtment genertes its own pressure volume loop tht, in turn, determines the pressure nd volume of the entire left ventricle. The mximum elsticity (which is relted to myocrdil contrctility) of the norml comprtment (E es1 ) is 5 mmhg ml 1, nd the mximum elsticity of the ischemic comprtment (E es2 ) is 1.5 mmhg ml 1. The cnine crdiovsculr model shown in Fig. 3 lso includes the dynmic model of the Hemopump shown in Fig. 2. To simulte the typicl clinic setting (FRAZIER et l., 199), the inlet of the pump in our model is inserted into the left ventricle, where the pressure is denoted s P LV. The outflow of the pump is dischrged into the descending ort, where the pressure is denoted s P [4], where the numer 4 refers to the forth ortic segment. As result, P in nd P out in Fig. 2 ecome P LV nd P [4], respectively. explined y the fct tht, when the pump speed is incresed, more lood is expelled y the pump, nd the ventriculr cvity is reduced. As result, the contriution of the hert to the pump flow is reduced, which is illustrted y the decrese in the upstroke in flow during the ejection phse t high speeds. In our simultion, the contrctility nd end-distolic filling volume Computer simultions nd results The suject of the computer simultion ws dog in lying position, with regionl ischemi in its left ventricle. The hert rte of the dog ws 1 ets min 1. The computer progrm ws written in Delphi lnguge nd run on n IBM comptile computer. The time intervl for computtion ws chosen to e.1 s. During ech time intervl, the pressure, flow nd volume of ech lock were computed nd updted sequentilly, strting from the left nd right ventricles. 3.1 Pump flow nd pressure difference during norml crdic cycle In the current pplictions, the Hemopump lwys runs t constnt rottion speed. Consequently, we studied the ssistnt effects of the pump operted t certin constnt speed. For the HP31, the speed cn e chosen from etween 17 revolutions min 1 (speed 1) nd 26 revolutions min 1 (speed 7) with n increment of 15 revolutions min 1. In Fig. 4, the flow pressure difference (Q DP) reltionships of the working pump t speeds 1, 3 nd 5 re shown. At ech speed level, the Q DP curve shows hysteresis, resulting in loop tht proceeds clockwise during crdic cycle. This phenomenon, which is due to the inertil property of the lood within the cnnul nd pump, ws lso oserved previously y MEYNS et l. (1996) in their in vivo study of the pump. The hysteresis of the loop decreses s pump speed increses. This cn e Fig c Reltionship of pump flow nd pressure difference of working pump during crdic cycle t () speed 1, () speed 3 nd (c) speed 5. ( s ) systolic period; ( ) distolic period Medicl & Biologicl Engineering & Computing 2, Vol. 347

5 of the left ventricle were set so tht the resultnt rnge of pressure differences cross the pump ws consistent with tht reported y MEYNS et l. (1996) in their in vivo experiment. Fig. 5 depicts the pump flow during one crdic cycle (.5 s, corresponding to hert rte of 1 min s 1 ) t pump rottion speeds 1 5. At ech speed, especilly t low speed, the pump flow shows significnt pulstion. As the pump speed rises, the pulstion of the pump flow decreses. This cn e ttriuted to the decrese in the pulstion of the pressure difference from speed 1 to speed 5, s shown in Fig. 4. We lso notice tht t speed 1, ckflow hppens round end systole. The ckflow my e deleterious to the filing hert nd should e voided. 3.2 Effects of Hemopump on vrious hemodynmic vriles Incorporting the Hemopump model into the cnine circultory model, we cn study the effects of the pump on vrious hemodynmic vriles t different rottion speeds. Fig. 6 shows the ortic pressure during crdic cycle t ech of the five rottion speeds of the pump. As the rottion speed increses, the men ortic pressure increses, nd the pulstion Fig. 5 Wveform of pump flow during crdic cycle when pump is operted t one of five speeds: ( j ) 1;( u ) 2; ( n ) 3; ( s ) 4;( ) ortic pressure, mmhg time, s left ventriculr flow, m s time, s left ventriculr volume, ml time, s c left ventriculr pressure, mmhg left ventriculr volume, ml d left tril volume, ml time, s e Fig. 6 Effects on vrious hemodynmic vriles of Hemopump when operted t different speeds. With exception of (d), vlue of ech vrile is plotted s function of time during one crdic cycle. () Aortic pressure; () lood flow pumped out through ortic vlve y left ventricle; (c) volume of left ventricle (d) pressure volume reltionship of left ventricle during crdic cycle; (e) volume of left trium.(), (c) (e) speed: ( þ) 1;( u ) 2; ( n ) 3; ( s ) 4;( ) 5; () speed: ( þ) 1;( u ) Medicl & Biologicl Engineering & Computing 2, Vol.

6 of the ortic pressure diminishes. The sme trends hve een reported in clinicl experiments (DREYFUS, 1996; MEYNS et l., 1995; LACHAT et l., 1999; PETERZEN et l., 1996; WALDENBERGER et l., 1995). Fig. 6 plots the lood flow pumped out y the left ventricle. Only t speed 1 is there noticele lood flow pumped out y the left ventricle during erly systole. As the pump rottion speed is further incresed, the mount of lood pumped out y the left ventricle ecomes negligile. This oservtion is lso consistent with the results reported y PETERZEN et l. (1996). They noticed tht the ortic vlve ws lmost lwys closed when the pump ws working. The reson tht, so fr, we hve not reported the simultion results for speeds 6 nd 7 cn e explined y Fig. 6c, which shows the volume of the left ventricle during the crdic cycle when the pump is in opertion. As the rottion speed of the pump is incresed from speed 1 to speed 5, the volume of the left ventricle decreses to rther smll vlue. When the pump speed is further incresed to speed 6 or speed 7, the volume of the left ventricle pproches zero t some moment, nd the simultion comes to hlt. This sitution is discussed in Section 3.4. Fig. 6d depicts the pressure volume loop of the left ventricle in one crdic cycle. As the pump speed increses, the loop moves to the left (the men volume decreses), nd the re of the loop decreses, indicting decrese in the worklod of the left ventricle (WALDENBERGER et l., 1995). Finlly, Fig. 6e shows the chnges in the left tril volume during the crdic cycle. As the pump speed increses, the left tril volume decreses, which my explin the potentil collpse of the left trium t high speeds reported in literture (CHEN nd YU, ). ml et 1 stroke volume, ml et speed level 3.3 Beneficil effects of Hemopump on filing hert The min eneficil effects of the Hemopump to filing hert include n increse in the stroke volume, reduction in oxygen consumption, s result of the decresed worklod of the left ventricle, nd n improved oxygen supply due to n increse in the coronry lood flow. Ech of these eneficil effects ecomes more significnt when the pump rottion speed increses, s shown in Fig. 7. In Fig. 7, the stroke volume is the comined volume of the lood pumped out y the left ventricle nd tht pumped out y the Hemopump during crdic cycle. As the contriution of the left ventricle to pumping lood quickly ecomes insignificnt s the pump rottion speed increses (see Fig. 6), the increse in the stroke volume is lmost entirely due to the increse in the pump flow. In Fig. 7, the myocrdil oxygen consumption V O2 of the left ventricle is determined y the following three equtions, sed on the work of SUGA (1979): V O2 ¼ V O2 ð1þþv O2 ð2þ ð13þ V O2 ð1þ ¼B PVAð1ÞþCE es1 ð1 RmÞþDð1 RmÞ ð14þ V O2 ð2þ ¼B PVAð2ÞþCE es2 Rm þ D Rm ð15þ where V O2 (1) nd V O2 (2) re the volumes of oxygen consumed y the norml comprtment nd y the ischemic comprtment of the left ventricle, respectively; PVA(1) nd PVA(2) re the res of the individul pressure volume loop of ech comprtment (see Section 2.3); nd E es1 nd E es2 re the mximum elsticities of the norml region nd the ischemic region of the left ventricle, respectively. The vlues of the three coefficients B, C nd D re otined from the work of SUGA et l. (1987). (13) (15) indicte tht the oxygen consumption is directly relted to the re of the pressure volume loop. Figure 6d indictes tht, when the pump speed increses, the re of the pressure volume (P V) loop of the left ventricle Fig. 7 decreses (lthough not plotted, the individul P V loop of the norml comprtment or tht of the ischemic comprtment shows similr trend). As result, the oxygen consumption decreses s the pump speed increses. Alterntively, the decrese in oxygen consumption of the left ventricle cn e explined y the reduction in its prelod tht is relted to the left trium volume nd the left ventriculr end-distolic volume. When the pump speed increses, oth the left trium volume nd the left ventriculr end-distolic volume decrese, s indicted in Figs 6e nd c. Consequently, the oxygen consumption decreses. Figure 7 lso shows the volume of the myocrdil oxygen supply (V OS ) t ech of the five pump speeds. The volume of the myocrdil oxygen supply is clculted from the totl coronry flow during one crdic cycle FTC V OS ¼ ða T Þ O speed level Assistnt effects of Hemopump t different rottion speeds: () stroke volume (totl lood volume pumped out y left ventricle nd Hemopump during one crdic cycle); () ( u) myocrdil oxygen consumption nd ( j) myocrdil oxygen supply FT C ð16þ where A is the volume percentge of the oxygen content in the coronry rteril lood, nd T is vrile tht depicts the ility of the myocrdil oxygen sorption. The typicl vlues of A nd T re determined from the work of WALLEY et l. (1988), nd finl vlue of V OS ¼ :15FT C is used in this study. As the pump rottion speed increses, the ortic pressure increses Medicl & Biologicl Engineering & Computing 2, Vol. 349

7 Tle 2 Vlues of vrious hemodynmic vriles when Hemopump is operted t five different rottion speeds Speed Q mpm,mls P mo, mmhg P osy, mmhg P odi, mmhg P po, mmhg P lvsy, mmhg V lvsy, ml V ldi, ml SV, ml et V oc, ml et V os, ml et (Fig. 6), nd the left ventriculr pressure decreses (Fig. 6d). As result, the coronry flow increses, s does the oxygen supply. In summry, the Hemopump ssists filing hert y relieving its worklod while supplying it with more oxygen. These eneficil effects of the Hemopump re lso reported y PETERZEN et l. (1996), sed on their clinic experiments. The results of our computer simultion regrding the pump s eneficil effects in terms of the vlues of severl relevnt hemodynmic vriles t five pump speeds re summrised in Tle 2. The nottions used in Tle 2 re s follows: Q mpm ¼ men pump flow; P mo ¼ men ortic pressure; P osy ¼ ortic pek systolic pressure; P odi ¼ ortic minimum distolic pressure; P po ¼ pulstion of ortic pressure (P osy P odi ); P lvsy ¼ left ventricle pek systolic pressure; V lvsy ¼ left ventricle endsystolic volume; V ldi ¼ left trium end-distolic volume; SV ¼ stroke volume; V OC ¼ volume of myocrdil oxygen consumption; nd V OS ¼ volume of myocrdil oxygen supply Over-unlod of left ventricle t pump speeds 6 nd 7 When the pump speed incresed to speed 6 or speed 7, the computer simultion cme to hlt fter severl crdic cycles. By trcing the volume of the left ventricle, which ws given n initil vlue of 7 ml t end-distole, we found the volume of the left ventricle pproched zero fter severl crdic cycles, nd the hlt in our progrm ws due to restrint tht the volume of the left ventricle cnnot e negtive. Our progrm, in fct, simulted condition referred to s the left ventricle eing over-unloded, which ws oserved y SIESS et l. (1996) in their experiment with sheep hving rther smll ventriculr cvity nd the pump eing operted t speeds 6 nd 7. According to these uthors, left ventricle over-unloding ws ccompnied y hmpered inflow of the pump, rndomised tip-to-wll contct nd possile rrhythmi nd therefore should e voided Effect of physiologicl sttus of right ventricle on pump performnce It hs een suggested tht the performnce of the pump depends upon the physiologicl sttus of the hert, not only of the left ventricle ut lso of the right ventricle (SIESS et l., 1996; MEYNS et l., 1996; ROBERT, 1). To study the effect of the right ventricle on the opertion nd performnce of the pump, we decresed the elsticity of the myocrdium of the right ventricle from mximum vlue of 2 mmhg ml 1 to 1 mmhg ml 1 nd then oserved its effects on the loop of the pump flow nd pressure difference (Fig. 8), s well s on the loop of the pressure nd volume of the left ventricle (Fig. 9), during crdic cycle. As indicted y the two Figures, when the contrctility of the right ventricle decreses, the pump flow nd the rnge of the pressure difference re oth Fig c Effects of myocrdil contrctility of right ventricle on reltionship of pump flow nd pressure difference when pump is operted t () speed 1, () speed 3 nd (c) speed 4. ( ) right ventriculr E es ¼ 2 mmhg ml 1 ;( s ) right ventriculr E es ¼ 1 mmhg ml 1 reduced (Fig. 8), nd the men pressure nd men volume of the left ventricle re lso oth reduced (Fig. 9). These effects re more pronounced t higher pump speed, n oservtion tht is consistent with the results of in vivo experiments otined y MEYNS et l. (1996). 35 Medicl & Biologicl Engineering & Computing 2, Vol.

8 left ventriculr pressure, mmhg left ventriculr pressure, mmhg left ventriculr pressure, mmhg Fig left ventriculr volume, ml Another oservtion mde from our computer simultion is tht, with filing right ventricle, the left ventricle is more prone to e over-unloded. In fct, with decresed contrctility of the right ventricle, our computer simultion cn only e crried out up to pump speed 4. At speed 5, the volume of the left ventricle pproched zero fter severl crdic cycles, nd the progrm left ventriculr volume, ml left ventriculr volume, ml c Effects of myocrdil contrctility of right ventricle on reltionship etween pressure nd volume of left ventricle when pump is operted t () speed 1, () speed 3 nd (c) speed 4. ( ) right ventriculr E es ¼ 2 mm Hgml 1 ; ( s ) right ventriculr E es ¼ 2 mmhgml 1 cme to hlt. Such phenomenon is not unexpected. As the contrctility of the right ventricle decreses, less lood will e driven into the left ventricle nd e ville for the pump to withdrw. This oservtion suggests tht, if the Hemopump is to e pplied for ptient whose right ventriculr function is lso hmpered, i-ventriculr ssistnce should e considered to chieve the full efficcy of the pump. 3.6 Comprisons of synchronous nd non-synchronous opertions of Hemopump Thus fr, we hve only considered the Hemopump eing operted t constnt speed throughout the crdic cycle, referring to the non-synchronous (with the hert) opertion. Fig. 6 indictes tht, under such opertion, the ortic pressure wveform ecomes quite flt, especilly t high pump speed. Considering the prospective long-term usge of the Hemopump, we cnnot ignore the long-stnding controversy regrding the physiologicl effects of non-pulstile circultion. Although NOSE (1993) reported tht long-term non-pulstile iventriculr ypss did not produce hrmful physiologicl effects in nimls, recent studies hve suggested tht prolonged non-pulstile left hert ypss cn produce certin effects on the rteril structure nd function, such s the wll thickness, smooth muscles nd vsoconstrictive function of the vessels (NISHIMURA et l., 1998; NISHINAKA et l., 1). To oserve the effects of the Hemopump working in the synchronous mode, we let the pump operte t speed 1 during distole (to void ckflow) ut t different speed during systole. Fig. 1 compres the stroke volumes for the two opertion modes, where the white rs re for the non-synchronous opertion of the pump rotting t constnt speed from speed 1 to speed 5, nd the lck rs re for the synchronous opertion. Under the synchronous mode, the pump lwys rottes t speed 1 during distole, ut the rottion speed chnges from speed 1 to speed 7 during systole, s shown in Fig. 1. The roken horizontl line in Fig. 1 indictes the norml level of stroke volume, 14 ml et 1, ccording to the work of MA stroke volume, ml et speed level Fig. 1 Comprison etween two opertion modes of pump: ( u) (non-synchronous mode): stroke volume produced y model when pump is operted t constnt speed throughout crdic cycle; ( j) (synchronous mode): stroke volume produced y model when pump is operted t speed 1 during distole nd t speeds 1 7 during systole; ( ) level of typicl stroke volume of 14 ml et 1 for norml hert Medicl & Biologicl Engineering & Computing 2, Vol. 351

9 ortic pressure, mmhg Fig time, s Comprison etween ortic pressure wveforms when pump is operted in two opertion modes to chieve sme stroke volume of 14 ml et 1. For non-synchronous mode, pump is operted t constnt speed 2 throughout crdic cycle. For synchronous mode, pump is operted t speed 1 during distole nd t speed 6 during systole. ( ) pump rottes constntly during one crdic cycle. ( s ) pump rottes synchronously with nturl hert et l. (1979). Figure 1 indictes tht the pump cn produce stroke volume of 14 ml et 1 t speed 2 under the nonsynchronous opertion mode. On the other hnd, to produce the sme stroke volume under the synchronous opertion mode, the pump hs to rotte t speed 6 during systole. This oservtion suggests tht the pump is more effective when operting in the non-synchronous mode. In Fig. 11, we compre the ortic pressure wveforms when the pump is operted in either the synchronous mode or the nonsynchronous mode to otin the sme stroke volume of 14 ml et 1. We notice tht, under the synchronous opertion mode, the pulstion of the ortic pressure is lrger, nd the wveform is closer to nturl one elonging to norml circultory system without ssistnce. This oservtion then suggests tht, when the pump is operted in the synchronous mode, the resultnt hemodynmic vriles of the circultory system re more comptile with those of nturl one. As result, there my e fewer long-term negtive physiologicl effects when the Hemopump is operted in the synchronous mode. 4 Discussion nd conclusions A dynmic model for the pump hs een developed sed on theoreticl nlysis s well s in vitro nd in vivo experimentl dt. The pump model is incorported into cnine circultory system model to study the reltionship etween the pump flow nd pressure difference reltionship of the pump in living circultory system, the effects of the Hemopump on vrious hemodynmic vriles of the circultory system, the ssistnt effects of the Hemopump on filing left ventricle, the effects of the physiologicl sttus of the right ventricle on the Hemopump performnces, nd the comprison etween the synchronous nd non-synchronous opertion modes of the pump. When the effects of inertil property of lood re included in the pump model, the curve of the pump flow ginst pressure difference during crdic cycle shows relistic hysteresis tht ws clerly oserved in the in vivo experiments. Mny other predictions from the model re lso in good greement with the reported results of clinicl nd niml experiments. The direct effects of the Hemopump on the hemodynmic vriles of the circultory system include n increse in men ortic pressure, n increse in stroke volume, decrese in left ventriculr volume, decrese in lood flow pumped out y the left ventricle, decrese in the re of the pressure volume loop of the left ventricle during crdic cycle, nd decrese in left tril volume. The increse in men ortic pressure increses the coronry flow, which in turn increses the oxygen supply to the hert. On the other hnd, the decrese in the left ventriculr volume nd the mount of lood pumped out y the left ventricle imply reduction in the worklod of the left ventricle. In ddition, the decrese in the re of the pressure volume loop of the left ventricle indictes decrese in the oxygen consumption of the hert. As result, the pump cn effectively ssist the filing hert y incresing the oxygen supply while decresing the oxygen consumption. The incresed men ortic pressure nd stroke volume lso men more lood flow eing delivered to the vitl orgns of the ody. The simultion results lso indicte tht ll the eneficil effects of the Hemopump re enhnced when the pump rottion speed increses. However, when the pump is operted t very high speed, oth our simultion nd in vivo experiments hve shown tht the volume of the left ventricle cn pproch zero t certin time during the crdic cycle, phenomenon referred to s the left ventricle eing over unloded. As left ventricle over-unloding cn e ccompnied y hmpered inflow of the pump, rndomised tip-to-wll contct nd possile rrhythmi, such sitution should e voided in clinicl pplictions of the Hemopump. On the other hnd, high sher stresses will occur owing to high rottionl speed, nd red lood cells cn e dmged. The pproches of hemolysis nlysis in such micro-xil lood pumps re now under investigtion y mens of computtionl fluid dynmics (APEL et l., 1). The question of wht the optimum pump speed is for given hert my then rise. It hs een suggested tht, for ptient with low crdic output, lower pump speed my e more desirle to chieve higher totl crdic output (SIESS et l., 1996). The min rgument for such strtegy is to mintin etter filling nd inflow conditions into the pump. If there is no limittion to operte the pump t constnt speed during the entire crdic cycle, etter strtegy my e to operte the pump t high speed when the left ventriculr volume is lrge, nd to reduce the pump speed when the left ventriculr volume ecomes smll. Direct implementtion of such strtegy requires sensor tht cn red the instntneous volume of the left ventricle. On the other hnd, s the timing for the left ventricle to rech minimum volume is known pproximtely (ner end-systole), the desired control of the pump speed my e chievle y using the ECG wveform rther thn specil volume sensor. Another interesting question is whether it is possile to find trget function to e either mximised or minimised y control of the opertion of the Hemopump. The vriles tht need to e incresed cn include ortic pressure nd stroke volume, nd the vriles tht need to e reduced cn include the re of the pressure volume loop of the left ventricle nd the highest pump rottion speed. The weight of ech vrile however, cn e ffected y the physiologicl conditions of the left ventricle, the right ventricle, nd the ort. The model descried in this pper should provide useful tool to investigte nd test vrious strtegies for optimum control of the Hemopump. Finlly, the results from the modelling study should lso provide useful guidelines for clinicl testing of vrious control strtegies. Acknowledgment This work is supported y Ntionl Nturl Science Foundtion of Chin nd Tsinghu University. 352 Medicl & Biologicl Engineering & Computing 2, Vol.

10 References APEL, J., PAUL, R., KLAUS, S., SIESS, T., nd REUL, H. (1): Assessment of Hemolysis relted quntities in microxil lood pump y computtionl fluid dynmics, Artif. Orgns, 25, pp BAI, J., nd ZHAO, B. (): Simultion evlution of crdic ssist devices, Methods of Inf. Med., 39, pp BULTER, K. C., MOISE, J. C., nd WAMPLER, R. K. (199): The Hemopump new crdic prothesis device, IEEE Trns. Biomed. Eng., 37, pp CHEN, E., nd YU, X. Q. (): The Hemopump s design nd its experimentl study, J Biomed. Eng., 17, pp DEBAKEY, M. E. (1971): Left ventriculr ypss pump for crdic ssistnce: clinicl experience, Am. J. Crdiol., 27, pp DREYFUS, G. D. (1996): The Hemopump 31, the sternotomy Hemopump clinicl experience, Ann. Thorc. Surg., 61, pp FRAZIER, O. H., WAMPLER, R. K., DUNCAN, J. M., MARIS, M.P., PARNIS, S. M., nd FUQUA, J. M. (199): First humn use of the Hemopump, ctheter-mounted ventriculr ssist device, Ann. Thorc. Surg., 49, pp FREED, P. S., WASFIE, T., AZDO, B., nd KANTROWITZ, A. 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H498 SUGA, H., YASAMURA, Y., NOZAWA, T., FUTAKI, S., LGARASHI, Y., nd GOTO, Y. (1987): Prospective prediction of O 2 consumption from pressure-volume re in dog herts, Am. J. Physiol., 25, p. H1258 WALDENBERGER, F. R., WOUTERS, P., DERUYTER, E., nd FLAMENG, W. (1995): Mechnicl unloding with miniture xil flow pump (Hemopump): n experimentl study, Artif. Orgns, 19, pp WALLEY, K. R., BEEKER, C. J., HOGAN, R. A., TEPLINSKY, K., nd WOOD, L. D. H. (1988): Progressive hypoxemi limits left ventriculr oxygen consumption nd contrctility, Circ. Res., 63, p. 849 ZHOU, X. Q., BAI, J., nd ZHAO, B. (1998): Simultion study of the effects of regionl ischemi of left ventricle of crdic performnce, Automedic, 17, pp Author s iogrphy XIONG LI ws orn in Hunn Province, Chin, in She received her BS in Biomedicl Engineering from Tsinghu University, Beijing, Chin, in. She is currently working towrds her MS in the Deprtment of Electricl Engineering t Tsinghu University. Her min reserch interests include modelling nd computer simultion of the crdiovsculr system nd simultion studies of crdic ssist devices. Medicl & Biologicl Engineering & Computing 2, Vol. 353