Preliminary Hydraulic Design and Test of A Centrifugal Blood Pump

Transcription

1 Preliminary ydraulic Design and Test of A Centrifugal Blood Pum Maruay Anansukkasam, Ruma Chaijinda, and Asi Bunyajitradulya* Deartment of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University Bangkok 0330, Thailand * Corresonding Author: Tel: , Fax: , asi.b@chula.ac.th Abstract The aer resents the design scheme and considerations for the reliminary hydraulic design of a centrifugal blood um, the evaluation of the design via model testing, and finally the more realistic rediction of the rototye erformance arameters based on the results of the model testing. The design is based on one-dimensional Euler s turbomachine equations and the design seed of,000 RPM, together with heart arameters, and some blood trauma and mechanical considerations. A X scale-u model is subsequently constructed and tested. The initial test of the model shows that the um cannot achieve the rototye-equivalent desired head-flow at the design seed. Subsequently, a series of additional model tests are erformed, and the result shows that the characteristic dimensionless headflow curve of this um, C 5,43C 0.66C 0. 65, is Reynolds number (Re) indeendent over the range of Re tested of.4-.9x0 6, yet still 0 times higher than the rototye Re of.x0 5. Similarity scaling, based on the Re-indeendent assumtion of the newly acquired dimensionless headflow curve, is then used to redict the required oerating seed of the rototye,,85 RPM, aroximately 0% above the design value. Additional test at this RPM confirms the rediction and shows that the model um can successfully achieve the rototye-equivalent head-flow at this seed. The more realistic erformance arameters of the rototye, based on the results of the model testing, are then redicted. It is subsequently concluded that, if the dimensionless head-flow curve of this um is indeendent of Re down to the rototye Re, the rototye should be able to deliver the desired headflow successfully at,85 RPM. The remaining issue is then whether the assumtion of Re indeendence down to the rototye Re is valid. Keywords: centrifugal blood um, ventricular assist device, VAD, hydraulic design, um test

2 Fig.. Control volume and notations for geometric variables., ê = tangential direction and tangential unit vector, ositive in the direction of U ; also, blade subtended angle r, eˆ r = radial direction (and radius) and radial unit vector, ositive away from the center V = absolute fluid velocity U = blade eriheral velocity = blade angle, measured from ê and away from ê r = angle of absolute fluid velocity V, N ê r P measured from ê r and towards ê = rotational seed = imeller angular velocity d = imeller diameter b = imeller width d : d / d b : b / b subscrits ê ê P o r, = imeller inlet and exit, resectively m, = model, rototye : = equal by definition Other notations are given in the text. ê. Introduction A blood um, or ventricular assist device (VAD), is a medical device that is used for assisting the function of the heart in uming blood in heart disease atients. Commercially, b b r r ê z ê z the aroved VADs are available from a few comanies [e.g., -3]. Presently, though, they need to be imorted at high cost and the local availability is still rare even for the imorts. This initiates the resent reliminary design and test roject. Naturally, there are many asects in the design and develoment of a VAD, for examle, fluid dynamics, rotor dynamics, strength and wear, drive, and blood trauma. owever, here we focus rimarily on the hydraulic design. The objective of the aer is to resent our design scheme and considerations for the reliminary design of a (centrifugal) blood um and to resent the evaluation of our design scheme via the result of the model testing. In the design rocess, the heart arameters and, to the first-order, the blood trauma, esecially hemolysis, is considered. The design is based on one-dimensional Euler s turbomachine equations. The result of the design is evaluated for the um erformance by the testing of a X scale-u model. While the hemolysis is reliminarily considered in the design rocess, it is, however, not yet tested.. Design Secification Parameters The fluid is blood with density of,050 kg/m 3 and dynamic viscosity of 4x0-3 ascalsecond. The design flowrate and head corresond to the rest state (designated A) with blood volume flowrate of A = 5.8 L/min and mean arterial ressure A = 93 mmg [4]. Note that at exercise state (designated B), B = 5.5 L/min and B = 0 mmg. At resent, we target the design at the rest state A.

3 3. Pum Design The current hydraulic design rocess can be divided into 3 major stes: um tye selection, imeller design, and casing design. 3.. Pum Tye Selection For the aroriate um tye, we consider the dimensionless secific seed s, defined by 3/4 s : /( g), where is the angular velocity (rad/s), is volume flowrate (m 3 /s), and is total hydraulic head (m). While we have some degree of freedom in choosing the design rotational seed and consequently the tye of machine (i.e., radial-flow vs axial-flow), in order to avoid the comlications of wear and drive we target the design rotational seed in the tyically low range of,000-4,000 RPM and choose the design rotational seed at,000 RPM. Taking into account the design oint A, this results in s of , which fall in the radial-flow tye range [5-6] and we choose to design a radial-flow machine. Note that if we choose instead a higher target range of rotational seed in the order of a few ten thousands RPM, this will result in an axial-flow tye machine. 3.. Imeller Design For the imeller design, we use the control volume as shown in Fig. and follow the set of Euler s turbomachine equations, with the target design oint at the rest state (A) and with the following assumtions: radial-entry flow ( 0 ) shockless entry/exit condition (relative fluid velocity with resect to the rotating blade is tangent to the blade angle at inlet and exit) straight blade constant absolute radial velocity along the blade assage neglect all losses. The notations for geometric variables are given in Notations and Fig.. Design Scheme and Analysis Our design scheme can be summarized with Eq. (), where K : A A A b, () b : tan tan tan d d () is the arameter that is a function of the geometries of the machine (,, d, b ) and the flow ( ). Secifically, we cast the combination ( K ) of the design secification arameters,, and (at the design oint A) in terms of the dimensionless and dimensional design geometric variables,, d, b,, and b, resectively, and the fluid density. As a result, K /( ) : A A A is a constant. Note that Eq. () can be derived from the set of Euler s turbomachine equations, which can be cast in terms of the geometric variables as follows. The velocity triangle relations: sin V i U i i, cos( i i ) sin sin V i U i i i, cos( i i ) cos sin V ir U i i i, (3) cos( i i ) where i is or, the inlet or exit cross section. Conservation of mass: V V r db. (4) r

4 (deg) o b 5 mm d < 0 cm d, b ( mm) 0., 0 Design oint Straight blade with d 0. [Eq. ()], 5, 0, 5 0., 0, 5, 0, 5 0.3, 0, 5, 0, 5 0.4, 0, 5, 0, 5 Volume flowrate: tan b r. (5) tan tan Euler s hydraulic torque mr V r T h tan tan T h V 4 b r tan :. (6) ydraulic ower ( ): mg T h tan tan mg b tan 3 4 r. (7) ydraulic head: tan r g tan tan. (8) Static ressure rise (neglect kinetic and otential head): tan r tan tan. (9) For simlicity, we choose to design straightblades. Thus, we have the following additional relations: Geometric relations for straight blade: (0) and, according to the sine law for the triangle op P in Fig., o 90 arcsin d sin(90 ) o. () In order to reduce the otential of flow searation in the blade assage, we choose the scheme of constant absolute radial velocity V r, Fig.. The design chart: the relation for ;, ) (deg) which is equivalent to constant relative radial velocity with resect to the rotating blade. Therefore, we have d b and rb r b () and the blade width rofile: b r) rv r (. (3) With the assumtion of radial-flow entry ( 0), and the conditions of straight blade ( ) and constant absolute radial velocity ( ), we can rewrite Eq. () as tan d b tan d / tan Kb d, (4) where ( ; d, b ; K). ere, the two semicolons are used to differentiate what we consider indeendent variables, variable arameters, and constant arameters, resectively. For a given fluid ( ), Eq. (4) is the relation for the blade subtended angle in terms of the dimensionless design geometric variables and, the dimensional design geometric d. ( d b variable b, and the design secification arameter K. Choosing as the variable, and d and b as the arameters, we can lot this relation as shown for the ranges of d = 0.

5 0.4 and b = 0 5 mm in Fig.. Figure is then used as a design chart. Note that all oints on the lines on this chart corresond to the same value of the design secification arameter K. Design Constraints and The Design Solution In order to choose the suitable design solution, we imose further constraints on the design solutions on the chart (Fig. ) as follows. Manufacturing limitation, 7 o : Therefore, most of the black lines ( d = 0.4) in Fig. are not suitable. Size limitation, d < 0 cm: For a tyical blood um, the inlet diameter is in the order of cm. If we choose d = 0., this will make d = 0 cm, not yet including the casing. The blue lines ( d = 0.) are therefore considered not suitable. Exit blade width limitation, b 5 mm: The remaining solutions are the solid green d, b ( mm) = (0.3,0) and the remaining reds d, b ( mm) = (0.,0-5). Since b / d, the solid green ( b = 3.33) with b = 0 mm and the reds ( b = 5) with 0-0 mm will give b < 5 mm, these are therefore considered not suitable. As a result, we are left with the one that we consider suitable under the constraints to be b = the dashed-dotted red line, i.e., d, b ( mm) = 0., 5 mm. The solution: While all oints on this line satisfy the secified K and the foregoing assumtions, not all oints on this line satisfy the condition of straight blade. Secifically, for a straight blade, we also have the geometric relation Eq. (). Thus, for a given d of 0., we find the solution on the line d, b ( mm) = 0., 5 to be = 7.73 o and = o. Finally, can be determined from Eq. (0), r from Eq. (5), V r from Eq. (3) evaluated at inlet, and blade width rofile b (r) also from Eq. (3) with constant Vr V r and. Table summarizes the geometric variables for the rototye, and Table at the back summarizes imortant erformance arameters for the design of the rototye (in comarison to those of the model test results). Note that this is a backward, straight blades imeller. Table. The geometry of the imeller. Geometric Variables (deg) 7.73 o (deg) o d (mm) 3.6 d (mm) b (mm) 5 b (mm) 5 d 0. b 5 (deg) The uestion of The Number of Blades With the blade shae determined, the issue of the aroriate number of blades and blade thickness, which are related to flow quality, blockage effect at imeller inlet, and mechanical strength, remain. At resent, the issue is not yet fully addressed, and we lan to address the issue more elaborately in the future. On the other hand, since we set out to test this design with a model made from acrylic for future flow measurement and observation, giving the riority to the mechanical strength, we determine the required blade thickness to be.5 mm. Subsequently, considering and avoiding excessive blockage effect, we decide on six blades. This results in the blockage ratio at the imeller inlet diameter of.9%. ere, blockage

6 ratio is defined as the total radial area blocked to the total radial area, B ntsin /( d), where n is the number of blades and t is the blade thickness. Note that for a future rototye, which will be made from a more suitable material, the restriction from the blade thickness is exected to be less severe; and, thus less blockage. Predicted Off-Design ead-flow Curve of The Prototye at Constant RPM In order to redict the off-design head-flow curve of the rototye at constant RPM, we cannot use the design relations (5)-(9) since they are restricted to shockless entry/exit condition of the velocity diagrams. Instead, we need to emloy the original Euler s torque and hydraulic head equations, T h mr V ( V = 0) and ( mg )/ mg Th / mg UV / g. Solve V from the velocity diagram, we have V U Vr cot. Rewrite V r in terms of [Eq. (3)] and substitute the resulting V in terms of into the equation for above, we finally have U cot U db g g. (5) The resulting ideal dimensional head-flow curve for the rototye from Eq. (5) is shown later in Fig. 5, together with the model test result. Briefly, we see that the ideal head decreases linearly and slowly with the flow, according to the sloe ( U cot)/( db g). Note that the sloe of Eq. (5) can be used as a guide in the design of the characteristic sloe of the dimensional head-flow curve of the um. If we define the dimensionless head C as C : g / d, the dimensionless flow C (a) (b) Fig. 3. The X scale-u model: (a) imeller, (b) assembly of the imeller and the um casing. 3 as C : / d, and the Reynolds number Re as Re : d /, where d is chosen for the characteristic diameter d, Eq. (5) can be rewritten as C d cot C b 4. (6) The resulting ideal dimensionless head-flow curve for the um from Eq. (6) is shown later in Fig. 6, together with the model test result. Again, C varies linearly and slowly with C, according to the sloe d cot /(b ). Note that this sloe, unlike its dimensional counterart which still deends on the velocity U, deends on geometric variables alone. Similar to Eq. (5), the sloe of Eq. (6) can be used as a guide in the design of the characteristic sloe of the dimensionless head-flow curve of the um Casing Design For the volute shae, with similar reason as the blade assage, in order to reduce the otential of flow searation we choose the scheme of constant tangential velocity throughout the volute assage. Preliminarily, we also consider the hemolysis. Yamane et al. [7-8] suggest that the suitable shear rate should be below 00,000 sec -. Since the maximum shear rate otentially occurs at the ga between the rotating imeller and the casing at the volute

7 inlet, we choose the ga width to be.5 mm; resulting in the shear rate at this location of,300 sec -. At this oint, it is imortant to note that hemolysis is related to the local shear and therefore can occur at the location where the local shear is high. Thus, the current consideration is only to the first-order. 4. Model, Similarity Scaling, Model Testing Model In order to evaluate the erformance of the current design, we choose to make a X scaleu model, made from acrylic, for ease of future flow observation and measurement. Figure 3 shows the resulting x scale-u model, which is the result of the current design scheme. Note that the volute assage cross section is rectangular. In order to fit to a -inch ie, we design a diffuser that changes the rectangular cross section to -inch diameter circular cross section. Similarity Scaling Law In scaling, we emloy similarity scaling law C f C,Re, (7) where the head and flow coefficients, and the Reynolds number is defined in Sec. 3.. The uestion of Reynolds Number To strictly follow this similarity law, the Reynolds number must be taken into account. The design rototye Reynolds number at A is calculated to be.x0 5. Given the X scale-u model, this can be done either by, for examle, using glycerine-water solution in order to get the kinematic viscosity of the blood so that the model can be run at reasonable seed ( Nm N / 4 ) but the head will be relatively low ( m / 4), or Motor using water ( blood / water = 4.7), but the test seed and the head will both be very low, N m ~ N / 0 and m ~ / 00. At this stage, we decide to first neglect the effect of Re, i.e., C f ( C ), use water as working fluid, and run the model at the same design seed as for the rototye, i.e.,,000 RPM, for ease of measurement. This corresonds to Re of.3x0 6, aroximately 0 times higher than that of the rototye. The effect of Re will be artially addressed in this work but will be addressed in more detail in the future. Thus, we have the scaling laws between the model and the rototye as m N N 8 m and m 4 N N m. (8) Finally, in this work we choose to test the model and deduce the erformance of the rototye from the scaling law at equal seed. Thus, we have the scaling laws, from Eq. (8), m 8 igh Gage Pum Model Low Gage Flow Venturi m and 4. (9) Model Pum Testing Figure 4 shows the schematic diagram of the test rig. Briefly, it is a closed loo test rig with uer reservoir oen to atmoshere. Two ressure gauges are installed at 0 ie diameters away from the um inlet and exit for reservoir Valve Fig. 4. Schematic diagram of the um test rig.

8 Prototye um head (m) Model um head (m) C.5 6 Ideal at,000 RPM Design oint A 0.3 Ideal Prototye RPM C from Ex Trace A Design Point A (@,000 RPM) 85 RPM Ideal C-C Linear (C from Ex) 0.5 (m) 4,85 RPM,000 RPM RPM Model A Model ead-flow A,85 RPM Model A C Data oints at,85 RPM (green triangles) Prototye RPM Poly. (C from Ex) Poly. (C from Ex) Linear fit: y = -.339x R = Parabolic fit: y = -543x x R = Cubic fit: y = x x +.068x R = Third degree olynomial does not do better than nd degree. 0 Fig. 5. Dimensional head-flow curves for the model and the rototye. the measurement of static ressures. Volume flowrate is measured by a venturi. The total hydraulic head is determined from g Model um volume (L/min) flowrate (L/min) Prototye um volume flowrate (L/min) V V z z g g g, (0) where, because of equal inlet and exit ie diameters, the kinetic heads cancel and the reading of the ressure gages is corrected for the elevation. Overall, the total hydraulic head deends essentially on the static ressure rise across the um. 5. Model Pum Test Results Dimensional Performance The model um test result is shown in Fig. 5. Presently, we test the um at,000 RPM. Focus first on the data oints at,000 RPM; the data oints at,85 RPM will be exlained later in Sec. 7. The result shows that the head changes relatively little with the flow over the test range (the variation is aroximately 4% of the average value, and well within the uncertainty of measurement), qualitatively in agreement with the ideal head-flow curves from Eq. (5). At the same volume flowrate, the Trace of rototye A at varying RPM Fig. 6. Dimensionless head-flow curve from model testing and the rediction of the oerating seed of the rototye. C C actual total hydraulic head is about 70% of the ideal value in the test range. Although not shown, since the head is aroximately constant, the hydraulic ower (= m g ) naturally increases with the volume flowrate. The maximum efficiency ( ) at this seed is found to be 9.8%. Effect of Re and Dimensionless Performance In order to get some reliminary information on the effect of Reynolds number, we make additional tests to a total of 7 seeds, evenly saced from 600,00 RPM or Re from.4-.5x0 6. Figure 6 shows the scatter lot of the head against the flow coefficients of all data oints. Disregard first the data oints at,85 RPM in the figure; they are not included in the resent analysis. The uncertainties of both C and C are estimated to be 0% of the reading value. Firstly, the result shows that the dimensionless head-flow curve is in qualitative agreement with the ideal one, C varies slowly with C. More imortantly, the result suggests that the effect of Reynolds number on the dimensionless head-flow curve in this range of

9 Re is small, albeit Re is varied only by a factor of and has not yet reached the rototye Re. If we assume that the effect of Re is small and, as a result, aly one arabolic-curve fit to all the data oints (excluding at,85 RPM), we find C a C ac ao, () where the constant a s are found to be a = - 5,43, a = 0.66, and a o = The reason for the arabolic fit is due to the exected square-loss in the hydraulic head and is aarently suggested by the data. The linear and cubic fits are also shown as the light grey lines in the lot for comarison. Finally, if we define the hydraulic ower coefficient as C : mg /( 3 d 5 m g ), we find Cm g CC, () where Cm g can be written in terms of C via Eq. (). 6. Prediction of The Prototye Pum Oerating Seed Figure 5 also shows the redicted rototye um erformance by also showing the scales of the rototye um head-flow at the same seed as that of the model on the secondary x and y axes according to the scaling law, Eq. (9). This can also be seen in dimensionless form in Fig. 6. From both figures, it is obvious that we have not yet achieved the rototyeequivalent desired head-flow at oint A when we run the um at the design seed of,000 RPM. In order to redict the required oerating seed for the rototye um oerating at headflow of oint A, we emloy the dimensionless head-flow curve and aly similarity scaling as follows. If we assume that the dimensionless head-flow curve does not deend on Re, i.e., C f ( C ), then the dimensionless head-flow curve shown in Fig. 6 is the head-flow curve of this um in this range of C. We can then trace the oerating oint A of the rototye um on the C C lane by using the set of arametric equations C, ( ) A and ga, C 3 ( ) d, d,, (3) where is the varying arameter, A, and A, are the flow and head at oint A of the rototye um, and d, is the diameter of the rototye um. The result is shown in Fig. 6. Theoretically, the oints on this trace corresond to different ossible similarity states of all ossible ums that have the diameter of size d, and that can oerate at the rototye head-flow at A at the corresonding, not of the same similarity state. The intersection oint of this trace with the dimensionless head-flow curve of this um from measurement then gives the dimensionless co-ordinates ( C, C ) of the oerating oint and the corresonding seed for this um. The determination of the oerating seed of the rototye as described is basically the alication of the similarity scaling law between the model and the rototye at the intersection oint. In this case, the result redicts that in order to achieve the desired flowrate and head at A, we need to oerate the rototye at,85 RPM, aroximately 0% above the design seed. This corresonds to C =.73x0-3, C = 0.77, and s = 0.9, and the arameters of

10 the rototye (not model) of Re =.4x0 5 and K =.03x0 6 Pa-s /m 3. Finally, while C C curve is relatively indeendent of Re, at least within the current range of arameters, our reliminary result suggests that the efficiency deends more strongly on Re; the lower the Re, the lower the efficiency. 7. Test of The Prediction In order to test the rediction from the dimensionless head-flow curve and similarity scaling law as described in Sec. 6, we roceed to make one additional test of the model at the same redicted seed for the rototye, i.e.,,85 RPM. The dimensional and dimensionless test results are shown in Figs. 5 and 6, resectively. As is obvious from Fig. 5, we now achieve the rototye-equivalent desired headflow at A for the model and, if the dimensionless head-flow curve is Re indeendent down to the rototye Re, also for the rototye. In addition, the dimensionless data oints also collase nicely onto the dimensionless head-flow curve from revious seeds, Fig. 6. This additional test therefore, confirms the similarity scaling between this model oerating at different seeds, and further extends the validity of the dimensionless head-flow curve for this um as described by Eq. () to a little higher Re; in other words, confirms the Reindeendence assumtion in this range of Re. In fact, after this test we also make one more test at the seed of,300 RPM, and the result still confirms the validity of the dimensionless head-flow curve nicely. Table summarizes some of the imortant arameters from the initial design of the rototye, the model tests, and the redicted erformance of the rototye after incororating the results of the model tests. Table. Summary of imortant arameters. Designed Predicted Model Model Prototye Prototye Fluid Blood Water Water Blood N (RPM),000,000,85,85 (L/min) (m of fluid) s C 3.4x0-3.73x0-3 C Re.x0 5.3x0 6.7x0 6.4x0 5 K ( Pa-s /m 3 ).x x x0 6 (%) ? m g (W) Excet Re and, the values in the model columns are calculated from similarity at the intersection oint of the measured dimensionless head-flow curve and the trace of the oerating oint A in Fig. 6; i.e., C =.73x0-3 and C =0.77. The efficiency for the model columns are interolated from the measured data at C =.73x0-3. When comare the oint of maximum efficiency (mentioned in Sec. 5, = 9.8%) and the similarity oint ( = 7.4%) to the desired oerating oint at,000 RPM of the model in Table, we see that while the desired oerating oint is not the oint of maximum efficiency, it is close. Its efficiency is lower than the maximum efficiency by aroximately 0% of the maximum efficiency value. When comare the efficiencies at the same similarity state (same C and C, models at,000 and,85 RPM) but different Re, we see that the efficiency deends on Re. Finally, since the efficiency deends on Re, we

11 make no rediction of the efficiency for the redicted rototye at this oint. 8. Summary and Conclusion In this work, the design scheme for a centrifugal blood um based on onedimensional Euler s turbomachine equations is devised; the design is conducted; and a model is manufactured and tested. The resulting geometric arameters from the design are summarized in Table. In order to test the design at this early stage, a X scale-u model is used and the Re indeendence in the similarity scaling law is assumed. The model is then tested at the design rototye seed of,000 RPM, which corresonds to Re =.3x0 6, aroximately 0 times higher than that of the rototye which is at.x0 5. The model test result at this single Re shows that the actual total hydraulic head is about 70% of the ideal value and the maximum efficiency is 9.8%, and the designed um cannot yet achieve the desired head-flow. In order to redict the required oerating seed of the rototye to oerate at the desired head-flow at A, the effect of Re and Re deendence is then investigated. Additional tests are consequently conducted with the Re range extended down to.4-.5x0 6 (600-,00 RPM), but not yet reach the rototye Re. It is found that the dimensionless head-flow curve, given by Eq. (), is indeendent of Re in this range. This dimensionless head-flow curve is then used to redict the required oerating seed of the rototye; and the rediction gives the seed of,85 RPM, aroximately 0% higher than the design value. In order to test the rediction, the model is then tested at this redicted seed of the rototye. The test confirms the rediction; and, the model achieves the rototye-equivalent desired head-flow at A. In another asect, the test confirms the similarity scaling law for the model oerating at different seeds and, together with another test at,300 RPM, extends the validity of Re-indeendence dimensionless head-flow curve of this um to Re.4-.9x0 6. Finally, the erformance arameters of the rototye, after incororating the more realistic data from the model testing, are redicted and given in the last column of Table. It is concluded that if the dimensionless head-flow curve of this um is indeendent of Re down to the rototye Re, the rototye should be able to deliver the desired head-flow at A successfully at,85 RPM. The remaining issue is then whether the assumtion of Re indeendence down to the rototye Re is valid. 9. Acknowledgement This roject is funded by Stimulus Package (SP) of Ministry of Education under the theme of Green Engineering for Green Society. The authors also would like to thank the ead of The Mechanical Engineering Deartment, Aj. Chinate Benyajati, and Aj. Somsak Chaiyainunt who initiate and suort the roject, and to Aj. Werayut Srituravanich who hels managing the funding. They also greatly areciate Dr. Takashi Yamane s visit and resentation. They would like to thank also Mr. Kitiong Kangvanskol for his hel in conducting some of the tests.

12 0. References [] Thoractec. URL: htt:// medical-rofessionals/vad-roduct-information /index.asx [] Jarvik eart. URL: htt:// com/home.as. [3] eartware. URL: htt:// au/irm/content/usa/roducts_vad.html. [4] Levitzky, M. G., 997. Cardioulmonary Physiology in Anesthesiology, McGraw-ill, New York. [5] Gülich, J. F., 00. Centrifugal Pums, Second Edition, Sringer, Berlin. [6] EBARA Cororation, 00. The EBARA Pum System Engineering andbook, EBARA Cororation. [7] Yamane, T., Maruyama, O., Nishida, M., Kosaka, R., Sugiyama, D., Miyamoto, Y., Kawamura,., Kato, T., Sano, T., Okubo, T., Sankai, Y., Shigeta, O., and Tsutsui, T., 007. emocomatibility of a hydrodynamic levitation centrifugal blood um, J. Artif Organs, Vol. 0, [8] Yamane, T., 00. Imlantable Non-ulsatile Artificial eart - Study with flow visualization, Thailand-Jaan Worksho, Nov. 7, 00, Chulalongkorn University, Bangkok.