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Haemodynamic approach to reducing thrombosis and haemolysis in an impeller pump
Haemodynamic and haemolysis
approach to reducing thrombosis in an impeller pump
Kun-xi Qian Shanghai
Second Medical University,
Peoples Republic
of China
Received September 1989, accepted March 1990
ABSTRACT In the experimentaland clinical support of the failing heart, the impeller-type centri&al pumps continue to be of interest because of their inherent advantages; however, the blood compatibility of these pumps still remains to be improved. From the viewpoint of haemodynamics, thrombosis and haemolysis could be reduced by eliminating the stagnation and turbulence of blood J?OW within the pump, which frequently tahes place near the blood contracting su faces of thepump, when the impeller contours do not coincide with the stream su@Zacesof the blood. It is suggested that it could be advantageous to design impeller contours according to the stream sufaces, by solving the partial dijj%rerttial equations of continuity, motion and energy. An impeller shroud and vane based on this approach would be filly rinsed by non-turbulent flow and there would then be neither stagnation nor turbulence within the pump, with the result that thrombosis and haemoljsis could be reduced. A new impellerpump, developed according to this method, wa.s evaluated as a le@ ventricular device in four dogs. The bypassJlow was controlled at 40-50s of the totaljow, each test lasting 6 h. All of the haematologicalparameters, measured every 2 h, remained within normal range. There was no thrombosis, and coagulation in the pump was avoided by a small dose of heparin to maintain the activated coagulation time (ACi’J under 200” in the experiments. Keywords: Impeller pump, thrombosis, haemolysis, stream surfaces, in vivo evaluation
INTRODUCTION Although diaphragm pumps have been much more extensively studied, impeller centrifugal blood pumps continue to be of interest in support of the failing heart, experimentally or clinically. They have inherent advantages in their function, construction, control, blood compatibility and cost, amongst which blood compatibility still remains to be studied in greater detail’. Thrombosis and haemolysis are both corn licated rocedures; there are many medical, met R anical, and surface-related facE iochemical, haemodynamic tors which cause thrombosis and haemolysis2y3. From oint, the thrombosis and the haemodynamic vie haemolysis would take wp p ace in stagnant and turbulent areas, and form as a result of incorrect design of the impeller4. When the impeller contour and other surfaces of the pump do not blood contacting coincide with the stream surfaces of blood flow, there would be stagnation and turbulence within the ump, especially near the impeller shroud and vane PFigure 7). The stagnation and turbulence could be eliminated by designing the impeller shroud and vane according to stream surfaces. In this way the thrombosis and haemolysis of the impeller pump could be reduced. Correspondence and reprint requests to: Dr Kun-xi Qan, c/o Institut Physiologic, Pauwelsstr. (Klinikum) 5100, Aachen, FRG 0 1990 Butteworth-Heinemann 0141-~5425/90/060533-03
The stream surfaces of the blood flow in an impeller pump are quite difficult both to calculate theoretically, and to visualize experimentally. The velocity distributions and the stream surfaces could only be calculated approximately if the viscosity of the blood in the pum were taken into consideration, and under this con B ition the calculation is tedious and the results rarely useful. It is better to achieve an analytical result by neglecting the viscosity, if it is possible, rather than to obtain an inaccurate result, with consideration of the viscosity.
IMPELLER CONTOUR In a common cylindrical coordinate system, r, 6 and L are components of radius, rotational an le and axial distance respectively (Figure 2). B Pood is assumed to be a non-viscous ideal fluid with density p = 1, and the effect of gravity is neglected. The principal equations of continuity, motion and energy are: div W= 0
(1)
d@ --02F+2Wx dt
$‘= -grad
P
p+$?$po
(3
for BES J. Biomed. Eng. 1990, Vol. 12, November
533
Haemodynamic approach to reducing thrombosis and haemolysis in an impeller pumf:
K.-K. Qian
This is the relative velocity distribution in a diagonal impeller. There is a relationship between velocity and stream surfaces: @= -w-m
b
a
Figure 1 Stagnation and turbulence would occur near blood contacting surfaces if impeller contours did not coincide with the stream surfaces of blood flow in the pump. a, Impeller shroud in axial pump; b, impeller vane in radial pump
grad $1 x grad $2
(6)
in which $1 and $2 are three-dimensional stream surfaces. Combining (5) and (6), $r, $2 can be obtained analytically7> : $1: z=c1 &: 0=c2ln
r2 r
(7)
This means that the shroud of the impeller should be a parabola and the vane of the impeller should be a logarithmic spiral. Figure 3 shows the parabolic shroud and logarithmic spiral vanes of a diagonal impeller.
IN WV0 EVALUATIONS
Figure 2 In a common cylindrical coordinate system, r, 0, z represent the components of radius, rotating angle and axial distance
in which W is the relative velocity of the blood cells in the impeller; w is angular speed of the impeller (8= w); r is the radial vector in the c lindrical coordinate (r, 8, z); u = wr ; P is the bloo dypressure pumped; and 4 is atrium ressure. Differentiating equation P3) and then inserting into equation (a), it follows: rot k?= -20”
(4) Equation (4) is analytically solvable in some special cases5,6. For a diagnonal pump ‘, the solution is: W, = c*/r w,=
-Wo+cCp/r
Wz=cs where cl, cp, c3 are integral constants.
a
A newly developed diagonal pump was evaluated in vim (Figure 4). The pump was used as a left ventricular bypass device, delivering blood from the left atrium to the aorta. The experimental animals were four dogs weighing 15-25 kg. The by ass ratio was controlled at 40-50% of the total flow PFigure 5). Because the impeller pump is both preload and afterload sensitive, its output seemed to be pulsatile corresponding to aortic pressure. To increase the pump flow, ‘Rigitine’ was infused during the experiments to decrease the mean aortic pressure of the dogs to 100 mmHg. Blood cell counts, the haemoglobin, the haematocrit and free haemoglobin, platelet aggregation and microgranules (lo-50pm) were measured before the operation, at the beginning of pumping and every 2 h. Most of the haematological ammeters remained unchanged and the plasma Kaemo lobin increased slowly but within the normal range PTable 7). Table 7 demonstrates that the pump did not damage the blood in a short bypass period. Free haemoglobin remained within an acceptable range in spite of its gradual increase. After the experiments the pump was dismantled immediately. Though low dosage of heparin was used and ACT was kept at under 200”, there was no
b
Figure 3 a, Impeller vane should be logarithmic spiral shaped; and b, the impeller shroud should be parabola shaped in a diagonal pump
534 J. Biomed. Eng. 1990, Vol. 12, November
Figure 4 Impeller pump was used as a left ventricular assist device in dogs during in vivo evaluations
thrombosis and haemolysis in an impellerpump: K.-K. @an
Haemodynnmicapproachto Table 1
Haematologicalparameter measured before operation,
Parameter
Preoperative
RBC (lo4 ml-‘) WBC (IO.’ ml ‘) PLT (IO’ ml ‘) HGB (g ‘%I) HCT (“/n) Free Hb (mg O/o) P1.T Aggregation (1%) Microgranule (ml-‘)
5.1 (1.0)
5.8 (2.3) 18.0 (6.5) 11.7 (1.2) 29.5 (4.9) 1.48 (0.24) 60.2 (11.7) 17536 (18583)
thrombosis or blood coagulation in all four experiments.
at beginning
Pump on 4.7 (0.8) 5.1 (2.3) 21.8 (2.1) 11.3 (1.2) 29.8 (4.6) 2.47 (0.50) 60.2 (3.5) 7153 (6387)
found in the pump
DISCUSSION A haemodynamic approach for designing impeller contour is presented. The impeller shroud and vane
of pumping
and every 2 h
(&SD)
2h 5.2 (0.5) 3.8 (1.5) 19.8 (2.1) 11.6 (2.0) 31.4 (2.9) 8.05 (5.77) 56.2 (7.8) 45 15 (2362)
4h 4.8 (0.2) 6.6 (1.6) 20.2 (2.1) 10.9 (1.0) 19.3 (1.0) 16.05 (6.77) 58.4 (10.9) 5030 (4553)
6h 4.7 (0.8) 8.0 (1.5) 21 .o (2.2) 9.3 (2.2) 28.1 (4.2) 28.58 (11.5) 67.42 (7.5) 24200 (37412)
are shaped according to the stream surfaces of blood flow, obtained by solving the relevant partial differential equations. Thus the blood contacting surfaces in the pump would be fully rinsed by non-turbulent flow. There would be neither stagnation nor turbulence thereafter and less thrombosis and lower haemolysis within the pump. All these theoretical results were demonstrated by acute animal experiments. An im eller pump with improved blood compatibility an x other inherent advantages may have more extensive ap lications in animal experiments in addition to cPinical trials. The development of the diaphragm pump has occupied 30 years; another 30 years may be necessary to perfect it. If only a fraction of the attention given to the diaphragm pump could be concentrated on an impeller pum , the prospect for an artificial heart would be much ! righter.
IWFERENCES
Figure 5
Haemodynamic parameters ments with dogs. AP, aortic pressure; PO, pump output; HO, heart output
in left ventricular assist experiCVP, central venous pressure;
1. Qan RX. Electric total artificial heart: with impeller or diaphragm? ES40 Proc, Bmo, CSSR, 1988. 2. Schoen FJ, Clagett GP, Hill JD, Chenoweth DE, Anderson JM, Eberhart RC. The biocompatibility of artificial organs. Tranr AWO1987; 33: 824. Ringoir S, Vanholder R. An introduction to biocompatibility. Artf07gan-s 1986; 10: 20-7. Qan RX. A new total artificial heart via impeller pumps. J Biomater A&+& 1990; 4: 405-18. @an RX. progress in impeller pumps in Shanghai. Assisted Circulation, 1989; 3: 195-214. Qan RX, Fei Q Lin KD, pi KD, Wang YP. The realization of pulsatile implantable impeller pump with low hemolysis. ArtifOrgans 1989; 13: 162-9. 7. Qan RX. The applications of 3-dimensional theory in designing impeller of the blood pumps. Chn J Eng Maths 1987; 4: 99-101. 8. @an RX. An analytical method of impeller design and its application in blood pumps. GhnJBiomechs 1987; 2: 46-52.
J. Biomed.
Eng. 1990. Vol. 12, November
535
approach to reducing thrombosis in an impeller pump
Kun-xi Qian Shanghai
Second Medical University,
Peoples Republic
of China
Received September 1989, accepted March 1990
ABSTRACT In the experimentaland clinical support of the failing heart, the impeller-type centri&al pumps continue to be of interest because of their inherent advantages; however, the blood compatibility of these pumps still remains to be improved. From the viewpoint of haemodynamics, thrombosis and haemolysis could be reduced by eliminating the stagnation and turbulence of blood J?OW within the pump, which frequently tahes place near the blood contracting su faces of thepump, when the impeller contours do not coincide with the stream su@Zacesof the blood. It is suggested that it could be advantageous to design impeller contours according to the stream sufaces, by solving the partial dijj%rerttial equations of continuity, motion and energy. An impeller shroud and vane based on this approach would be filly rinsed by non-turbulent flow and there would then be neither stagnation nor turbulence within the pump, with the result that thrombosis and haemoljsis could be reduced. A new impellerpump, developed according to this method, wa.s evaluated as a le@ ventricular device in four dogs. The bypassJlow was controlled at 40-50s of the totaljow, each test lasting 6 h. All of the haematologicalparameters, measured every 2 h, remained within normal range. There was no thrombosis, and coagulation in the pump was avoided by a small dose of heparin to maintain the activated coagulation time (ACi’J under 200” in the experiments. Keywords: Impeller pump, thrombosis, haemolysis, stream surfaces, in vivo evaluation
INTRODUCTION Although diaphragm pumps have been much more extensively studied, impeller centrifugal blood pumps continue to be of interest in support of the failing heart, experimentally or clinically. They have inherent advantages in their function, construction, control, blood compatibility and cost, amongst which blood compatibility still remains to be studied in greater detail’. Thrombosis and haemolysis are both corn licated rocedures; there are many medical, met R anical, and surface-related facE iochemical, haemodynamic tors which cause thrombosis and haemolysis2y3. From oint, the thrombosis and the haemodynamic vie haemolysis would take wp p ace in stagnant and turbulent areas, and form as a result of incorrect design of the impeller4. When the impeller contour and other surfaces of the pump do not blood contacting coincide with the stream surfaces of blood flow, there would be stagnation and turbulence within the ump, especially near the impeller shroud and vane PFigure 7). The stagnation and turbulence could be eliminated by designing the impeller shroud and vane according to stream surfaces. In this way the thrombosis and haemolysis of the impeller pump could be reduced. Correspondence and reprint requests to: Dr Kun-xi Qan, c/o Institut Physiologic, Pauwelsstr. (Klinikum) 5100, Aachen, FRG 0 1990 Butteworth-Heinemann 0141-~5425/90/060533-03
The stream surfaces of the blood flow in an impeller pump are quite difficult both to calculate theoretically, and to visualize experimentally. The velocity distributions and the stream surfaces could only be calculated approximately if the viscosity of the blood in the pum were taken into consideration, and under this con B ition the calculation is tedious and the results rarely useful. It is better to achieve an analytical result by neglecting the viscosity, if it is possible, rather than to obtain an inaccurate result, with consideration of the viscosity.
IMPELLER CONTOUR In a common cylindrical coordinate system, r, 6 and L are components of radius, rotational an le and axial distance respectively (Figure 2). B Pood is assumed to be a non-viscous ideal fluid with density p = 1, and the effect of gravity is neglected. The principal equations of continuity, motion and energy are: div W= 0
(1)
d@ --02F+2Wx dt
$‘= -grad
P
p+$?$po
(3
for BES J. Biomed. Eng. 1990, Vol. 12, November
533
Haemodynamic approach to reducing thrombosis and haemolysis in an impeller pumf:
K.-K. Qian
This is the relative velocity distribution in a diagonal impeller. There is a relationship between velocity and stream surfaces: @= -w-m
b
a
Figure 1 Stagnation and turbulence would occur near blood contacting surfaces if impeller contours did not coincide with the stream surfaces of blood flow in the pump. a, Impeller shroud in axial pump; b, impeller vane in radial pump
grad $1 x grad $2
(6)
in which $1 and $2 are three-dimensional stream surfaces. Combining (5) and (6), $r, $2 can be obtained analytically7> : $1: z=c1 &: 0=c2ln
r2 r
(7)
This means that the shroud of the impeller should be a parabola and the vane of the impeller should be a logarithmic spiral. Figure 3 shows the parabolic shroud and logarithmic spiral vanes of a diagonal impeller.
IN WV0 EVALUATIONS
Figure 2 In a common cylindrical coordinate system, r, 0, z represent the components of radius, rotating angle and axial distance
in which W is the relative velocity of the blood cells in the impeller; w is angular speed of the impeller (8= w); r is the radial vector in the c lindrical coordinate (r, 8, z); u = wr ; P is the bloo dypressure pumped; and 4 is atrium ressure. Differentiating equation P3) and then inserting into equation (a), it follows: rot k?= -20”
(4) Equation (4) is analytically solvable in some special cases5,6. For a diagnonal pump ‘, the solution is: W, = c*/r w,=
-Wo+cCp/r
Wz=cs where cl, cp, c3 are integral constants.
a
A newly developed diagonal pump was evaluated in vim (Figure 4). The pump was used as a left ventricular bypass device, delivering blood from the left atrium to the aorta. The experimental animals were four dogs weighing 15-25 kg. The by ass ratio was controlled at 40-50% of the total flow PFigure 5). Because the impeller pump is both preload and afterload sensitive, its output seemed to be pulsatile corresponding to aortic pressure. To increase the pump flow, ‘Rigitine’ was infused during the experiments to decrease the mean aortic pressure of the dogs to 100 mmHg. Blood cell counts, the haemoglobin, the haematocrit and free haemoglobin, platelet aggregation and microgranules (lo-50pm) were measured before the operation, at the beginning of pumping and every 2 h. Most of the haematological ammeters remained unchanged and the plasma Kaemo lobin increased slowly but within the normal range PTable 7). Table 7 demonstrates that the pump did not damage the blood in a short bypass period. Free haemoglobin remained within an acceptable range in spite of its gradual increase. After the experiments the pump was dismantled immediately. Though low dosage of heparin was used and ACT was kept at under 200”, there was no
b
Figure 3 a, Impeller vane should be logarithmic spiral shaped; and b, the impeller shroud should be parabola shaped in a diagonal pump
534 J. Biomed. Eng. 1990, Vol. 12, November
Figure 4 Impeller pump was used as a left ventricular assist device in dogs during in vivo evaluations
thrombosis and haemolysis in an impellerpump: K.-K. @an
Haemodynnmicapproachto Table 1
Haematologicalparameter measured before operation,
Parameter
Preoperative
RBC (lo4 ml-‘) WBC (IO.’ ml ‘) PLT (IO’ ml ‘) HGB (g ‘%I) HCT (“/n) Free Hb (mg O/o) P1.T Aggregation (1%) Microgranule (ml-‘)
5.1 (1.0)
5.8 (2.3) 18.0 (6.5) 11.7 (1.2) 29.5 (4.9) 1.48 (0.24) 60.2 (11.7) 17536 (18583)
thrombosis or blood coagulation in all four experiments.
at beginning
Pump on 4.7 (0.8) 5.1 (2.3) 21.8 (2.1) 11.3 (1.2) 29.8 (4.6) 2.47 (0.50) 60.2 (3.5) 7153 (6387)
found in the pump
DISCUSSION A haemodynamic approach for designing impeller contour is presented. The impeller shroud and vane
of pumping
and every 2 h
(&SD)
2h 5.2 (0.5) 3.8 (1.5) 19.8 (2.1) 11.6 (2.0) 31.4 (2.9) 8.05 (5.77) 56.2 (7.8) 45 15 (2362)
4h 4.8 (0.2) 6.6 (1.6) 20.2 (2.1) 10.9 (1.0) 19.3 (1.0) 16.05 (6.77) 58.4 (10.9) 5030 (4553)
6h 4.7 (0.8) 8.0 (1.5) 21 .o (2.2) 9.3 (2.2) 28.1 (4.2) 28.58 (11.5) 67.42 (7.5) 24200 (37412)
are shaped according to the stream surfaces of blood flow, obtained by solving the relevant partial differential equations. Thus the blood contacting surfaces in the pump would be fully rinsed by non-turbulent flow. There would be neither stagnation nor turbulence thereafter and less thrombosis and lower haemolysis within the pump. All these theoretical results were demonstrated by acute animal experiments. An im eller pump with improved blood compatibility an x other inherent advantages may have more extensive ap lications in animal experiments in addition to cPinical trials. The development of the diaphragm pump has occupied 30 years; another 30 years may be necessary to perfect it. If only a fraction of the attention given to the diaphragm pump could be concentrated on an impeller pum , the prospect for an artificial heart would be much ! righter.
IWFERENCES
Figure 5
Haemodynamic parameters ments with dogs. AP, aortic pressure; PO, pump output; HO, heart output
in left ventricular assist experiCVP, central venous pressure;
1. Qan RX. Electric total artificial heart: with impeller or diaphragm? ES40 Proc, Bmo, CSSR, 1988. 2. Schoen FJ, Clagett GP, Hill JD, Chenoweth DE, Anderson JM, Eberhart RC. The biocompatibility of artificial organs. Tranr AWO1987; 33: 824. Ringoir S, Vanholder R. An introduction to biocompatibility. Artf07gan-s 1986; 10: 20-7. Qan RX. A new total artificial heart via impeller pumps. J Biomater A&+& 1990; 4: 405-18. @an RX. progress in impeller pumps in Shanghai. Assisted Circulation, 1989; 3: 195-214. Qan RX, Fei Q Lin KD, pi KD, Wang YP. The realization of pulsatile implantable impeller pump with low hemolysis. ArtifOrgans 1989; 13: 162-9. 7. Qan RX. The applications of 3-dimensional theory in designing impeller of the blood pumps. Chn J Eng Maths 1987; 4: 99-101. 8. @an RX. An analytical method of impeller design and its application in blood pumps. GhnJBiomechs 1987; 2: 46-52.
J. Biomed.
Eng. 1990. Vol. 12, November
535