Technical n o t e Design of heparin infusion pump for a wearable artificial kidney" Keywords--Heparinisation, Artificial kidney, Drug infusion

WITHIN the last decade, the artificial kidney has become a practical, widely used clinical haemodialysis device (Nos~, 1971). However, current limitations faced by the patient are the lengthy dialysis sessions, high cost, and physiological effects of variations in his metabolic toxin levels as a result of intermittent dialysis. To overcome these limitations, a novel wearable artificial kidney system is being proposed and developed at Stanford University ( W A L L A C E , 1973). Other workers have reported membrane and materials-limitations studies as a step toward a compact artificial kidney (LEVINE and LA COURSE, 1967; BROWN and KRAMER, 1968; COONEY, 1971). Inherent in the design of any artificial organ is the prevention of thrombosis. Anti-coagulant infusion, e.g. 2 cm a of heparin per hour, is normally used with current kidney machines (GORDONet aL, 1956; LINDHOLM and

portable infusion pumps, battery or spring-driven, are available, their characteristics are still far from ideal for this usage. We propose a new type of heparin infusion pump--one which is very compact, simple and requires no external power source.

Prototype design The venturi infusion pump (v.i.p.) has two basic parts: a heparin reservoir and infusion venturi. The design is shown in Fig. 1. In the reservoir, blood flows through a flexible, cylindrical membrane, while heparin fills the annular volume between the membrane and the heparin reservoir case. Thereby, the heparin is pressurised by the patient's blood pressure. In the venturi, flow acceleration reduces the static pressure to a level slightly lower than that in the heparin reservoir. This pressure drop results

2 inches

F

rilling port

heparin reservoir Ct9 .L~?-

_L

_"o o o o

~infusion venturi

oo%

o

--J--b,ood

r-

membrane Fig. 1 Schematic of venturi infusion regulated haparinisation

pump

for

MURRAY, 1964). A motor-driven infusion pump is generally employed to supply the proper drug flow during dialysis. With present stationary kidney machines, the size, weight and power requirements of these infusion pumps are not burdensome. For a wearable artificial kidney, anti-coagulant infusion is still a necessity. But the portable nature of the wearable kidney places stringent requirements on the size, weight and power supplies of its components. Even though *First received 20th November 1973 and in final form 14th March 1974

478

in a flow of heparin from the reservoir into the blood stream in the venturi. An orifice controls the exact flow rate. Consequently, the patient's blood pressure itself drives and controls heparin infusion. The equation governing the performance of the venturi infusion pump can be developed. The pressure difference between the reservoir and the venturi is given by the Bernoulli equation (SHEPARD, 1965). Assuming a onedimensional flow, low viscosity and low friction losses P,-

P ( v o 2 - v , 2) . . . . . zgc

Po = - w : -

(1)

where P denotes static pressure, t' denotes fluid density,

Medical and Biological Engineering

May 1975

gc is the gravitational constant, V denotes fluid velocity, and the subscripts r and v denote reservoir and venturi, respectively. The heparin infusion resulting from this pressure difference is given by the orifice equation (McCABEand SMITH, 1956), assuming a negligible pressure drop from friction in the heparin carrying-tubes:

Q~ = CAo

P

where Q~ is the heparin volumetric flow rate, C is the orifice coefficient, usually equal to about 0'6, and Ao is the orifice area. Combining eqns. 1 and 2 with the continuity equation Q~ = Av Vv

.

.

.

.

.

.

.

.

.

(3)

where Qv is the blood flow rate, Ao is the venturi area, and Vv is the velocity of blood in the venturi section. Assuming that V2v >> V 2, and that all velocities are at steady state, we obtain the governing equation for heparin infusion rate, Qn: Q, ---,~C

Qb

Ao

Ao

.

.

.

.

.

.

.

(4)

"5 1.0 E

,

region A

U

w O4

Experimental To demonstrate the manner in which a small concentration of heparin can be infused into the blood stream with no external power source, a prototype was made. Its actual size was approximately twice that necessary for the wearable artificial kidney (WALLACE, 1973). Materials of fabrication included rigid plastic tubing, a rubber membrane, and a small needle valve for use as the metering orifice. The venturi diameter was about onethird of the main-flow diameter. Water played the functional role of blood, and a dye solution that of heparin. 1C-

5 ~oOE

i o.4, "0

o

1.2 "O

L

.

Eqn. 4 predicts, moreover, that the heparin infusion concentration should be independent of time, blood flow rate, and orientation of the patient. Time does not appear in eqn. 4 because steady-state conditions were assumed; orientation does not appear because any gravitational pressure drop on the blood side of the fluid circuit will be exactly balanced by an equal gravitational pressure drop on the heparin side.

c

In our tests, the effects of four independent variables were studied: orientation, time, flow rate and orifice size. The dye concentration in the effluent water was determined by a visual comparison of collected samples with standards of known dye concentration. 1. Orientation. The effluent dye concentration was not affected by orientation. It was found that gravity played no role in the performance of the venturi infusion pump, as expected from eqn. 4. Obviously, insensitivity to the patient's position is of importance. 2. Time. Fig. 2 shows the variation in the dye concentration with time. The slight change is likely to be due to a gradual contact between the membrane and the reservoir walls as the dye supply becomes depleted and the membrane expands outward. Fig. 2 indicates that an excess heparin capacity of about 2 0 ~ will ensure an essentially uniform heparinisation between fillings.

~

0.7 ,

0

0.2

,

,

i

i

i

i

i

i

0.4 0.6 08 1.0 relative water flowrate

i

112

Fig. 3 Effect of relative water flow rate on effluent dye concentration

3. Flow rate. The effect of flow rate was evaluated because the blood flow rate in an artificial kidney may vary somewhat during haemodialysis due to changes in the patienrs blood pressure. Fig. 3 indicates that the dye concentration was slightly dependent on the flow rate. This dependence may be accounted for by changes in the orifice coefficient with flow rate, and by small frictional pressure losses elsewlaere in the heparin flow path; both of these effects would be more significant at low flow rates. But proper design can ensure that the result would become negligible. Fig. 3 indicates that by operating in a flow-insensitive region, such as region A, a 2 5 ~ change in the water flow rate results in only a 4 ~ change in the dye concentration. 4. Orifice area. The effect of the orifice area was also evaluated. At a constant water flow rate, the dye concentration could be reproducibly varied by a factor of 10. This indicates that the heparin dosage could be adjusted to each patient's clotting behaviour by selecting the proper orifice size.

Discussion

2 4 6 time after starting with full reservoir, min

Fig. 2 Effect of time on dye concentration in effluent water (acting as a blood substitute)

Medical and Biological Engineering

May 1975

The general performance characteristics of the venturi infusion pump should be the same for both water and blood. The concentration of the infused liquid is governed mainly by the area ratio Ao lay (eqn. 4), and by the orifice coefficient which is affected by the viscosities and the density ratio of water and blood. Thereupon relating to the performance of the venturi pump prototype, the concentration of the infused heparin in the patient's

479

blood could be expected to be (a) essentially independent of the blood flow rate, (b) essentially constant with time, and (c) independent of the patient's orientation. One factor not yet investigated experimentally is the effect of a pulsatile arterial blood flow. We believe that blood-pressure pulsations would not significantly affect the performance of the heparin infusion pump. The pressure pulsations propagate rapidly so that the v.i.p. sees a uniform blood pressure at any time. Cyclic fluctuation of the blood pressure also has essentially no effect on the performance of the venturi infusion pump, since the device's behaviour does not depend on the absolute pressure level. Blood-velocity pulsations, however, would cause a pulsatile heparin infusion. This should not be a problem since only the average heparin infusion dosage really matters. Of course, the pulsatile heparin flow will affect the constant, C in eqn. 4, but this constant will be determined experimentally. For regional heparinisation, one venturi infusion pump (v.i.p.) would infuse heparin into the blood as it enters the wearable artificial kidney; a second r.i.p, would infuse protamine neutraliser into the blood stream as it exits from the wearable artificial kidney unit. Thus, only the blood in the wearable kidney would have a high clotting time, e.g. one hour. In summary, a new type of infusion pump is being proposed for continuous regional heparinisation in a wearable artificial kidney. The v.i.p, is simple, compact, and is powered by the patient's own blood pressure. Tests of a prototype indicate general suitability of the design for the intended application.

References Nos~, Y. (1971) The artificial kidney. In Advances in biomedical engineering and medical physics. Ed., LEVIN~, S. N., Vol. 4, 163-224.

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WALLACE, R. A. (1973) Wearable artificial kidney. US Patent in preparation and unpublished results, Stanford University, Stanford, Calif. LEVINE, S. N. and LA COURSE, W. C. (1967) Materials and design considerations for a compact artificial kidney. J. Biomed. Materials Res. 1, 275-284. BROWN, C. E. and KRAMER, N. C. (1968) Factors in membrane design and selection as a step toward a wearable artificial kidney. Trans. Am. Soc. Artif Int. Organs 14, 36--42. COON~Y, D. O. (1971) Materials limitations in the design of a microcapsule artificial kidney. J. Biomed. Materials Res. 5, 407-410. GORDON, L. A., RICnARDS, V. and PERrdNS, H. A. (1956) Preliminary report of a method using simultaneous infusion of heparin and protamine. New England J. Med. 255, 1053-1066. LINDHOLM, D. D. and MURRAY,J. S. (1964) A simplified method of regional heparirdzation during hemodialysis according to a predetermined dosage formula. Trans. Am. Soc. Artif Int. Organs 10, 92-95. Sn~I'ARD, D. G. (1965) Elements offluid mechanics, p. 123. Harcourt Brace, New York. MCCABE,W. L. and SMITh, J. C. (1956) Unit operations of chemical engineering, p. 100. McGraw-Hill, New York. ALAN K. MILLER* RICHARDA. WALLACE~" Department of Materials Science & Engineering Stanford University Stanford, Calif. 94305, USA "Hertz Foundation Fellow tNew Professor of Polymer Science, Oregon Graduate Center for Study & Research, 19600 N.W. Walker Rd., Beaverton, Oregon 97005, USA

Medical and Biological Engineering

May 1975

Design of heparin infusion pump for a wearable artificial kidney.

Technical n o t e Design of heparin infusion pump for a wearable artificial kidney" Keywords--Heparinisation, Artificial kidney, Drug infusion WITHIN...
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