Mass Transfer Characteristics
August, 1979
M a s s Transfer Characteristics of Hollow-Fiber Dialyzers and Hemoperfusion Devices David 0. Cooney and John S. Daly ABSTRACT Clearance versus time tests were carried out on three charcoal-based hemoperfusion devices (Sandev, Becton-Dickinson and Gambro) using solutions of 1 gm/L sodium salicylate in a pH 7.4 buffer and in bovine blood at flow rates of 200 rnl/min. Similar tests were performed on a Cordis Dow 2.5 m2hollowfiber dialyzer at a tube side flow rate (QB) of 200 ml/min. Buffer was pumped through the dialysate side at a flow rate (QD)of 400 ml/min. Two dialyzers were run in series at QB = 200 ml/min and QD = 500 or 1000 ml/min. Mass transfer resistances were computed from the test results. These values are useful in that they constitute an index of the intrinsic initial kinetics of solute transfer in each device. However, the clearance versus time curves indicate that these initial kinetics decrease at different rates for each hemoperfusion unit as sorption capacity begins to be depleted. I n contrast, the initial clearances for the dialyzers remain at their initial values. These data reveal much about the relative mass transfer characteristics of these devices.
tive therapy (use of a respirator, administration of stimulants) is often sufficient. For serious cases, when the patient is in a deep coma for example, enhancement of toxin removal by additional means must be employed to prevent permanent damage to vital organs (e.g., the brain, liver or lungs). Measures such as forced diuresis and peritoneal dialysis are helpful; however, hemodialysis is generally more efficient. The relatively new technique of hemoperfusion (perfusing of the patient's blood through a packed bed of a n adsorbent material, such as activated charcoal granules) has been promoted as perhaps the best general approach to enhancing toxin removal. T h e existing literature consists mostly of reports of 1) clinical case studies in which various devices were used to treat actual drug overdose victims or patients suffering from renal or hepatic failure, and 2) in vitro tests of the removal of specific solutes (e.g., drugs, endogenous toxins, amino acids) by such devices. Although most of these reports have been qualitative in nature, there has been a substantial number of papers in which methods for mathematically modeling the behavior of dialyzers have appeared. With respect to hemoperfusion devices, mathematical modeling h a s received much less attention, but a few theoretically-oriented papers have been published,'-4 I n the present paper, the authors wish to add to this growing body of literature which attempts to characterize hemoperfusion devices according to certain fundamental indices of behavior. Analysis of a dialyzer h a s been included for comparative purposes. Specifically, the capabilities of a commercially available hollow-fiber hemodialyzer device and three commercially available hemoperfusion devices for extracting a typical drug from flowing streams of a buffer solution and from blood were studied and compared.
m a s s transfer, hemoperfusion, dialyzers, clearances, kinetics Nomenclature total external area for mass transfer fluid phase concentration overall mass transfer coefficient volumetric flow rate RT total mass transfer resistance external surface area per unit length of column S W total solute transfer rate z axial length Subscripts B blood or buffer D dialysate
A C K Q
INTRODUCTION The treatment of victims of poisoning and severe drug overdose is a n important but complex area of biomedical engineering technology. For milder cases of poisoning or drug overdose, simple suppor-
MATERIALS AND METHODS The hemodialyzer tested was the Cordis Dow Model 5 Artificial Kidney (C-DAK, Cordis Dow Corp., Miami, Florida, U.S.A.) having a 2.5 m2 effective sur-
From the Chemical Engineering Department, Clarkson College of Tech. nology, Potsdam, New York, 13676, U.S.A.
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face area. This device, containing 20,000 fibers of 200 pm I.D. and 21 cm length, was first marketed i n July, 1974. The hemoperfusion devices studied were 1)the Sandev Haemocol unit (Sandev, Ltd., Gilston Park, Harlow, Essex, England; 300 gm of 2-4 mm diameter charcoal particles covered with a 5 pm acrylic hydrogel coating and packed in a column highly tapered on both ends); 2) the Becton-Dickinson Hemodetoxifier unit (B-D Drake Willock, Portland, Oregon, U S A . ; 94 gm of 0.3-0.84 mm diameter uncoated charcoal granules affixed to a polyester film which is wound into a spiral coil and placed into a 9.3 cm diameter X 13.6 cm long cylindrical shell); and 3) the Gambro Adsorba 300C unit (Gambro, Lund, Sweden; 300 gm of 1mm diameter X 2 mm long cylindrical extruded charcoal pellets coated with a 3-5 p m cellulose membrane a n d packed into a cylindrical - 7.8 cm diameter X 30 cm long - shell). Hollow-Fiber Dialyzer Studies New C-DAK units were obtained from t h e Cordis Dow Corporation. A representative unit (determined by preliminary screening tests) was chosen and clearance tests were performed. On the “blood side’’ (tube side), a solution of 1.0 gm/L of reagent grade sodium salicylate in a pH 7.4 sodiumpotassium phosphate buffer was pumped at a flow rate (QB)of 200 ml/min. The buffer was of the same pH (7.4) and ionic strength as blood. The reason for using sodium salicylate as the test solute was that the authors wished to relate these studies to drug removal in general and felt that sodium salicylate was typical of a range of common drugs i n terms of molecular size and acidlbase properties. The “dialysate side” (shell side) fluid was pure buffer and was pumped countercurrently a t a flow rate (QD)of 400 ml/min. Sodium salicylate concentrations in the outlet streams were determined by ultraviolet spectrophotometry a t a 330 nm wavelength. For QB= 200 ml/min and QD= 400 ml/min, the C-DAK clearance was found to be 152.0 ml/min. Clearance is defined as the tube side flow rate X the fractional extraction of solute from the tube side fluid, that is
The reciprocal of KA can be termed the overall mass transfer resistance, RT. Using this equation, RT was computed for the QB = 200, QD= 400 run with buffer solutions to be 2.64 min/L. Next, two runs were made on a system consisting of two C-DAK units in series, with the 1 gm/L salicylate-in-buffer solution pumped through the tube side at 200 ml/min and buffer pumped countercurrently through the shell side at either 500 ml/min (first run) or 1000 ml/min (second run). The measured clearances were 186.6 ml/min and 193.3 ml/min, respectively, and the overall mass transfer resistances were 1.37 m i n / L a n d 1.27 m i n / L , respectively. Finally, runs were performed using sodium salicylate dissolved to the extent of 1 gm/L in freshly collected bovine blood which was heparinized i n the amount of 6-8 I.U./ml a t the time of collection. About 12 liters of blood was available for each run, permitting tests of approximately 60 minutes duration (QB = 200 ml/min, QD = 400 ml/min). A roller-type blood pump was used in these runs. A bubble trap on the inlet line was used to prevent the introduction of a n y air bubbles into the C-DAK. The blood in the feed reservoir was very gently stirred from time to time to prevent any significant sedimentation of cells from occurring. Analysis for the salicylate was done by the well-known method involving Trinder’s reagent.6 The blood temperature was 25 f l.2”C at all times. H e m o p e r f u s i o n C o l u m n Studies The three hemoperfusion devices described earlier were each tested for their ability to adsorb sodium salicylate from a 1 gm/L solution of this in the pH 7.4 phosphate buffer. At a flow rate of 200 ml/min, effluent samples were periodically taken and analyzed for salicylate concentration. Then, using equation (l), clearances were computed. Figure 1 presents the clearance versus time results obtained for each device along with those for the C-DAK system. A full discussion of these curves, and other data concerning overall and individual mass transfer resistances and clearances versus time behavior of these units is given by Cooney, Infantolino and Kane.’ It will not be reported here. Instead, the focus i n this study is the comparative mass transfer characteristics of the hemoperfusion devices and the C-DAK units. The hemoperfusion device clearance curves can be analyzed to yield KA and RT values for each device. The analysis begins with the differential mass transfer rate expression
Clearance = QB(CB~” - CB,,,~)/CB~,, Theoretical analyses’ indicate t h a t in a countercurrent dialyzer of this type, the total drug extraction rate, W (gm/min), can be characterized with the equation (2)
dW = -&BdC = KS(C-C*) dz
where A is the total external hollow-fiber surface area, a n d K is a n overall mass transfer coefficient.
(3)
It is easy to demonstrate that near time zero, for
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Mass Transfer Characteristics I
I
I
I
I
I
160
0
I
I
I
I 200
100 Tlm.,
I
I
t
1
J
300
m1nul.m
FIG. 1. Clearance characteristics using salicylate in phosphate buffer. Time, minutes
FIG. 2. Clearance characteristics using salicylate in bovine blood.
which C* (the value of C which would be in equilibrium with the adsorbent phase, if equilibrium existed) is essentially zero, this equation can be integrated to give
that, in actual practice, it is really the product KA t h a t matters in determining clearance, a n d not the value of either K or A alone. For those who are interested, however, an estimate can be offered of w h a t t h e authors believe a r e t h e approximate values of A for the hemoperfusion columns studied: B-D, 1.24 m2;Gambro, 2.12 m2;and Sandev, 0.75 m2. These areas are less t h a n t h a t of a single C-DAK unit. Each hemoperfusion column was then r u n using 1 gm/L sodium salicylate in bovine blood at a blood flow rate of QB = 200 ml/min. All methods were similar to those used i n the blood run with the C-DAK unit. The resulting clearance curves are shown in Figure 2, where they are compared to the single C-DAK system. Values of RT were computed using equation (4).
The equivalence of this equation and equation (2) when CD= 0 everywhere shows that the efficiency of a dialyzer having a reasonably high QD(hence, CD= 0) can be compared to the initial efficiency of a hemoperfusion column, as Radcliffe and Gaylor have previously d i ~ c u s s e d . ~ For any experimental run, QB and CBin are fixed. The value of CB,,~corresponding to time zero can be obtained by extrapolating CB,,~data back to time zero. KA or RTc a n then be computed from equation (4). One might wonder why the sorbent's total external area, A, is lumped together with K a n d is not computed separately, so that a n estimate of K alone can be made. The reason is that the surface of a charcoal particle is typically not a t all smooth but is rough a n d irregular (the Gambro particles do appear to be somewhat smooth, but the Sandev and B-D ones clearly are not). Because of this, there is no way to determine the true surface area. Even if the sorbent particles did have smooth external surfaces, the particles typically possess a significant range of sizes rather than being all of a single size. What size should be chosen as representative of the whole lot, s o that the specific surface area (specific area i n cm2/cm3 = G/diameter in cm) can be computed? Should one use a n arithmetic, geometric, logarithmic, or some other mean particle size? The answer is unclear. A final reason for lumping A in with K is
RESULTS M a s s T r a n s f e r Resistance V a l u e s Table I lists RT values for each device in both the buffer and blood environments. Time-Averaged Clearance Values Holland et aL2 have pointed out the important idea that, in terms of quantifying the total amount of solute removed over certain time periods from the beginning of a hemoperfusion, clearance values should be time-averaged over such time periods. In accordance with this idea, the authors have integrated the areas under the clearance curves in Figures 1 and 2 and have determined the time-averaged values presented in Table 11. The time periods chosen were one and two hours from the beginning of the tests.
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Vol. 3, No. 3 TABLEI1 TIME-AVERAGED CLEARANCE VALUES (ML/MIN) Buffer Tests Blood Tests 1 hr 2 hrs 1 hr
TABLEI MASS TRANSFER RESISTANCES (RT) IN MIN/L USING SODIUM SALICYLATE IN BUFFER OR BOVINE BLOOD AT QB = 200 ML/MIN Buffer Tests Blood Tests B-D Column 1.32 4.39 Gambro 1.62 5.03 Sandev 4.18 8.36 C-DAK (QD = 400) 2.64 7.65 TWO C-DAKs 1.37 (QD = 500)
B-D Column Gambro Sandev C-DAK (QD = 400) TWO C-DAK’s (QD = 500)
DISCUSSION The RTvalues for the hemoperfusion columns reflect the intrinsic kinetics of each device. On this basis, the B-D unit appears to be best, a n d the Sandev unit (having large charcoal granules) is decidedly the worst. Another important factor is total column capacity, however, as indicated at least approximately by the amount of charcoal in each unit. The B-D device h a s only 94 gm of charcoal as compared to 300 gm of charcoal in each of the other devices. Hence, as Figure 1 clearly shows, the B-D unit approaches saturation much faster t h a n the other units. It h a s also been demonstrated, however, that for drugs t h a t are normally present i n the blood in lower than 1 gm/L concentrations in overdose cases (e.g., barbiturates with concentrations more like 0.1 gm/L) the B-D column clearance remains higher than the clearances for the other two hemoperfusion devices for a much longer period of time.’ The loss of kinetic performance due to saturation effects is also reflected by the average clearances presented in Table 11. In the buffer tests, the B-D unit (which has the best initial kinetics) is now the worst unit in terms of solute removal if one considers a n extended time period, such as one or two hours. This makes it quite clear t h a t indices of initial kinetics and of longer-term, time-averaged kinetics can have very different implications. In the blood tests, the B-D unit is, perhaps unexpectedly, the best of the four systems tested over a one-hour period. One reason for this is that solute uptake rates are much lower with blood than with buffer, and the rate of saturation of the B-D unit is, therefore, not as marked. Table I indicates that the RT values are much elevated (by roughly a factor of three) when blood is used, as opposed to buffer. This is, perhaps, a n unexpectedly large effect, but can be explained on the basis of cell and protein deposition and flow nonuniformities. T h e decreases i n t h e one-hour timeaveraged clearances when blood is used, as opposed
95.3 173.4 115.6 152.0
186.6
53.4 (est.) 137.3 104.7 152.0 186.6
102.7 95.6 77.7 96.0 -
to buffer, are not as dramatic as the increase in the
RT values (e.g., the clearances fall by 44.9,32.8 and 36.8% for the Gambro, Sandev and single C-DAK systems, respectively); for the B-D unit, the average clearance with blood is actually 7.8% higher than with the buffer. The reason for the rise i n clearance noted with the B-D device is not clear - while one would not necessarily expect much of a decrease in clearance when switching from buffer to blood, one would not expect an increase. The most likely explanation is that, because of its unique spiral-wound design, different B-D units could easily have quite different flow pattern behaviors, which lead to different clearance efficiencies. I t becomes evident from Figures 1 and 2 that one advantage of the C-DAK type of system is t h a t its clearance, although initially lower t h a n the clearances of the B-D and Gambro hemoperfusion devices, remains relatively constant with time, a n d ultimately becomes higher. Thus, the C-DAK system might be preferable for long-term perfusions. Figure 1 suggests, as does Table I, that two C-DAK’s in series would be almost as good as any of the hemoperfusion devices. Two C-DAK’s could easily be used since their priming volumes are only about 200 ml (hence, 400 ml for two). The B-D, Gambro a n d Sandev columns have priming volumes of 255, 300 a n d 330 ml, respectively, and it is more risky to use two of these in series (the B-D unit has, however, been recommended for two-in-series operation). The comparison between the hemoperfusion columns a n d the single C-DAK or double C-DAK systems cannot be taken too literally from Figures 1 and 2, except near time zero. The rate of clearance fall in hemoperfusion devices i n any real application will be affected by the fact t h a t the inlet drug concentration will decrease progressively with time due to 1)drug metabolism i n the patient and 2) drug removal in the hemoperfusion devices. Also, the behavior of the hemoperfusion devices will depend
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crucially on the chemical nature of the drug, i.e., on the affinity of charcoal for adsorbing the drug. The C-DAK system is affected mainly by the drug’s molecular size (this affects t h e hemoperfusion units also). Although the fact t h a t clearances do not fall with time suggests that the C-DAK system should be considered for long-term perfusions, the early time period is often critical in preventing organ damage i n drug overdose victims. Clearly, t h e hemoperfusion devices may often be more effective during this period. The choice of which of these four devices to use will depend heavily on the specific drug involved a n d its concentration in the patient. However, one should only select hemoperfusion over hernodialysis 1) when the identity of the drug involved has been definitely established and 2) when it is known, from clinical results, that the hemoperfusion device to be used is indeed better than the dialyzer that would normally be employed.
Mass Transfer Characteristics kinetics, the systems rate as follows: B-D, excellent; two C-DAK’s, excellent; Gambro, very good; single C-DAK, good; and Sandev, moderate. I n terms of sorption capacities, the hemoperfusion units rate a s follows: Gambro and Sandev, very good probable capacity; and B-D, a much lower probable capacity.
References 1. COONEY,D. O., INFANTOLINO, W., KANE, R. Comparative
2.
3.
4.
5.
CONCLUSIONS The results obtained suggest that in terms of initial
6.
257
studies of hemoperfusion devices. I. I n uitro clearance characteristics. Biomater Med Dev Artif Organs, 6199, 1978. HOLLAND,F. F., DONNAUD, A., GIDDEN,H. E., KLEIN,E. Methods of measurement of m a s s transfer rates and capacities of hemoperfusion cartridges. T r a n s Am SOCArtif Intern Organs, 23:573, 1977. DUNLOP,E. H., GAZZARD, B. G., LANGLEY, P. G., WESTON, M. J., Cox, L. R., WILLIAMS, R. Design features of haemoperfusion columns containing activated charcoal. Med Biol Eng, 14:220, 1976. RADCLIFFE,D. F., GAYLOR, J. D. S. Interpretation of haemoperfusion column performance using the “equivalent haemodialyzer” concept. Abst ASAIO, 7:47, 1978. COONEY,D. 0. Biomedical Engineering Principles. Dekker, New York, New York, U.S.A., p. 318, 1976. TRINDER, P. Rapid determination of salicylates in biological fluids. Biochem J, 57:301, 1954.
August, 1979
M a s s Transfer Characteristics of Hollow-Fiber Dialyzers and Hemoperfusion Devices David 0. Cooney and John S. Daly ABSTRACT Clearance versus time tests were carried out on three charcoal-based hemoperfusion devices (Sandev, Becton-Dickinson and Gambro) using solutions of 1 gm/L sodium salicylate in a pH 7.4 buffer and in bovine blood at flow rates of 200 rnl/min. Similar tests were performed on a Cordis Dow 2.5 m2hollowfiber dialyzer at a tube side flow rate (QB) of 200 ml/min. Buffer was pumped through the dialysate side at a flow rate (QD)of 400 ml/min. Two dialyzers were run in series at QB = 200 ml/min and QD = 500 or 1000 ml/min. Mass transfer resistances were computed from the test results. These values are useful in that they constitute an index of the intrinsic initial kinetics of solute transfer in each device. However, the clearance versus time curves indicate that these initial kinetics decrease at different rates for each hemoperfusion unit as sorption capacity begins to be depleted. I n contrast, the initial clearances for the dialyzers remain at their initial values. These data reveal much about the relative mass transfer characteristics of these devices.
tive therapy (use of a respirator, administration of stimulants) is often sufficient. For serious cases, when the patient is in a deep coma for example, enhancement of toxin removal by additional means must be employed to prevent permanent damage to vital organs (e.g., the brain, liver or lungs). Measures such as forced diuresis and peritoneal dialysis are helpful; however, hemodialysis is generally more efficient. The relatively new technique of hemoperfusion (perfusing of the patient's blood through a packed bed of a n adsorbent material, such as activated charcoal granules) has been promoted as perhaps the best general approach to enhancing toxin removal. T h e existing literature consists mostly of reports of 1) clinical case studies in which various devices were used to treat actual drug overdose victims or patients suffering from renal or hepatic failure, and 2) in vitro tests of the removal of specific solutes (e.g., drugs, endogenous toxins, amino acids) by such devices. Although most of these reports have been qualitative in nature, there has been a substantial number of papers in which methods for mathematically modeling the behavior of dialyzers have appeared. With respect to hemoperfusion devices, mathematical modeling h a s received much less attention, but a few theoretically-oriented papers have been published,'-4 I n the present paper, the authors wish to add to this growing body of literature which attempts to characterize hemoperfusion devices according to certain fundamental indices of behavior. Analysis of a dialyzer h a s been included for comparative purposes. Specifically, the capabilities of a commercially available hollow-fiber hemodialyzer device and three commercially available hemoperfusion devices for extracting a typical drug from flowing streams of a buffer solution and from blood were studied and compared.
m a s s transfer, hemoperfusion, dialyzers, clearances, kinetics Nomenclature total external area for mass transfer fluid phase concentration overall mass transfer coefficient volumetric flow rate RT total mass transfer resistance external surface area per unit length of column S W total solute transfer rate z axial length Subscripts B blood or buffer D dialysate
A C K Q
INTRODUCTION The treatment of victims of poisoning and severe drug overdose is a n important but complex area of biomedical engineering technology. For milder cases of poisoning or drug overdose, simple suppor-
MATERIALS AND METHODS The hemodialyzer tested was the Cordis Dow Model 5 Artificial Kidney (C-DAK, Cordis Dow Corp., Miami, Florida, U.S.A.) having a 2.5 m2 effective sur-
From the Chemical Engineering Department, Clarkson College of Tech. nology, Potsdam, New York, 13676, U.S.A.
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Vol. 3, No. 3
face area. This device, containing 20,000 fibers of 200 pm I.D. and 21 cm length, was first marketed i n July, 1974. The hemoperfusion devices studied were 1)the Sandev Haemocol unit (Sandev, Ltd., Gilston Park, Harlow, Essex, England; 300 gm of 2-4 mm diameter charcoal particles covered with a 5 pm acrylic hydrogel coating and packed in a column highly tapered on both ends); 2) the Becton-Dickinson Hemodetoxifier unit (B-D Drake Willock, Portland, Oregon, U S A . ; 94 gm of 0.3-0.84 mm diameter uncoated charcoal granules affixed to a polyester film which is wound into a spiral coil and placed into a 9.3 cm diameter X 13.6 cm long cylindrical shell); and 3) the Gambro Adsorba 300C unit (Gambro, Lund, Sweden; 300 gm of 1mm diameter X 2 mm long cylindrical extruded charcoal pellets coated with a 3-5 p m cellulose membrane a n d packed into a cylindrical - 7.8 cm diameter X 30 cm long - shell). Hollow-Fiber Dialyzer Studies New C-DAK units were obtained from t h e Cordis Dow Corporation. A representative unit (determined by preliminary screening tests) was chosen and clearance tests were performed. On the “blood side’’ (tube side), a solution of 1.0 gm/L of reagent grade sodium salicylate in a pH 7.4 sodiumpotassium phosphate buffer was pumped at a flow rate (QB)of 200 ml/min. The buffer was of the same pH (7.4) and ionic strength as blood. The reason for using sodium salicylate as the test solute was that the authors wished to relate these studies to drug removal in general and felt that sodium salicylate was typical of a range of common drugs i n terms of molecular size and acidlbase properties. The “dialysate side” (shell side) fluid was pure buffer and was pumped countercurrently a t a flow rate (QD)of 400 ml/min. Sodium salicylate concentrations in the outlet streams were determined by ultraviolet spectrophotometry a t a 330 nm wavelength. For QB= 200 ml/min and QD= 400 ml/min, the C-DAK clearance was found to be 152.0 ml/min. Clearance is defined as the tube side flow rate X the fractional extraction of solute from the tube side fluid, that is
The reciprocal of KA can be termed the overall mass transfer resistance, RT. Using this equation, RT was computed for the QB = 200, QD= 400 run with buffer solutions to be 2.64 min/L. Next, two runs were made on a system consisting of two C-DAK units in series, with the 1 gm/L salicylate-in-buffer solution pumped through the tube side at 200 ml/min and buffer pumped countercurrently through the shell side at either 500 ml/min (first run) or 1000 ml/min (second run). The measured clearances were 186.6 ml/min and 193.3 ml/min, respectively, and the overall mass transfer resistances were 1.37 m i n / L a n d 1.27 m i n / L , respectively. Finally, runs were performed using sodium salicylate dissolved to the extent of 1 gm/L in freshly collected bovine blood which was heparinized i n the amount of 6-8 I.U./ml a t the time of collection. About 12 liters of blood was available for each run, permitting tests of approximately 60 minutes duration (QB = 200 ml/min, QD = 400 ml/min). A roller-type blood pump was used in these runs. A bubble trap on the inlet line was used to prevent the introduction of a n y air bubbles into the C-DAK. The blood in the feed reservoir was very gently stirred from time to time to prevent any significant sedimentation of cells from occurring. Analysis for the salicylate was done by the well-known method involving Trinder’s reagent.6 The blood temperature was 25 f l.2”C at all times. H e m o p e r f u s i o n C o l u m n Studies The three hemoperfusion devices described earlier were each tested for their ability to adsorb sodium salicylate from a 1 gm/L solution of this in the pH 7.4 phosphate buffer. At a flow rate of 200 ml/min, effluent samples were periodically taken and analyzed for salicylate concentration. Then, using equation (l), clearances were computed. Figure 1 presents the clearance versus time results obtained for each device along with those for the C-DAK system. A full discussion of these curves, and other data concerning overall and individual mass transfer resistances and clearances versus time behavior of these units is given by Cooney, Infantolino and Kane.’ It will not be reported here. Instead, the focus i n this study is the comparative mass transfer characteristics of the hemoperfusion devices and the C-DAK units. The hemoperfusion device clearance curves can be analyzed to yield KA and RT values for each device. The analysis begins with the differential mass transfer rate expression
Clearance = QB(CB~” - CB,,,~)/CB~,, Theoretical analyses’ indicate t h a t in a countercurrent dialyzer of this type, the total drug extraction rate, W (gm/min), can be characterized with the equation (2)
dW = -&BdC = KS(C-C*) dz
where A is the total external hollow-fiber surface area, a n d K is a n overall mass transfer coefficient.
(3)
It is easy to demonstrate that near time zero, for
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Mass Transfer Characteristics I
I
I
I
I
I
160
0
I
I
I
I 200
100 Tlm.,
I
I
t
1
J
300
m1nul.m
FIG. 1. Clearance characteristics using salicylate in phosphate buffer. Time, minutes
FIG. 2. Clearance characteristics using salicylate in bovine blood.
which C* (the value of C which would be in equilibrium with the adsorbent phase, if equilibrium existed) is essentially zero, this equation can be integrated to give
that, in actual practice, it is really the product KA t h a t matters in determining clearance, a n d not the value of either K or A alone. For those who are interested, however, an estimate can be offered of w h a t t h e authors believe a r e t h e approximate values of A for the hemoperfusion columns studied: B-D, 1.24 m2;Gambro, 2.12 m2;and Sandev, 0.75 m2. These areas are less t h a n t h a t of a single C-DAK unit. Each hemoperfusion column was then r u n using 1 gm/L sodium salicylate in bovine blood at a blood flow rate of QB = 200 ml/min. All methods were similar to those used i n the blood run with the C-DAK unit. The resulting clearance curves are shown in Figure 2, where they are compared to the single C-DAK system. Values of RT were computed using equation (4).
The equivalence of this equation and equation (2) when CD= 0 everywhere shows that the efficiency of a dialyzer having a reasonably high QD(hence, CD= 0) can be compared to the initial efficiency of a hemoperfusion column, as Radcliffe and Gaylor have previously d i ~ c u s s e d . ~ For any experimental run, QB and CBin are fixed. The value of CB,,~corresponding to time zero can be obtained by extrapolating CB,,~data back to time zero. KA or RTc a n then be computed from equation (4). One might wonder why the sorbent's total external area, A, is lumped together with K a n d is not computed separately, so that a n estimate of K alone can be made. The reason is that the surface of a charcoal particle is typically not a t all smooth but is rough a n d irregular (the Gambro particles do appear to be somewhat smooth, but the Sandev and B-D ones clearly are not). Because of this, there is no way to determine the true surface area. Even if the sorbent particles did have smooth external surfaces, the particles typically possess a significant range of sizes rather than being all of a single size. What size should be chosen as representative of the whole lot, s o that the specific surface area (specific area i n cm2/cm3 = G/diameter in cm) can be computed? Should one use a n arithmetic, geometric, logarithmic, or some other mean particle size? The answer is unclear. A final reason for lumping A in with K is
RESULTS M a s s T r a n s f e r Resistance V a l u e s Table I lists RT values for each device in both the buffer and blood environments. Time-Averaged Clearance Values Holland et aL2 have pointed out the important idea that, in terms of quantifying the total amount of solute removed over certain time periods from the beginning of a hemoperfusion, clearance values should be time-averaged over such time periods. In accordance with this idea, the authors have integrated the areas under the clearance curves in Figures 1 and 2 and have determined the time-averaged values presented in Table 11. The time periods chosen were one and two hours from the beginning of the tests.
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Vol. 3, No. 3 TABLEI1 TIME-AVERAGED CLEARANCE VALUES (ML/MIN) Buffer Tests Blood Tests 1 hr 2 hrs 1 hr
TABLEI MASS TRANSFER RESISTANCES (RT) IN MIN/L USING SODIUM SALICYLATE IN BUFFER OR BOVINE BLOOD AT QB = 200 ML/MIN Buffer Tests Blood Tests B-D Column 1.32 4.39 Gambro 1.62 5.03 Sandev 4.18 8.36 C-DAK (QD = 400) 2.64 7.65 TWO C-DAKs 1.37 (QD = 500)
B-D Column Gambro Sandev C-DAK (QD = 400) TWO C-DAK’s (QD = 500)
DISCUSSION The RTvalues for the hemoperfusion columns reflect the intrinsic kinetics of each device. On this basis, the B-D unit appears to be best, a n d the Sandev unit (having large charcoal granules) is decidedly the worst. Another important factor is total column capacity, however, as indicated at least approximately by the amount of charcoal in each unit. The B-D device h a s only 94 gm of charcoal as compared to 300 gm of charcoal in each of the other devices. Hence, as Figure 1 clearly shows, the B-D unit approaches saturation much faster t h a n the other units. It h a s also been demonstrated, however, that for drugs t h a t are normally present i n the blood in lower than 1 gm/L concentrations in overdose cases (e.g., barbiturates with concentrations more like 0.1 gm/L) the B-D column clearance remains higher than the clearances for the other two hemoperfusion devices for a much longer period of time.’ The loss of kinetic performance due to saturation effects is also reflected by the average clearances presented in Table 11. In the buffer tests, the B-D unit (which has the best initial kinetics) is now the worst unit in terms of solute removal if one considers a n extended time period, such as one or two hours. This makes it quite clear t h a t indices of initial kinetics and of longer-term, time-averaged kinetics can have very different implications. In the blood tests, the B-D unit is, perhaps unexpectedly, the best of the four systems tested over a one-hour period. One reason for this is that solute uptake rates are much lower with blood than with buffer, and the rate of saturation of the B-D unit is, therefore, not as marked. Table I indicates that the RT values are much elevated (by roughly a factor of three) when blood is used, as opposed to buffer. This is, perhaps, a n unexpectedly large effect, but can be explained on the basis of cell and protein deposition and flow nonuniformities. T h e decreases i n t h e one-hour timeaveraged clearances when blood is used, as opposed
95.3 173.4 115.6 152.0
186.6
53.4 (est.) 137.3 104.7 152.0 186.6
102.7 95.6 77.7 96.0 -
to buffer, are not as dramatic as the increase in the
RT values (e.g., the clearances fall by 44.9,32.8 and 36.8% for the Gambro, Sandev and single C-DAK systems, respectively); for the B-D unit, the average clearance with blood is actually 7.8% higher than with the buffer. The reason for the rise i n clearance noted with the B-D device is not clear - while one would not necessarily expect much of a decrease in clearance when switching from buffer to blood, one would not expect an increase. The most likely explanation is that, because of its unique spiral-wound design, different B-D units could easily have quite different flow pattern behaviors, which lead to different clearance efficiencies. I t becomes evident from Figures 1 and 2 that one advantage of the C-DAK type of system is t h a t its clearance, although initially lower t h a n the clearances of the B-D and Gambro hemoperfusion devices, remains relatively constant with time, a n d ultimately becomes higher. Thus, the C-DAK system might be preferable for long-term perfusions. Figure 1 suggests, as does Table I, that two C-DAK’s in series would be almost as good as any of the hemoperfusion devices. Two C-DAK’s could easily be used since their priming volumes are only about 200 ml (hence, 400 ml for two). The B-D, Gambro a n d Sandev columns have priming volumes of 255, 300 a n d 330 ml, respectively, and it is more risky to use two of these in series (the B-D unit has, however, been recommended for two-in-series operation). The comparison between the hemoperfusion columns a n d the single C-DAK or double C-DAK systems cannot be taken too literally from Figures 1 and 2, except near time zero. The rate of clearance fall in hemoperfusion devices i n any real application will be affected by the fact t h a t the inlet drug concentration will decrease progressively with time due to 1)drug metabolism i n the patient and 2) drug removal in the hemoperfusion devices. Also, the behavior of the hemoperfusion devices will depend
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crucially on the chemical nature of the drug, i.e., on the affinity of charcoal for adsorbing the drug. The C-DAK system is affected mainly by the drug’s molecular size (this affects t h e hemoperfusion units also). Although the fact t h a t clearances do not fall with time suggests that the C-DAK system should be considered for long-term perfusions, the early time period is often critical in preventing organ damage i n drug overdose victims. Clearly, t h e hemoperfusion devices may often be more effective during this period. The choice of which of these four devices to use will depend heavily on the specific drug involved a n d its concentration in the patient. However, one should only select hemoperfusion over hernodialysis 1) when the identity of the drug involved has been definitely established and 2) when it is known, from clinical results, that the hemoperfusion device to be used is indeed better than the dialyzer that would normally be employed.
Mass Transfer Characteristics kinetics, the systems rate as follows: B-D, excellent; two C-DAK’s, excellent; Gambro, very good; single C-DAK, good; and Sandev, moderate. I n terms of sorption capacities, the hemoperfusion units rate a s follows: Gambro and Sandev, very good probable capacity; and B-D, a much lower probable capacity.
References 1. COONEY,D. O., INFANTOLINO, W., KANE, R. Comparative
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5.
CONCLUSIONS The results obtained suggest that in terms of initial
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studies of hemoperfusion devices. I. I n uitro clearance characteristics. Biomater Med Dev Artif Organs, 6199, 1978. HOLLAND,F. F., DONNAUD, A., GIDDEN,H. E., KLEIN,E. Methods of measurement of m a s s transfer rates and capacities of hemoperfusion cartridges. T r a n s Am SOCArtif Intern Organs, 23:573, 1977. DUNLOP,E. H., GAZZARD, B. G., LANGLEY, P. G., WESTON, M. J., Cox, L. R., WILLIAMS, R. Design features of haemoperfusion columns containing activated charcoal. Med Biol Eng, 14:220, 1976. RADCLIFFE,D. F., GAYLOR, J. D. S. Interpretation of haemoperfusion column performance using the “equivalent haemodialyzer” concept. Abst ASAIO, 7:47, 1978. COONEY,D. 0. Biomedical Engineering Principles. Dekker, New York, New York, U.S.A., p. 318, 1976. TRINDER, P. Rapid determination of salicylates in biological fluids. Biochem J, 57:301, 1954.
