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Computer Simulation of Low-Density Lipoprotein Removal in the Presence of a Bioreactor Containing Phospholipase A2 Samuel D. Shefer, Joshua Breslau, and Robert Langer* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
High concentrations of low-density lipoproteins (LDL) in the blood can lead to coronary heart disease, the primary cause of death in the Western hemisphere. A new treatment t o reduce LDL levels is now being tested on rabbits, which are model animals for hypercholesteremia. The treatment involves using a n immobilized enzyme within a bioreactor that is incorporated in a n extracorporeal circuit. The enzyme modifies LDL to a form that is much more rapidly removed from the circulation. A mathematical model to describe LDL metabolism in the presence of the bioreactor was developed to give a better understanding of the biodistribution of modified LDL during and following treatment. A four-compartment model was developed on the basis of previous studies on human lipid metabolism, with the specific values of the constants taken from the experimental data on rabbits. A Macintosh I1 computer with a Stella I1 modeling program was used t o simulate the treatment and to predict LDL levels over time given different values for initial enzyme activity, length of treatment, rate of enzyme denaturation, and other relevant parameters. The model provided a close fit with the experimental results for the change in total cholesterol. It confirmed the observed delay in the plasma cholesterol rebound level after the end of the extracorporeal treatment. One conclusion derived from both the experimental data and the model is that during the first 1.5 h, the limiting step for LDL removal is the rate a t which modified LDL is taken up by the liver. However, bioreactor cessation becomes the limiting step in maintaining low LDL levels for a n extended term. The study suggests that continuous modification of LDL, possibly using an implantable device, is required to maintain low levels of plasma LDL.
Introduction Lipoproteins are a class of macromolecules primarily composed of proteins and lipids, whose main function is to act as carriers for plasma cholesterol. Lipoproteins are often categorized by their density, which is a function of the ratio between lipids and proteins. Lipoproteins with a high ratio of protein to lipids have high densities and are classified as high-density lipoproteins (HDL, d > 1.063 g/mL). As the relative quantity of the lipid component grows, the density decreases and drops to the values for low-density lipoproteins (LDL, 1.019 < d < 1.063 g/mL), intermediate-density lipoproteins (IDL, 1.006 < d < 1.019 g/mL), and very low-density lipoproteins (VLDL, d < 1.006 g/mL). The total cholesterol in the human plasma circulation is calculated as a weighted sum of the HDL, LDL, and free triglycerides. Ingested fat forms chylomicrons, lipid particles that enter the bloodstream through the thoracic duct. These are used in the formation of VLDLs in the liver. In the body, VLDLs gradually lose lipids and gain density, passing through the IDL range and finally becoming LDLs. HDLs in the plasma pick up lipids from surrounding tissue, lose density, and also become LDLs. LDL is removed from circulation mainly by the liver. A danger of high concentrations of LDL is atherosclerosis, in which lipoproteins form a permanent deposit on artery walls, eventually restricting blood flow and leading to coronary heart disease (CHD) (Goldstein et al., 1973). This problem is especially acute for people with familial hypercholesterolemia, a genetic condition in which the
* Address correspondence and reprint requests to this author.
LDL receptors on liver cells that normally remove LDL from the blood are absent. Potential treatments for this condition, or for general hypercholesterolemia, must reduce the concentration of LDL in the blood. One way in which this can be accomplished is by enzymatic modification of the LDL to a form that is removed from circulation more rapidly (Labeque et al., 1993). Phospholipase A2 (PLAz),an enzyme derived from the venom of the snake Crotalus atrox, modifies LDL into a form that is rapidly taken up by the liver (Labeque et al., 1993). Its function is to cleave phospholipids, another important component of LDLs. The faster rate of uptake of PLA2-LDL results in an overall reduction of the amount of plasma LDL. Treatment with PLA2, then, seems to have the potential to be a useful way of reducing the risk of CHD. Such a treatment is being developed and tested on rabbits (Labeque et al., 1993),which provide a good model for human atherosclerosis. The treatment involves extracorporeal circulation of the plasma of a hypercholesterolemic New Zealand white or Watanabe rabbit through a bioreactor containing immobilized PLAz on agarose beads for a period of approximately 90 min. This has been found to reduce the cholesterol level by as much as 40%, depending on the enzyme activity in the bioreactor (Shefer et al., 1993b). Important questions are as follows: What are the metabolic pathways that account for the results obtained with the enzymatic treatment in the bioreactor? Can a knowledge of these pathways help optimize the method of treatment? In order to be able to trace the metabolic pathways without sacrificing the rabbits, we performed computer simulations based on experimental data. While experi-
8756-7938/95/3011-0133$09.00/0 0 1995 American Chemical Society and American Institute of Chemical Engineers
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ments only provided us with data on the changes in the total blood cholesterol, the simulation could also describe processes occurring in the internal organs such as the accumulation of modified LDL in liver, which could not be measured directly without sacrificing the rabbits. Various considerations motivated us to construct a mathematical model to describe the process of LDL removal. We wanted to determine the relationships among the various physiological and engineering parameters controlling the process. The analysis of the model may help in the determination of the limiting step for the overall removal of plasma LDL (bioreactor performance or physiological processes). In addition, a mathematical model may be used to derive further conclusions that could eventually minimize the number of animals needed for these studies. The construction of the mathematical model consisted of the following steps. First, we made use of previous concepts of human lipoprotein pathways and kinetics. On the basis of known metabolic pathways of LDL and the biodistribution of LDL and PLAZ-LDL in New Zealand white rabbits, we constructed a mathematical model. The model describes the continuous changes in the native and modified LDL biodistributions due to the introduction of a bioreactor that modifies LDL particles. The validity of the model was verified by comparison with actual concentrations of lipoproteins measured over time.
Experimental Section Software. The work was done on an Apple Macintosh I1 personal computer running the Stella I1 modeling software (High Performance Systems, Inc., Hanover, NH). The model was run for periods of 2.5-30 h, depending on the duration of the associated experiment, using a step time (dT) of 0.05 h and the Runge-Kutta 4 integration option to solve equations simultaneously for all variables over time. Procedures. The procedure for in vivo.experiments with rabbits is as previously described (Shefer et al., 1993a). In general, hypercholesterolemic New Zealand white rabbits (HNZW)were used for this study. A bioreactor containing PLA2 immobilized onto agarose beads was incorporated in an extracorporeal circuit. Blood was circulated for 90 min with a flow rate of 5 mL/ min, as described previously (Shefer et al., 1993a,b). Total cholesterol, HDL, and triglycerides (TG)were measured directly, making possible the evaluation of the LDL concentration (mg/dL) (Friedwald et al., 1972). The total cholesterol used in the model is estimated by using the formula for total cholesterol in humans as an approximation (Friedwald et al., 1972): total cholesterol = HDL
+ LDL + 0.2TG
The previous Friedwald approximation was needed because there is no direct way to measure the LDL level in rabbits. Enzyme decay rates were measured experimentally (Shefer et al., 199313). One unit of enzyme activity is defined as the amount of protein that produces one micromole of fatty acids a t 37 "C. The activity was measured by titrating the fatty acids produced by the enzymatic reaction with sodium hydroxide in a mixed batch reactor a t 37 "C (Dennis et al., 1973).
Results and Discussion Construction of the Model. The first assumption made in the construction of the model is that LDL is the
Turn-over to other organs / lipoprotein
A
k'
I
W
Figure 1. Schematic representation of human LDL biodistribution as a two-compartment model.
main particle to be modified, and the levels of HDL, IDL, and VLDL remain constant over the 90 min duration of the extracorporeal treatment. This is a simplification because the enzyme actually modifies all particles with phospholipids. However, the simplification is partially justified by the fact that LDL molecules occur in much higher quantities than other plasma lipoproteins in hypercholesterolemic rabbits (Shefer et al., 1993a), and previous studies indicate a high affinity of PLA2 for LDL compared with HDL (Natarajan et al., 1990). The first phase in the construction of the model made use of a previously existing two-compartment model for LDL biodistribution (Figure 1)in humans (Berman et al., 1982). One compartment contains the LDL in the plasma (68%)(compartment A, Figure 1);the other contains the extravascular LDL, most of which is presumed to be in the liver (19%)(compartment B, Figure 1). In this model, the LDL enters the plasma from digested food (at a constant rate of 122) and the liver (at a rate k4). The LDL leaves the plasma compartment and travels to the liver (at a rate of k3), to other organs, or to other lipoproteins (at rate kl) (Berman et al., 1982). We assume that LDL biodistribution in humans is parallel to that in rabbits. The turnover rate and kinetic constants were measured in the study with rabbits. All of the rate constants in this phase of the model are assumed to be first-order, except for the rate of flow of LDL into the plasma from outside the system, which was zero-order. This is justified because the rabbits were kept on a fixed high-cholesterol diet (Shefer et al., 199313). It is further assumed that the system is a t equilibrium before the introduction of the bioreactor containing immobilized PLA2. Therefore, in the absence of enzyme, the LDL concentration would remain constant over the period of time of the treatments (90 min). The second phase in building the model was the introduction of the bioreactor and a compartment for modified LDL (PLA2-LDL) in the plasma (compartment C, Figure 2) and liver (compartment D, Figure 2). The rate a t which PLA2-LDL is taken up by the liver is defined as kg. In this model, the only source of PLA2-LDL is modification of the plasma LDL by the bioreactor. We assume that the modified LDL is taken up only by the liver (Labeque et al., 1993). The modified LDL uptake rate is taken as constant, equal to 1.16h for New Zealand White (NZW)rabbits (Labeque et al., 1993). This is the value used for the (first-order) LDL removal constant, kg. The amount of enzyme is assumed to be the limiting factor in the modification process. The rate of conversion is then determined by the rate of the enzyme activity and the plasma LDL concentration. The enzymatic deactivation rate is assumed to be exponential with time (as found in preliminary studies). After 90 min of blood circulation,
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Biotechnol. Prog., 1995, Vol. 11, No. 2 Table 1. Decay of (Immobilized Enzyme) Bioreactor Activity within 90 min of Extracorporeal Treatment
number 1 2 3 4
A I
Plasma LDL A
D
I
Plasma PLAgLDL
1
Figure 2. Biodistribution of LDL in the human body; modification of the two-compartment model by the introduction of a bioreactor that modifies LDL.
the modification rate becomes 0 as the bioreactor is disconnected. The bioreactor activity rate r (in h-l) is determined by
r = (initial activity) exp(enzyme decay x time) where time time).
reaction time (r = 0 when time
enzyme decay =
(1)
=- reaction
ln(fina1 fractional enzyme activity) reaction time (2)
The kinetics of LDL and PLA2-LDL flux among the compartments can be summarized by the following differential equations. LDL change in plasma with time:
-dA - -k,A - k d - rA dt
+ k,B + k,
(3)
liver LDL change with time: -= k
dt
plasma P%-LDL
d - k,B
(4)
change with time:
-dC - rA - k,C dt
liver P%-LDL
change with time:
e = k,C dt where A is LDL in the plasma (mg), B is LDL in the liver (mg), C is PLA2-LDL in the plasma (mg), D is PLA2LDL in the liver (mg), kl is the LDL removal rate from the plasma (h-l), k2 is the LDL flow rate into plasma (mg h-l), k3 is the LDL removal rate by the liver (h-l), k4 is the LDL liver release rate (h-l), and k g is the PLA2-LDL removal rate into the liver (h-l). Quantification. The plasma LDL removal rate in NZW rabbits (k3) is approximately 0.069 h-l. LDL
initial activity (units) 3.6 15 15.9 6.72
final activity (units) 2.8 2 4.24 2.17
decrease (8) 22.22 86.67 73.4 67.71
content in NZW rabbit liver is 19% (wt), while 68% (wt) is in the plasma (Labeque et al., 1993). These data allow the values of the four rate constants, k1, k2,k3, and k4, to be determined. The initial value of LDL concentration in plasma, A, was determined by experimental measurement. The initial value of LDL in liver, B, was set to 19/68(theinitial value of A), the ratio between the amounts of LDL in the liver and LDL in the plasma (Labeque et al., 1993). The initial values of the modified LDL in plasma, C, and in liver, D, were set to 0. Constant k1 was found to be 0.0132, determined by trial and error and producing a good fit of the data. The value used for k2 was 0.0132 multiplied by the initial value of A, which establishes equilibrium in the absence of a bioreactor, plus an integer ranging from 5 to 15, depending on the size of the rabbit, to reflect the fact that hypercholesterolemic NZW rabbits have a continuously increasing cholesterol level due to their diets. The values of k3 and k4 were selected such that the ratio between them would be 19/68 (Labeque et al., 1993). A value of 0.069 was used for k3, which set 124 equal to 0.247. The value of ks was set a t 1.16 for the removal of PLA2-LDL from NZW rabbits (Labeque et al., 1993). During the treatment, the reactor rate, r, decays exponentially (Table 1). To determine a proportion between the measured enzyme activity and the reaction rate used in the model, we measured initial and final enzyme activity. A constant of proportionality between measured units of enzymatic activity and the units used by the Stella computer program was selected to give the best possible fit of the data. The conversion constant varied slightly between rabbits, with a range of 0.25 (SD = f0.07). This conversion value was found by trial and error to best fit the experimental data. Solution of the Model. The equations (eqs 1-5) as they stand are analytically tractable with certain simplifications made, but the analytic solution is unenlightening. We therefore chose to solve the equations numerically and then plot the result. This solution presented graphically gives a clear indication of the type of behavior predicted by the model and is easy to compare with experimental data for assessment of the model's value. This is why graphical methods were chosen for the solution of the equations. The equations given in the Appendix were used for the computer simulation. The graphical flow sheet for the program applied is described in Figure 3. Prediction with the Model. The model was used to predict the changes in total cholesterol over a period of time when bioreactors with different initial activities were used (Figure 4). In the absence of enzyme (control case), the total cholesterol continuously increases with time due to high cholesterol in-flow. The predicted reduction in total cholesterol profile when enzyme is present can be described as a sharp reduction within the extracorporeal treatment time, followed by a return to the initial level within several hours. The computer simulation predicts only a slight decrease (5%)when less than 2 units of enzyme are applied. For a higher amount of enzyme a significant reduction in total cholesterol is
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Biotechnol. Prffg., 1995, Vol. 11, No. 2
Liver-Pla2-LDL
I
Enzyme-Remaining
Modified-to-Liver
Figure 3. Schematic representation of the complete model used by Stella of a two-compartment model incorporating the bioreactor. The compartments containing plasma LDL, liver LDL, and PLA-LDL in the plasma and in liver are represented by boxes. The thick arrows leading between the boxes represent the possible flow of LDL. The circles labeled LDL Inflow, Removal Rate, LDL to Liver, LDL to Plasma, and Modified to Liver represent the rate constants. Thin arrows between circles represent general mathematical relationships that are defined in the equations in the Appendix. P L A r L D L comes from plasma LDL that is modified by the immobilized enzyme in the bioreactor. The reactor activity determines the rate at which the plasma LDL is modified, which depends on the initial activity of the enzyme, the rate at which the enzyme deactivates, and the duration of the treatment. 1.2
1.o
0.2
0.0
10
5
15
Time (hr)
Figure 4. Prediction curve for plasma total cholesterol levels as expected from the model, when bioreactors with different activities are used: (-) control, 0 units of enzyme, (- - -) 2 units, (- * -1 4 units, (- -) 10 units, and 20 units of activity. (a*.)
predicted. The higher the bioreactor activity, the higher the decrease in total cholesterol and the longer the rebound time (time in which total cholesterol reaches the initial level).
Comparison between Computer Simulation and Measured Data. A comparison of the predicted (computer simulation) and observed (measured) values for the rabbits is given in Figure 5A-D. The shape of the data suggests that the model is a qualitatively good approximation of the measured data. The model correctly predicts the observed decrease in plasma total cholesterol with time. The comparison between prediction and observation is based on a limited amount of matching points. This limitation results from restrictions on the blood volume that could be taken from the rabbits after extracorporeal treatment. The good agreement between the model predictions and the observed data allowed us to simulate LDL removal in different unmeasured conditions. The model was used to simulate the reduction in total cholesterol when the LDL modification process continued for unlimited duration (>24 h). The model predicts that cholesterol and LDL will eventually stabilize at a new level of about 25% of the initial amount. This situation may not be practically realized with an extracorporeal setup as used in this study because the patient would have to be attached to a complicated system (pumps, circuit, etc.). However, the need for continuous LDL removal might trigger the development of future therapy: technology that will minimize the system size or that will apply an implanted bioreactor. An important parameter of the process is the rebound time of total cholesterol. The rebound time is used to plan the succeeding extracorporeal treatments in order to maintain low levels of plasma total cholesterol in the
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t
e
0.4.
1
0.0;
5
10
Time (hr) 1.a
\
B
0.8
0.8
- 0
z&
0.6
2-
E
0-
e
0,
0.4
0.2
0.2
0.0 J
1
2
3
Time (hr)
'
0.OJ
5
10
15
20
Time (hr)
Figure 6. (A-D) Total cholesterol kinetics; comparison between the measured data ( 0 )and the simulation model (-1.
patients. For a control rabbit (without enzyme in the bioreactor), the model correctly predicts that no change in the total cholesterol level will occur over time. The results presented in Figure 4 indicate that the larger the amount of enzyme in the bioreactor, the longer the rebound time. The rebound times, as observed and as predicted by the model, are presented in Table 2. The measured data provide rebound times comparable to those from the computer simulation. The inconsistency between the measured values and the various amounts of bioreactor activity results from the difficulty of making a precise measurement of the rebound time. In most cases, due to limitations in blood volume drawn from rabbits, we estimated (by extrapolation or interpolation) from the measured points (Table 2). It should also be noted that the model is not expected to be accurate for a period of more than 24 h due to variance in the individual diet uptake rate during this time. Analysis of Metabolic Pathways. The model is able to elucidate the process of PLA2-LDL accumulation that occurs in the liver during treatment. The simulated
Table 2. Simulated and Measured Rebound Times as a Function of the Amount of Bioreactor Activity
enzyme activity 0
simulated (h) 0
measured (h) 0
2.2 2.8 4.2 6.8
24 23 27 27
24 20 26 24
values of PLAZ-LDL are shown together with the measured values of total cholesterol for several tested rabbits in Figure 6A-D. During and immediately following the extracorporeal treatment, the level of LDL in the liver falls slightly, while the level of PLA2-LDL in the liver increases rapidly. When extracorporeal treatment ceases, most of the PLA2-LDL accumulates in the liver, and the concentration of liver LDL gradually returns to its original level. The accumulation of modified LDL in the liver occurred unnaturally and thus is nondegradable. Further modeling of the lipoprotein cellular metabolism was studied by Yuan et al. (1991).
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! 0
10
n
20
"0
Time (hr)
20
10
Time (hr)
400"1 300
\
0
0
Time (hr)
Time (hr) Figure 6. (A-D) Simulation of accumulation of PLA2-LDL (. .-) and LDL ((- -) concentrations with time.
We focused on two significant events: the time in which plasma total cholesterol reaches a minimum level and the time in which modified LDL cholesterol reaches a maximum level in the liver. The minimum level of total cholesterol indicates the removal rate by the liver as a result of the bioreactor activity. By assuming that all PLAZ-LDL produced is immediately taken up by the liver, the accumulation of PLAZ-LDL in the liver simulates the amount of modified LDL that passes from the plasma. In all cases (Table 3), the time at which a minimum concentration of total cholesterol occurs is earlier than the time at which the maximum level of LDL is reached in the liver ( p < 0.05 by t-test). The significance of this observation will be discussed when we analyze the limiting step of the overall process. The overall process of LDL removal is divided into two main steps. In the first step, the LDL is modified by the immobilized PLAz in the bioreactor and is then circulated back into the body. In the second step, the modified LDL is removed from the bloodstream due to uptake by the liver cells (Figure 7). The efficiency of the bioreactor in modifying plasma LDL was discussed previously (Shefer et al., 1993a).
2
1
- -1
in liver and changes in plasma total cholesterol
Table 3. Occurrence of Critical Events: Time in Which Plasma Total Cholesterol Reaches a Minimum Level and Time in Which Modified LDL Reaches a Maximum Level in the Livers of Four Different Rabbits time minimum time maximum reactor level plasma TC" level modified LDL number activity (h) is reached (h) in liver is reached (h) 1 1.5 3.3 4.5 2 1.5 3.81 5.17 3 1.5 2.8 4.5 4 a
1.5
4.2
6.2
TC: total cholesterol.
Generally, we observed higher amounts of total LDL removal for increasing bioreador activity. Within 90 min treatments, most of the rabbit's blood was circulated through the system. Under these conditions, we observed 90% modification of the rabbit's LDL by the bioreactor (Shefer et al., 1993a). Therefore, we concluded that the level of bioreactor activity is not a limiting factor in the overall LDL removal process. The second step of the process is the uptake of modified LDL by the liver cells. The cellular removal mechanism of this process is not completely clear. Various hypoth-
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Extracorporeal Bioreactor
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Patient's Body (liver)
Definition of D. 4. LiverJLA2LDL = LiverJLA2LDL + dt*(ModifieLUptake) 4.1 INIT(Liver-PLA2LDL) = 0 Total Cholesterol Calculation. 5. Cholesterol = HDL PlasmaJDGConc + ModifiehConc 0,2*Triglycerides 5.1 HDL = 24 5.2 Triglycerides = 50 5.3 ModifiehConc = Plasma-PLA2LDL/Plasmavolume 5.4 PlasmaVolume = 1.35 Normalization of Cholesterol Values. 6. CholN = CholesteroV336.0 Enzyme Degradation. 7. EnzymeDegradation = LOGN(Enzyme3emaining)/(-Reactor-time) 7.1 EnzymeRemaining = 0.266 7.2 InitialReactorAct = 01.0 7.3 ReactorActivity = IF (TIME 1.5 h), after the extracorporeal treatment ceases. In the future, we plan to design a bioreactor that is able to modify LDL over long periods of time, such as an implanted device. This may be useful for sustaining a low level of total cholesterol and might be applied as a therapy for CHD.
+
Literature Cited Acknowledgment The authors thank Mr. J. P. M. Ferreira for his assistance with analyzing the enzyme activity and Dr. Achim Goepferich and Dr. Claude Mullon for reviewing the manuscript. The research was supported by W. R. Grace and Co., Lexington, MA, and NIH Grant GM 25810. Appendix The followingare the equations and data input as used for the Stella software with the Macintosh 11. The numbers in italics are given as an example. Definition of A. 1.PlasmaLDL = PlasmaLDL dt*(-LDGUptake LDLJnflow - LDLRemoval - Modification) 1.1INIT(P1asmaLDL) = 407.7 1.2 Modification = ReactorActivity*PlasmaLDL 1.3 PlasmaLDGConc = PlasmaLDLPlasmaVolume Definition of B. 2. LiverLDL = LiverLDL dt*(LDL-Uptake) 2.1 INIT(LiverLDL) = 113.9 2.2 LDL-Uptake = (LDGtoLiver*PlasmaJDL)(LDL-to_Plasma*LiverLDL) Definition of C. 3. PlasmaPLA2LDL = P l a s m d L A 2 L D L dt*(Modification - ModifiehUptake) 3.1 INIT(PlasmaPLA2LDL) = 0 3.2 LiverLDL-Conc = LiverLDUPlasmaVolume 3.3 Liver_PLA2-Conc = Liver_PLA2LDL/Plasmavolume 3.4 ModifieLUptake = Modifiehto-Liver*PlasmaPLA2LDL
+
+
+
+
Berman, M.; Grundy, S. M.; Howard, B. V. In Lipoprotein Kinetics and Modeling; Academic Press: New York, 1982;p 486. Dennis, E. A. Kinetic Dependence of Phospholipase-A2 Activity on Detergent Triton X-100.J. Lipid Res. 1973,14, 152- 159. Friedwald, W. T.; Levy, I. R.; Fredrickson, D. S. Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge. Clin. Chem. 1972,18,499-502. Goldstein, J. L.; Hazzard, W. R.; Schrott, H. G.; Bierman, E. C.; Motulsky, A. G. Hyperlipidemia in Coronary HeartDisease-Lipoprotein Characteristics of a Classification Based on Genetic Analysis. J. Clin. Invest. 1973,52, 1533-1544. Labeque, R.; Mullon, C. J.-P.; Ferreira, J. P. M.; Lees, R. S.; Langer, R. Enzymatic modification of plasma low density lipoprotein: A potential treatment for hypercholesterolemia. Proc. Natl. Acad. Sei. U S A . 1993,90, 3476-3481. Natarajan, M. K.;Fong, S. B.; Angel, A. Enhanced Binding of Phospholipase-A2 Modified Low Density Lipoprotein by human Adipocytes. Biochem. Cell. Biol. 1990, 68, 1243- 1249. Shefer, S.D.; Payne, R. G.; Langer, R. Design of a biomedical reactor for plasma low density lipoprotein removal. Biotechnol. Bioeng. 1993a, 42, 1252-1262. Shefer, S. D.; Ferreira, J. P. M.; Mullon, C. J.-P.; Langer, R. Physioligical response to the extracorporeal removal of low density lipoprotein in rabbits: Efficacy and safety. Int. J. Artif. Organs 1993b, 15, 218-228. Yuan, F.; Weinbaum, S.; Pfeffer, R.; Chien, S. A mathematical model for he receptor mediated cellular regulation of the low density lipoprotein metabolism. J. Biomech. Eng. 1991,113, 1-10. Accepted July 22, 1994.@ Abstract published in Advance ACS Abstracts, October 15, 1994. @
