Novel Devices for the Predictable Delivery of NitricOxide to Aqueous Solutions

Mahendra Kavdia, Shravan Nagarajan, and Randy S. Lewis*

School of Chemical Engineering, Oklahoma State University, Stillwater, Oklahoma 74078

Received May 20, 1998

Nitric oxide (NO), a recently discovered biological molecule synthesized by many cells, hasmany physiological roles including blood pressure regulation, neurotransmission, and inhibitionof platelet adhesion. However, NO and reactive species formed in the presence of oxygen andsuperoxide can also be cytotoxic, mutagenic, or carcinogenic. Two novel devices were developedto deliver controlled and predictable amounts of NO to aqueous solutions for studying theeffects of NO on biological systems. The devices contained either a slit or a tube composed ofa gas-permeable membrane. Aqueous solution flowed on one side of the membrane while theother side of the membrane was exposed to NO gas. Mathematical models were used to predictthe bulk or mixing-cup NO concentration in the aqueous solution at the exit of each deliverydevice following exposure to NO gas. Model predictions were in good agreement withexperimental values at both 25 and 37 °C. One of the delivery devices was also connected toa well-stirred and oxygenated chamber. Model predictions of the chamber NO concentration,which included the reaction of NO with O2, were in excellent agreement with experiments.

Introduction

Nitric oxide (NO)1 is synthesized by many cells includ-ing macrophages, neutrophils, endothelial cells, andhepatocytes. Important physiological roles of NO includeblood pressure regulation, neurotransmission, and inhi-bition of platelet adhesion (1). However, NO and reactivespecies formed in the presence of oxygen and superoxidecan also be cytotoxic, mutagenic, or carcinogenic (1, 2).In light of both the physiological and pathophysiologicalactions of NO, controlled and quantitative delivery of NOwould be beneficial for studying the effects of NO andits reactive products on biological systems.

Current methods for delivering or generating NO inbiological systems include the release of NO from NO-donor compounds, the stimulation of NO synthase en-zymes in cellular systems, the addition of NO-saturatedsolutions, and the permeation of NO through polymericmembranes (3-8). The majority of research investigat-ing the role of NO on biological systems utilizes the firstthree methods.

An advantage of using NO-donor compounds is thatthe NO-release rates can be modified based upon thestructure of the donor compound (3, 8). However, light,pH, and the aqueous medium can affect the NO-releaserate. In addition, the nonconstant release rate of NO andthe reactivity and/or toxicity of the NO-donor compoundfollowing the release of NO can be problematic (8, 9).Stimulation of NOS to produce NO is a viable approachfor in vivo studies and for producing a near-constantrelease of NO. However, other species generated or

existing within a cell, such as superoxide, can react eitherintracellularly or extracellularly with NO to form otherpotentially damaging species. Addition of NO-saturatedsolutions to biological solutions has the drawback of theinability to maintain steady-state concentrations of NO,especially in a reactive environment.

Permeation of gaseous NO through polymeric mem-branes enables a constant NO delivery rate that leadsto steady-state NO concentrations, even in the presenceof species which react with NO. A previous studyincorporating NO permeation through a membrane re-sulted in constant formation of NO2

- in the presence ofO2, suggesting that the NO concentration achieved steadystate (7). However, the delivery rate was only semiquan-tifiable, and the aqueous NO concentrations were notpredictable or measured. In all methods of NO delivery,it is often advantageous to deliver NO at a constant andcontrolled rate to maintain a desired and predictable NOconcentration in a biological environment. Knowledgeof the concentration is beneficial for assessing the effectsof NO on biological systems, especially when assessingthe physiological relevance of the NO exposure level.

In view of the advantages of a constant NO deliverymethod in which predictable and steady-state NO con-centrations can be maintained, two devices for deliveringNO through permeable membranes and into a flowingsolution have been developed and modeled. The advan-tages of these devices are that (1) a controlled amount ofNO is delivered to maintain a steady-state NO concen-tration, (2) the NO concentrations are predictable frommodels, (3) the pH and light effects on the delivery rateare avoided, and (4) the addition of undesired species iseliminated to avoid undesired reactions. An applicationof the delivery device is described for maintaining aconstant and predictable NO concentration in a well-stirred chamber.

* Address correspondence to this author at the School of ChemicalEngineering, 423 EN, Oklahoma State University, Stillwater, OK74078. Telephone: (405) 744-5280. Fax: (405) 744-6338. E-mail:lewis@gibbs.cheng.okstate.edu.

1 Abbreviations: NO, nitric oxide; sccm, standard cubic centimetersper minute.

1346 Chem. Res. Toxicol. 1998, 11, 1346-1351

10.1021/tx980112s CCC: $15.00 © 1998 American Chemical SocietyPublished on Web 10/15/1998

Materials and Methods

Note: Due to the potential toxicity of NO, all NO gas wasvented to a hood.

Reagents. Ultrahigh pure nitrogen, after passage throughan O2 trap, was mixed with a mixture of 10% NO, balance N2

using controlled gas flow meters (Porter Instrument Co., Hat-field, PA) to obtain the desired NO gas concentration. Phosphate-buffered saline (PBS, 0.01 M) was obtained from Life Technolo-gies (Grand Island, NY). Potassium iodide and glacial aceticacid were obtained from Sigma (St. Louis, MO).

Delivery Devices. Two devices, one composed of a perme-able tube and one composed of a thin slit bounded by twopermeable sheets, were designed for physical delivery of NO toa flowing solution. Advantages of these devices are that thephysical dimensions can easily be modified to vary the NOdelivery rate and they are simple to fabricate.

The slit-flow device is shown in Figure 1. The central portionof the device is made of stainless steel and contains a rectan-gular opening through which aqueous solution flows. Theopening is 15.2 cm long with a cross section 0.5 cm wide and0.3 cm high. A membrane, Plexiglas, gasket, and gas inlet/outletchamber are attached to each side of the central portion usinghex bolts, although only attachments on one side are shown inthe 3-D profile. A semipermeable poly(dimethylsiloxane) mem-brane (MEM-100, 0.005 in. thick; Membrane Products, Albany,NY) is laminated to a 0.2 cm thick rectangular sheet of Plexiglasusing silicone adhesive. The Plexiglas contains a rectangularopening of 2.5 cm length and 0.5 cm width to expose the flowingsolution to gas permeating through the membrane. The Plexi-glas opening is 10.2 cm downstream of the flow inlet. ThePlexiglas opening can be lengthened to allow for a greater gasexposure area if required. The membrane, following compres-sion between the Plexiglas and stainless steel, prevents theliquid from leaking upon initiation of flow through the device.

A rubber gasket is placed between the Plexiglas and the gasinlet/outlet chamber to prevent gas leaks. The chamber contains

a section (15.2 cm long, 0.5 cm wide, 0.3 cm deep) through whichgas flows. Tube fittings are threaded into the chamber forattachment of gas lines. As depicted in the side profile of thedelivery device, solution flowing through the central portion isseparated from the gas stream by only the membrane in onesection of the device. In this section, a gas containing NO canpermeate through the membrane and into the solution.

The tube delivery device is shown in Figure 2. The deviceconsists of Silastic tubing (VWR Products, 0.147 cm i.d., 0.196cm o.d.) attached to Teflon tubing (0.132 cm i.d., 0.193 cm o.d.)placed inside a stainless-steel Swagelock cross. Heat shrinktubing (made of polyolefins), which is significantly less perme-able to gas as compared to Silastic, is utilized to attach theTeflon tubing to the Silastic tubing. A section (3.0 cm) of theSilastic tubing is left exposed such that gas flowing across thetube permeates through the exposed Silastic tube and into aflowing solution. The exposed section or the NO gas concentra-tion can easily be adjusted to permit more or less gas frompermeating into the solution.

Delivery Device Experiments. For both delivery devices,PBS was continuously pumped through the slit or tube at a flowrate of 3 mL/min using a peristaltic pump (Masterflex R, Model77390-00, Cole-Palmer Instrument Co., Vernon Hills, IL). Thus,the residence times (volume divided by volumetric flow rate) inthe region of gas exposure were 1.0 and 7.5 s for the tube deviceand slit-flow device, respectively. A gaseous mixture of NO andN2 of a specified concentration continuously flowed through thegas chamber or across the exterior of the Silastic tubing. TheNO concentration was measured at the delivery device outletand compared to model predictions. Experiments were per-formed at both 25 °C and 37 °C. For the 37 °C experiments,both delivery devices were autoclaved for 25 min at 250 °F priorto each experiment. The devices were autoclaved to assess thepredictability of NO delivery for applications in which steriledelivery devices are desired.

Nitric Oxide Analysis. The aqueous NO concentration,following exposure to NO gas, was measured using either a

Figure 1. Slit-flow delivery device. The device is composed of a stainless-steel central portion through which solution flows. Agas-permeable membrane, Plexiglas, gasket, and gas inlet/outlet chamber are attached to each side of the central portion using hexbolts. Gas that contains NO can permeate through the membrane and into the solution in the section where the flowing solution isseparated from the gas stream by only the membrane. All dimensions are described in the text.

Nitric Oxide Delivery to Aqueous Solutions Chem. Res. Toxicol., Vol. 11, No. 11, 1998 1347

chemiluminescence analyzer (Model NOA 270B, Seivers Corp.,Boulder, CO) or an amperometric probe (ISO-NOP, WorldPrecision Instrument, Sarasota, FL). For the chemilumines-cence method, aqueous samples were drawn using a gastightsyringe (Hamilton Co., Reno, NV), and 0.1 or 0.25 mL wasinjected into 10 mL of solution composed of 0.2 M potassiumiodide and glacial acetic acid mixed in a 1:3 volumetric ratio.The solution was contained in a glass vial and was continuouslystirred and bubbled with N2 at 200 sccm1 to purge NO from thesolution and transport the NO into the chemiluminescencedetector. The concentration of NO in the sample was obtainedby comparison with NO2

- standards since NO2- is instanta-

neously converted to NO in the solution (10). The calibrationcurve was linear over the range of concentrations studied. Theminimum detection limit is 25 pmol.

For the amperometric probe measurements, the probe wasinserted into a tee at the point of measurement. For experi-ments at 37 °C, the probe was located in an incubator since theprobe response is sensitive to temperature. The probe wascalibrated at both 25 °C and 37 °C. The calibration consistedof bubbling known concentrations of NO gas into deoxygenatedPBS. The saturated NO aqueous concentrations were obtainedfrom NO solubility data which are 2.53 and 2.14 µM/mmHg forNO at 25 and 37 °C, respectively (11). The saturated solutionwas pumped at 3.0 mL/min through the tee containing the probeto obtain the calibration curve. For 37 °C experiments, thesolution was recirculated through the tee. At both tempera-tures, linear calibration curves were obtained over the range ofconcentrations studied.

Model for Prediction of the NO Concentration. Thebulk (or mixing-cup) NO concentration exiting the deliverydevice (Cb) was modeled and compared with experiments. Theaqueous NO concentration (C) in the delivery device is obtainedfrom the steady-state dimensionless continuity equation for NOwhich is

The dimensionless concentration (θ) is (C - Co)/(Ci - Co) whereCo is the aqueous NO concentration in equilibrium with thegaseous NO to which the delivery device is exposed and Ci isthe aqueous NO concentration at the inlet. For this study, Ci

) 0. The value of Co is the product of the NO solubility (H)and the gas partial pressure of NO. The dimensionless param-eter ê is z/L where the z coordinate represents the direction offlow (z ) 0 at the flow inlet) and L is the length of the membranethrough which NO gas permeates. Equation 1 is based on fullydeveloped laminar flow with a homogeneous fluid. The reactionof NO with aqueous O2 was not included in eq 1 since thereaction is slow for the NO concentrations of this studycompared to the residence time of the solution in the slitchamber.

For the tube device, η is r/R where the r coordinate representsthe radial direction (r ) 0 at tube center) with a tube innerradius of R. The parameter A is DL/UmR2, where D is theaqueous NO diffusivity and Um is the maximum velocity. Thevalue of Um is twice the average velocity. The parameter B is1/η. For the slit-flow device, η is y/h where the y coordinaterepresents the slit height direction (y ) 0 at the slit center) witha slit height of 2h. The value of B is 0. The dimensionlessparameter A is DL/Umh2.

For a slit in which the width-to-height ratio is .1, the slitcan be approximated as having an infinite width. For such anapproximation, the velocity profile [which is Um(1 - η2) withUm equal to 3/2 of the average velocity] is independent of thewidth of the slit. Thus, the two-dimensional form of eq 1 wherethe width dimension is omitted is valid for predicting the NOconcentration profile. The slit-flow device for this study has awidth-to-height ratio of 1.7. Thus, the above assumption thatthe velocity profile is independent of the slit width is not entirelyvalid.

The velocity profile has been solved for a rectangular slit inwhich the slit width is wide enough that only the nearest edgeinfluences the velocity profile (12). The velocity profile re-sembles Um(1 - η2), but Um is a function of the slit width withvalues between 0 and 3/2 the average velocity. For this study,the model predictions for Cb shown in the figures for the slit-flow device were obtained by assuming Um is 3/2 of the averagevelocity across the entire slit width (the infinite width ap-proximation). Analysis using the velocity profile as a functionof the slit width results in model predictions for Cb estimatedto be approximately 25% higher. Thus, the best design for aslit-flow device would have a width-to-height ratio >10 foraccurately predicting Cb or the NO concentration profile basedupon eq 1 with Um equal to 3/2 the average velocity.

The initial and boundary conditions to solve eq 1 are

The Sherwood number (NShw) at the wall is kwh/D and kwR/Dfor the slit-flow device and tube device, respectively. The masstransfer coefficient characterizing the transport of NO throughthe permeable membrane is kw.

The solution to eq 1 yields θ ) f(ê,η). The solution can beobtained using a numerical package such as Matlab. Thus, theNO concentration profile within the delivery device is obtained.The predicted value of the bulk (mixing-cup or velocity-weighted) NO concentration (Cb) exiting the NO delivery device(at ê ) 1) is

Analytical solutions for Cb for both slit-flow and tube deviceshave previously been solved (13, 14).

For the model, the average velocity was obtained from thegeometric dimensions and the volumetric flow rate. The valueof D in PBS was assumed similar to that in water which is 2.7× 10-5 cm2/s at 25 °C and 5.1 × 10-5 cm2/s at 37 °C (15). Thevalue of kw was obtained from the NO permeability (P) of poly-

Figure 2. Tube delivery device. The device is composed ofSilastic tubing (0.147 cm i.d., 0.196 cm o.d.) attached to Teflontubing (0.132 cm i.d., 0.193 cm o.d.) and placed inside aSwagelok cross. Heat shrink tubing covers all but 3.0 cm of theSilastic tubing to allow for NO permeation into solution follow-ing exposure of the tubing exterior to NO gas.

(1 - η2)∂θ∂ê

) A[∂2θ∂η3

+ B∂θ∂η] (1)

ê ) 0 all η θ )1 (2)

all ê η ) 0 ∂θ/∂η ) 0 (3)

all ê η ) 1 ∂θ/∂η ) -NShwθ (4)

θb )∫0

1(1 - η2)θú)1 dη

∫0

1(1 - η2) dη

)Cb - Co

Ci - Co(5)

1348 Chem. Res. Toxicol., Vol. 11, No. 11, 1998 Kavdia et al.

(dimethylsiloxane) membranes (i.e., Silastic) according to kw )P/Hδ for slit flow and kw ) P/[HR ln(Ro/R)] for flow in a tube.The membrane thickness is δ, and the tube outer radius is Ro.The value of P for NO is 2.3 × 10-13 mol cm-1 s-1 mmHg-1 at25 °C (16). The permeability at 37 °C is approximately twicethe reported value at 25 °C in order to account for the effect ofheating the membrane during autoclaving (17). The value ofH for NO is 2.53 and 2.14 µM/mmHg at 25 and 37 °C,respectively (11).

Delivery Device Application. The slit-flow delivery devicewas connected to a stirred chamber to demonstrate an applica-tion of the delivery device. The accuracy of predicting the NOconcentration in an O2 reactive environment was also assessed.The stirred chamber, shown in Figure 3, is stainless steel andwas designed to include a Teflon stir bar. The chamber internaldimensions are 5.5 cm in diameter by 0.8 cm high. Therectangular stir bar (4.4 cm long, 0.6 cm wide, 0.3 cm high) wasfabricated by placing small magnets in each end of the bar andsealing each end with silicone adhesive. The stir bar rotatedaround a screw that held the stir bar in place. The stir barwas 0.3 cm from the bottom of the stirred chamber. Thus, acell culture plate containing adhering cells could be placed inthe bottom of the chamber if desired. The chamber could thenbe utilized to expose cells to steady-state aqueous NO concen-trations for any specified length of time. The aqueous NOconcentration could also be adjusted at any time by changingthe NO gas concentration to which the delivery device isexposed.

PBS was continuously pumped through the delivery deviceand stirred chamber at 3.0 mL/min while the chamber wasstirred at 30 rpm. The device and chamber were connected with15.5 cm of Teflon tubing (0.16 cm i.d.) such that the residencetime of the tubing was 0.1 min. The theoretical residence timeof the 21.0 mL chamber was 7.0 min. A residence timedistribution study confirmed that the stirred chamber was wellmixed and that the measured and theoretical residence timeswere the same. The delivery device was exposed to various NOgas concentrations at both 25 and 37 °C. The outlet NOconcentration of the stirred chamber, which is the same as theconcentration in the chamber for a well-mixed fluid, wasmeasured using an amperometric probe as described above.

Results and Discussion

Aqueous NO Concentration in Exiting Perfusate.The bulk or mixing-cup NO concentration (Cb) in theperfusate at the exit of each delivery device was meas-ured as a function of the NO gas concentration to whichthe semipermeable membranes were exposed. Figure 4shows the measured aqueous NO concentrations atsteady state exiting both delivery devices. The steady-state aqueous NO concentrations were obtained within2 min of changing the NO gas concentration, of whichpart of the time was due to the time required for the NOgas concentration to obtain steady state. The measuredaqueous NO concentrations are shown relative to the NOconcentrations (Co) which would be in equilibrium with

the NO gas. The equilibrium NO gas concentrationswere obtained using NO solubility data as previouslygiven. Model predictions are also shown which aredescribed later.

The average values of Cb/Co at all NO gas exposurelevels were 0.043 ( 0.005 (n ) 28), 0.064 ( 0.008 (n )16), and 0.107 ( 0.011 (n ) 15) for slit flow at 25 °C, slitflow at 37 °C, and tube flow at 37 °C, respectively. Themeasured values were obtained using chemiluminescenceand the amperometric probe for the tube and slit-flowdevices, respectively. In addition, the NO concentrationexiting the tube device at 37 °C was also measured usingthe amperometric probe, with an average value for Cb/Co of 0.120 ( 0.019 (n ) 8) over a similar range of Co.This shows that the NO concentrations as measuredusing the amperometric probe or chemiluminescence aresimilar. Thus, bioavailable NO is exiting the deliverydevices. As shown, Cb/Co is not a function of Co asexpected from model predictions explained later. It isalso evident that the aqueous NO concentration is notsaturated at any of the gas exposure levels, with only amaximum of 10% saturation achieved. A higher percent-age of the saturated conditions was obtained with thetube device as compared to the slit-flow device due to thedifference in geometry, exposure area, and flow velocities.By increasing the membrane exposure area and/or de-creasing the flow rate, the NO concentration relative toequilibrium can be increased. Although at the highestgas exposure level the aqueous NO concentration ap-proached 2 µM, higher concentrations are obtainable byincreasing the NO gas exposure level, adjusting the flowrate, or modifying the delivery device dimensions.

Figure 3. Stirred chamber. The stirred chamber is composed of stainless steel with a Plexiglas cover attached with hex bolts. Thechamber contains a stir bar located 0.3 cm from the bottom of the chamber. The volume of the chamber, with the stir bar in place,is 21.0 mL.

Figure 4. Delivery device NO concentrations at the outlet (Cb)are shown relative to NO concentrations (Co) that would be inequilibrium with the NO gas exposed to the delivery device.Means ( SD are shown as discrete symbols for slit and tubedelivery devices at 25 and 37 °C. The dashed lines representmodel predictions as described in the text.

Nitric Oxide Delivery to Aqueous Solutions Chem. Res. Toxicol., Vol. 11, No. 11, 1998 1349

Model Predictions of Exiting NO Concentration.Although the bulk aqueous NO concentrations weremeasured in the exiting perfusate of both deliverydevices, it is useful to predict the NO concentrations.Predictions would be beneficial for selecting a desired NOconcentration without experimental measurements basedon adjustments in the flow rate or device dimensions (i.e.,membrane exposure area). The value of Cb at thedelivery device exit was predicted using the models forboth the slit-flow and tube geometries. The values of Cb/Co predicted by the models are shown in Figure 4. Themodels show good agreement with experiments for bothdelivery devices at all temperatures studied, irrespectiveof the size and geometry of the delivery device. It isnotable that the model parameters were obtained inde-pendent of the experiments. The general agreement ofthe model predictions with experimental results suggeststhat the models can be utilized to effectively predict theoutlet NO concentrations of the delivery devices. Ifdesired, the models can also be used to obtain the spatialconcentration profiles within the slit or tube.

Delivery Device Application. One application of thedelivery device is the connection of the device to a stirredchamber to maintain a specified NO concentration withinthe chamber for a period of time. The chamber could beused for biological studies in which a specified NOconcentration is desired. For any application, it isimportant to assess the effects of reacting species withNO, such as O2, to predict the NO concentrations to whichbiological systems are exposed. For a small stirredchamber connected downstream of the slit-flow deliverydevice, the steady-state NO concentration in the chamber(Cc) was experimentally measured as shown in Figure 5.The measured aqueous NO concentrations are shownrelative to the NO concentrations (Co) which would be inequilibrium with the NO gas. The steady-state concen-trations in the stirred chamber were obtained in ap-proximately 30 min following the exposure of NO gas tothe delivery device. This time is consistent with eq 6shown below for a step change in the chamber inlet NOconcentration.

A model was developed to predict the NO concentrationexiting the stirred chamber following exposure of thedelivery device to a specified NO gas concentration. The

NO concentration exiting the stirred chamber will be lessthan that coming out of the delivery device because ofthe reaction with O2. For a well-stirred chamber, the NOconcentration in the chamber (Cc) is

The value of Cb, predicted from the delivery device model,was assumed constant in the tubing between the deliverydevice and the stirred chamber due to the short residencetime of 6 s. The rate constant (k) for the reaction of NOwith O2 is 2.1 × 106 and 2.4 × 106 M-2 s-1 at 25 and 37°C, respectively (18). The stirred chamber residence time(τc) is 7.0 min. At steady state when dCc/dt ) 0, Cc ispredictable from eq 6 using the predicted value of Cb fromthe delivery device model. For the model, it is appropri-ate to assume that the aqueous O2 concentration remainsconstant due to its large excess at saturated conditionsas compared to the NO concentration exiting the NOdelivery device. The saturated O2 concentrations are 265and 223 µM at 25 and 37 °C, respectively (11).

The model results for the stirred chamber are alsoshown in Figure 5 for both an oxygenated and a deoxy-genated solution. The model predictions are shown inthe absence of O2 to illustrate the effect that reactivespecies can have on predicting the NO concentration. Itis notable that the oxygenated and deoxygenated modelpredictions approach each other at low NO concentrationssince the reaction becomes less significant with decreas-ing NO concentration. The excellent agreement betweenthe predicted and experimental NO concentrations showsthat NO concentrations are predictable in experimentalsystems as long as the kinetics of significant reactionsinvolving NO are known. The NO concentrations canalso be maintained at steady state.

Conclusions

In view of the importance of delivering predictablequantities of NO to biological systems for investigatingthe biological effects of NO, two simple delivery deviceswere designed. For applications of the delivery deviceto study the effects of NO exposure to biological systems,several methods can be utilized which incorporate thedelivery devices. Cell adhesion (such as platelets) tovarious proteins coated on the permeable membrane canbe studied in the presence or absence of NO delivery toassess the effects of NO on the adhesion process. Thedelivery device can be included in a circulating ornoncirculating loop connected to a stirred chamber toexpose cells in the chamber to steady-state NO condi-tions.

In all designs, it is important to assess the effects ofreacting species with NO in order to predict the NOconcentrations to which biological systems are exposed.NO is a highly reactive molecule and can react withspecies such as superoxide, metal-containing proteins, oroxygen. Previous studies have shown that NO concen-trations resulting from the delivery of NO to oxygenatedculture medium containing serum were predictable whileonly accounting for the reaction with O2 (9). However,if other unknown but significant reactions with NO exist,the models described in this work can be used to providean upper estimate of the NO concentration.

Figure 5. NO concentrations (Cc) at the outlet of a well-stirredchamber exposed to oxygen are shown relative to NO concentra-tions (Co) that would be in equilibrium with the NO gas exposedto the slit-flow delivery device. Means ( SD are shown asdiscrete symbols at 25 and 37 °C. Model predictions accordingto eq 6 are shown for both oxygenated (solid lines) anddeoxygenated (dashed lines) solutions.

dCc

dt)

Cb - Cc

τc- 4k[Cc]

2[O2] (6)

1350 Chem. Res. Toxicol., Vol. 11, No. 11, 1998 Kavdia et al.

Acknowledgment. This work was supportedby a grant from the National Institutes of Health(R15DK51327).

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