Medical Device Link.

Originally Published IVD Technology June 2004

Processing Technologies

Figure 1. The Sun integrated lancing and blood testing device (Pelikan Technologies Inc.; Palo Alto, CA) with its prototype sensor arrangement (click to enlarge).

During development of macroscopic medical diagnostic devices such as conventional blood chemistry analyzers or flow cytometers, it is usually possible to mount flow sensors, temperature probes, and optical detectors at various positions along the instrument pathway to experimentally determine optimal operational parameters for the device. That approach often fails with microdevices, however. This is because standard sensors and probes are typically of the same scale as the device and interfere so much with its behavior that the measured data do not represent actual device performance. Therefore, the most useful experimental data for diagnostic microdevice development tend to be external measurements from which the internal physics of the device can be induced.

Mathematical modeling of microscale processes is a useful alternative to taking internal measurements. Microscale chemical and physical processes generally follow deterministic physical laws that can be accurately represented in mathematical models, unlike macroscale processes, for which the effects of turbulence must be approximated, and those at the nanoscale level, where fluids do not behave as a continuous material and the physical laws that apply are still debated. Once correlated to external measurements, microscale modeling can predict internal behavior within the microdevice at any point in space and time. New insights and optimization techniques can follow. Many developers of diagnostic microdevices employ this powerful approach of simultaneous modeling and experimentation.

Figure 2. The sensor modeled at the stage following initial contact with the sample. The embedded photo is a close-up of the sensor membrane with the emulsion of hydrophobic microdroplets dispersed in hydrophilic phase. Photo source: University of Virginia (click to enlarge).

The large surface-to-volume ratio that is characteristic of microdevices frequently leads to unexpected process behavior. For example, microvolumes of physiological fluids evaporate, cool, and heat extremely rapidly. Modeling often is necessary to accommodate, or leverage, such heat-transfer and evaporation processes and their impact on the system. And at microdevices’ typical low Reynolds numbers, signifying slow flows, mixing is often problematic. Here, modeling guides the design toward the achievement of mixing requirements.

The modeling of laminar flow is rarely an end in itself, but knowledge of the flow field enables determination of its effect on other important physical processes. The resulting multiphysics model is very useful to experimentalists tasked with sorting out the effects of a microdevice that involves complex physics. Many researchers have used this approach to develop devices for the extraction of analytes from fluids,¹ the measurements of pH, viscosity, and diffusion coefficient,^2-4 quantitative analysis,⁵ and sample preparation.⁶ Others have used it to develop laminate-based microfluidic devices for biomedical applications.^7-9

This article shows how modeling can accelerate the development of diagnostic products, by describing the development of a microfabricated glucose sensor.

A Modeled System

An international team led by Pelikan Technologies Inc. (Palo Alto, CA) and including MicroPlumbers Microsciences LLC (Seattle), with researchers from the University of Virginia (Charlottesville, VA), the Michigan Molecular Institute (Midland, MI), Cranfield University (Silsoe, Beds, UK), Cambridge Consultants Ltd. (Cambridge, UK), and thinXXS GmbH (Mainz, Germany), undertook to develop a novel microfabricated point-of-use glucose sensor to be integrated within an automated low-volume lancet-based blood collection device, the Pelikan Sun. The blood collection device, now in prototype, is optimized to achieve almost painless acquisition of approximately 200 nl of blood per sample (a hundredth of a drop). The integrated glucose sensor was developed to be compatible with such small fluid volumes, as well as to provide a response time below 10 seconds and precision of ±5% over the clinical range. In the prototype, sensors are clustered in units of five for each sample measurement and within a microchannel along which a blood sample flows (see Figure 1).

Table I. Kinetic constants of enzyme reactions, including turnover numbers and Michaelis-Menton constants (click to enlarge).

This is a new type of fluorescence-optical glucose biosensor. The membrane consists of an emulsion that incorporates the enzyme glucose oxidase (GOX) to catalytically consume sample glucose and to coconsume oxygen. The emulsion additionally contains an oxygen-quenchable fluorescent indicator that determines the concentration, and hence consumption, of oxygen within the sensor by exhibiting a change in fluorescence related to the sample glucose concentration. The indicator is carried in hydrophobic droplets dispersed within a hydrophilic matrix containing GOX. Using an emulsion for the membrane makes possible single-step deposition of the sensor, simplifies manufacturing, and maintains optimal microenvironments for the GOX and the fluorescent indicator. Other significant advantages are expected to be realized, such as faster response times.

The sensor model mathematically replicates the significant physical and chemical processes taking place in the sensor and sample (see Figure 2).
Prior to contact between the sample and the sensor layers, the whole blood sample contains red blood cells (RBCs) at a given hematocrit level, plasma, and, dissolved in the plasma, oxygen (bound to hemoglobin inside the RBCs and equilibrated with the surrounding plasma), human catalase (with no significant exchange of catalase between the RBCs and plasma), glucose (which is the analyte), and hydrogen peroxide. The sample is assumed to contain no GOX at this point. Other blood constituents that diffuse into the sensor layer are not expected to have a significant impact on the sensor chemistry at the concentrations they are able to attain within 60 seconds after exposure.

Table II. Glucose solution characteristics (click to enlarge).

Before contact with the sample, the dispersed-phase sensor membrane contains a fluorescent indicator in the form of a ruthenium complex (ruthenium-diphenylphenantroline; Ru(dpp)3 2+) immobilized within microdroplets of a hydrophobic material (a siloxane-containing polymer) that are of known concentration and size distribution and embedded in a continuous hydrogel matrix of known water, polymer, and GOX content (see inset photo in Figure 2). The membrane additionally has an oxygen concentration that is in equilibrium with the atmosphere.

When the sensor is exposed to the sample initially, the diffusion of all species is affected by the presence of the dispersed hydrophobic droplets. The diffusion rate of each diffusing species may be increased or decreased depending on its diffusion and partition coefficient. GOX starts to diffuse out of the sensor and into the sample at a slower rate than the small diffusing species. As the glucose molecules reach the GOX molecules, they are metabolized and converted, with the coconsumption of oxygen and production of hydrogen peroxide, to gluconic acid, which in turn is instantaneously and nonreversibly hydrolyzed to gluconolactone.

The ruthenium complex in the hydrophobic microdroplets is initially in equilibrium with the ambient oxygen concentration, and its fluorescent lifetime is quenched to some degree. As oxygen is consumed by the GOX enzyme reaction, a concentration gradient is generated between the hydrophobic microdroplets and the surrounding hydrogel, causing oxygen to diffuse out of the microdroplets. At the same time, oxygen from the plasma in the sample (which is continuously replenished by the RBCs) is diffusing into the sensor and locally counteracting the reduction in oxygen concentration brought about by the GOX enzyme reaction. The net effect of this activity is a location-dependent reduction in the oxygen concentration in the microdroplets.

Figure 3. The rates of enzyme reactions as a function of cross-sectional distance through sample and sensor after exposure of the sensor membrane to the sample: (a) the rate at which catalase converts hydrogen peroxide back to oxygen and (b) the rate at which GOX metabolizes and converts glucose (click to enlarge).

The fluorescence of the dispersed ruthenium complex within the microdroplets is thus quenched to a value somewhere between the value for ambient and that for 0-mbar oxygen. Fluorescence lifetimes for oxygen-quenched systems tend to be in the low microsecond range. While hydrogen peroxide, a by-product of the GOX reaction in the hydrophilic phase, is also known to be a fluorescence quencher, its concentration within the hydrophobic microdroplets, and thus its quenching effect, is insignificant.

Modeling Methodology

The sensor model mathematically implements the physics just described via a finite-volume method. This is an alternative to the finite-element method. At regular intervals throughout the assay, and simultaneously, the model solves a species conservation equation for each modeled constituent—oxygen, glucose, GOX, catalase, and hydrogen peroxide—that assumes no mass transfer across the outer boundary of the region containing both sample and sensor. The concentration of any of these constituents (f) at any time (t) and at any point in the modeled region with local diffusion coefficient (D) is obtained through its conservation equation, which in vector calculus notation is

ðf/ðt = D—2f + S.

The equation states that the accumulation rate (the term on the left) is the sum of the molecular diffusion and the production/destruction rate, S. The production rates of oxygen, glucose, and hydrogen peroxide are calculated from their stoichiometry and reaction rates either as a Michaelis-Menton reaction (for oxygen and hydrogen peroxide due to catalase)—

1/VMM = Km/(Vmax [O2]) + 1/Vmax
—or a Ping-Pong Bi-Bi reaction (for oxygen and glucose due to GOX)—

1/VPPBB = Kmoxygen/(Vmax [O2]) + Kmglucose/(Vmax [glucose]) + 1/Vmax.

The values of the kinetic constants for these equations are listed in Table I. Production rates are as follows:

• Soxygen = –VPPBB + VMM.
• Sglucose = –VPPBB.
• SH2O2 = VPPBB – 2VMM.

Figure 4. Concentrations of the reactants oxygen (a), hydrogen peroxide (b), and glucose (c) along the sample-sensor interface as a function of location in the sample and sensor. The concentration jump is due to different solubilities in the sample and sensor (click to enlarge).

The sensor model must track the diffusion of each important chemical component of the emulsion and the sample, the chemical reactions between them, and the signal resulting from oxygen depletion. When the oxygen mass-transfer rate in a hydrophobic droplet and the surrounding hydrophilic phase is sufficiently fast, the concentration of oxygen in the two phases will always be close to equilibrium.

The time required for oxygen equilibration in response to a change in oxygen concentration in the surrounding hydrogel was determined from the infinite series solution for unsteady diffusion in a sphere (t Ž R2/[2•DO2]) as 10 milliseconds when the droplets are 5 µm in diameter and the diffusion coefficient of oxygen in the hydrophobic phase is 3.0 ¥ 10–4 mm2/sec. This equilibration time is three orders of magnitude shorter than the assay time. It allows a welcome simplification in that the emulsion can be considered a single continuous material with volume-averaged properties rather than two segregated materials, one for each phase, that require constant updating of the local oxygen flux between them. The volume-averaged properties are diffusion coefficient, partition coefficient, and initial concentration of each modeled chemical species.

Using oxygen concentration in the sensor membrane as an example, the initial millimolar concentration is fAqSO2Aq + fSiSO2Si. The effective partition coefficient is calculated as

HO2 = fAq + fSi • SO2Si/SO2Aq,

and the diffusion coefficient as

DO2 = fAqDO2Aq + fPoly(1 – fSi)DO2Poly + fSiDO2Si,

where fSi is the volume fraction of the emulsion that is siloxane-containing hydrophobic phase and fAq and fPoly are the volume fractions of the hydrophilic phase that are aqueous and polymer, respectively. The diffusion coefficients of oxygen in water, hydrogel polymer, and hydrophobic phase are DO2Aq, DO2Poly, and DO2Si. The solubilities of oxygen in water and in hydrophobic phase at initial conditions are SO2Aq and SO2Si. Actual values of diffusion coefficients and initial concentrations in the glucose solution are listed in Table II. Of the five modeled chemical species, only oxygen is appreciably soluble in the hydrophobic phase. Its diffusion coefficient is 3.0 ¥ 10–4 mm2/sec and solubility in standard atmosphere at 25°C is 2.4 mmol.

Solution of each constituent’s conservation equation at regular intervals throughout the assay, as each constituent is affected by chemical reactions with others, produces the predicted concentrations of oxygen, glucose, GOX, catalase, and hydrogen peroxide throughout the sensor membrane and sample.

Results from Model and Experiment

Information generated by the model and the corresponding experiment for one set of initial conditions and sensor parameters was plotted (see Figures 3–7 and discussion immediately following). Glucose-loaded saline solutions were used to provide tightly controlled samples as data sources.

Enzyme Reaction Rates. The reaction rates for catalase from Aspergillus niger, present in the sensor layer as a contaminant of GOX (see Figure 3a), and for GOX from A. niger (see Figure 3b) as a function of cross-sectional distance through the sample (1 mm) and sensor (0.047 mm) were plotted. The curves in the plot correspond to rates 5, 10, 15, and 20 seconds after simulated exposure of the sensor membrane to the sample. Both reactions occur almost solely in the sensor. Their initial rates are the highest. The GOX reaction is limited to the membrane near the interface where glucose diffuses in from the sample.

Figure 5. The change in fluorescence lifetime of the ruthenium complex as a function of location within the sensor membrane, calculated from oxygen concentration and Stern-Volmer relation (click to enlarge).

Concentrations of Reactants. Experiments have shown that the A. niger enzymes are somewhat immobilized in the sensor emulsion by an as yet unknown mechanism (possibly entrapment), diffusing approximately a thousand times more slowly than if free. This diffusion rate reduction is implemented in the model, which shows that the enzyme concentrations remain essentially constant in the sensor over the assay time. The small amount of enzyme that leaks out into the sample is allowed to diffuse as it normally would in an aqueous solution.

The concentrations of the reactants were modeled (see Figure 4). Oxygen was freely dissolved in the sample and sensor emulsion and hydrogen peroxide and glucose in the sample and sensor hydrophilic phase. These concentrations are affected by both diffusion and the processes of consumption and production through chemical reaction over time. Oxygen concentration in the emulsion is depleted by the GOX reaction. Its decrease in the hydrophobic phase is the cause of the change in fluorescence lifetime. The increase in hydrogen peroxide concentration shown in Figure 4b is produced by the GOX activity; hydrogen peroxide that diffuses into the sample largely escapes the catalase reaction. Figure 4c shows that glucose is consumed as it diffuses into the sensor from the sample.

Fluorescence Lifetime. The change in fluorescent lifetime of the ruthenium complex from the original lifetime when equilibrated with 20% oxygen at 1 atm is calculated from local oxygen concentration and the Stern-Volmer relation (see Figure 5). The change is a function of location in the sensor emulsion layer; there is no ruthenium complex in the sample. It is not perfectly uniform throughout the sensor because the GOX reaction keeps the oxygen in disequilibrium.

Sensor Calibration and Response. The dynamic response of a sensor with good overall response characteristics—fast response, dynamic range in the physiologically important range, and a large enough signal change to be useful—was simulated (see Figure 6). The sensor has a hydrophobic-to-hydrophilic volume fraction of 40/60, has an overall thickness of 47 µm, and is 70% water in the hydrophilic phase.
In the simulated calibration graph (Figure 6a), plotted for different times after initial sensor exposure to the sample, the sensor shows a solid response over the whole glucose range in less than 10 seconds.

Figure 6. Simulated dynamic calibration (a) and response (b) graphs for a modeled glucose sensor (click to enlarge).

Simulated response curves plotted for different glucose concentrations show the sensor reaching a plateau for the high glucose level after less than 10 seconds (Figure 6b). The medium and low glucose levels exhibit an acceptable response over a similar period in kinetic measurement mode. For reference, the normal range of glucose concentration in capillary blood is 3.5 to 6 mmol. The 25-mmol case thus represents an extremely high, critical glucose level. In Figure 6b, the signal for even the high glucose level never reaches 100%, which would be equivalent to complete consumption of all oxygen present in the sensor, but rather attains a steady-state value above 95%. The discrepancy is due to oxygen diffusion from the sample. The fact that oxygen diffusion is relatively minor is advantageous in that the sensor will not display significant sensitivity to variations in oxygen concentrations in the sample.

Experimental test data were taken with a prototype sensor membrane using the same initial conditions and sensor parameters as supplied to the sensor model for Figure 6—a 40/60 hydrophobic-to-hydrophilic volume fraction, thickness of 47 µm, and 70% aqueous hydrophilic phase (see Figure 7). The predicted response (see Figure 6b) agrees with the test data, especially at the higher glucose loading. The data from the prototype membrane display some variability and a reduced dynamic range relative to what was predicted.

Discussion

Figure 7. The experimentally obtained response curve of a sensor designed according to the sensor model predictions displayed in Figure 6b. Source: Cranfield University (click to enlarge).

The international project discussed here—a distinctly new type of glucose sensor with a novel emulsion-based sensing layer—proceeded from abstract concept to working prototypes in only a few months. One reason for this speed and success was the excellent coordination between the experimental teams and the modelers. They worked synchronously on the physical prototypes and mathematical models, using the same proposed sensor parameters and test conditions. Experimental validation strengthened the modeling enterprise, while modeling strengthened the experimental effort by identifying anomalous test results before the testing program could veer off course. Experience showed that the design envelope is more quickly explored when variations from tested conditions are fed to the model, thus adding value to the experimental results.

Nevertheless, it must be noted that the combined modeling and experimental approach is not always the best development path. While computational software is now capable of multiphysics simulations, including chemical reactions, surface binding, heat transfer, diffusion, hydrodynamics, electrokinetics, sedimentation, and mixing of fluids with different viscosities and phases, some processes still are costly to model, are not well represented mathematically, or have poorly defined boundary conditions. And desired physical and chemical properties, especially for novel or unusual materials, can be hard to find.

In addition, very complex models can be prohibitively expensive. They certainly cost much more than an inexpensive experimental series. For example, in the research reported here, it was more cost-effective to test combinations of fluorescent dyes and hydrophobic matrices experimentally in order to optimize fluorescence intensity and decay time.

Several benefits of coordinating experimental and modeling work have been found.

The model was instrumental at the beginning of the development project in predicting that a rapid sensor response of under 10 seconds was indeed possible—this at a time when the experiments were still showing a response time in minutes. (The slow experimental response was due to material incompatibilities that were later corrected.)

In addition, comparison of modeling and experimental results led to discovery that GOX activity at concentrations higher than 5 mmol in the sensor layer became nonlinear with respect to GOX concentration, and that there was an inhibitory effect on GOX activity at those concentrations. This freed the experimental teams from trying to push the GOX concentration in the sensor to the solubility limit.

The experimental teams decided that, because of manufacturing limitations, it would be necessary to design sensors that were less than 50 µm thick. The model, however, had predicted that a sensor of approximately 100 µm thickness would exhibit the optimum balance between response time and cross-sensitivity to sample oxygen. So, the model was exercised repeatedly to explore the design space. It predicted that if the GOX concentration were changed to 3 mmol, it would be possible to achieve a similar balance between fast response time, good dynamic range, and low cross-sensitivity.

A temporarily puzzling phenomenon was explained by the model. The experimental teams had noticed a significant drop-off of glucose signal—an increase in fluorescence lifetime or, more accurately, in hybrid fluorescence phosphorescence lifetime—after only short exposure of the sensor to the sample. Then it was discovered through modeling that the sensor had in fact used up—metabolized—all the glucose in the sample solution. The volume of the sample was subsequently increased.

Ultimately, qualitative design rules were developed, based on model results and experimental corroboration, as follows:
• The thickness of the whole blood sample layer has no significant effect unless the sample layer is very thin (<100 µm) and is not shielded from the atmosphere.
• A thinner sensor will be faster, but oxygen diffusion from the sample will start to be noticeable with sensors thinner than 100 µm. A higher GOX concentration can compensate for this effect. Oxygen- or glucose-controlled GOX behavior is not a function of layer thickness but of the ratio between hydrophilic- and hydrophobic-phase volume and GOX concentration.
• GOX concentration has to be balanced with the hydrophobic-phase volume fraction to ensure a good dynamic range as well as a glucose-controlled reaction mechanism.
• An 80:20 ratio of hydrophilic to hydrophobic phase is ideal, but this can be modified as long as GOX concentration is modified as well. Increasing the ratio produces effects that enhance each other and decrease sensor response time. Glucose diffuses faster in the hydrophilic phase because less-impenetrable hydrophobic material is in the way, and oxygen is removed from the hydrophobic phase more quickly because less stored oxygen is available. Also, the greater preponderance of hydrophilic phase allows more GOX to be used.
• Both layer thickness and the ratio of hydrophilic to hydrophobic phase will have an impact on the overall fluorescence intensity that can be obtained from the sensor.
• A low polymer fraction in the hydrogel—that is, a higher water content—yields sensors with faster response.
• Catalase contamination in the hydrogel layer converts hydrogen peroxide back into oxygen, thus removing half of the oxygen-consuming effect the consumption of glucose had on the hydrophobic layer. GOX with low catalase contamination is consequently required.
• Droplet sizes below 5 µm will ensure that oxygen diffusion inside the droplets is not a controlling parameter.

Conclusion

An exclusively experimental approach of device building and testing is usually not a viable one for development of microscale diagnostic devices, because nanoscale sensors for prototype testing generally are not available. An appropriate combination of prototype modeling and testing is crucial for the rapid development of microanalytical devices for in vitro diagnostic testing.

References

1. MR Holl et al., “Optimal Design of a Micro Fabricated Diffusion-Based Fluid Constituent Extraction Device,” in Micro-Electro-Mechanical Systems (MEMS), proceedings of the ASME International Mechanical Engineering Congress and Exposition, vol. DSC-59 (New York: American Society of Mechanical Engineers, 1996), 189–195.

2. P Galambos, FK Forster, and BH Weigl, “A Method for Determination of pH Using a T-Sensor,” in Proceedings of the 1997 International Conference on Solid-State Sensors and Actuators (Transducers ’97), vol. 1, 535–538 [accessed 14 May 2004], available from Interenet: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=13397&page=9.  

3. P Galambos and FK Forster, “An Optical Micro-Fluidic Viscometer,” in Micro-Electro-Mechanical Systems (MEMS), proceedings of the ASME International Mechanical Engineering Congress and Exposition, ed. CJ Kim et al., vol. DSC-66 (New York: American Society of Mechanical Engineers, 1998), 187–191.

4. P Galambos and FK Forster, “Micro-Fluidic Diffusion Coefficient Measurement,” in Micro Total Analysis Systems, ed. DJ Harrison and A van den Berg, (Dordrecht, Netherlands: Kluwer Academic Publishers, 1998), 299–302.

5. AE Kamholz et al., “Quantitative Analysis of Molecular Interaction in a Microfluidic Channel: The T-Sensor,” Analytical Chemistry 71, no. 23 (1999): 5340–5347.

6. CR Cabrera, B Finlayson, and P Yager, “Formation of Natural pH Gradients in a Microfluidic Device under Flow Conditions: Model and Experimental Validation,” Analytical Chemistry 73, no. 3 (2001): 658–666.

7. BH Weigl et al., “Lab-on-a-Chip Sample Preparation Using Laminar Fluid Diffusion Interfaces—Computational Fluid Dynamics Model Results and Fluidic Verification Experiments,” Fresenius Journal of Analytical Chemistry 371, no. 2 (2001): 97–105.

8. BH Weigl et al., “Design and Rapid Prototyping of Thin-Film Laminate-Based Microfluidic Devices,” Biomedical Microdevices 3, no. 4 (2001): 267–274.

9. RL Bardell et al., “Microfluidic Disposables for Cellular and Chemical Detection—CFD Model Results and Fluidic Verification Experiments,” in Biomedical Instrumentation Based on Micro- and Nanotechnology: Proceedings of SPIE BIOS 2001, ed. RP Mariella Jr and DV Nicolau, vol. 4265-02 (Bellingham, WA: SPIE: The International Society for Optical Engineering, 2001): 1–13.

10. BH Weigl et al., "Standard and High-Throughput Microfluidic Disposables Based on Laminar Fluid Diffusion Interfaces," Proceedings of SPIE BIOS 4626D, no. 72, ed. RP Mariella Jr. and CJ Murphy (2002): 421–428. 

Bernhard H. Weigl, PhD, and Ron L. Bardell, PhD, are cofounders of MicroPlumbers Microsciences LLC (Seattle). They can be reached at bernhardw@microplumbers.com and ronb@microplumbers.com, respectively. Thomas H. Schulte, PhD, is research and development program director at Pelikan Technologies Inc. (Palo Alto, CA). He can be reached at tom.schulte@pelikantechnologies.com. David C. Cullen, PhD, is reader in biophysics and biosensors and academic director at the Institute of BioScience and Technology at Cranfield University (Silsoe, Beds, UK). He can be reached at d.cullen@cranfield.ac.uk.  James N. Demas, PhD, is professor of chemistry at the University of Virginia (Charlottesville, VA). He can be reached at jnd@virginia.edu. 

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