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Monitoring of bacteria growth using a wireless, remote query resonant-circuit sensor: application to environmental sensing
Biosensors & Bioelectronics 16 (2001) 305– 312 www.elsevier.com/locate/bios
Monitoring of bacteria growth using a wireless, remote query resonant-circuit sensor: application to environmental sensing K.G. Ong a,1, J. Wangb,1, R.S. Singha,1, L.G. Bachas b, C.A. Grimes a,* a
Department of Electrical Engineering & Materials Research Institute, The Pennsyl6ania State Uni6ersity, 204 Materials Research Lab, Uni6ersity Park, Pennsyl6ania, PA 16802, USA b Department of Chemistry, 217 Chemistry/Physics Building, The Uni6ersity of Kentucky, Lexington, KY 40506, USA Received 23 August 2000; received in revised form 12 December 2000; accepted 1 March 2001
Abstract A new technique is presented for in-vivo remote query measurement of the complex permittivity spectra of a biological culture solution. A sensor comprised of a printed inductor-capacitor resonant-circuit is placed within the culture solution of interest, with the impedance spectrum of the sensor measured using a remotely located loop antenna; the complex permittivity spectra of the culture is calculated from the measured impedance spectrum. The remote query nature of the sensor platform enables, for example, the in-vivo real-time monitoring of bacteria or yeast growth from within sealed opaque containers. The wireless monitoring technique does not require a specific alignment between sensor and antenna. Results are presented for studies conducted on laboratory strains of Bacillus subtilis, Escherichia coli JM109, Pseudomonas putida and Saccharomyces cere6isiae. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Sensor; Biosensor; Complex permittivity; Bacteria; Yeast; Remote query
1. Introduction Microbiological impedance devices (FirstenbergEden and Eden, 1984; Felice et al., 1992; Asami and Yonezawa, 1995a; Markx and Davey, 1999; Felice et al., 1999; Felice and Valentinuzzi, 1999; Noble et al., 1999; Noble, 1999; Owens et al., 1992; Owens, 1985) are routinely used in the food industry and by public health agencies to estimate product shelf life and to screen for microbial contamination. These devices monitor microbial metabolism in growth medium by immersing electrodes directly into the medium and measuring the permittivity and/or conductivity of the medium. While direct characterization techniques offer many advantages, disadvantages include the necessity of test chamber penetration offering the potential for contamination, polarization of the probe electrode, and bubble formation at the electrode surface. Harris and * Corresponding author. Tel.: + 814-865-2262; fax: + 814-8652326. E-mail address: [email protected] (C.A. Grimes). 1 These authors contributed equally to this work.
coworkers (Harris et al., 1987) used a four-terminal impedimetric device to eliminate the effect of electrode polarization, however, the metallic electrodes were still subject to bubble formation. Recently Asami and coworkers (Asami and Yonezawa, 1996; Asami et al., 1996, 1998, 1999) designed an electrode-less method of measuring the impedance of a medium through monitoring the induction current on a pair of immersed inductive coils. Although the described electrode-less method eliminates bubble formation and electrode polarization, physical connections are still required to connect the coils to the electronic instruments offering the unwanted possibility of sample contamination. In this work we present application of a new remote query, wireless-telemetry sensor platform. The sensor, referred to as the LC sensor, consists of a series-connected interdigital capacitor (IDC) and a spiral inductor printed on a thin substrate (see Fig. 1). Referring to Fig. 2, the inductor –capacitor pair has a resonant frequency fo defined as the frequency at which the real portion of the impedance is at maximum amplitude, and a zero-reactance frequency fz defined as the frequency at which the imaginary portion of the
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K.G. Ong et al. / Biosensors & Bioelectronics 16 (2001) 305–312
Fig. 1. (a) The LC sensor. (b) The conductor pattern on the sensor surface.
impedance is zero. The resonant frequency and the zero-reactance frequency are dependent upon the inductance, capacitance and resistive loss of the circuit elements that comprise the LC sensor. As non-magnetic mediums are examined in this work the inductance of the LC sensor remains constant. In contrast, as the complex permittivity of the medium in which the sensor is immersed changes so does the capacitance of the interdigital capacitor, and the associated resistive losses, and these effects shift the resonant frequency and the zero-reactance frequency of the sensor. Consequently, the complex permittivity of a bacteria or yeast culture can be determined by monitoring the changes in the sensor resonant frequency and zero-reactance frequency. The LC sensor is monitored using a loop antenna (Ong and Grimes, 2000), with the antenna impedance spectrum measured using an impedance analyzer. Mutual inductance coupling between the loop antenna and the sensor inductor alters the antenna impedance. Using a circuit model, the resonant frequency ( fo) and zero-reactance frequency ( fz) of the sensor can be extracted from the change in the antenna impedance. Finding the resonant frequency and the zero-reactance frequency of the sensor enables determination of the complex, real and imaginary, permittivity of the medium in which the sensor is immersed; m%− jm¦. The sensor platform enables monitoring m*= r of bacterial growth without any physical connections to the sensor. Furthermore alignment between sensor and monitoring antenna is not important as the resonant frequency and zero-reactance frequency are independent of sensor location and orientation.
In this paper, we present results on the application of the new sensor technology to monitoring the growth of Bacillus subtilis, Escherichia coli JM109, Pseudomonas putida grown in Luria Bertani medium, and Saccharomyces cere6isiae (yeast) grown in a sugar– oatmeal mixture. The permittivity magnitude of the E. Coli, measured using the LC sensor platform, is shown to correlate with optical density measurements.
2. Theory of operation The complex permittivity of the medium in which the sensor is located is calculated from the sensor resonant frequency and zero-reactance frequency using a circuit model. As shown in Fig. 3 the sensor is modeled as an RLC circuit; is the inductance of the
Fig. 2. Typical measured impedance spectra of the LC sensor when the sensor is immersed in the bacteria culture solution. The resonant frequency and zero-reactance frequency are indicated in the figure.
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Rearranging Eq. (5), the zero-reactance frequency of the sensor fz, defined as the frequency at which the reactive portion of the sensor impedance is zero (see Fig. 2), is: z 1 = 2y 2y
fz =
'
1 1 − 2 2 LC R C
(6)
To find the resonant frequency of the sensor fo the real part of Eq. (4) is first differentiated and then equated to zero:
!
"
dRe{ZT} d 2M 2R = =0 d d R− 2RCL + 2L 2
(7)
Fig. 3. Equivalent circuit models for the sensor and the antenna. The antenna is modeled as an inductor La with a driving voltage source Vin. The sensor is modeled as an RLC circuit. The mutual inductance coupling between the antenna and the sensor is represented by two dependent voltage sources V12 and V21.
Solving Eq. (7), the resonant frequency of the sensor is given by:
spiral inductor, C is the capacitance of the sensor IDC, and R represents the resistive loss in the IDC. The antenna is a loop with inductance La. The mutual inductance between the sensor and antenna is represented with two dependent voltage sources V12 and V21. By performing standard circuit analysis (Paul, 1989) on the circuits in Fig. 3, the total measured impedance across the terminal of the loop antenna, ZT, is given as:
Rearranging Eq. (8), the capacitance C can be determined as:
2M 2 ZT =ZA + ZS
R=
(1)
where ZA is the intrinsic impedance of the antenna in Ohms, is the radian frequency in Hertz, M is the mutual inductance between the sensor and antenna in Henrys, and ZS can be found using standard circuit analysis as (Paul, 1989): R 1+j RC
fo =
C=
o 1 = 2y 2y
'
1 LC
(8)
1 L(2yfo)2
(9)
The resistance R can be determined by rearranging Eq. (6):
'
L C(1− (2yfz)2LC)
(10)
In Eqs. (9) and (10), the only two unknows are fo and fz, which are determined from the experiment. The inductance L, in Henrys, can be measured experimentally or calculated using Bryan, 1954:
L =1.39×10 − 6(OD + ID)NL5/3log10 4
OD + ID OD − ID
(2)
(11)
where j is −1, R is the resistance of the resistor in Ohms, L is the inductance of the inductor in Henrys, and C is the capacitance of the capacitor in Farads. A background subtraction is used to remove the intrinsic antenna impedance ZA from the measured response so that (Eq. (1)) becomes:
where OD and ID are the inner and outer diameters of the inductor in meters (see Fig. 1b), and NL is the number of the inductor turns. From Eqs. (9) and (10), the real part of the relative permittivity (m %) r at and the conductivity s can be calculated using Markx and Davey, 1999; Harris et al., 1987
ZS =j L +
ZT =
2M 2 ZS
(3)
2M 2R (R− RCL)2 + 2L 2
|=
2
+j
2M 2( RC(R − 2RCL) − L) (R− 2RCL)2 + 2L 2
(4)
To find the zero-reactance frequency, the imaginary part in Eq. (4) is equated to zero: RC(R− 2RCL)− L = 0
(12)
1 sR
(13)
and
Substituting Eq. (2) into Eq. (3) yields: ZT =
C − ms sm 0
m %r =
(5)
where m0 is the free space permittivity (o0 = 8.854× 10 − 12 Farads/meter), ms is the relative permittivity of the substrate (the substrate is electrically lossless, which is m %s = m %s = 4.1), and s is the cell constant of the interdigital capacitor defined as Endres and Drost, 1991):
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308
s=
2
l(NC −1)K[(1− (a/b) )] 2K[a/b]
1/2
(14)
where a, b and l are the IDC dimensions defined in Fig. 1b, NC is the number of capacitor electrodes, and K is the elliptic integral of the first kind. The imaginary part of the complex permittivity of the medium m %%r can be calculated from s as (Ramo et al., 1984; Markx and Davey, 1999): m %%r =
1 sR omo
(15)
It should be noted that this technique assumes the complex permittivity is equal at fz and fo, an assumption valid for our work as fz and fo are within 1.5% of each other, and we operate between 6 and 9 MHz, which is well below the resonant frequency of the culture medium.
3. Materials and experimental methods B. subtilis, E. coli JM109, P. putida, and S. cere6isiae (yeast) were our laboratory strains. A setup was made to continuously stir the culture solution and maintain a constant temperature using a water bath throughout the duration of the experiment (see Fig. 4). Culture medium, sensor, and the container used for the experiment were autoclaved at 120°C for 15 min prior to the experiment. The growth conditions adopted were as follows. Bacillus was grown in Luria Bertani (LB) medium at 25°C, E. coli was grown in LB medium at 37, 30, and 25°C, and Pseudomonas was grown in LB medium at 25°C. LB medium was obtained from Difco Laboratories (Detroit, MI). Yeast was grown in a sugar–oatmeal mixture (1/2 cup of sugar, 1 cup of oatmeal, and 2 cups of carbon-filtered tap water). A square LC sensor, as depicted in Fig. 1 and comprised of copper lines on a plastic substrate, of side length of
4 cm was used. The antenna was a 6-turn loop antenna with diameter of 9 cm. The sensor and antenna planes were parallel, and the separation between the sensor and antenna was approximately 8 cm. The output power of the antenna was 10 dBm. The impedance spectra were recorded using an HP 4192A Impedance Analyzer controlled through a Macintosh PowerPC via GPIB interfacing. The length of the cable between the antenna and the Impedance Analyzer was calibrated using the open/short calibration method (a built-in function in HP 4192A). The controlling software was written in C++. The sensor surface was protected by spray-coating a thin, : 200 mm, layer of polyurethane and allowed to dry before autoclaving and measurement. The polyurethane coating protected the copper conductor lines from corrosion in the bacteria/yeast culture. The coating was also used to prevent the bacteria/yeast culture, which is an electrically conductive medium, from damping the sensor resonance. The effect of the protective coating on the measurement is accounted for by use of two correction factors, one for m% and the other for m¦, that are a function of the coating thickness, coating permittivity, and medium permittivity. To find these correction factors the complex permittivity of various test liquids, with values ranging from 18–j1.4 to 97–j42 (isopropanal alcohol, glycerol, water with different salt and sugar concentrations), were first measured using a using a strip-line cavity (Waldron, 1964). The liquids were then measured using the polyurethanecoated sensor to determine the uncalibrated complex permittivity. Taking the ratio of the stripline cavity measured values to those obtained using the polyurethane-coated sensor, the correction factors for m% and m¦ at different permittivity values were calculated, from which a calibration function could be determined through curve fitting. The thickness of the protective coatings were determined using a surface profilometer.
4. Results and discussion
Fig. 4. The experimental set up for remote query bacterial growth monitoring.
The growth of the microorganisms was monitored over time, starting from a clear solution to a turbid solution. Fig. 5 shows the correlation between the optical density, measured using a UV-vis spectrometer, and the permittivity magnitude m * (5.66–5.98 MHz) r for E. coli culture at 27°C. The LC sensor can resolve changes in culture permittivity m * of less than 0.01, r corresponding to a culture-growth time increment of approximately 5 s. To monitor the bacteria growth, the changes in the real and imaginary parts of the relative complex permittivity, Dm %r and Dm ¦r were measured. Fig. 6a and b plot Dm %r and Dm ¦r of E. coli, Pseudomonas, and Bacillus cultures over a 48 h period, with the upward trend in
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ture, indicating the E. coli were dying due to the CO. By tracking the permittivity of a culture with time, information on the ambient environment can be obtained. For example, while the permittivity spectra of the E. coli culture decreases upon CO exposure, comparison between multiple cultures of different bacteria or yeast strains could be used to ascertain the relative amounts of different gases in the environment. The growth of yeast during a beer fermentation process was also monitored using the LC sensor platform for 4.5 days, and the results presented in Fig. 9; the permittivity of the starting solution was approxiFig. 5. Comparison between the magnitude of the complex permittivity m * measured using the LC sensor (5.66 –5.98 MHz) and the r optical density (OD) of E. Coli culture at 27°C. The line is a 2 quadratic curve fit: m* r =21.4OD + 48.7OD+ 89.6. The experiment started with a fresh culture, with a time interval between the consecutive data points of approximately 1 h.
permittivity indicating culture growth. The complex permittivities of the three starting solutions are variable, with m %r ranging from 118 to 137 and m ¦r ranging from 19 to 37, and so for comparison starting values have been normalized to zero. The initial difference in the measured m %r values is due to differences in the bacteria concentration of the initial solutions, while the difference in m ¦r is due largely to the difference in number of conducting ions within these bacteria cultures. Among the three bacteria strains E. coli has the fastest growth rate, with an increase of 13.1 in m %r and 2.0 in m ¦r within 48 h. Bacillus has the slowest growth rate with 5.1 increase in m %r and 0.8 in m ¦r within 48 h. Fig. 7a and b plot Dm %r and Dm ¦r with time for E.coli grown at 37, 30 and 25°C. Over the temperature range examined, higher temperature leads to more rapid growth. To study the effect of cell mortality, the complex permittivity of a 36 h at 25°C culture solution of E. coli was first measured, after which the culture solution was heated to 100°C and then cooled back to 25°C. It was found that after heating Dm %r of E. coli decreased from 12.1 to 7.8, a 36% reduction, while the Dm ¦r values showed a 22% reduction (from 1.89 to 1.48). The decrease in the measured permittivity is due to presence of dead cells, which have a leaky cell membrane, hence are less polarizable and less able to transduce electrical signals (Asami et al., 1996). It is known that carbon monoxide inhibits the growth rate of E. coli and other bacteria (Gee and Brown, 1981). Thus the effect of a carbon monoxide environment on E. coli growth was also investigated. E. coli culture was grown at 25°C under carbon monoxide atmosphere. Fig. 8a and b shows a negative relative change in the complex permittivity of the E. coli cul-
Fig. 6. The change in (a) m %r and (b) m ¦r of the Pseudomonas, E. coli and Bacillus cultures grown at 25°C as a function of time.
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5. Performance and limitations For a 4 cm square LC sensor monitored by a 6-turn, 9 cm diameter loop antenna, at power level of 10 dBm, the maximum distance between the sensor and the antenna that led to a detectable signal was found to be 14 cm. The ‘detection zone’, defined as the region where the sensor can be accurately monitored, is plotted in Fig. 10. The basal plane of the sensor can be rotated up to 80° with respect to the basal plane of the loop antenna without affecting operation. The size of the
Fig. 7. The change in (a) m %r and (b) m ¦r of E.coli culture over 48 h at constant temperatures of 25, 30, and 37°C.
mately m *= 85− j21. A LC sensor was immersed r within the fermentation vessel, and continuously monitored during fermentation. Similar to the behavior reported in (Asami and Yonezawa, 1995b), Fig. 9 shows a large step-wise change in Dm %r (step size of Dm %r 3.5) and a smaller step-wise change in Dm ¦r (step size of Dm ¦r 0.7) with culture growth. It should be noted that for many materials, liquids in particular, permittivity correlates with density, and density viscosity. Hence the sensor could also be used as a viscosity sensor once an appropriate calibration has been performed on the test material.
Fig. 8. The change in (a) m %r and (b) m ¦r of E. coli culture when it was exposed to normal atmospheric condition and a pure CO environment. The temperature was held constant at 25°C.
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311
lated fz, and curve-fitted the data points near fo with second-order polynomial functions and then solved for fo (Press et al., 1992); the resolution of m %r and m ¦r was increased to 0.01 and 0.002, respectively. The resolution of the complex permittivity can be further increased by increasing fo or decreasing fstep. It is observed that the stray capacitance effects of metallic structures within, approximately, 5 cm of the loop antenna, see Fig. 1, affects the measured signal. Hence the proposed method appears to be limited to monitoring microorganisms cultured in plastic, glass, or ceramic containers.
6. Conclusions Fig. 9. The change in (a) m %r and (b) m ¦r of the yeast culture during a beer fermentation process at 25°C.
detection zone can be increased by increasing the size of the sensor and antenna, the number of turns of the loop antenna, and the inductance of the sensor (Ong and Grimes, 2000). There is a small error in determining the resonant frequency and zero-reactance frequency associated to the change in mutual inductance coupling between sensor and antenna, which is dependent upon the location and orientation of the sensor relative to the loop antenna. For a moving sensor anywhere within the zone shown in Fig. 10, the error is less than 1% (Ong and Grimes, 2000). The 1% error in fo and fz limits the resolution of m %r and m ¦r to 1.0 and 0.2, respectively. In our experiments the position of the sensor was fixed at all times. Hence the resolution of m %r and m ¦r was higher, limited by the step size increment for the frequency sweep fstep, and the resonant frequency of the sensor fo. In our experiments fstep was 5 kHz, and fo was between 7 to 8 MHz. Using Eqs. (12) and (13), the resolution of m %r and m ¦r were calculated as 0.1 and 0.02. To further increase the resolution we linearly interpo-
Application of a new wireless, remote query sensor platform for the continuous monitoring of biological culture growth has been shown. The sensor consists of a printed-circuit inductor– capacitor pair, the impedance spectrum of which changes in response to the permittivity of the surrounding environment. The sensors are monitored using a loop antenna; hence, no connections to the sensor are required to obtain sensor information. This technique requires no specific alignment or orientation restrictions enabling the monitoring of conditions inside sealed, opaque containers. The LC sensors, which are inexpensively fabricated with printed circuit board technology, can be used on a disposable basis, significantly reducing the chances of sample contamination.
Acknowledgements This work was supported by the National Science Foundation under contracts ECS-9988598 and ECS9875104 (CAG), and by NASA (LGB).
References
Fig. 10. The shape and size of the sensor ‘detection zone’ for a 4 × 4 cm sensor monitored by a 6-turn, 9 cm diameter loop antenna at power of 10 dBm.
Asami, K., Yonezawa, T., 1995a. Dielectric analysis of yeast cell growth. Biochim. Biophys. Acta 1245, 99 – 105. Asami, K., Yonezawa, T., 1995b. Dielectric behavior of non-spherical cells in culture. Biochim. Biophys. Acta 1245, 317 – 324. Asami, K., Yonezawa, T., 1996. Dielectric behavior of wild-type yeast and vacuole-deficient mutant over a frequency range of 10 kHz– 10 GHz. Biophys. J. 71, 2192 – 2200. Asami, K., Yonezawa, T., Wakamatsu, H., Koyanagi, N., 1996. Dielectric spectroscopy of biological cells. Bielectrochem. Bioenerg. 40, 141 – 145. Asami, K., Gheorghiu, E., Yonezawa, T., 1998. Dielectric behavior of budding yeast in cell separation. Biochim. Biophys. Acta 1381, 234 – 240. Asami, K., Gheorghiu, E., Yonezawa, T., 1999. Real-time monitoring of yeast cell division by dielectric spectroscopy. Biophys. J. 76, 3345 – 3348. Bryan, H.E., 1954. Printed inductors and capacitors. Tele-Tech Electronic Ind. 14, 68 – 69.
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Endres, H.E., Drost, S., 1991. Optimization of the geometry of gas-sensitive interdigital capacitors. Sensors Actuators B 4, 95 – 98. Felice, C.J., Valentinuzzi, M.E., 1999. Medium and interface components in impedance microbiology. IEEE Trans. Biomed. Eng. 46, 1483 – 1487. Felice, C.J., Valentinuzzi, M.E., Vercellone, M.I., Madrid, R.E., 1992. Impedance bacteriometry: medium and interface contributions during bacterial growth. IEEE Trans. Biomed. Eng. 39, 1310 – 1313. Felice, C.J., Madrid, R.E., Olivera, J.M., Rotger, V.I., Valentinuzzi, M.E., 1999. Impedance microbiology: quantification of bacteria content in milk by means of capacitance growth curves. J. Microbiol. Methods 35, 37 – 42. Firstenberg-Eden, R., Eden, G., 1984. Impedance microbiology: Innovation in microbiology series 3. Letchworth, Hertfordshire, England, Research Studies Press, Wiley, NY. Gee, D.L., Brown, W.D., 1981. The effect of carbon monoxide on bacterial growth. Meat Sci. 5, 215 –222. Harris, C.M., Todd, R.W., Bungard, S.J., Lovitt, R.W., Morris, J.G., Kell, D.B., 1987. The dielectric permitivity of microbial suspensions at radio frequencies: a novel method for the real-time estimation of microbial biomass. Enzyme Microb. Technol. 9, 181 – 186. Markx, G.H., Davey, C.L., 1999. The dielectric properties of biolog-
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ical cells at radiofrequencies: applications in biotechnology. Enzyme Microb. Technol. 25, 161 – 171. Noble, P.A., 1999. Hypothetical model for monitoring microbial growth by using capacitance measurements: a mini review. J. Microbiol. Methods 37, 45 – 49. Noble, P.A., Dziuba, M., Harrison, D.J., Albritton, W.L., 1999. Factors influencing capacitance-based monitoring of microbial growth. J. Microbiol. Methods 37, 51 – 64. Ong, K.G., Grimes, C.A., 2000. A resonant printed circuit sensor for remote query monitoring of environmental parameters. J. Smart Mater. Struct. 9, 421 – 428. Owens, J.D., 1985. Formulation of culture media for conductimetric assays: theoretical considerations. J. Gen. Microbiol. 131, 3055 – 3076. Owens, J.D., Konirova, L., Thomas, D.S., 1992. Causes of conductance change in yeast cultures. J. Appl. Bacteriol. 72, 32 –38. Paul, C.R., 1989. Analysis of Linear Circuits. McGraw-Hill. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. (Eds.), 1992. Numerical Recipes in Fortran 77, Second ed. Cambridge Press, New York. Ramo, S., Whinnery, J.R., Van Duzer, T., 1984. Fields and Waves in Communication Electronics. Wiley Chapter 13. Waldron, R.A., 1964. Theory of a strip-line cavity for measuring of dielectric constants and gyromagnetic-resonance line-widths. IEEE Trans. Microwave Theory Tech. 1, 123 – 131.
Monitoring of bacteria growth using a wireless, remote query resonant-circuit sensor: application to environmental sensing K.G. Ong a,1, J. Wangb,1, R.S. Singha,1, L.G. Bachas b, C.A. Grimes a,* a
Department of Electrical Engineering & Materials Research Institute, The Pennsyl6ania State Uni6ersity, 204 Materials Research Lab, Uni6ersity Park, Pennsyl6ania, PA 16802, USA b Department of Chemistry, 217 Chemistry/Physics Building, The Uni6ersity of Kentucky, Lexington, KY 40506, USA Received 23 August 2000; received in revised form 12 December 2000; accepted 1 March 2001
Abstract A new technique is presented for in-vivo remote query measurement of the complex permittivity spectra of a biological culture solution. A sensor comprised of a printed inductor-capacitor resonant-circuit is placed within the culture solution of interest, with the impedance spectrum of the sensor measured using a remotely located loop antenna; the complex permittivity spectra of the culture is calculated from the measured impedance spectrum. The remote query nature of the sensor platform enables, for example, the in-vivo real-time monitoring of bacteria or yeast growth from within sealed opaque containers. The wireless monitoring technique does not require a specific alignment between sensor and antenna. Results are presented for studies conducted on laboratory strains of Bacillus subtilis, Escherichia coli JM109, Pseudomonas putida and Saccharomyces cere6isiae. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Sensor; Biosensor; Complex permittivity; Bacteria; Yeast; Remote query
1. Introduction Microbiological impedance devices (FirstenbergEden and Eden, 1984; Felice et al., 1992; Asami and Yonezawa, 1995a; Markx and Davey, 1999; Felice et al., 1999; Felice and Valentinuzzi, 1999; Noble et al., 1999; Noble, 1999; Owens et al., 1992; Owens, 1985) are routinely used in the food industry and by public health agencies to estimate product shelf life and to screen for microbial contamination. These devices monitor microbial metabolism in growth medium by immersing electrodes directly into the medium and measuring the permittivity and/or conductivity of the medium. While direct characterization techniques offer many advantages, disadvantages include the necessity of test chamber penetration offering the potential for contamination, polarization of the probe electrode, and bubble formation at the electrode surface. Harris and * Corresponding author. Tel.: + 814-865-2262; fax: + 814-8652326. E-mail address: [email protected] (C.A. Grimes). 1 These authors contributed equally to this work.
coworkers (Harris et al., 1987) used a four-terminal impedimetric device to eliminate the effect of electrode polarization, however, the metallic electrodes were still subject to bubble formation. Recently Asami and coworkers (Asami and Yonezawa, 1996; Asami et al., 1996, 1998, 1999) designed an electrode-less method of measuring the impedance of a medium through monitoring the induction current on a pair of immersed inductive coils. Although the described electrode-less method eliminates bubble formation and electrode polarization, physical connections are still required to connect the coils to the electronic instruments offering the unwanted possibility of sample contamination. In this work we present application of a new remote query, wireless-telemetry sensor platform. The sensor, referred to as the LC sensor, consists of a series-connected interdigital capacitor (IDC) and a spiral inductor printed on a thin substrate (see Fig. 1). Referring to Fig. 2, the inductor –capacitor pair has a resonant frequency fo defined as the frequency at which the real portion of the impedance is at maximum amplitude, and a zero-reactance frequency fz defined as the frequency at which the imaginary portion of the
0956-5663/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S0956-5663(01)00131-2
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Fig. 1. (a) The LC sensor. (b) The conductor pattern on the sensor surface.
impedance is zero. The resonant frequency and the zero-reactance frequency are dependent upon the inductance, capacitance and resistive loss of the circuit elements that comprise the LC sensor. As non-magnetic mediums are examined in this work the inductance of the LC sensor remains constant. In contrast, as the complex permittivity of the medium in which the sensor is immersed changes so does the capacitance of the interdigital capacitor, and the associated resistive losses, and these effects shift the resonant frequency and the zero-reactance frequency of the sensor. Consequently, the complex permittivity of a bacteria or yeast culture can be determined by monitoring the changes in the sensor resonant frequency and zero-reactance frequency. The LC sensor is monitored using a loop antenna (Ong and Grimes, 2000), with the antenna impedance spectrum measured using an impedance analyzer. Mutual inductance coupling between the loop antenna and the sensor inductor alters the antenna impedance. Using a circuit model, the resonant frequency ( fo) and zero-reactance frequency ( fz) of the sensor can be extracted from the change in the antenna impedance. Finding the resonant frequency and the zero-reactance frequency of the sensor enables determination of the complex, real and imaginary, permittivity of the medium in which the sensor is immersed; m%− jm¦. The sensor platform enables monitoring m*= r of bacterial growth without any physical connections to the sensor. Furthermore alignment between sensor and monitoring antenna is not important as the resonant frequency and zero-reactance frequency are independent of sensor location and orientation.
In this paper, we present results on the application of the new sensor technology to monitoring the growth of Bacillus subtilis, Escherichia coli JM109, Pseudomonas putida grown in Luria Bertani medium, and Saccharomyces cere6isiae (yeast) grown in a sugar– oatmeal mixture. The permittivity magnitude of the E. Coli, measured using the LC sensor platform, is shown to correlate with optical density measurements.
2. Theory of operation The complex permittivity of the medium in which the sensor is located is calculated from the sensor resonant frequency and zero-reactance frequency using a circuit model. As shown in Fig. 3 the sensor is modeled as an RLC circuit; is the inductance of the
Fig. 2. Typical measured impedance spectra of the LC sensor when the sensor is immersed in the bacteria culture solution. The resonant frequency and zero-reactance frequency are indicated in the figure.
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Rearranging Eq. (5), the zero-reactance frequency of the sensor fz, defined as the frequency at which the reactive portion of the sensor impedance is zero (see Fig. 2), is: z 1 = 2y 2y
fz =
'
1 1 − 2 2 LC R C
(6)
To find the resonant frequency of the sensor fo the real part of Eq. (4) is first differentiated and then equated to zero:
!
"
dRe{ZT} d 2M 2R = =0 d d R− 2RCL + 2L 2
(7)
Fig. 3. Equivalent circuit models for the sensor and the antenna. The antenna is modeled as an inductor La with a driving voltage source Vin. The sensor is modeled as an RLC circuit. The mutual inductance coupling between the antenna and the sensor is represented by two dependent voltage sources V12 and V21.
Solving Eq. (7), the resonant frequency of the sensor is given by:
spiral inductor, C is the capacitance of the sensor IDC, and R represents the resistive loss in the IDC. The antenna is a loop with inductance La. The mutual inductance between the sensor and antenna is represented with two dependent voltage sources V12 and V21. By performing standard circuit analysis (Paul, 1989) on the circuits in Fig. 3, the total measured impedance across the terminal of the loop antenna, ZT, is given as:
Rearranging Eq. (8), the capacitance C can be determined as:
2M 2 ZT =ZA + ZS
R=
(1)
where ZA is the intrinsic impedance of the antenna in Ohms, is the radian frequency in Hertz, M is the mutual inductance between the sensor and antenna in Henrys, and ZS can be found using standard circuit analysis as (Paul, 1989): R 1+j RC
fo =
C=
o 1 = 2y 2y
'
1 LC
(8)
1 L(2yfo)2
(9)
The resistance R can be determined by rearranging Eq. (6):
'
L C(1− (2yfz)2LC)
(10)
In Eqs. (9) and (10), the only two unknows are fo and fz, which are determined from the experiment. The inductance L, in Henrys, can be measured experimentally or calculated using Bryan, 1954:
L =1.39×10 − 6(OD + ID)NL5/3log10 4
OD + ID OD − ID
(2)
(11)
where j is −1, R is the resistance of the resistor in Ohms, L is the inductance of the inductor in Henrys, and C is the capacitance of the capacitor in Farads. A background subtraction is used to remove the intrinsic antenna impedance ZA from the measured response so that (Eq. (1)) becomes:
where OD and ID are the inner and outer diameters of the inductor in meters (see Fig. 1b), and NL is the number of the inductor turns. From Eqs. (9) and (10), the real part of the relative permittivity (m %) r at and the conductivity s can be calculated using Markx and Davey, 1999; Harris et al., 1987
ZS =j L +
ZT =
2M 2 ZS
(3)
2M 2R (R− RCL)2 + 2L 2
|=
2
+j
2M 2( RC(R − 2RCL) − L) (R− 2RCL)2 + 2L 2
(4)
To find the zero-reactance frequency, the imaginary part in Eq. (4) is equated to zero: RC(R− 2RCL)− L = 0
(12)
1 sR
(13)
and
Substituting Eq. (2) into Eq. (3) yields: ZT =
C − ms sm 0
m %r =
(5)
where m0 is the free space permittivity (o0 = 8.854× 10 − 12 Farads/meter), ms is the relative permittivity of the substrate (the substrate is electrically lossless, which is m %s = m %s = 4.1), and s is the cell constant of the interdigital capacitor defined as Endres and Drost, 1991):
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s=
2
l(NC −1)K[(1− (a/b) )] 2K[a/b]
1/2
(14)
where a, b and l are the IDC dimensions defined in Fig. 1b, NC is the number of capacitor electrodes, and K is the elliptic integral of the first kind. The imaginary part of the complex permittivity of the medium m %%r can be calculated from s as (Ramo et al., 1984; Markx and Davey, 1999): m %%r =
1 sR omo
(15)
It should be noted that this technique assumes the complex permittivity is equal at fz and fo, an assumption valid for our work as fz and fo are within 1.5% of each other, and we operate between 6 and 9 MHz, which is well below the resonant frequency of the culture medium.
3. Materials and experimental methods B. subtilis, E. coli JM109, P. putida, and S. cere6isiae (yeast) were our laboratory strains. A setup was made to continuously stir the culture solution and maintain a constant temperature using a water bath throughout the duration of the experiment (see Fig. 4). Culture medium, sensor, and the container used for the experiment were autoclaved at 120°C for 15 min prior to the experiment. The growth conditions adopted were as follows. Bacillus was grown in Luria Bertani (LB) medium at 25°C, E. coli was grown in LB medium at 37, 30, and 25°C, and Pseudomonas was grown in LB medium at 25°C. LB medium was obtained from Difco Laboratories (Detroit, MI). Yeast was grown in a sugar–oatmeal mixture (1/2 cup of sugar, 1 cup of oatmeal, and 2 cups of carbon-filtered tap water). A square LC sensor, as depicted in Fig. 1 and comprised of copper lines on a plastic substrate, of side length of
4 cm was used. The antenna was a 6-turn loop antenna with diameter of 9 cm. The sensor and antenna planes were parallel, and the separation between the sensor and antenna was approximately 8 cm. The output power of the antenna was 10 dBm. The impedance spectra were recorded using an HP 4192A Impedance Analyzer controlled through a Macintosh PowerPC via GPIB interfacing. The length of the cable between the antenna and the Impedance Analyzer was calibrated using the open/short calibration method (a built-in function in HP 4192A). The controlling software was written in C++. The sensor surface was protected by spray-coating a thin, : 200 mm, layer of polyurethane and allowed to dry before autoclaving and measurement. The polyurethane coating protected the copper conductor lines from corrosion in the bacteria/yeast culture. The coating was also used to prevent the bacteria/yeast culture, which is an electrically conductive medium, from damping the sensor resonance. The effect of the protective coating on the measurement is accounted for by use of two correction factors, one for m% and the other for m¦, that are a function of the coating thickness, coating permittivity, and medium permittivity. To find these correction factors the complex permittivity of various test liquids, with values ranging from 18–j1.4 to 97–j42 (isopropanal alcohol, glycerol, water with different salt and sugar concentrations), were first measured using a using a strip-line cavity (Waldron, 1964). The liquids were then measured using the polyurethanecoated sensor to determine the uncalibrated complex permittivity. Taking the ratio of the stripline cavity measured values to those obtained using the polyurethane-coated sensor, the correction factors for m% and m¦ at different permittivity values were calculated, from which a calibration function could be determined through curve fitting. The thickness of the protective coatings were determined using a surface profilometer.
4. Results and discussion
Fig. 4. The experimental set up for remote query bacterial growth monitoring.
The growth of the microorganisms was monitored over time, starting from a clear solution to a turbid solution. Fig. 5 shows the correlation between the optical density, measured using a UV-vis spectrometer, and the permittivity magnitude m * (5.66–5.98 MHz) r for E. coli culture at 27°C. The LC sensor can resolve changes in culture permittivity m * of less than 0.01, r corresponding to a culture-growth time increment of approximately 5 s. To monitor the bacteria growth, the changes in the real and imaginary parts of the relative complex permittivity, Dm %r and Dm ¦r were measured. Fig. 6a and b plot Dm %r and Dm ¦r of E. coli, Pseudomonas, and Bacillus cultures over a 48 h period, with the upward trend in
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ture, indicating the E. coli were dying due to the CO. By tracking the permittivity of a culture with time, information on the ambient environment can be obtained. For example, while the permittivity spectra of the E. coli culture decreases upon CO exposure, comparison between multiple cultures of different bacteria or yeast strains could be used to ascertain the relative amounts of different gases in the environment. The growth of yeast during a beer fermentation process was also monitored using the LC sensor platform for 4.5 days, and the results presented in Fig. 9; the permittivity of the starting solution was approxiFig. 5. Comparison between the magnitude of the complex permittivity m * measured using the LC sensor (5.66 –5.98 MHz) and the r optical density (OD) of E. Coli culture at 27°C. The line is a 2 quadratic curve fit: m* r =21.4OD + 48.7OD+ 89.6. The experiment started with a fresh culture, with a time interval between the consecutive data points of approximately 1 h.
permittivity indicating culture growth. The complex permittivities of the three starting solutions are variable, with m %r ranging from 118 to 137 and m ¦r ranging from 19 to 37, and so for comparison starting values have been normalized to zero. The initial difference in the measured m %r values is due to differences in the bacteria concentration of the initial solutions, while the difference in m ¦r is due largely to the difference in number of conducting ions within these bacteria cultures. Among the three bacteria strains E. coli has the fastest growth rate, with an increase of 13.1 in m %r and 2.0 in m ¦r within 48 h. Bacillus has the slowest growth rate with 5.1 increase in m %r and 0.8 in m ¦r within 48 h. Fig. 7a and b plot Dm %r and Dm ¦r with time for E.coli grown at 37, 30 and 25°C. Over the temperature range examined, higher temperature leads to more rapid growth. To study the effect of cell mortality, the complex permittivity of a 36 h at 25°C culture solution of E. coli was first measured, after which the culture solution was heated to 100°C and then cooled back to 25°C. It was found that after heating Dm %r of E. coli decreased from 12.1 to 7.8, a 36% reduction, while the Dm ¦r values showed a 22% reduction (from 1.89 to 1.48). The decrease in the measured permittivity is due to presence of dead cells, which have a leaky cell membrane, hence are less polarizable and less able to transduce electrical signals (Asami et al., 1996). It is known that carbon monoxide inhibits the growth rate of E. coli and other bacteria (Gee and Brown, 1981). Thus the effect of a carbon monoxide environment on E. coli growth was also investigated. E. coli culture was grown at 25°C under carbon monoxide atmosphere. Fig. 8a and b shows a negative relative change in the complex permittivity of the E. coli cul-
Fig. 6. The change in (a) m %r and (b) m ¦r of the Pseudomonas, E. coli and Bacillus cultures grown at 25°C as a function of time.
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5. Performance and limitations For a 4 cm square LC sensor monitored by a 6-turn, 9 cm diameter loop antenna, at power level of 10 dBm, the maximum distance between the sensor and the antenna that led to a detectable signal was found to be 14 cm. The ‘detection zone’, defined as the region where the sensor can be accurately monitored, is plotted in Fig. 10. The basal plane of the sensor can be rotated up to 80° with respect to the basal plane of the loop antenna without affecting operation. The size of the
Fig. 7. The change in (a) m %r and (b) m ¦r of E.coli culture over 48 h at constant temperatures of 25, 30, and 37°C.
mately m *= 85− j21. A LC sensor was immersed r within the fermentation vessel, and continuously monitored during fermentation. Similar to the behavior reported in (Asami and Yonezawa, 1995b), Fig. 9 shows a large step-wise change in Dm %r (step size of Dm %r 3.5) and a smaller step-wise change in Dm ¦r (step size of Dm ¦r 0.7) with culture growth. It should be noted that for many materials, liquids in particular, permittivity correlates with density, and density viscosity. Hence the sensor could also be used as a viscosity sensor once an appropriate calibration has been performed on the test material.
Fig. 8. The change in (a) m %r and (b) m ¦r of E. coli culture when it was exposed to normal atmospheric condition and a pure CO environment. The temperature was held constant at 25°C.
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lated fz, and curve-fitted the data points near fo with second-order polynomial functions and then solved for fo (Press et al., 1992); the resolution of m %r and m ¦r was increased to 0.01 and 0.002, respectively. The resolution of the complex permittivity can be further increased by increasing fo or decreasing fstep. It is observed that the stray capacitance effects of metallic structures within, approximately, 5 cm of the loop antenna, see Fig. 1, affects the measured signal. Hence the proposed method appears to be limited to monitoring microorganisms cultured in plastic, glass, or ceramic containers.
6. Conclusions Fig. 9. The change in (a) m %r and (b) m ¦r of the yeast culture during a beer fermentation process at 25°C.
detection zone can be increased by increasing the size of the sensor and antenna, the number of turns of the loop antenna, and the inductance of the sensor (Ong and Grimes, 2000). There is a small error in determining the resonant frequency and zero-reactance frequency associated to the change in mutual inductance coupling between sensor and antenna, which is dependent upon the location and orientation of the sensor relative to the loop antenna. For a moving sensor anywhere within the zone shown in Fig. 10, the error is less than 1% (Ong and Grimes, 2000). The 1% error in fo and fz limits the resolution of m %r and m ¦r to 1.0 and 0.2, respectively. In our experiments the position of the sensor was fixed at all times. Hence the resolution of m %r and m ¦r was higher, limited by the step size increment for the frequency sweep fstep, and the resonant frequency of the sensor fo. In our experiments fstep was 5 kHz, and fo was between 7 to 8 MHz. Using Eqs. (12) and (13), the resolution of m %r and m ¦r were calculated as 0.1 and 0.02. To further increase the resolution we linearly interpo-
Application of a new wireless, remote query sensor platform for the continuous monitoring of biological culture growth has been shown. The sensor consists of a printed-circuit inductor– capacitor pair, the impedance spectrum of which changes in response to the permittivity of the surrounding environment. The sensors are monitored using a loop antenna; hence, no connections to the sensor are required to obtain sensor information. This technique requires no specific alignment or orientation restrictions enabling the monitoring of conditions inside sealed, opaque containers. The LC sensors, which are inexpensively fabricated with printed circuit board technology, can be used on a disposable basis, significantly reducing the chances of sample contamination.
Acknowledgements This work was supported by the National Science Foundation under contracts ECS-9988598 and ECS9875104 (CAG), and by NASA (LGB).
References
Fig. 10. The shape and size of the sensor ‘detection zone’ for a 4 × 4 cm sensor monitored by a 6-turn, 9 cm diameter loop antenna at power of 10 dBm.
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