2172
Anal. Chem. 1988, 58, 2172-2178
Measurement of 13C02/12C02 Abundance by Nondispersive Infrared Heterodyne Ratiometry as an Alternative to Gas Isotope Ratio Mass Spectrometry Charles S. Irving, Peter D. Klein,* Philip R. Navratil, and Thomas W. Boutton USDAIARS Children’s Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, and Texas Children’s Hospital, Houston, Texas 77030
We report the performance of a prototype nondlspersive Infrared heterodyne ratlometer In the ana&& of seven reference gas samples contalnlng 3.0% COP in alr, and isotopic enrichments from -85 to +329 6%~ vs. PDB as measwed by gas Isotope ratio mass spectrometry. The instrument response in volts-‘ (V-’) varled from -0.51 to 1.22 over the range of -85 to +329L. A mean instrument response wHh a 0.0015 standard deviation (0.375%) requlred 110 s of signal averaging at a 1-s sampllng rate. The callbration curve of instrument response vs. 6%0 was hear over the entlre range and had a slope of 6.003 89 f 0.000 03 (SD), an intercept of -0.168 f 0.005, and a standard error of 0.009. With thls curve, 45 s of data acquloltion at a mean Instrument response of -0.280 V-’ attalned a standard deviation of &1.3%~at -28.7%0. Nondlsperslve Infrared heterodyne ratiometry can anatyre the laccontent of reapiratory gas samples with acceptable accuracy and sensitivity for cilnlcai studies.
The gas isotope ratio mass spectrometer is the most widely used means to determine the isotopic composition of carbon dioxide and in particular the abundance of 13C. Such instrumentation has been of fundamental importance in geochemical, environmental,and ecological studies concerned with variations in natural abundance, as well as in biomedical applications employing compounds enriched in 13C (1). The latter differ from geochemical measurements in two important respects. First, the precision of the isotope ratio is affected by dietary and physiological processes which result in fluctuations in the basal values of respiratory 13C02(2). Second, the large numbers of samples generated require automated sample isolation, purification, introduction, and analysis (3). Even though such instrument capabilities exist, biomedical studies impose further requirements, e.g., high reliability, minimal downtime, low maintenance demands, and facile operation. In 1973, the National Institute of General Medical Science (NIGMS) learned of a novel method for I3C measurement based on a newly patented technique called nondispersive infrared heterodyne ratiometry ( 4 ) . The rising interest in stable isotope usage and the central role of I3C/l2C measurements prompted the NIGMS t~ issue a contract t~ Andros Analyzers, Inc., of Berkeley, CA, in 1975 to design and fabricate a working model for biomedical applications. In 1981, our laboratory responded to a Request for Applications for analytical and clinical evaluation of this instrument and was awarded its custody upon arrival in July 1983. The effort and cost spent to develop this instrument mandated a stringent
* Address correspondence to this author at Stable Isotope Laboratory, Medical Towers Bldg., 1709 Dryden, Suite 519, Houston, TX 77030.
0003-2700/86/0358-2172$0 1.50/0
assessment of its capability in an environment dedicated to I3CO2determinations. The outcome reported here suggests that nondispersive infrared heterodyne ratiometry is the candidate method for 13C abundance measurements in a clinical setting.
PRINCIPLE OF OPERATION Nondispersive infrared heterodyne spectrometry can be used to quantitate components of a gas mixture. Such a spectrometer measures the intensity of a heterodyne signal generated from the partial absorption of amplitude-modulated infrared radiation by a pressure-modulated gas sample. The method does not require monochromatic infrared radiation but does require that the intensity of the radiation transmitted through the sample be selectively modulated at the absorption wavelengths of the gas of interest. This process is accomplished by transmitting radiation through a sample of the gas while the density of the gas is modulated in a sinusoidal manner. The theory of the successive attenuation of infrared radiation that passes serially through density-modulated gas samples is complex and has not been fully analyzed (4). Dimeff (4) treated the case in which light of wavelength X and initial intensity lox is transmitted serially through two optical cells of length l1 and 12 containing gases with mean densities in the light path of p1 and p2 and molecular absorption coefficients of p1and h.The gases are sinusoidally modulated at frequencies w1 and w2, respectively, to produce density changes of Apl and Apz, respectively. The ratio of the intensities of radiation leaving the second cell I x compared with the radiation entering the first cell lox is given by eq 1 (1) ~ A / ~ O= A exp[-(Ao + AI + Ad1
+ P212P2
(2)
A, = plllApl COS wlt
(3)
A2 = p212Ap2
(4)
A0
=P
1 h
COS
Wpt
where A,, is the static component defined by eq 2 and A1 and A2 are the dynamic components defined by eq 3 and 4,respectively. Expansion of eq 1 yields IX/~OX = [ l - (Al A2) ( l / 2 ) ( A l 2 + AZ2+ 2A1A2) - ...I e-& (5)
+
+
which contains a product term, A1A2, that corresponds to additional frequency components of the intensity modulation at the heterodyne frequencies, w1 f w2. The heterodyne signal is denoted by H1,2and is defined at the frequency w1 - w2 by = [(I/ ~ ) P I P z ~ I ~ z A P I ACOS P z (WI - m2)t]e-& (6)
The amplitude of the heterodyne signal is directly proportional to the absorption coefficients of the two gases at wavelength X. The amplitude of the heterodyne signal is also proportional to the lengths of the two optical cells, hl and X2, and to the 0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986 Optical Cell
c
Cell 2
Cell 1
Modulator
Fi
I
'2C02
wo2
Sample
m
m
M
Fl F2
W
Fiz
II
"12
W
W
Frequency Domain Flgure 1. Schematic representation of the generation of fundamental and heterodyne signals. Curves depicting amplitude modulation of transmmed radiation represent the ac compomnt of radktlon Intensity over approximately 100 ms. Symbol definitions are ghren In the text.
W
i3c/12c isotopic ratio of coz. Reference,
(8)
1.
Sample
FR FiZFl.3
W
(7) The principle of nondispersive infrared heterodyne spectrometry is shown schematically in Figure 1. Radiation, uo, is modulated to yield ul, as it is transmitted through an optical cell containing a gas with a mean density p1 that is densitymodulated to Apl at frequency wl. The power spectrum in the frequency domain of the transmitted radiation intensity shown in Figure 1 displays a single fundamental line, Fl, at wl. The partial absorption of intensity-modulated infrared radiation by a second gas sample with density pz at wz results not only in the generation of a second fundamental signal, F2, at wz, but also in two heterodyne signals at wz f wl. The signal at w2 + w1 is not shown in the figure. The intensity of the Hl,zsignal is directly proportional to Ap2, which is the product of the density modulation Ap2 of the entire gas sample and the concentration of the absorbing gas, C2 Nondispersive infrared heterodyne spectrometry can be used for trace gas analysis since the concentration of the molecular species that selectively abcorbs the modulated radiation in cell 2 can be calculated easily from the intensity of the H1,2signal. Nondispersive infrared heterodyne spectrometry can be extended to isotope ratio measurements of carbon dioxide because 12C02and 13C02behave as two distinct molecular species in their responses to the incident IR beam (5). This is due to the absence of significant overlap of individual rotational-vibrational lines in the u3 fundamental vibrational bands of 13C02and 12C02centered at 4.375 pm (2284.5 cm-l) (6) and 4.256 pm (2349.3 cm-') (7),respectively. The simplest form of COP isotopic measurement is shown in Figure 2. Infrared radiation is transmitted through a cell containing l2CO2 modulated at w12 and then through a cell containing 13C02modulated at ~ 1 3 .This produces amplitude-modulated infrared radiation with two fundamental components, F12and FI3,whose amplitudes are given by
W
Frequency Domain Flgure 2. Schematic representation of the simplest use of nondispershre Infrared heterodyne spectrometry for the determination of the
magnitude of the density changes, Apl and Ap2 For a detectable heterodyne signal to be produced, the individual vibrational-rotational lines of the two gas samples must overlap. The problem of interference by other substances is thus reduced and the method can be used to analyze complex mixtures. In practice, infrared radiation from a nondispersive infrared source is passed through a broad-band interference fiter before entering the first optical cell. Therefore, eq 6 must be integrated, as in eq 7, over all wavelengths transmitted through the broad-band interference filter.
FlZ = ~ 1 2 ~ 1 2 A P 1 2
2173
W
FSFR% F13
W
Frequency Domain Flgure 3. Schematlc representatlon of the use of a reference optical
cell in nondisperslve infrared heterodyne ratiometric measurement of the %/12C isotopic enrichment of a sample of C02 compared with that of a reference gas. Bimodulated IR radiation is generated by 12C02and 13C02optical cells, shown in Figure 2. The heterodyne signals generated by the reference cell and the sample cell have the following origins: (1) H,,, (2) Hi2,ri (3) Hi3,rl (4) H12.., and (5) HI^,..
No Hi213 heterodyne signal is generated because the product eq 6 is negligible at all wavelengths in the 4-pm region. When this bimodulated radiation is passed through a C02gas
p12/113 in
sample modulated at w, heterodyne signals at w12 - w, and ~ 1 -3 w, are produced. Their amplitudes are given by
where where AP, is the change in the pressure of the sample gas and C2: and C,U are the concentrations of l2CO2and 13C02in the sample gas. As seen in eq 12, the ratio H13,s/H12,sis proportional to the 13C/12Cratio in the gas sample. In practice, however, variations in Aplz and ApI3restrict the precision and accuracy of the isotope-ratio measurement. A four-cell, four-frequency design employing an internal reference has been used to compensate for instabilities in Aplz and hp13 (5). This method is described schematically in Figure 3. Bimodulated infrared radiation obtained from reference 12C02and l3CO2cells is passed through a third reference cell containing COz with natural isotopic abundances that is modulated (Ap,) at a third frequency, w., This process produces two more heterodyne signals, H12,, and H13.1,at w12 w, and 013 - or, respectively. These signals monitor Ap12 and Ap13 and thus serve as internal references. Subsequent
2174
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986 Reference
,
Sample
Bimodulated IR Source
wS=wR APS
w R ApR
$3 =-$I?
W
W
W
Frequency Domain
Flgwe 4. Schematic representation of the pressure servo mode of nondisperstve infrared heterodyne ratiimetric anaiysis of the ISC/'*C isotopic enrichment of a sample of COP 4sand 9, refer to the phase of the densky modulations of the sample and reference cells, respectively.
transmission of the beam through the sample cell produces (among others) heterodyne signals Hlz, and H13+. In addition, because the sample and reference cells contain 12COzand 13C02,an HsJheterodyne signal is generated at w, - a,. More importantly, however, the 13C/12C ratio of the sample gas, normalized to that of the reference gas, can be derived from the amplitudes of four heterodyne signals as shown in eq 13.
Rs - = - -H13,e H12,s
RI
H12,r
(13) H13,1
Initial isotopic analyses of C02carried out by Andros Analyzers, Inc., were based on this method and utilized four phase-sensitive Ithaco Dynatrac-3 signal analyzers to determine the amplitudes of the four heterodyne signals. In practice, the precision of these measurements was found to be limited by differential drifts in the four signal analyzers
(8). A novel pressure servo scheme, shown in Figure 4, was used by Andros Analyzers, Inc., to overcome these drift problems. In the pressure servo mode, the sample and reference cells are modulated at the same frequency, we = w,; however, the phase of the pressure modulation in the reference cell is shifted by 180° with respect to the sample cell. Only two heterodyne signals are observed and these represent the difference between reference and sample heterodyne signals. As seen in eq 14 and 15, the signal AHlz a t w12 - ws,, is the difference between the H12,,and Hlz, signals, and the signal AH13 at 013 - wsJ is the difference between the H13,s and H13,, signals. In m i 2
Figure 5. Block diagram of the components of the nondispersive infrared heterodyne ratlometer Instrument. See Instrumentation section for a description of components by number. two other observable parameters, A H 1 3 and F13,to yield eq 20, which relates the instrument response, m 1 3 / ( F 1 3 + AP,), defined in arbitrary units, to the absolute difference between 13C/12C isotopic ratios of C 0 2 in the reference and sample gases. The principles of the instrument operated in the pressure servo mode are summarized in eq 20. In practice, the term instrument response = A . H 1 3 / F 1 3 A P r = to express the difference in isotopic content between the sample and reference (Re- R,) has been replaced by isotopic enrichment expressed in delta units (R, - R,)/R,, which approximates the former term since R, approximates 1.0 X In addition to isotope ratio values, the instrument also measures the level of COz in the sample gas. The COz concentration of the sample is determined from the ratio of the pressure modulations in the reference and sample cells given in eq 21, obtained by rearranging eq 16.
= H12,a - Hn,r = P ~ ~ ~ @ P ~ - A@rC,'21r) P ~ C ~ ~ ~ ~ ~ (14)
HI^,^ - H13,r = ~ 1 3 ~ 1 1 3 A ~ 1 3 ( f l ~ C s-' ~@$rl31J ls (15)
APsC,'2ls =
AP,c,121,
(16)
the pressure servo mode, the modulation of the reference cell, AP,,is adjusted continuously to null the AHlz signal. The isotopic composition of the gas in the sample cell can then be derived from the AH13 signal. The intensity of the F13 signal (eq 9) is substituted in eq 15 to yield eq 17. By substituting in eq 17 the expression for AP, (eq 181, derived from eq 16, and rearranging the terms for gas concentrations, one obtains eq 19. Because AP,is monitored continuously by a pressure m13/F13
= p13(flsCsl3ls - Prc1'~1r)
APS =
APrC,'21,/C,'21,
= p13L?LP,1rCr12(Rs - Rr)
(17) (18)
(19) transducer in the reference cell, i t can be combined with the m13/F13
INSTRUMENTATION
The components of the Andros instrument are shown in Figure 5. Infrared radiation obtained from an automobile cigarette lighter, 1, operated at 9 V and 4.5 A passes through a 4.0-4.4 pm interference filter, 2, an optical cell containing 100% natural abundance COz, 3, four pressure-modulated optical cells containing 100% 12C C02 (lZC99.9%) (Monsanto Mound Laboratory HH-3-77-49), 4 , 5 % 13C C 0 2 (I3C 99.3%) (MSD Isotopes, MS-2163) in dry air, 5, 15% COz of natural abundance in dry air, 6, breath sample containing 1.0-4.5% COz, 7, and a second nonmodulated optical cell containing 100% COz of natural abundance, 8. The two nonmodulated cells attenuate the 12Csignal in relation to the 13Csignal. The light path in optical cells 1, 2, and 3 is approximately 2 cm per cell and in 4 is approximately 6 cm. Each cell is fitted with a pair of sapphire windows. The pressure-modulated optical cells act as quarter-wave closed-pipe resonators. In each optical cell, a 10-cm diameter, 10-W full-range speaker (Radio Shack 40-1197) generates an acoustic wave that is channeled through a horn machined in the top of the cell. The four optical cells, whose lengths perpendicular to the light path
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
have been adjusted to achieve acoustic resonance, are driven at 781, 895, 575, and 575 Hz, respectively. The speakers are driven by a k9-V signal obtained from four sine wave generators, 10 and 11, and power amplifiers, 12. Pressure modulation in each optical cell is measured by a pressure transducer, 13, whose voltage and frequency are monitored by a pressure signal demodulator/reference signal generator, 14. To prevent changes in the gas density in the optical cells and consequent effects on the resonance frequency and pressure modulation, the temperature of the optical cells is maintained a t 15 f 0.1 "C by chilled water from a Neslab CFT-33 refrigerated recirculating bath. Infrared radiation is detected by an InSb crystal maintained at -198 "C. In the detector preamplifier 15, the photovoltaic output from the crystal is mixed with four fundamental suppression signals, 16, obtained from the pressure signal demodulator/reference signal generator. These fundamental suppression signals are generated from the pressure transducer outputs and are phase-shifted 180' with respect to the Flz,F13, and ~ 1 - wI2 signals. After being mixed with the fundamental suppression signals, the detector output is biased, amplified, and fed to three signal demodulators. The AHl2-pressureservo system operates in the following manner: a reference signal for AHlz is generated by 14 from the pressure transducer of the comparison cell. The reference signal is used by an Ithaco Dynatrac-3 signal analyzer, 18,to monitor the in-phase and quadrature components of the AHl2 signal obtained from the preamplifier, 15. The pressure servo circuit, 19, controls the signal that is synthesized in 11that drives the comparison cell speaker. The amplitude of the speaker drive is adjusted so that the output from the AH12 demodulator, 18, is minimal. The AH13 heterodyne signal is monitored by another Ithaco Dynatrac-3 signal analyzer, 20, that receives its reference signal from 14. The servo system that suppresses the fundamental signal operates as follows: the preamplifier output is fed into custom-designed fundamental signal demodulators, 21. The amplitude of the F12,F13, and fundamental suppression signals is adjusted by 16 to maintain a low, preset output from the fundamental signal demodulator. Systems 10-21 thus constitute the analog electronics of the original instrument designed by Andros Analyzers, Inc., and operate in the manner described. The data acquisition and computational components perform three major functions: (1) control the gas manifold system; (2) digitize the analog signals from signal demodulators and calculate and time-averagem13/(F13hpr), the instrument response; and (3) calculate breath-test parameters, generate reports and graphics, and document test results. The system consists of a Columbia personal computer, 22, equipped with a 12-bit analog and digital 1/0 system (Data Translation DT2801). The gas manifold system consists of (1) a microprocessorbased valve-controlunit, 25, capable of driving 32 Mini-Mizer 0.5-W air valves (Humphrey M3E1), (2) a 20-port sample-inlet manifold, 27, and a detachable sample-transport unit, 26, consisting of 20 1-L sample collection bags, (3) a manifold of seven cylinders of calibration gases, 28, and (4) a utility manifold and vacuum pump, 29. When the instrument is to be started, the personal computer sends a command via the serial port to the valve-controller unit which, in turn, activates the valves in the utility manifold to evacuate the sample cell, flush with air, and reevacuate the cell. The valve controller then fills the sample cell with 400 mL of calibration gas from the f i t cylinder in the calibration gas manifold. Upon completion of the first set of calibration measurements, the cell is evacuated, flushed, and reevacuated and the next calibration gas is introduced. Upon completion of the seven-point calibration
3
2175
routine, the instrument is ready to analyze samples from the sample inlet manifold in a similar manner. For on-line breath test analyses, the utility manifold is connected directly to the subject's face mask or to a mixing chamber downstream from the mask. The time required to evacuate, flush, reevacuate, and introduce a sample is less than 1 min. Digitization and analysis of analog signals obtained from the analog control electronics and demodulators are carried out in the following manner. One set of A/D conversions is performed on the AP12,M13, AP,,and AP,signals, 17, obtained from 14, the pressure signal demodulator/reference signal generator. These dc signals are proportional to the amplitude of the ac corqponents of the pressure transducer signals. The other 'set of A/D conversions is performed on the quadrature (QAH13) and in-phase (IAHI3)output voltages from the AH13 demodulator, 20, and the quadrature (QF13) and in-phase (IF13) output voltages from the F13 demodulator, 21. Instrument response ( V I ) is calculated as (QAH13' + I ~ 1 3 2 ) ' / 2 / ( ~ , ( Q F 1 3 2ZF132)'/2). Measurements were performed at a rate of one per second; during each cycle the running mean and standard deviation of the averaged instrument response were computed. The standard deviation of the mean is estimated for band-limited Gaussian noise and is given by the square root of the variance divided by U T ,where B, the noise bandwidth, is 0.2 for the 1.25-s time constant of the signal demodulator and Tis the acquisition time (seconds). This cycle is repeated until a specified precision has been achieved or until the signal time has exceeded 4 min. Diagnostic information on the system operation generated by the analog control electronics in the form of an 8-bit digital signal is monitored by the personal computer. The dc output from a temperature probe in the sample cell is also used to monitor the optical cell temperature. Breath test curves are displayed graphically on the video display terminal, 23, and reports are generated with an Epson RX-80F/T dot matrix printer, 24. Data are also archived on floppy d i s h .
+
METHODS AND MATERIALS Materials. 12COz(99.9% 12C) was obtained from Mound 13C02 (99.3% 13C) was Laboratory Monsanto ("-3-77-49). obtained from MSD Isotopes (MS-2163). Compressed air (UN 1002),3.06% COz (natural abundance) in 96.94% air (185107&A), and 5.16% COz (natural abundance) in 94.84% air were prepared by Big Three Industries, Houston, TX, from NF- or USP-grade gases. All gas samples were used without further purification. Calibration Gas Samples. Seven COz concentration gas standards (320 L) ranging from 1to 5% COPin air were prepared by dilution of a sample of 5.15% COz with air. The composition of the resulting mixture was determined by gas chromatography as previously described (9). Seven 13CCOz calibration standards (1140 L) with isotopic enrichments ranging from approximately -85 to +3295 vs. PDB were prepared by the addition of either 12COzor l3CO2to 3.06% COz (13C,-27%0)in air. The final isotopic enrichments of the standards were determined by triplicate geochemical grade mass spectrometric gas isotope ratio measurements (R. Dunbar, Ph.D., Department of Geology, Rice University, Houston, TX). Aliquots (115 L) were transferred to Luxfer C5 gas cylinders in the calibration gas manifold of the Metabolic Carbon Analyzer. Each instrument calibration curve required a 400-mL sample of each of the W02 calibration standards. l3COZCalibration Routine. The seven 13C02standard calibration gases were analyzed in order of increasing enrichment y i n g the following method. the sample cell was evacuated, flushed $th air, reevacuated, filled with calibration standard to a pressure af 5 psi, and then vented to atmospheric pressure. Instrument responses ranged from approximately -0.5 to 1 V-l. Signal averaging was continued until a standard deviation of the mean of 0.0015 V-l of the instrument response was achieved or the accumulation time exceeded 240 s. Upon completion of the seven
2176
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
analyses, linear regression methods were used to determine the standard error, slope, and intercept of the regreasion line, together with the standard deviations and the uncertainty associated with use of the calibration curve for interpolation of instrument response to obtain the isotopic enrichment of a sample. CO, Concentration Calibration Curve. Nylon sample bags fabricated from 0.002 x 54 in. Wrightlon 4500 (452541.5M International Plastics Products, Carson, CA) were f i e d with 5OO-mL aliquots of each of the seven COz concentration standard gas samples,placed on the sample inlet manifold, and analyzed using the method described above. Upon completion of the seven analyses, linear regression analysis of P,/Ps vs. % COzwas carried out on the five samples in the 2-4% C02range and a calibration curve was plotted. Test of Intra- and Intersample Precision. A sample bag was filled with 30 L of 3.05% COz (13C,-26.77~)in air and was attached to one of the ports of the sample inlet manifold. The bag was sampled repetitively over 120 min and analyzed following the same procedure used for the calibration test. After each measurement,the time of sampling,instrument response, standard deviation of the mean, calculated 13C abundance as 7~ vs. PDB, COz concentration, and sample cell temperature were recorded and the measured % vs. PDB was plotted against the time of sample analysis. The mean and standard deviation of each value throughout the run were then calculated and compared with the intrasample standard deviation set for individual measurements. Test of Residual Sample Bias. Two sample bags were filled with 3 L of the -85.57~calibration standard and attached to sample ports 1 and 3. Another sample bag was filled with 3 L of the 329% calibration standard and attached to sample port 2. Five successive samples from ports 1, 2, and 3 were analyzed as described above. Test of the Effect of l80Content on '%O, Measurements. Standard water samples with l80enrichments of 25,100,200,500, and 1000% above natural abundance were prepared by the addition of HzlsO (l8010 atom % excess) to water samples. Oxygen-18 enriched water standards were equilibrated with natural abundance COz, and the resulting l80enrichment of the COzwas determined by using the method described by Schwller et al. (IO). Aliquots of the oxygen-enriched COz samples were placed in Wrightlon sample bags and analyzed as described above.
-29 d3d
5 dB /OIV
-59 -29 d3'i
5
dE /DIV
-59 START
Flgure 6. Frequency domain spectra of preamplifier output of the nondispersive infrared heterodyne ratiometer in the pressure servo mode with acoustic drive to the reference cell (top)off and (bottom) on. The signals observed with reference cell drlve off (top)are (1) H12,s (205 Hz), (2) (269 Hz),(3) F , (575 Hz), (4) F,, (781 Hz), and (5) F I 3(845 Hz). In the pressure servo mode with the reference cell drive on (bottom),note that the AHl2 signal at 205 Hz is nulled and the AH,3 signal (2) at 269 Hz is attenuated with respect to the H,3,8 signal in A. Spectra were obtained with a Hewlett-Packard 3561A dynamic signal analyzer.
RESULTS Demonstration of Nondispersive Infrared Heterodyne Spectrometry Using the Pressure Servo System. Figure 6 (top) displays the semilog plot of the fast Fourier transform (FIT) spectrum in the frequency domain from 175 to 975 Hz. This represents the output of the detector preamplifier signal before demodulation. The spectrum was obtained without acoustic modulation in the reference cell and displays the H1za, H13+,F,, F12, and F13signals at 205, 269,575, 781, and 845 Hz, respectively. Aside from two minor extraneous signals, the frequency spectrum is pure over a range of 40 dl3. Suppression of the F,, Flz,and F13fundamental signals in the detector preamplifier has reduced their intensities to the levels of the heterodyne signals. Operation of the instrument in the pressure servo mode in which the reference cell was driven 180° out of phase with the sample cell (Figure 6, bottom) resulted in the complete nulling of the AHlzsignal at 205 Hz and reduced the intensity of the AHl3 signal a t 269 Hz with respect to the H13#signal in Figure 6A. The additional signals seen in the FFT spectrum have not been assigned, but do not affect the measurement of the AH13 and F13 signals. The F, signal in Figure 6B arises from modulation in both the sample and reference cells. I t is larger and broader than the corresponding signal in Figure 6A, due to the varying pressure modulation in the reference cell that occurs in the pressureservo mode. These spectra demonstrate that the instrument operates in the pressure servo mode, as described in the Principle of Operation and Instrumentation sections. l3CO2 Calibration Curve. The instrument response, AH13/(F13APc), obtained for seven calibration gas standards consisting of 3% C 0 2 in air with 13C isotopic enrichments of
-200
-100
0
100
200
300
400
Delta per mil vs PDB
Flgure 7. Plot of instrument response vs. the isotopic enrichment of calibration gas standards given in units of 6% vs. PDB. Solid line represents the least-squares regression line, whose parameters are given in the text.
-85.5, -26.7, +46.0, +94.1, +124.4, +230.6, and +329.0%0vs. PDB, respectively, is plotted in Figure 7 against isotopic enrichment. Instrument response was linear over the range of 4007~.The data could be fitted to a regression line with slope and intercept of 0.003895 f 0.000027 (SD) (V-'.%o-') and -0.1681 0.0046 V I , respectively. Instrument response, which ranged from -0.51 to 1.2, could be determined with a precision of 0.0015 (standard deviation of the mean) within 110 s of data acquisition for all calibration samples. This response was equivalent to a precision of 0.38700for less than 2 min of data acquisition of a sample containing approximately 3% COB. An additional measure of instrument performance was obtained, when the calibration data were used to estimate the uncertainty of a hypothetical sample at an interpolated re-
*
ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
2177
Table I. Daily Log of ISCCalibration Curve Parameters date
slope
intercept
SE'
6% vs. PDBb
02-20 02-21 02-22 02-25 02-26 02-27 02-28 03-01 03-04 03-05 03-06 03-07 03-08 03-11 03-13 03-14 03-15 03-18 03-20 03-21 03-22 04-08 04-09 05-15
3895 f 27' 3924 f 28 3938 f 29 3312 f 26 3308 f 24 3304 f 26 3323 f 25 3905 f 39 3314 f 29 3293 f 24 3274 f 22 3311 f 27 3271 f 27 3289 f 25 3288 f 31 3253 f 34 3268 f 28 3277 f 25 3275 f 25 3266 f 24 3267 f 31 3180 f 21 3186 f 23 3004 f 17
-1681 f 46 -1670 f 41 -1645 f 48 -1376 f 44 -1299 f 40 -1366 f 44 -1404 f 39 -1504 f 46 -1314 f 49 -1440 f 41 -1318 f 36 -1379 f 46 -1317 f 45 -1175 f 43 -1470 f 36 -1439 f 40 -1480 f 41 -1522 f 41 -1363 f 43 -1397 f 41 -1433 f 52 -1758 f 35 -1748 f 39 -1605 f 20
0.0095 0.0098 0.0100 0.0092 0.0086 0.0092 0.0081 0.0113 0.0102 0.0085 0.0076 0.0096 0.0094 0.0089 0.0086 0.0099 0.0099 0.0086 0.0087 0.0085 0.0109 0.0073 0.0081 0.0049
-28.7 f 1.35 -28.8 f 1.39 -29.2 f 1.41 -43.0 f 1.62 -45.4 f 1.48 -43.4 f 1.61 -42.0 f 1.41 -33.2 f 1.40 -44.8 f 1.80 -41.3 f 1.49 -45.3 f 1.36 -42.9 f 1.67 -45.3 f 1.68 -49.4 f 1.61 -40.4 f 1.36 -41.8 f 1.52 -40.4 f 1.74 -39.0 f 1.51 -43.9 f 1.55 -43.0 f 1.51 -41.8 f 1.93 -32.8 f 1.28 -33.0 f 1.43 -39.8 f 0.83
a Standard error of the regression line. Lark, P. D.; Craven, B. R.; Bosworth, R. C. L. The Handling of Chemical Data; Pergamon Press: Oxford, 1968; Chapter IV. bPDB, Pee Dee belemnite. Standard deviation.
sponse to -0.284 V1.Forty-five 1-s measurements at this instrument response would result in a standard deviation of f 1 . 3 7 ~a t an isotopic enrichment of -28.7% This point on the calibration curve was selected because it represents the lowest 13C abundance normally encountered in respiratory COz. Each time the instrument was turned off after use, it was recalibrated on start up. The effect of powering-up the instrument on the calibration curve parameters as well as the long-term drift in these parameters is seen in Table I. The daily calibration curve parameters obtained over a 1-month period are listed, starting with the calibration curve data displayed in Figure 7. The precision of the slope and intercepts and the standard error of the regression did not vary greatly from day to day over the course of a month. However, slope and intercept did change slightly, which justified automatic recalibration of the instrument on power up. The abrupt change in the slope and intercept from one day to the next is the consequence of operational changes made in the pressure modulation of one of the optical cells. Precision and Sample Analysis Time. To determine the intra- and intersample variation and average sample analysis time under actual operating conditions, repetitive sampling and ratiometric analysis were carried out on a sample of 3% COz (13C, -26.77~)in air over 120 min. Data acquisition was carried out for a minimum of 110 s and terminated when the standard deviation of the instrument response reached 0.0015 (0.375%). Over the course of 120 min, 32 analyses were obtained, with approximately 2 min devoted to data acquisition in each cycle. The 13C enrichments measured are plotted as a function of sampling time in Figure 8. The mean of the 32 measurements was -27.47 f 0.56760, which corresponds to the ability to measure a change of 1.68% at the 3a level. The level of precision attainable with 120 s of signal averaging permits the instrument to carry out on-line measurements of breath 13C02sampled repetitively from a face mask, hood, or mixing chamber. COz Concentration Calibration Curve. The values of APc/AP, (v/v) obtained from analysis of seven COz concentration standards over a range of 1-5% COz in air. The
i -25 /
-351
0
"
20
"
40
"
60
"
'
80
I
100
.
'
120
Time ( m i d
Figure 8. Isotopic enrichments in 6760vs. PDB of repetitive samples of 3% CO, (13C -263%) in air plotted as a function of the sampling time. The solid line designates the mean of the 32 measurements (-27.47%), while the standard deviation of f0.56%0 is designated by the dashed line. This plot demonstrates the rate at which samples can be measured as well as the long-term instrument precision.
Table 11. Memory Effect of Low or High 13CEnrichment Alteration on Sequential Measurements enrichment measd by GIRMS,"%o -85.5 329.0 -85.5 a
L measurement 2 3 4
1
5
std mean, dev, %o L
-85.1 -85.6 -85.9 -88.3 -87.5 -86.5 h1.3 328.1 328.0 331.8 329.0 327.8 328.8 f1.3 -86.5 -86.9 -87.5 -88.2 -88.3 -87.5 f0.8
Gas-isotoDe-ratiomass sDectrometrv.
response was linear over the range of 2-470 COz,in which most breath test samples fall. The regression line through these points had a slope and intercept of 0.3595 f 0.0027 (%-I) and 0.0275 f 0.0085, respectively, with r = 0.999 91. Interpolation of a mean value for APc/AP,of 1.0 (obtained from averaging of 42 1-s readings of AP,f AP,into the calibration curve yields a COz concentration of 2.8585 f 0.0058%. The instrument thus not only provides an estimate of the isotopic enrichment of C 0 2 but also yields a precise estimate of the COz content of the sample. Bias Due to Residual Sample Gases. To determine the magnitude of memory effects resulting from residual gases left in the sample cell from previous analyses, five samples of -85.5% COzwere analyzed followed by five samples of 3297~ COz. The analyses were repeated on a second lot of five samples of -85.5% COz. As seen in Table 11, after five determinations of the depleted COz,no bias toward lower values was detected in the analyses of the first enriched samples. Although a slight bias to more negative values is seen in the second set of determinationson the depleted samples, a similar trend was seen in the first set of analyses of this sample. For all practical purposes, no memory effects could be detected. Interference by C1802,To determine the extent to which 12C180160is detected as 13C160160by the instrument, five samples of 3% C 0 2 (13C,-26.57~)in air were equilibrated with a standard of Hz180 to obtain standards of COz with l80 enrichments of 33.9,94.7,223,513,and 989% vs. SMOW. The apparent 13C enrichments of these samples were -28.7, -25.5, -20.7, -7.9, and +12.7%0,respectively. Linear regression analysis of the apparent 13Cenrichment of COz as a function of the actual l80enrichment of the sample yielded a slope and intercept of 0.043 13 0.00037 and -29.99 0.19, respectively, and a standard error of 0.291. This slope indicates that on a mole fraction basis, the effect of 1zC180160 on the instrument response is 24.1% that of the effect of 13C160160. The sensitivity of the instrument to 1zC180160 probably arises from an overlap of the spectral lines. In practice, any biological
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 11, SEPTEMBER 1986
enrichment of lsO levels in COz would be so small as to have a negligible effect on 13C measurements. Overall Performance Characteristics. The daily start up of the instrument consists of cooling the optical cells to 15 "C, cooling the IpSb detector to liquid Nz temperature, and turning on power to the instrument and computer. If the optical cells are at room temperature, approximately 1h is required to achieve operating temperature. Cooling of the IR detector requires approximately 5 min. Once these temperatures are achieved, the calibration program can be initiated. A t this stage, the instrument can be restarted immediately after a power failure. Calibration of the instrument is completely automatic and requires only that the operator fill the liquid NzDewar.
DISCUSSION Measurements of excess 13C02in breath after the administration of 13C-labeledsubstances have biomedical applications that range from monitoring energy metabolism and substrate utilization to the assessment of organ function. Current gas isotope ratio mass spectrometers have the ability to measure isotopic abundances of 13C to within *0.01%0. In human tracer studies, the excretion of I3C varies with the metabolic fuel being oxidized and this variation has been shown to be *0.7%0 (standard deviation) over a 6-h period. Thus, analytical precisions greater than 0 . 3 4 5 % are of little use in physiological studies with 13C-enriched substrates. Moreover, conventional tracer studies are concerned with relative responses, i.e., changes from base line abundance, so that the requirement for accuracy with which the absolute abundance is determined, typically f0.5-1.0%, is less stringent than in other (e.g., geochemical) applications. Although the developmentof the original instrument system faltered before completion, use of the principle of nondispersive infrared heterodyne spectrometry to determine 13COz/12COz ratios is clearly established by the present instrument. The instrument is capable of measuring 13C abundance over a range of -100 to 320% with a precision of 0.4% and an accuracy of 1 . 3 7 ~within 120 s on a sample of 3% COP No memory effect is displayed, and following our modifications,the instrument has a sample introduction time of 60 s and an overall sample analysis cycle of 3.75 min. Thus the metabolic carbon analyzer is capable of providing rapid
analyses, including on-line measurements of 13Cabundance in respiratory COP. The instrument now has the capability to conduct an automatic seven-pointcalibration, requiring less than 30 min and is equipped with a 20-port sample manifold under computer control. With the experience gained from this assessment, the limitations in the original design that must be overcome have become evident. These include reliance on acoustical resonance and the attendant 400-mL sample requirement, the use of an InSb detector, which must be maintained at liquid N2 temperatures, and, finally, the use of analog technology to demodulate multicomponent ac signals. All of these limitations can be and are being overcome in the hture development of this instrument into a clinically useful system for 13C abundance measurements.
ACKNOWLEDGMENT K. Williams, Andros Corporation, provided substantive background and perspective on original prototype designs. Manuscript preparation by S. Wahl and S. Perez and editorial review by Y. Garza are also appreciated. Registry No. 13C02, 1111-72-4;COz, 124-38-9. LITERATURE CITED (1) Klein, P.; Klein, E. R. J. Pedlatr. Gastroenferol. Nufr. 1085, 4 , 9-19. (2) Schoeller, D. A.; Schnekler, J. F.; Solomons, N.; Watkins, J. B.;Klein, P. D. J. Lab. Clin. Med. 1077, 9 0 , 412-417. (3) Schoeller, D. A,; Klein, P. D. Biomed. Mass Specfrom. 1970, 6 , 350-355. (4) Dimeff, J. 1072, US. Patent 3679899. (5) Davies. D. W. 1977, US. Patent 4 027 972. (6) Herzberg, G. Molecular Spectra and Mdecular Structure; D. Van Norstrand: Princeton, NJ, 1945; Vol. 11, p 274. (7) Nielsen, A. H. fhys. Rev. 1038, 53, 983-985. (8) Wnllams, K., personal communication, 1983. (9) Irving, C. S.; Wong, W. W.; Shulman, R. J.; Smith, E. 0.; Klein, P. D. Am. J . Physiol. 7083, 245, R190-R202. (10) Schoeller, D. A.; van Santen. E.;Peterson, D.; Dietz, W.; Jaspan, J.; Klein. P. 0.Am. J. Clin. Nutr. 1080, 33, 2686-2697.
RECEIVED for review September 30, 1985. Resubmitted January 24, 1986. Accepted May 5, 1986. This work was supported by GM 28783, AM 28129, by the USDA/ARS Children's Nutrition Research Center, Department of Pediatrics, Baylor College of Medicine, and Texas Children's Hospital, and by BCM Technologies, Inc.
