Anal. Chem. 2008, 80, 2097-2104
Tailoring Noise Frequency Spectrum between Two Consecutive Second Derivative Filtering Procedures to Improve Liquid Chromatography-Mass Spectrometry Determinations Shau-Chun Wang,*,† Chiao-Juan Lin,† Shu-Min Chiang,† and Sung-Nien Yu‡
Department of Chemistry and Biochemistry and Department of Electrical Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung, Chia-Yi 621, Taiwan
This paper reports a simple chemometric technique to alter the noise spectrum of a liquid chromatographymass spectrometry (LC-MS) chromatogram between two consecutive second-derivative filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. This technique is to multiply one second-derivative filtered LC-MS chromatogram with another artificial chromatogram added with thermal noises prior to the other secondderivative filter. Because the second-derivative filter cannot eliminate frequency components within its own filter bandwidth, more efficient peak S/N ratio improvement cannot be accomplished using consecutive second-derivative filter procedures to process LC-MS chromatograms. In contrast, when the second-derivative filtered LC-MS chromatogram is conditioned with the multiplication alteration prior to the other second-derivative filter, much better ratio improvement is achieved. The noise frequency spectrum of the second-derivative filtered chromatogram, which originally contains frequency components within the filter bandwidth, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the other regimes, the other second-derivative filter, working as a band-pass filter, is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC-MS chromatograms, of which 5-fold peak S/N ratio improvement achieved with two consecutive second-derivative filters remains the same S/N ratio improvement using a onestep second-derivative filter, are improved to accomplish much better ratio enhancement, approximately 25-fold or higher when the noise frequency spectrum is modified between two matched filters. The linear standard curve using the filtered LC-MS signals is validated. The filtered LC-MS signals are also more reproducible. The more accurate determinations of very low-concentration samples (S/N ratio about 5-7) are obtained via standard addition * To whom correspondence should be addressed. E-mail:
[email protected]. † Department of Chemistry and Biochemistry. ‡ Department of Electrical Engineering. 10.1021/ac702222m CCC: $40.75 Published on Web 02/16/2008
© 2008 American Chemical Society
procedures using the filtered signals rather than the determinations using the original signals. Temporal or spatial signals are often smoothed or filtered prior to extracting their characteristic frequency components. Similarly, the signal and noise spectra of a trajectory or an image can also be modified in frequency domain in order to recognize the temporal or spatial features more clearly. Recently the applications of spectral analysis or noise modification to assist temporal and spatial filters have been used in biomedical engineering technologies such as deciphering the electroencephalographic (EEG) morphology for the control of a brain-computer interface and improving the qualities of digital radiographic images.1,2 Similar approaches can also be utilized in analytical technologies; for instance, the noise spectrum modification technique has been used to improve the LC-MS/MS peak signals.3 This technique multiplies one match-filtered or low-pass filtered chromatogram with another artificial chromatogram of similar peak features containing only thermal noises. These multiplication procedures can smear the bandwidth-limited noise frequency spectrum of a filtered chromatogram to a wider range. As a result, the noise on the modified chromatogram can be more efficiently removed with the second filtering procedure to achieve better signal-to-noise (S/N) ratio improvement. This noise spectrum modification technique has been used to remedy the deficiency of matched filters to remove spike-like noises on liquid chromatographytandem mass spectrometry (LC-MS/MS) signals.3,4 In theory, the above noise spectrum modification is also applicable to implementation with a band-pass filtered chromatogram. The second derivative filter, of which the properties are of a band-pass filter, has been used to suppress the background drifting problem inherent in liquid chromatography-mass spectrometry (LC-MS) chromatograms.5 The second derivative filter (1) Krusienski, D. J.; Schalk, G.; McFarland, D. J.; Wolpaw, J. R. IEEE Trans. Biomed. Eng. 2007, 54, 273. (2) Saunders, R. S.; Samei, E. Med. Phys. 2003, 30, 3006. (3) Wang, S.-C.; Huang, C.-M.; Chiang, S.-M. J. Chromatogr., A 2007, 1061, 192. (4) Wang, S.-C.; Chiang, S.-M.; Huang, C.-M. Anal. Chim. Acta 2006, 556, 20. (5) Danielsson, R.; Bylund, D.; Markides, K. E. Anal. Chim. Acta 2002, 454, 167.
Analytical Chemistry, Vol. 80, No. 6, March 15, 2008 2097
is to perform the cross-correlation of a chromatogram with the second-order derivative profile of a model chromatographic peak. Since the second-order derivative of a fluctuated chromatogram background is zero, the background drifting problem is therefore remedied. In addition, the cross-correlation procedures preserve the original signal peak although the 2-fold differentiation results in the second-order derivative shape of a filtered peak. The frequency response for the second derivative filter shows its bandpass properties. Other groups of signal processing techniques such as wavelet transform and multivariate analysis have also been used to suppress the background shifting of chromatograms or spectrum and improve the S/N ratios of their signal peaks.6-10 These methods usually require more sophisticated software procedures and sometimes tedious trials in their computational procedures. In this paper, we develop a simple chemometric technique to modify the noise frequency spectrum of second-derivative-filtered LC-MS chromatograms via multiplying the filtered chromatogram with the other simulated chromatogram containing only random thermal noises. This simulated chromatogram sc(t) is the summation of a smooth peak s(t) and noise n(t). The features of s(t) are estimated with these of a second-derivative-filtered chromatographic peak sdf(t). When the second-derivative-filtered chromatogram sdf(t) is multiplied by sc(t), the expansion can be expressed as eq 1,
sdf(t)sc(t) ) sdf(t)s(t) + sdf(t)n(t)...
(1)
Because the features of sdf(t) are similar to these of s(t), the first term sdf(t)s(t) maintains the signal peak. Therefore, the tailored noise spectrum of the above multiplication product is mainly contributed to by the second term sdf(t)n(t). The multiplication of two time-dependent waveforms is in equivalence to the convolution between the two frequency spectra of these time-dependent waveforms. The Fourier transform of the multiplication product sdf(t)n(t) to frequency domain is proportional to the convolution of two spectra SDF(ν) and N(ν), which are the Fourier transforms of sdf(t) and n(t), respectively,
∫
[sdf(t)n(t)] exp(-iωt) dt ) 1 2π
∫SDF(v)N(ω - v) dv...
(2)
Because the second derivative filter works as a band-pass filter, SDF(ν), the Fourier transform of a second-derivative-filtered peak, therefore only contains the frequency components of a narrow band. SDF(ν) is estimated as a Gaussian profile in Figure 1A. The profile of N(ν), the Fourier transform of random noises n(t), is a flat line in Figure 1B. Figure 1C shows, although SDF(ν) covers only a limited range of frequency, the convolution of SDF(ν) with a flat line N(ν) results in a wider frequency spectrum. Therefore, (6) Visentini, J.; Kwong, E. C.; Carrier, A.; Zidarov, D.; Bertrand, M. J. J. Chromatogr., A 1995, 712, 31. (7) Gemperline, P. J.; Cho, J. H.; Archer, B. J. Chemom. 1999, 13, 153. (8) Bernabe-Zafon, V.; Torres-Lapasio, J. R.; Ortega-Gadea, S.; Simo-Alfonso, E. F.; Ramis-Ramos, G. J. Chromatogr., A 2005, 1065, 301. (9) Shao, X.; Cai, W.; Pan Z. Chemom. Intell. Lab. Syst. 1999, 45, 249. (10) Felinger, A.; Kare, M. Chemom. Intell. Lab. Syst. 2004, 72, 225.
2098 Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
Figure 1. (A) The simulated frequency spectrum of one secondderivative filtered chromatographic peak. (B) The simulated frequency spectrum of the thermal noise. (C) The convolution results of the spectra in parts A and B.
on the modified chromatogram, its noise spectrum is spread to a wider frequency regime. Because the noise spectrum is no longer squeezed at the frequency regime within a narrow band, the other second derivative filter efficiently removes more noise to obtain higher S/N ratio peaks. On the other hand, because the dc and low-frequency components on the noise spectrum of the conditioned chromatogram remain suppressed, the baseline of the final chromatogram was therefore not fluctuated or shifted. The noise modification steps can be implemented between two second-order derivative filters to develop more efficient filtering procedures. Intensity adjustment and position correction steps are sometimes needed after each set of filtering or modification steps. Figure 2 shows the flow chart describing these procedures. The computation procedures will be discussed in the Experimental Section in more details.
Figure 2. The flow chart shows the filtering procedures using the noise modification steps between two second-order derivative filters.
To demonstrate that these noise-modification based filtering procedures are applicable to improve the signals on LC-MS chromatograms, pharmaceutical samples spiked in the matrix of polymer suspension solutions are purified and then injected into the LC-MS to acquire chromatograms. The chromatograms are processed with the noise modification procedures to show the improvement of the signal-to-noise (S/N) ratio and the signal reproducibility. The processed chromatographic signals are also used to validate the standard curve linearity and to determine the sample concentrations. EXPERIMENTAL SECTION Materials. Chemicals such as desipramine and diphenhydramine are obtained from Sigma. Acetonitrile solvent was purchased from J.T. Baker (Phillipsburg, NJ). The acetic acid reagent is obtained from Tedia Company Inc. (Fairfield, OH). The chromatographic column used in this study is C8 Luna (5 µm; 2 mm × 50 mm) from Phenomenex (Torrance, CA). Ibuprofen suspension liquid from U-Liang Pharmaceutical company (Taiwan) is used as the matrix of the polymer suspension solution. Apparatus. Samples are dissolved in acetonitrile/0.1% acetic acid solution (50/50, v/v) and then loaded into the vials of an automated injection system (400 Standard, Varian, CA). The elution of liquid chromatography is driven with a ProStar 220 isocratic solvent delivery system (Varian) at a flow rate of 0.2 mL/ min. The mobile phase composition is the same as that of the injection solvent. Injection volumes of 20 µL are used whereas a triple quadrupole mass spectrometer system Quattro Ultima (Micromass, U.K.) is used to acquire the LC-MS/MS signals. The mass spectrometer is equipped with a Z-spray electrospray ionization source. Typical source conditions are as follows: capillary 2.5 kV; source temperature 100 °C; desolvation temperature 350 °C; cone gas flow 100 L/h; desolvation gas flow 500 L/h. The first and third stages of the quadrupole mass analyzers
are set to follow the fragmentation transition of the precursor ion at m/z 256 to the product ion at m/z 166, to detect diphenhydramine of which the most abundant isotopic molecular weight is calculated as 255.4. Similarly, the mass analyzers are also used to follow the transition of m/z 267 f 72 to detect desipramine of which the most abundant isotopic molecular weight is calculated as 266.3. Both quadrupole analyzers are set at LM (low mass) resolution 12 and HM (high mass) resolution 12, providing a resolution ∆m/z approximately equal to 1.0 at full width at halfmaximum (fwhm) when tracing the above fragmentation transitions. The ion energy settings of the first and second stage quadrupole mass filters are 1.0 and 0.5, respectively. The photomultiplier voltage is set as 650 V. Ion signals are recorded in the positive multiple-reaction-monitoring (MRM) mode with the following conditions: interchannel delay 0.02 s, mass span 0 amu, dwell time 0.07 s, and recording time 5.0 min. The collision cell parameters are as follows: collision gas is argon (purity 99.9%); collision energies are set at 10 and 20 eV to induce the fragmentation reactions of m/z 256 f 166 and m/z 267 f 72, respectively; pirani pressure is kept at 1.8 × 10-3 mbar. The mass spectrometer is controlled with Masslynx 3.5 to acquire the LC-MS chromatograms. Data are exported from a Masslynx file into a personal computer for processing with software codes developed in our laboratory using the MATLAB 6.1 (Mathworks, MA) package. The details of the processing procedures are described in the following section. Sample Preparations and Standard Curve Establishment Procedures. Stock solutions are prepared using the mixture solution of methanol and ammonium acetate (pH 4; 0.1% w/w) at the ratio 1:1. Both diphenhydramine and despiramine of 1.0 mg are dissolved in the above mixture solution of 10 mL to prepare stock solutions of 100 µg/mL. The stock solutions of diphendydramine and despiramine are diluted to prepare working solutions at 1 and 10 µg/mL, respectively. The adequate amounts of the diphenhydramine working solution are spiked into 10 µL polymer suspension solution and diluted to 1.0 mL with 50% acetonitrile solution to prepare standard samples at the concentrations 1, 10, 50, 75, and 150 ng/mL, respectively. Each standard sample of 1.0 mL is mixed with 50 µL of sodium carbonate (1 M; pH 11). The organic solvent mixture of about 1.0 mL consisted of n-hexane, dichloromethane, and isopropyl alcohol (20:10:1 v/v/v) and is added into the mixture and shaken for 5 min. The diphenhydramine extract is siphoned after 5 min centrifugation (5000 rpm). The extracts are dried down using nitrogen gas at room temperature and dissolved in 50% acetonitrile to 1.0 mL to determine with the LC-MS instrument. Similarly, the adequate amounts of the despiramine working solution are spiked into 10 µL of polymer suspension solution and diluted to 1.0 mL with 50% acetonitrile solution to prepare standard samples at the concentrations 10, 20, 50, 75, 150, and 200 ng/mL, respectively. Each standard solution at the amount of 200 µL is filtered using 0.22 µm filtration membrane and diluted to 1.0 mL prior to LC-MS determination. Standard Addition Method Procedures. Each of the five purified aliquots of the 5 µL spiked diphenhydramine sample at 0.8 or 3.2 ng/mL and the spiked despiramine sample at 5 ng/mL is filled into five vials labeled as A, B, C, D, and E. Standard solutions of the same concentration of 0, 5, 10, 15, and 20 µL are added into the vials A, B, C, D, and E, respectively. The mobile Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
2099
phase solvents are then filled into the vials to adjust the final total volumes of each vial to 25 µL. Each sample is loaded into the LC-MS to acquire its chromatogram. The chromatographic peaks are processed with the noise modification procedures to obtain the improved signal intensities. These intensity values are used to obtain one linear curve at various addition volumes via regression procedures. This curve is extrapolated across the addition volume axis. The value of the crossing point (Vc) is used to estimate the sample concentration (Cs) using eq 3
Cs ) VcCstd/Vs ...
(3)
where Vs is the sample aliquot volume and Cstd is the concentration of the standard solution. Signal Processing Procedures. Like the filtering procedures described in the flow chart (Figure 2), LC-MS chromatograms of diphenhydramine or despiramine samples are first processed with second-derivative filter procedures. As illustrated in eq 4, the cross correlation between the analyte chromatogram Chrom(t) and one reference signal ref1(t) is computed.
SDF1(t) )
∫chrom(t)ref (t + τ) dτ ...
∑chrom(T )ref (T j
1
i+j)
...
(5)
j
where j ) 0, 1, 2, ..., k and i range from -k to +k. When i + j < 0, ref1(Ti+j) ) ref1(Tj+k) and when i + j > k, ref1(Ti+j) ) ref1(Tj-k). When the parameters of ref1(t) including the peak center tc, width 4σ, and height A1 are specified,
{ [
ref1(Ti) ) A1 exp -
]}
(Ti - tc)2 2σ2
′′
...
(6)
where exp(Ti) represents the exponential function of Ti and the superscript ′′ represents the second-order derivative of this exponential function. ref1(Ti) in eq 6 can be also rewritten as
ref1(Ti) )
( )[
A1 (Ti - tc)2 σ2
σ2
] [
- 1 exp -
]
(Ti - tc)2 2σ2
... (7)
When eq 7 is substituted into eq 5, SDF1(Ti) can be expressed as 2100
∑
{( )[
chrom(Tj)
j
A1 (Ti+j - tc)2 σ2
σ2
[
exp -
]
-1 ×
]}
(Ti+j - tc)2 2σ2
... (8)
Because the original chromatograms contain only a finite number of data points (k), the intensities of filtered chromatogram points at the center will inevitably be much larger than those at the edge. Therefore, the filtered chromatogram is adjusted with a normalization function, which is the cross correlation result between one flat-line of unity and the reference signal, ref1(Ti).
NSDF1(Ti) )
∑C
j
j
{( )[
SDF1(Ti)
A1 (Ti+j - tc)2 σ2
σ2
] [
- 1 exp -
]}
(Ti+j - tc)2 2σ2
... (9)
(4)
1
In eq 4, this reference signal ref1(t) is one simulated chromatogram with the second-derivative curve of a Gaussian peak. The peak center tc, width 4σ, and height A1 of this Gaussian peak are estimated with the features of the LC-MS peak obtained with analyte standards of high concentration (100 ng/mL or higher). In practice, to compute the cross-correlation of two digitized chromatograms of total length k points Chrom(Tj) and ref1(Ti), the following equation can be used.
SDF1(Ti) )
SDF1(Ti) )
Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
where all Ci are equal to 1. Equation 9 results in a digitized chromatogram of length 2k + 1. To adjust the shifted retention time, T0 is designated as retention time t ) tc,
ANSDF1(Ti) ) NSDF1(Ti + tc)...
(10)
Also, only the points ANSDF1(T0) to ANSDF1(Tk) are kept for further processing. The multiplication product result of the filtered chromatogram with another simulated chromatogram, which contains the second derivative curve of one Gaussian peak added with additional thermal noises, is obtained.
MP(Ti) ) ANSDF1(Ti)[ref2(Ti) + N(Ti)]...
(11)
where the term MP(Ti) represents the multiplication operation and the operation result, respectively. In eq 11, ANSDF1(Ti) is the same computation result as that in eq 10. The signal ref2(Ti) is also the cross-correlation function between one Gaussian peak and its second derivative curve. The peak center tc, width 4σ, and height A1 of this Gaussian peak are estimated with the features of the LC-MS peak Chrom(Tj) in eq 5. The term N(Ti) represents the random noises added on the Gaussian peak ref2(Ti). The noises N(Ti) are generated with a random number generator of the distribution function that is normal with the zero mean. The variance of this distribution function is the one-tenth of the ref2(Ti) peak height. Similarly, when the parameters of ref2(t) including the peak center tc, width 4σ, and height A1 are specified and the correlation result is intensity-normalized,
ref2ua(Ti) )
∑A j
1
{ [
]} { [
2
exp -
(Tj - tc) 2σ2
∑C j
{ [
(Ti+j - tc)
A1 exp -
exp -
j
]}
2σ2
′′
(Ti+j - tc)2 2σ2
]}
2
CAMP(Ti) ) AMP(Ti)sign(Ti)...
... (12)
The corrected chromatogram is processed with the matched filter procedures one more time to obtain the final results.
SDF2(Ti) )
ref2(Ti) ) ref2ua(Ti + tc)...
SDF2(Ti) )
∑A
MP(Ti)
...
(14)
|ref2(Ti)| + 〈N〉
where |ref2(Ti)| represents the absolute value of ref2(Ti) and AMP(Ti) indicates the adjustment result. When ref2(Ti) is substituted with eq 13, eq 14 becomes
AMP(Ti) )
|{( )[
(Ti - tc)
4σ2
4σ2
] [
- 1 exp -
]}|
(Ti - tc)2 8σ2
... (15) + 〈N〉
ref2(Ti)
...
|ref2(Ti)|
{ [
]} { [ ]} ∑ { [ ]}
exp -
1
(Tj+k - tc)2
A1 exp -
2σ2
Ck exp -
Ti+j+k2 2σ2
′′
Ti+j+k2
(14)
where |ref2(Ti)| also represents the absolute value of ref2(Ti). The corrected multiplication product CAMP(Ti) becomes
′′
(17)
...
2σ2
Because AMP(Ti) also contains high frequency noises, the other second-derivative filter is able to accomplish efficient noise reduction. When the amplitudes of all CAMP(Ti) have been normalized via similar procedures to those in eq 7,
NSDF2(Ti) )
∑C
{
∑A
i
j
{ [
1
SDF2(Ti)
]} { [ ]} ∑ { [ ]}
exp -
(Tj - tc)2 2σ2
Ci exp -
j
A1 exp -
Ti+j2
Ti+j2 2σ2
′′
2σ2
}
′′
... (18)
where all Ci in eq 18 are equal to 1 and the parameters A1, tc, and σ are the same as those in eq 12. Similarly the positions of Ti are shifted toward the positive direction by tc.
ANSDF2(Ti) ) NSDF2(Ti + tc)...
Because eq 15 only results in intensity adjustment, the noise frequency range of AMP(Ti) should be similar to that of MP(Ti). However, because ANSDF1(Ti) and ref2(Ti) contain similar curve features, the value of each MP(Ti) in eq 11 is always positive. The curve features of the second derivative function ref2(Ti) is therefore distorted. To remedy this feature distortion, AMP(Ti) is multiplied with a sign correction function sign(Ti),
sign(Ti) )
(16)
i
k
Tj
A2
i+j)...
∑CAMP(T ) × j
(13)
Only the points ref2(T0) to ref2(Tk) are kept for further processing. In eq 11, the second-derivative filtered chromatogram ANSDF1(Ti) with the noises containing the frequencies only within the filter bandwidth is multiplied with a simulated second-derivative curve containing random noises N(Ti), and the modified chromatogram MP(Ti) no longer contains only the noise frequencies within the filter bandwidth. The noise frequency spectrum range of MP(Ti) becomes wider via this modification. Equation 14 shows that each point on the modified chromatogram MP(t) is then divided by the summation of its corresponding point on the simulated chromatogram ref2(t) and the average intensity of noises 〈N〉 to adjust the exaggerated peak intensity.
MP(Ti)
2
j
The reference signal ref2(Ti), the same as that in eqs 12 and 13, is used in the other second-derivative filter procedures. When eqs 12 and 13 are substituted into eq 16, SDF2(Ti) becomes
k
2
∑CAMP(T )ref (T j
where the superscript ′′ represents the second-order derivative of this exponential function. The cross-correlation function in the denominator is used to normalize the intensities. Equation 12 also results in a digitized chromatogram of length 2k + 1. To adjust the shifted retention time, T0 is designated as retention time t ) tc,
AMP(Ti) )
(15)
′′
(19)
Also only the points ANMF2(T0) to ANMF2(Tk) are kept. These filtering procedures are able to maintain the signal intensity linearity. When the signal peak Chrom(Tj) in eq 4 is multiplied by a factor k, the same multiplication k will appear in the final results of ANMF2(Ti) in eq 17. RESULTS AND DISCUSSION Figure 3A shows one LC-MS chromatogram, obtained with the diphenhydramine sample (1 ng/mL). The signal peak on this chromatogram has a S/N ratio of approximately 3. The secondderivative filtered chromatogram, of which the signal peak has S/N ratio of 14, is shown in Figure 3B. The S/N ratio improvement is about 4.6 times. This improvement result is close to the ideal case about 5.0 times, which can be estimated using the formula Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
2101
Figure 3. (A) LC-MS chromatogram of diphenhydramine (1 ng/mL). (B) LC-MS chromatogram of part processed with matched filter. The imbedded graph shows the frequency spectrum of chromatogram in part B. (C) Intensity-adjusted chromatogram via performing the multiplication using part with another simulated chromatogram, containing a second-derivative curve of one Gaussian peak with thermal noise. The imbedded graph shows the frequency spectrum of chromatogram in part C. (D) Final LC-MS chromatogram via processing (part C) with the other secondderivative filter.
0.38xd, where d is the number of data points within the chromatographic peak.3,4 As the introduction section points out, the second-derivative filter works as a band-pass filter. The second filtering process immediately following the first filter therefore provides only negligible improvement (filtered chromatogram not shown). Figure 3C shows the intensity-adjusted results of the multiplication product of the chromatogram in Figure 3B with another simulated chromatogram. This adjusted chromatogram contains a second-derivative curve of one Gaussian peak with the features similar to those in Figure 3B. The conditioned chromatogram in Figure 3C shows the S/N ratio of the signal peak similar to that in Figure 3B, but the noise pattern is significantly different from that in Figure 3B. The appearance of noise in Figure 3C shows more high-frequency components. Like the previous discussion, when the noise spectrum of the conditioned chromatogram is shifted toward other frequency ranges outside the filter bandwidth, the other second-derivative filter procedures are able to eliminate noises more efficiently. Consistent with our prediction, the final chromatogram (Figure 3D) indeed shows better S/N improvement. The S/N ratio of the peak in Figure 3D 2102
Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
is close to 70, indicating the improvement result is almost 25fold. Table 1 illustrates the results of the diphenhydramine LCMS chromatograms processed by two consecutive secondderivative filter procedures with and without performing additional multiplication steps prior to the second filtering computation. Similar to the result shown in Figure 3D, the diphenhydramine S/N ratio improvement results with noise conditioning steps are between 23 and 30 times approximately. The ratio improvement results without noise conditioning are similar to the results in Figure 3B, 4.0-5.2 times. Table 1 also lists the results of the despiramine LC-MS chromatograms (10 ng/mL), on which the signal-to-noise ratios of the original peaks are about 6-7, processed by two consecutive second-derivative filter procedures with and without performing additional multiplication steps prior to the second filtering computation. The S/N ratio improvement results of despiramine with noise conditioning steps are between 30 and 46 times approximately, somewhat higher than the diphenhydramine results. The ratio improvement results without noise conditioning are still similar, 4.4-5.3 times.
Table 1. Signal-to-Noise Ratio (SNR) Improvement Results of Diphehydramine and Despiramine LC-MS/MS Chromatograms Processed with One or Two Second Derivative Filters Consecutively and Conditioned with Multiplication Modification between Two Second Derivative Filters data set no.
SNR of unfiltered peak SNR of filtered peak processed with one second derivative filters SNR improvement (folds) SNR of filtered peak conditioned with multiplication modification between two second derivative filters SNR improvement (folds) SNR improvement of filtered peak processed with two consecutive second derivative filters (folds) SNR of unfiltered peak SNR of filtered peak processed with one second derivative filters SNR improvement (folds) SNR of filtered peak conditioned with multiplication modification between two second derivative filters SNR improvement (folds) SNR improvement of filtered peak processed with two consecutive second derivative filters (folds)
no. 1
no. 2
no. 3
no. 5
no. 6
no. 7
no. 8
no. 9
no. 10
average
3.43 16.7
4.21 19.7
Diphenhydramine 3.02 3.06 3.81 17.4 15.7 18.3
3.63 17.2
3.52 17.6
3.85 18.8
3.23 15.1
3.75 18.1
3.55 17.5
4.87 90.1
4.69 95.1
5.76 89.0
5.14 88.3
4.80 94.1
4.88 102
4.99 80.3
4.99 107
4.67 96.1
4.83 96.7
4.95 93.9
26.3 4.87
22.6 4.69
29.5 5.76
28.9 5.14
24.7 4.80
28.1 4.88
22.8 4.99
27.8 4.89
29.8 4.67
25.8 4.83
26.6 4.95
8.32 36.8
8.70 45.5
Despiramine 8.52 6.60 39.4 31.4
7.31 34.2
7.44 39.7
8.12 36.7
7.64 40.5
6.96 30.6
7.00 31.3
7.66 36.6
4.42 297
5.23 317
4.62 395
4.76 251
4.67 268
5.34 330
4.52 244
5.29 230
4.40 229
4.47 227
4.77 279
35.7 4.42
36.5 5.23
46.3 4.62
38.0 4.76
36.6 4.67
44.4 5.34
30.0 4.52
30.1 5.29
32.9 4.40
32.4 4.47
36.3 4.77
Table 2. The Regression and Determination Results of Using the Standard Curves with Original and Filtered Signal Peaks
standard curves using original signal peaks determination errors (%) determination precision (standard deviation %); original peak SNR ∼ 3a standard curves using filtered signal peaks determination errors (%) determination precision (standard deviation %); original peak SNR ∼ 3a a
diphenhydramine
desipramine
y ) 1.1311x + 1.3477 R2 ) 0.9977b
y ) 0.4213x - 0.8527 R2 ) 0.9973b
-921
469.59
26.35
44.44
y ) 3.6077x + 0.8458 R2 ) 0.9952b
y ) 0.1166x - 0.4005 R2 ) 0.9988b
-100.1
512.1
9.47
11.47
SNR: signal-to-noise ratio. b R2: correlation coefficient.
As described previously, the multiplication of two chromatograms at the time domain is in equivalence to the convolution between the two frequency spectra of these chromatograms. When the remaining frequency noises, which are within the filter bandwidth, on the second-derivative filter chromatogram are multiplied with the random noises on the simulated chromatogram, the noise spectrum of this multiplication product no longer contains only the components within the filter bandwidth. The range of noise spectrum becomes wider. The imbedded graphs in parts B and C of Figure 3 show the frequency spectra of these two chromatograms, respectively. Clearly, the frequency spectrum
no. 4
Table 3. Signal Intensity Reproducibility of Original and Second-Derivative Filtered Peaks (Diphenhydramine and Despiramine) diphenhydramine
no. 1 no. 2 no. 3 no. 4 no. 5 no. 6 average standard deviation (%)
despiramine
original signal intensity (SNR ∼ 5)
filtered signal intensity
original signal intensity (SNR ∼ 3)
filtered signal intensity
18.6 18 12.6 14 15.5 16.2 13.56 16.95 %
341 264 243 277 305 283 285.5 11.9 %
4.8 9.9 17.7 29.3 n/a n/a 15.425 69.1 %
24 29 30 43 n/a n/a 31.5 25.7 %
imbedded in Figure 3B shows almost no frequency components outside the filter bandwidth. The remaining noises within the filter bandwidth cannot be eliminated with the other second-derivative filter or any other types of band-pass filter. In contrast, when the noises are modified to shift toward the other frequency regimes in Figure 3C, they can be efficiently eliminated with the other second-derivative filter to obtain better S/N ratio improvement. Table 2 shows the regression results of diphenhydramine and despiramine peaks versus sample concentrations with and without using noise spectrum modifications. The linearity (R2 values) of the processed curves is the same as that of the original curves. The curve linearity of using processed peaks is validated. However, more accurate determinations using this standard curve still cannot be obtained because the linearity has not been improved. Table 3 illustrates the signal intensity (peak height) reproducibility of diphenhydramine peaks (1 ng; S/N ratio about 5) and Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
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Table 4. Concentration Determinations of Diphenhydramine and Despiramine Using Standard Addition Methods with Original and Filtered Signal Peaks relative errors (%) Diphenhydramine prepared concn (ng/mL) 0.8 determined concn (ng/mL) 1.68 110 using original signals (no. of replicates, 3) determined concn (ng/mL) 1.21 51 using filtered signals (no. of replicates, 3) prepared concn (ng/mL) 3.2 determined concn (ng/mL) 4.74 48 using original signals (no. of replicates, 3) determined concn (ng/mL) 3.51 11 using filtered signals (no. of replicates, 3) Despiramine prepared concn (ng/mL) 5.0 determined concn (ng/mL) 7.67 using original signals (no. of replicates, 2) determined concn (ng/mL) 5.54 using filtered signals (no. of replicates 2)
standard deviation (%)
14 4.8
7.1 19.7
53.4
27.8
10.7
4.0
despiramine peaks (1 ng; S/N ratio about 3) with and without noise spectrum modifications. The signal reproducibility of processed peaks (standard deviations 12% and 26% of diphenhydramine and despiramine, respectively) is better than that of the original peaks (standard deviations 17% and 69%, respectively). Assuming signal reproducibility does not vary over a short concentration range, the above reproducibility improvement can result in more accurate determinations when standard addition procedures are employed. Table 4 shows the determination results of diphenhydramine at 0.8 and 3.2 ng/mL and the results of despiramine at 5 ng/mL, respectively, obtained via standard addition method procedures. The original S/N ratios of 0.8 and 3.2 ng/mL diphenhydramine peaks are 3 and 7, respectively. The original S/N ratio of the despiramine peak is 5. More accurate quantification of peaks in which the S/N ratio is less than the
2104 Analytical Chemistry, Vol. 80, No. 6, March 15, 2008
limit of quantitation (S/N ratio ∼ 10) is obtained via the standard addition method when the intensities of processed peaks are used. CONCLUSIONS We successfully implement a noise conditioning technique multiplying one second-derivative filtered LC-MS chromatogram containing noise only within the filter bandwidth with another simulated chromatogram containing thermal noise. The conditioned chromatogram is processed with the second secondderivative filter to obtain a much better peak S/N ratio than the ratio using two consecutive second-derivative filters without noise conditioning. Compared with the S/N ratios of the original LCMS/MS peaks, the ratios are enhanced to ∼25-fold or higher and ∼5-fold with and without performing noise conditioning steps, respectively. This noise tailoring technique is to shift the noise spectrum of the second-derivative filtered chromatogram, which is only within the filter bandwidth, toward the other frequency ranges. As a result, the noise on the conditioned chromatogram can be removed more efficiently using the other second-derivative filter, which works as a band-pass filter. The linear standard curve using the filtered LC-MS signals is validated. The filtered LCMS signals are also more reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 5-7) are obtained via standard addition procedures using the filtered signals than the determinations using the original signals. Developing software to implement this noise tailoring technique is simple. In addition, unlike other signal processing procedures using multivariate analysis or wavelet transform,4-8 our noise conditioning procedures do not require any tedious trials. Potentially this noise modification technique can be also used between any two band-pass filters to remedy the deficiency of these filters to improve the determinations using LC-MS signals. ACKNOWLEDGMENT The authors thank the financial support of National Science Council, Taiwan (Grant NSC 95-2113-M-194-010). The manuscript preparation assistance of Hui-Ju Liao is acknowledged. Received for review December 21, 2007. AC702222M
October
28,
2007.
Accepted
