Fit chromatographic peaks to an exponential-gaussian hybrid or gaussian profile

Fit peak parameters using exponential-gaussian hybrid or gaussian function.

Usage

fit_peaks(
  x,
  lambda,
  pos = NULL,
  sd.max = 50,
  fit = c("egh", "gaussian", "raw"),
  max.iter = 1000,
  estimate_purity = TRUE,
  noise_threshold = 0.001,
  ...
)

Arguments

x: A chromatogram in matrix format.
lambda: Wavelength to fit peaks at.
pos: Locations of peaks in vector y. If NULL, find_peaks will run automatically to find peak positions.
sd.max: Maximum width (standard deviation) for peaks. Defaults to 50.
fit: Function for peak fitting. (Currently exponential-gaussian hybrid egh, gaussian and raw settings are supported). If raw is selected, trapezoidal integration will be performed on raw data without fitting a peak shape. Defaults to egh.)
max.iter: Maximum number of iterations to use in nonlinear least squares peak-fitting. (Defaults to 1000).
estimate_purity: Logical. Whether to estimate purity or not. Defaults to TRUE.
noise_threshold: Noise threshold. Input to get_purity.
...: Additional arguments to find_peaks.

Value

The fit_peaks function returns a matrix, whose columns contain the following information about each peak:

rt: Location of the peak maximum.
start: Start of peak (only included in table if bounds = TRUE).
end: End of peak (only included in table if bounds = TRUE).
sd: The standard deviation of the peak.
tau: \(\tau\) parameter (only included in table if fit = "egh").
FWHM: The full width at half maximum.
height: Peak height.
area: Peak area.
r.squared: The R-squared value for linear fit of the model to the data.
purity: The spectral purity of peak as assessed by get_purity.

Again, the first five elements (rt, start, end, sd and FWHM) are expressed as indices, so not in terms of the real retention times. The transformation to "real" time is done in function get_peaks.

Details

Peak parameters are calculated by fitting the data to a gaussian or exponential-gaussian hybrid curve using non-linear least squares estimation as implemented in nlsLM. Area under the fitted curve is then estimated using trapezoidal approximation.

Note

The fit_peaks function is adapted from Dr. Robert Morrison's DuffyTools package as well as code published in Ron Wehrens' alsace package.

References

* Lan, K. & Jorgenson, J. W. 2001. A hybrid of exponential and gaussian functions as a simple model of asymmetric chromatographic peaks. Journal of Chromatography A 915:1-13. doi:10.1016/S0021-9673(01)00594-5 .

* Naish, P. J. & Hartwell, S. 1988. Exponentially Modified Gaussian functions - A good model for chromatographic peaks in isocratic HPLC? Chromatographia, /bold26: 285-296. doi:10.1007/BF02268168 .

Author

Ethan Bass

Examples

data(Sa_pr)
fit_peaks(Sa_pr[[1]], lambda = 220)
#>           rt start end        sd           tau      FWHM      height
#> 1   30.69332    14  46 6.2865644    1.20769992 14.773426   8.9910726
#> 2   50.94330    46  52 0.5711967  -11.41366848  1.342312   0.3652505
#> 3   61.44532    53  61 3.2042222    2.37308275  7.529922  12.7874585
#> 4   69.97526    61  78 2.7067311   -1.01879444  6.360818 118.1461826
#> 5   82.42709    78  85 1.3744994   -0.73109961  3.230074   1.5745430
#> 6   89.64284    85  93 1.5296385    0.61202488  3.594650   2.3360448
#> 7  104.49707    93 114 2.1826134   -0.19394678  5.129142 878.3558848
#> 8   81.84177   114 118 2.4690722   22.61770113  5.802320   9.6411867
#> 9  119.85327   118 123 5.2832737  -13.86056689 12.415693   8.5707183
#> 10 131.85675   123 139 1.8315236    0.11513594  4.304081 418.7796260
#> 11 141.10828   139 147 4.1299082   -4.37157201  9.705284   8.5085781
#> 12 156.09501   149 161 1.7963783   -0.01487998  4.221489   5.8543152
#> 13 167.73853   161 171 1.6517982   -0.14556475  3.881726  25.5505898
#> 14 183.22815   171 188 2.0807233   -0.22145455  4.889700 350.1547326
#> 15 193.98654   188 200 2.4682084   -1.29245512  5.800290 119.6729349
#> 16 216.44045   200 228 1.8375563   -0.13007408  4.318257 319.6260534
#> 17 234.50440   228 238 1.9619252   -0.17648212  4.610524  35.8686113
#> 18 243.58113   238 254 4.9483859    0.66568143 11.628707  15.8252538
#> 19 262.00099   254 264 1.8302984   -0.98597515  4.301201  17.3957395
#> 20 272.87432   264 279 3.0837104    0.05107119  7.246719  96.9289225
#> 21 284.45995   279 293 1.8712197   -0.34947351  4.397366 121.3286776
#> 22 298.28530   293 303 2.0217365   -0.90317976  4.751081  14.6884289
#> 24 320.15708   315 323 1.2587749    0.34042184  2.958121   0.6212100
#> 25 336.89949   323 347 2.2339189   -0.82019092  5.249709 157.2481960
#> 26 351.82167   347 363 4.3854006    2.73641711 10.305691   7.1109632
#> 27 379.01651   363 383 9.6193330  -13.36671566 22.605432   3.8470521
#> 28 389.96461   383 390 0.4505398  -11.19848606  1.058768   5.0689224
#> 29 396.32753   390 401 7.3086188   -2.14825864 17.175254   6.6276427
#> 30 410.94947   401 411 1.7808715 -123.44165218  4.185048   5.5950637
#> 31 419.42472   411 421 4.8293966  -14.83514636 11.349082   7.4589610
#>           area r.squared     purity
#> 1   141.609052 0.9869708 0.63636364
#> 2     1.533815 0.7267476 1.00000000
#> 3    44.203814 0.9997068 1.00000000
#> 4   844.468381 0.9954198 0.17647059
#> 5     7.929626 0.9529150 1.00000000
#> 6     9.913595 0.9974965 1.00000000
#> 7  4895.362421 0.9991512 0.08333333
#> 8    37.726631 0.8292605 0.60000000
#> 9    36.686028 0.9637970 1.00000000
#> 10 2149.825149 0.9991802 0.15384615
#> 11   42.867284 0.9910774 1.00000000
#> 12   31.941462 0.9960339 1.00000000
#> 13  116.325582 0.9997472 0.90909091
#> 14 2159.863516 0.9987345 0.15384615
#> 15  749.502596 0.9870224 0.18181818
#> 16 1996.653868 0.9988400 0.50000000
#> 17  231.767485 0.9889112 0.72727273
#> 18  148.058988 0.8325459 0.52941176
#> 19   88.004196 0.9912112 0.63636364
#> 20  713.899661 0.9118992 0.46666667
#> 21  753.063438 0.9843055 0.26666667
#> 22   84.486071 0.9455491 0.72727273
#> 24    2.923839 0.9897500 1.00000000
#> 25  972.579141 0.9950354 0.33333333
#> 26   70.695956 0.7701393 1.00000000
#> 27   63.752468 0.9955775 1.00000000
#> 28   30.677295 0.9392470 1.00000000
#> 29   64.992481 0.8411157 1.00000000
#> 30   54.963920 0.8662737 1.00000000
#> 31   67.504644 0.8950062 1.00000000