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Fit chromatographic peaks

Source: R/fit_peaks.R
fit_peaks.Rd

Peak parameters are estimated by fitting one of several models to the data using nonlinear least squares (nlsLM). Supported models include Gaussian, bidirectional exponentially modified Gaussian, or exponential-Gaussian hybrid functions. The area under each fitted curve is estimated using trapezoidal approximation.

Usage

fit_peaks(
  x,
  lambda,
  pos = NULL,
  sd_max = NULL,
  fit = c("egh", "bemg", "gaussian", "raw"),
  max_iter = 1000,
  estimate_purity = FALSE,
  purity_args = list(),
  noise_variance = NULL,
  baseline = c("none", "flat", "sloped"),
  ...
)

Arguments

x

A single chromatogram in matrix format.

lambda

Wavelength at which to fit peaks. Must correspond to a wavelength present in x.

pos

A data.frame of peak apices and boundaries, as returned by find_peaks, with columns pos, lower and upper giving row indices of x. If NULL (the default), find_peaks is run on x at lambda.

sd_max

Deprecated. Filter peaks by width with filter_peaks instead. If supplied, it is applied as a cutoff on FWHM of 2.355 * sd_max timepoints.

fit

Peak model. Options are bidirectional exponentially modified Gaussian ("bemg"), exponential-Gaussian hybrid ("egh"), "gaussian", or "raw". "raw" integrates the signal directly by trapezoidal approximation without fitting a model. Defaults to "egh". See Peak models in get_peaks.

max_iter

Maximum number of iterations to use in nonlinear least squares peak-fitting. Defaults to 1000.

estimate_purity

Logical. Whether to estimate purity. Defaults to FALSE, and is always FALSE when x holds a single wavelength.

purity_args

A named list of additional arguments passed to get_purity, e.g. list(background_correction = "none", metric = "max"). A lambdas element here selects the wavelengths used to compare spectra, not the wavelengths at which peaks are integrated.

noise_variance

Variance of noise, passed to get_purity. If not provided, it is estimated once for the whole chromatogram rather than once per peak.

baseline

Whether to measure each peak above a local baseline: "none" (the default), "flat" or "sloped". See Local baselines in get_peaks.

...

Additional arguments passed to find_peaks, such as smooth_window, smooth_type, min_prominence_snr, min_curvature and min_amplitude. See Choosing the smoothing window in find_peaks.

Value

A data.frame with one row per peak and the following columns:

  • rt: Apex of the fitted peak model, or of the detected peak when fit = "raw".

  • start: Peak start.

  • end: Peak end.

  • sd: Standard deviation of the Gaussian component of the fitted model, which is not the width of the peak unless fit = "gaussian". NA when fit = "raw".

  • tau: Exponential decay constant (only when fit = "egh").

  • tau_right: Time constant of the exponential tail on the right side of the peak, the reciprocal of its fitted rate (only when fit = "bemg").

  • tau_left: Time constant of the exponential tail on the left side of the peak, the reciprocal of its fitted rate (only when fit = "bemg").

  • h: The amplitude parameter of the fitted BEMG shape function. It scales the shape but is neither its value at center nor the peak height (only when fit = "bemg").

  • center: The center parameter of the fitted BEMG shape function, the location around which the exponential tails are applied. May differ from rt (only when fit = "bemg").

  • FWHM: The full width at half maximum of the peak, comparable across values of fit. NA for a "raw" peak whose integration window does not fall below half its height on both sides.

  • height: Peak height above the fitted baseline.

  • area: Peak area above the fitted baseline.

  • r.squared: Coefficient of determination (\(R^2\)) of the fitted curve over the peak window, 1 - SS_res / SS_tot. Negative when the fit is worse than a flat line at the mean. Not returned when fit = "raw".

  • purity: The spectral purity of peak as assessed by get_purity.

  • window_limited: 1 if a fitted shape parameter hit a limit set by the integration window, or a "gaussian" or "egh" fit narrowed to one sampling interval at half height, meaning the window or the sampling rather than the data determined the reported shape, and 0 otherwise. Not returned when fit = "raw".

  • converged: 1 if the optimizer reported convergence for the final step of the fit, and 0 otherwise, including when part or all of the fit was skipped or failed (see Fitting procedure in get_peaks). Not returned when fit = "raw".

  • floor: Constant baseline offset (only when baseline = "flat").

  • floor_start: Baseline level at the left edge of the peak window (only when baseline = "sloped").

  • floor_end: Baseline level at the right edge of the peak window (only when baseline = "sloped"). The table is in index units rather than retention times: rt, start, end and center are index positions; sd, FWHM, tau, tau_right and tau_left are widths on the index scale; and area is integrated over the index axis. get_peaks converts them to the chromatogram's time axis.

Details

Peaks that can't be fitted are dropped if they've been detected automatically with find_peaks. Otherwise, if the peak positions are provided explicitly through pos, height and area are set to NA and they are marked 0 in the converged column.

The peak models, local baselines and fitting procedure are described in get_peaks, under Peak models, Local baselines and Fitting procedure.

Note

The loop over peaks in fit_peaks is adapted from the fitpeaks function in Ron Wehrens' alsace package. The Gaussian peak shape and the interface of the internal fitting functions are adapted from Robert Morrison's DuffyTools 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, 26: 285-296. doi:10.1007/BF02268168 .

See also

find_peaks, get_peaks

Author

Ethan Bass

Examples

data(Sa_pr)
fit_peaks(Sa_pr[[1]], lambda = 220)
#>           rt start end        sd          tau      FWHM      height
#> 1   30.66114    14  48  6.101575   1.44697364 14.403076   8.9748818
#> 2   49.94050    48  54  1.181971  -1.10373785  2.886559   0.3915597
#> 3   70.01920    54  79  2.729871  -1.17486581  6.479732 123.7545250
#> 4   82.33054    79  86  1.482960  -0.43913100  3.505344   2.5630020
#> 5   89.65612    86  93  1.725862   0.74138982  4.096455   2.8793770
#> 6  104.49705    93 124  2.183908  -0.19404617  5.144468 894.3629580
#> 7  131.85646   124 149  1.833434   0.11605405  4.318157 468.3178181
#> 8  156.03382   149 161  1.858660   0.17723271  4.378535   7.4302224
#> 9  167.74077   161 173  1.681790  -0.15232333  3.961719  28.6002885
#> 10 183.20931   173 189  2.094857  -0.16099380  4.934272 414.2717933
#> 11 193.90505   189 201  2.400072  -0.87407104  5.684120 128.4663742
#> 12 216.44076   201 229  1.842958  -0.13155394  4.340793 433.8264796
#> 13 234.37947   229 240  2.087220   0.30929995  4.919702  47.6597945
#> 14 243.28110   240 255  3.721672   3.76517021  9.144208  16.0564058
#> 15 261.90773   255 265  2.102433  -0.57181758  4.966692  18.9817970
#> 16 272.86037   265 279  3.095311   0.09729706  7.289213  94.6165502
#> 17 284.46078   279 294  1.877091  -0.35653644  4.427114 161.9127876
#> 18 298.16377   294 311  1.928674  -0.35565627  4.548366  17.6025746
#> 19 320.10828   311 323  1.046951   0.27961372  2.472988   0.7954206
#> 20 336.89987   323 348  2.228935  -0.81884813  5.279340 171.3788902
#> 21 351.76261   348 364  3.699194   3.37989773  9.020474   6.9747887
#> 22 378.91468   364 384 10.262991  -7.88194072 24.777329   3.4392483
#> 23 396.45231   384 403  9.840007  -2.54701213 23.238604   5.8916446
#> 24 411.06601   403 412  7.643896 -97.75200512 70.106682   5.3320058
#> 25 419.24718   412 422  6.088367  -6.96651196 15.128362   7.2786470
#>            area r.squared purity window_limited converged
#> 1   136.6168187 0.9834201     NA              0         1
#> 2     0.9895294 0.1434314     NA              0         1
#> 3   861.2327696 0.9910190     NA              0         1
#> 4     9.2206621 0.9982737     NA              0         1
#> 5    11.6265191 0.9937378     NA              0         1
#> 6  4899.5751670 0.9985326     NA              0         1
#> 7  2153.0681287 0.9981330     NA              0         1
#> 8    34.3806776 0.9355800     NA              0         1
#> 9   120.5844854 0.9995746     NA              0         1
#> 10 2172.4932812 0.9960212     NA              0         1
#> 11  735.7342180 0.9970448     NA              0         1
#> 12 2005.0667012 0.9957840     NA              0         1
#> 13  247.0319456 0.9661289     NA              0         1
#> 14  145.4116996 0.9588278     NA              0         1
#> 15   96.0671652 0.9711060     NA              0         1
#> 16  710.5446283 0.8959060     NA              0         1
#> 17  758.8991868 0.9748398     NA              0         1
#> 18   82.6349173 0.9781477     NA              0         1
#> 19    2.0678877 0.1506531     NA              0         1
#> 20  969.4820324 0.9942008     NA              0         1
#> 21   64.0434095 0.8251971     NA              0         1
#> 22   57.4508700 0.9935989     NA              0         1
#> 23   94.7135320 0.8801906     NA              0         1
#> 24   46.5196604 0.8663922     NA              1         1
#> 25   64.5439100 0.9002292     NA              0         1