Mixture Model for the Deconvolution of Thermal Decay Curves

Deconvolution of thermal decay curves allows you to quantify proportions of biomass components in plant litter. Thermal decay curves derived from thermogravimetric analysis (TGA) are imported, modified, and then modelled in a three- or four- part mixture model using the Fraser-Suzuki function. The output is estimates for weights of pseudo-components corresponding to hemicellulose, cellulose, and lignin. For more information see: Müller-Hagedorn, M. and Bockhorn, H. (2007) <doi:10.1016/j.jaap.2006.12.008>, Órfão, J. J. M. and Figueiredo, J. L. (2001) <doi:10.1016/S0040-6031(01)00634-7>, and Yang, H. and Yan, R. and Chen, H. and Zheng, C. and Lee, D. H. and Liang, D. T. (2006) <doi:10.1021/ef0580117>.

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Why deconvolution?

Plant cell wall biomass is composed of a range of different types of carbon. Proportions of primary carbon types are useful for estimating kinetic decay parameters or for calculation of intrinsic plant traits. Traditional methods for calculation of these components involve wet chemistry methods that can be monetarily and environmentally costly. Thermogravimetric analysis is an alternative method, already in use in the biofuel field, that involves pyrolysing dry, ground plant litter and estimating components from resulting mass decay peaks. Since different carbon types break down relatively independently during different temperature phases, we can separate the multi-peaked rate of mass loss curve into constituent parts using a mixture model. This package conducts this peak separation analysis in a open-source and reproducible way using R. This methodology has been tested on a range of plant litter composed primarily of soluble carbohydrates, hemicellulose, cellulose, and lignin.

Installation

You can install mixchar from GitHub with:

install.packages("devtools")
devtools::install_github("smwindecker/mixchar")

Below we will show a basic implementation of the package. For a detailed step by step workflow, see the workflow vignette on the website.

For a detailed discussion of the methodology, please see the methodology vignette on the website.

Basic use

Data from thermogravimetric analysis is usually exported in one of two forms: as mass loss or mass remaining (mg) by temperature. An example dataset that contains mass loss data for the species Juncus amabilis is included in the package:

library(mixchar)
head(juncus)
#>   temp_C mass_loss
#> 1 31.453 -0.000931
#> 2 31.452 -0.001340
#> 3 31.450 -0.001350
#> 4 31.450 -0.001660
#> 5 31.450 -0.001680
#> 6 31.450 -0.001800

We can use the function process() to take the derivative of this data, resulting in rate of mass loss over temperature data. To do so you need to specify the dataset, the initial mass of sample, the name of the temperature data column, and the name of your mass loss or mass data column. If you have mass loss data you can specify with mass_loss argument, if it’s mass remaining data you can use the mass argument. You only need to provide one. The function defaults to temperature data in Celsius, but you can also indicate the data is provided in Kelvin, by adding temp_units = 'K'.

tmp <- process(juncus, 
               init_mass = 18.96, 
               temp = 'temp_C', 
               mass_loss = 'mass_loss')

The default plot function for the derivative data shows you both the mass with temperature curve and the derivative rate of mass loss curve.

Processed data then needs to be deconvolved into its constituent parts. The deconvolve function takes care of this step, by cropping the derivative data to exclude dehydration and then running the Fraser-Suzuki mixture model and estimating individual peak parameters and weights.

output <- deconvolve(tmp)

Although most biomass samples have only three main components (corresponding to hemicellulose, cellulose, and lignin), some have a second hemicellulose peak in the low temperature range. The function will decide whether three or four peaks are best, but you can override it by modifying the n_peaks argument. The function also has built in starting values for the nonlinear optimisation. If you’d like to modify those or the upper and lower bounds for the estimates, you can also do so with the start_vec, lower_vec, and upper_vec arguments to deconvolve().

The deconvolve() function results in a variety of outputs. You can use a accessor functions to look at these. component_weights() will display the weights of each carbon component, rate_data() will show you the modified dataset used for fitting, model_fit() will show you the model fit, and temp_bounds() will print the temperature values at which the data were cropped for analysis. You can also plot the resulting output using the default plotting function, which can be in black and white or in colour.

Contribution

This is still a work in progress! If you see any mistakes, or find that the code is not functioning well on your data, let us know by logging a bug on the issues page.

Acknowledgements

Thank you to Nick Tierney and David Wilkinson for valuable feedback during development. Thanks to the Holsworth Wildlife Reseach Endowment & The Ecological Society of Australia for support on this project.