Where...

1. A is the model matrix made up the unscaled individual signatures of the compounds being fit. The current locations of the peak clusters are taken into account when the A matrix is calculated.

2. x is a vector made up all of the compound concentrations to be optimized. Each component of the vector, xi, is bounded between li (lower bound) and ui (upper bound). Non-negative restraints are imposed (li ≥ 0) since concentrations cannot be negative.

3. b is the spectral subtraction line, i.e. the experimental spectrum minus the contribution of all compounds part of the current profile that are not part of the optimization process. In other words, if a compound has been fit and his not part of the fitting process, its contribution is subtracted from the experimental spectrum before the process starts.

4. W is a weight vector, which is used to modulate the relative importance of each spectral point. Optionally, the algorithm can increase the weight of the points that are overfit though an iterative penalization process.

   IMPORTANT NOTE: The optimization process will not modify the location of the peak clusters.

How to use COMPLETE Autofit

1. Open your processed CNX file within the Profiler Module.

2. Go to Tools -> Batch Operations -> "COMPLETE Autofit"

3. Select Files to Fit Automatically

   • Select Files or Folders to Fit Automatically: COMPLETE Autofit will do a complete profile of one, or several CNX files. Select your unprofiled CNX files here.

   • Save Automated Fit Report to: A fit report in the form of a tabulated separated value (tsv) file will be generated, with each input file and the sum of residuals associated with each fit attempt. Specify the destination and name of the report file here.

4. Select the Compounds to Fit Automatically. You can either:

   • Choose to fit all the compounds already profiled in each file. In this case, compounds must be already present in their profile and all of the compounds will be included in the fit operation.

   • Choose compounds from and already profiled spectrum. Note that it is possible to select only a subset of those in the interface’s next step.

   • Choose compounds from a Chenomx library

   • Choose compounds from a customized compound list defined in Library Manager.

   IMPORTANT NOTE: DO NOT ATTEMPT TO FIT THE ENTIRE CHENOMX LIBRARY. THIS WILL RESULT IN OVERFITTING AND AN EXTREMELY LONG PROCESS. TARGET THE COMPOUNDS THAT SHOULD BE VISIBLE AND PRESENT FOR THE TYPE OF SAMPLES YOU HAVE.

5. Compound Selection Refinement

   • • Depending on your selection in the previous step, you may be presented with an option to further refine your compound selection. You can move compounds across list boxes to specify whether or not you want to include them in the fit.

   • • The checkbox option “Skip compounds that are already fit” is self-explanatory. It allows you to ignore compounds that are already fit. Their contribution will be calculated and taken in consideration to fit the reminder of the compounds, but their current state (cluster positions, concentrations) will not be modified.

6. Concentration Fitting Setup

   This interface is composed of two main sections: Regions Selection, and Concentration Fitting options. The role of each section is described below. The application Preferences panel can be used to control and set all the default values appearing in the interface.

   1. Region Selection: Comma-separated list of spectral regions (in ppm units) to be included or excluded in the fit. Each component of the lists must include a lower and upper bound in ppm, separated by a dash. For instance, “0.8-2.3, 3.0-4.2” is a valid list.

      • The Included Regions input field displays the limits of the currently selected spectral region (as selected with the Select Region Tool). If no region is currently selected, the Included Regions input field defaults to the entire spectrum.

      • The Excluded Regions input field will automatically include the region associated with the water peak. It is recommended that any peaks around the water region be excluded due to attenuation caused by water saturation. Similarly, the region associated with urea (5.4-6.0 ppm) should also be excluded if urea is present.

        Excluded regions have prevalence over any included regions, i.e. any spectral point falling within any of the listed excluded regions will automatically be ignored during the fit.

   2. Concentration Fitting Options: This group of options control the behavior of the optimization engine.

      • Resolution(bin) size:

        The spectrum can be fit using either its full representation, or a binned representation. This parameter controls the number of spectral points per bin. Set this parameter to 1 for full resolution. However, it is highly recommended to use a binned representation if the peak cluster positions have not been optimized. Fitting at full resolution will require more memory and CPU time.

      • Overfitting Penalty Factor:

        The amount of overfitting can be limited by increasing the weights of the spectral points where overfitting occurs. This will effectively increase the importance of the spectral points where this occurs relative to the other ones, adding a penalty to pay for predicting points over the spectrum line. For a given spectral point, the square of the difference between the experimentally observed spectrum intensity and the predicted/calculated one will be multiplied by the factor specified in this field if the difference is negative. The weights are adjusted iteratively and up to 5 cycles of optimizations are performed if the specified penalty factor is >1.

      • Concentration Upper Bounds and Penalty Factor:

        Non-negative constraints are used during the optimization process so that concentration values remain ≥ 0. Two different settings are offered to control their upper bounds. They can be set to be unlimited via the Unconstrained option, or limited according to their predetermined maximal potential concentration. The maximal potential concentration of a given compound is the highest concentration for which the compound signature would not exceed the experimental spectrum.

        Because of possible discrepancies between the compound library signatures and the experimental spectrum, mainly due to pH conditions, matrix effects, etc, the potential concentrations determined by Profiler may not be optimal and should only be regarded as guidelines. To give potential concentrations more wiggle room, potential concentrations can be pre-multiplied by a specified constant. The derived set of scaled potential concentration values will then be used as upper bounds.

      • NOTE: It very important to note that the baseline is not modeled from the residuals at any stage. It is therefore crucial that the baseline be properly corrected prior to concentration fitting.

7. Autofit Setup

   This panel controls the overall behaviour of automated fitting:

   1. The number of internal iterative rounds is related to the number of times, for each fit attempt of a given spectrum, the algorithm will position clusters and adjust concentrations. It is directly equivalent to the situation encountered with manual fitting, where an operator usually has to do several rounds of going through the list of compounds to be fit and adjust their peak cluster positions and height (concentration).

   2. The number of fit attempts control how many output files will be generated for each input spectrum cnx file. By analogy, it is related to how many people would be trying to fit the spectrum if there were a team of operators. Each one could potentially come up with a different solution that produces more or less the same fit quality in terms of sum of squares of the residual line.

   3. The number of CPUs control how many CPUs can be used for parallel computations. The number presented in the interface takes into account the maximum number of CPUs allowed and defined by the software license, and the number of CPUs that may already be used by another COMPLETE Autofit job.

8. Review and Finish

   • COMPLETE Autofit will generate multiple profiled CNX files for each input spectrum file that will be saved in the same location as the input source. It will not however modify the original source files themselves.

   • A fit report will be produced, showing the residuals chi-square value for each of the produced cnx file. For a given input file, the output solution with the lowest chi square (lowest fit error) is automatically saved with the label “_best” appended at the end of its filename.

   • A text file (.txt) will also be generated for each exported CNX file with the chi square value achieved for each internal round of iteration. Inspection of those text files can reveal whether or not the number of internal rounds that were specified is enough to achieve a minimum. If the best solution (lowest chi square) is generally obtained only at the last internal iterations, it is a sign that maybe a higher number of iterations is needed.

   • It is up to the user to choose the output solution that produced the best fit, if the decision parameter is other than the sum of residuals. For statistical analysis (PCA, PLS-DA, etc.), it may be more relevant to work with concentrations averaged over the series of exported fits rather than single values.

A Note about Legacy Autofit

Version 10 also reintroduces a form of automated fitting found in version 8.6 and earlier of the software, as “Legacy Autofit”. Legacy Autofit may be preferable to older users that want to maintain controls for a project initiated using older versions of Chenomx NMR Suite. For users starting a project using Chenomx NMR Suite Versions 9 or later, consider using more advanced Autofit techniques such as Compound Snapper / Fit Automatically or the COMPLETE Autofit Tool.

The difference between Legacy Autofit and COMPLETE Autofit is explained below.

1. Legacy Autofit first takes the raw spectrum and subtracts the contribution of all previously fit compounds that are not selected for the autofit.

2. Starting from the spectrum obtained in step #1, it scores the compounds selected for autofit to establish the order in which they will be fit.

3. Starting from the best potential candidate, it tries to simultaneously establish the position of the clusters for that metabolite and the maximum intensity (and therefore concentration) of that compound on the spectrum. (If it fails to establish where some clusters are located, they are left at their default/untransformed locations.)

4. The contribution of the potential candidate is then subtracted from the spectrum to yield another spectrum which serves as starting point for the processing of the second candidate compound, using the same procedure.

5. This cycle is repeated until the list of selected compounds for autofitting has been exhausted.

6. One can clearly see that the risk of errors increases at every step, and that eventually not all compounds will succeed in being autofitted. Moreover, as individual compounds are added at their maximal concentrations, the final result does not reflect a global optimization of all compounds, but reflects a successive series of individual optimization. (In order words, after adding compound #x, the algorithm does not reevaluate compound #x-1, #x-2, #x-3, etc.)