Human odor and forensics. Optimization of a comprehensive 1 two-dimensional gas chromatography method based on 2 orthogonality: how not to choose between criteria.

: 13 The use of comprehensive two-dimensional gas chromatography coupled with mass 14 spectrometry would be a real asset for the forensic profiling of human hand odor. This paper 15 focuses on the optimization of a comprehensive gas chromatography method using a 16 synthetic mixture of 80 compounds representative of human hand odor composition. In order 17 to rank the candidate column sets, instead of using a unique criterion, we used a chemometric 18 tool called desirability which is based on Derringer functions and enables to consider several 19 criteria simultaneously and hence to get the best compromise. Nine criteria including six 20 orthogonality criteria were used to evaluate the quality and the efficiency of the separation. 21 The desirability analysis lead to a straightforward ranking and an accurate overview of the 22 results in two situations, with an objective of routine analysis and without. In both cases, the 23 DB-1MS×DB-1701 set was found to be best suited for the separation of the considered 24 mixture, however with different gradients.


I) Introduction
Profiling human hand odor is a topic of current interest because it would be a considerable breakthrough in forensics, bringing more convincing evidence to magistrates than that of dogs alone.To give more relevance to the information obtained from dogs, there is a need to develop a better understanding of human odor.Indeed, relying only on animals whatever their capabilities is not suitable in courts: identification provided by dogs can merely be used as a corroborative evidence.Thus, the development of an objective analytical strategy to characterize human odor may be a promising complementary tool to the use of trained dogs [1,2].Hundreds of molecules are involved in human hand odor.To our knowledge however, two-dimensional (2D) techniques have not yet been used to characterize living human odor though comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC×GC-MS) may provide novel information regarding the complexity of the samples.
Like fingerprints, human odor is said to be specific of each individual [2].In 2014, de Lacy Costello et al. [3] published a comprehensive review of the volatiles emanating from a healthy human body.Different groups of chemical compounds were found in the headspace of biological samples: acids, alcohols, aldehydes, esters, hydrocarbons, ketones, heterocyclic compounds [4] and even sulfur-containing compounds in armpit samples [5].Considering the nature of the molecules involved, gas chromatography coupled with mass spectrometry (GC-MS) seems to be the most appropriate analytical technique [6].However, classic onedimensional (1D) GC-MS showed its limitations in term of peak capacity considering the number of compounds involved: using GC×GC-MS appeared natural to overcome the complexity of the samples.
The first thing to consider when developing a 2D method is the choice of the column set, and orthogonality is often used to characterize the performance of a 2D separation.A system is said to be orthogonal if the first and second dimensions columns are statistically independent.But the independence of the two retention mechanisms might not be sufficient to provide a better separation.Indeed, any change of selectivity between first and second dimension provides always a better separation than that obtained in 1D, but for an efficient separation, the surface coverage of the 2D chromatogram by the spots (compounds) also has to be homogenous.The evaluation of the quality of the separation is still in the center of many debates and there are many criteria for its evaluation, some of them characterizing the absence of correlation or independence, others the occupation of the separation space, and still others trying to combine the two.Schure and Davis recently compared several criteria used for the evaluation of 2D separations [7]: the choice of a criterion appears to be tough, each of them having its advantages and limitations.Though this paper aims neither at reviewing all criteria described in the literature, nor at comparing their performance, we propose here a short overview of the most representative ones.
Correlation coefficients (Pearson's, Kendall's and Spearman's) were used to evaluate the correlation between the retention times of the two dimensions of a 2D separation [8][9][10][11].Al Bakain et al. showed that Kendall's coefficient was a good indicator of orthogonality: contrary to Pearson's coefficient, Kendall's is not sensitive to extreme values and provides a good measure of nonlinear monotonous association [8].However, Gilar et al. stated that correlation coefficients were not well suited for measurement of chromatographic orthogonality, especially for systems with clustered data and outliers [12].Slonecker et al. proposed two criteria based on informational theory, the informational similarity and the percentage of synentropy, both based on the mutual information of the system [13], which is a measure of independence.
Other descriptors rather characterize the distribution of the peaks in the 2D space, using for example nearest neighbor distances (NND) between peaks.One can either sum distances, as discussed by Clark and Evans [14], or squared distances, as discussed by Brown and Rothery [15].Nowik et al. also used a NND approach in their work [16,17]; the arithmetic mean of the NND gives a good indication of peak spreading all over separation space, but is strongly impacted by long distances.The authors also used the geometric and harmonic means which are descriptors of homogeneity and are also sensitive to short distances.They concluded that the harmonic mean of the NND best characterizes orthogonality.Schure et al. proposed a measure of retention time spacing based on a power law fractal distribution [18].The boxcounting dimension is a measure of inter-peak spacing scales and, indirectly, of how effectively the separation space is used [12,18].The homogeneity of the surface coverage can also be more directly characterized by discretizing the 2D space in bins and evaluating the ratio between number of occupied bins and total number of bins [8,12,19].This method can be applied either on the original retention times, or on values normalized between the smallest and the largest one: in the latter case, the unused separation space on the borders is not taken into account.Leonhardt et al. compared the compound distribution in each dimension to the distribution of a fully orthogonal system to evaluate clustering [20].Ryan et al. measure directly the ratio between the area occupied by the spots and the unused separation space beneath the second dimension [21].The area of occupied space can also be estimated by a rectangular form.However, Semard et al. pointed out that a rectangle is too coarse to describe a complex geometry, and proposed to estimate the percentage of occupied separation space using Delaunay's triangulation algorithms based on the convex hull [22].Rutan et al. also used the minimum convex hull to determine a fractional coverage metrics characterizing the effective peak capacity [23].Another geometric approach consists in the calculation of the peak spreading angle [11,24].Gilar et al. concluded that surface coverage and box-counting dimension methods offer useful and intuitively understandable measures of orthogonality.These methods are robust enough for small samples commonly used in chromatographic practice [12].
In order to take both independence of the retention times and coverage of the separation space into account, Zeng et al. proposed a criterion based both on the bin coverage percentage and Pearson's linear correlation coefficient between the retention times [25].In order to account for a large variety of nonlinear relationships, Mani-Varnosfaderani et al. adapted this method by replacing Pearson's correlation by the maximal information coefficient [26].Jacova et al. evaluated different orthogonality assessment tools in GC×GC [27], and using simulation and statistics, they concluded that the geometric approach using a number of bins equal to the number of compounds [8,12] or the NND approach with the use of the arithmetic and the harmonic means [16,17] were the best ones.This short survey shows the extreme diversity of the criteria for the evaluation of 2D separations: considering a single criterion is not an option anymore [28].This is the reason why, in this paper, nine criteria including six orthogonality criteria were considered for the evaluation of the separation of a synthetic mixture of 80 representative of human hand odor [2].The criteria were selected for the complementarity of the information they provide.A chemometric tool called desirability [29,30] using Derringer functions was used to get an accurate overview of results [31].Its optimization led to the best compromise between the criteria and provided an overall quality score, enabling to rank the different column sets objectively.

II) Statistical analysis 1) Criteria
Six orthogonality criteria were selected: Spearman's correlation coefficient, the arithmetic and the harmonic means of the NND, the coefficient of orthogonality calculated with the Camenzuli's Asterisk equations [32], and the calculation of the separation space coverage with both normalized and raw data.The quality of the separation was also evaluated with three additional criteria: the number of coelutions, the number of detected compounds and the run time.The latter criteria and the reason why they were chosen will be detailed in the present section.
Let n be the number of detected compounds of the chromatogram, and  ! and  " the retention times of the first and second dimension respectively.Let " and #&' " be the retention times of the first and the last eluted compounds in each dimension.The normalized retention times of the first and second dimension " are calculated as follows: .

Spearman's correlation coefficient
If the peaks are well-spread all over the 2D separation space, the first and second dimension retention times should not be correlated.Thus, correlation coefficients can be used to evaluate orthogonality [8], with the advantage that they do not require the discretization of the separation space, nor the normalization of the retention times, and can be calculated easily.
Spearman's correlation coefficient ρ provides a measure of monotonous nonlinear correlations between retention times.The compounds are ranked according to their retention time in the first and second dimensions.Let ( $ *! ,  $ *" ) denote the ranks of a pair of coordinates of compound i , di = ri t1 -ri t2 , and n the number of compounds, then: Spearman's correlation coefficient is preferred to Pearson's which is not suited for the measure of nonlinear associations and is sensitive to extreme values.

Nearest Neighbor distance approach
A recent approach was proposed by Nowik et al. to assess the orthogonality of 2D separative systems using NND [16].The NND is defined as the shortest of all distances  $ of point i to all other points.All calculations were performed with normalized retention time, so that only the time window effectively occupied by the compounds, which is usually narrower than the whole separation space, is considered.Three different descriptors were defined by Nowik et al.: the arithmetic mean  ̅ (() , the geometric mean  ̅ (() and the harmonic mean  5 (() .

𝐴 ̅
The arithmetic and the geometric means are strongly influenced by long distances and give information about peak spreading, while the harmonic mean is more impacted by short distances and therefore gives information about clustering.

Asterisk equations
Camenzuli et al. proposed a new measure of orthogonality for multi-dimensional chromatography [32].Different equations -known as Asterisk equations -allowed the calculation of  1 which gave a measure of orthogonality.All calculations were performed with normalized retention times.Four parameters are calculated to characterize the peak dispersion around four lines.The peak dispersion around each line is compared to that of a uniform distribution.This technique does not require the discretization of the separation space and has the advantage of evaluating the dispersion around four different axes.

Occupied space -geometric criteria
This geometric criterion was used as an indicator of the coverage of the separation space and hence of orthogonality [8].It is impacted by the number of peaks and requires space discretization into    bins.In the present study, the mixture of standards contains 80 compounds.A value of p=9 was chosen to have a number of bins close to the number of targeted compounds: one compound per bin would lead to a space covering percentage of 98.7%.
This geometric criterion can be calculated using either raw or normalized data.Calculation with normalized data eliminates border areas of the chromatogram, and enables to consider only the relative spatial arrangement of the compounds, whereas working with raw data enables to take the undesired presence of empty areas into account.

Additional separation criteria
Three additional criteria were included for the optimization of the columns set and conditions.Since the developed methods will eventually be used routinely, the run time was taken into account to save time.The number of coelutions as well as the number of detected compounds -compounds of the mixture found on the considered chromatogram -were also evaluated to rank the different columns set.Plotting the number of coelutions versus the number of detected compounds for each analytical setup showed that these two indicators are absolutely not correlated (Pearson correlation coefficient of 6.10 -5 ).Indeed, the modulation system being a dual-jet cryomodulator applied to the second dimension column -on which the modulation is done -some compounds can be subject to an echo phenomenon.A cold-jet default of trapping can lead to the apparition of twin peaks separated by half a modulation time in the second dimension.Thus, an increase in the number of coelutions can be observed while the number of detected compounds remains the same.

2) Desirability parameters
Desirability evaluation is a multicriteria decision-making method using Derringer functions [31], which necessitates the definition of an individual desirability function for each criterion.
In this way, each measured response of interest is converted into a dimensionless number dk between 0 (criterion not satisfied) and 1 (criterion satisfied).The two bounds of the desirability curve will be described by the letters B0 and B1 (cf.figure 1).
The global desirability D of a column set is calculated as the product of the individual desirabilities: The desirability approach allows to get an accurate overview of results in a straightforward manner, as in [30,33,34] where it was successfully applied for multicriteria optimization.

1) Chemicals and reagents
To optimize the analytical methods, a mixture of 80 standards was prepared in heptane (10 mg/kg each).The detailed composition of this mixture is available as Supplementary Material.Compounds likely to be found in human hand odor were selected [2].A particular attention was given to cover a wide range of chemical properties (polarity, molecular weight, chemical family).

2) Comprehensive two-dimensional gas chromatography and mass spectrometry
Analyses were performed on a Thermo Trace GC×GC coupled with a Thermo ISQ MSD (Thermo, Villebon-sur-Yvette, France).This device was equipped with a Thermo Triplus autosampler.
Helium flow was set at a constant value of 1mL/min.The initial temperature was 40 °C, held for 1 min, then raised to 250 °C, and again held for 1 min, with gradients of 2, 2.5, 3 or 4 °C/min.The modulation was performed with a dual-jet CO2 thermal modulator, and modulation times of 6, 8 or 10 seconds were selected.The mass spectrometer was used with the electronic ionization source (70 eV) heated at 210°C.The acquisition was made in scan mode, with scan range 46-320 amu.A solvent delay of 9 minutes was used.Data were acquired with Xcalibur and processed with ChromCard (Thermo softwares).

4) Head-Space SolidPhase MicroExtraction (HS-SPME)
Given the volatility of most of the targeted compounds, injection was performed using HS-SPME.Such a technique enabled to minimize the solvent peak compared to classical liquid injection.This study was conducted with a focus on the separation and not on the limits of detection.No quantitation was performed and the areas of the different peaks of interest were not used.The SPME fiber used was a 75 µm DiVinylBenzene-Carboxen-PolyDiMethylSiloxane (DVB-CAR-PDMS) from Supelco (Sigma-Aldrich, Saint Quentin Fallavier, France).For HS-SPME procedures, standards were prepared by introducing 10 µL of the mixture of 80 standards in the 20 mL vial.The fully automated HS-SPME procedure was as follows.First, the vial was equilibrated at 70°C during 1 min, then the fiber was placed into the head-space of the sample for the extraction, still maintained at 70°C for 20 min.At the end of the extraction, the fiber was desorbed directly in the GC injector for 20 min at 250°C in split mode (1:10).

IV) Results and discussion
In this paper, 27 different analytical setups were evaluated, an analytical setup being defined by a column set, a gradient and a modulation time (cf.table 1).The optimization is mainly about the column set, but the gradient and the modulation time had to be adapted to each column set to get an enhanced separation, hence the relevance of the multicriteria strategy implemented in this paper.A preliminary study was performed to define which ranges of gradient and modulation time were relevant for each column set.The modulation time should not exceed 10 seconds to avoid overloading the modulator jet, but it has to be long enough to minimize wrapping around.In a first step, all analytical setups were tested with a gradient of 3°C/min and a modulation time of 6 seconds.The eight column sets, the four different gradients (2, 2.5, 3 or 4 °C/min) and the three different modulation times (6, 8 or 10 s) led to a total of 96 different analytical setups, but a first selection was made as some analytical setups were more promising than others.The fact that developed methods could be used for routine analysis had also to be considered.Thus, data were processed with two different objectives.First, criteria were chosen to get the best separation in a reduced run time.The second objectives did not take the run time into account and gave more weight to the quality of the separation.

1) Calculation of individual desirabilities
Prior to data processing, the bounds B0 and B1 were set (cf. table 2).The arithmetic mean of NND provided information about peak spreading and extreme points, while the harmonic mean provided a complementary information about peak clustering.In Nowik et al., the orthogonality of several data sets evaluated with the harmonic mean ranged from 0.017 to 0.054, a value of 0.047 being considered satisfactory.Hence the bounds B1 and B0 were set to 0.05 and 0.045 respectively.For the arithmetic mean, the values were in the interval [0.040 ; 0.084], hence our choice of the bounds B1 and B0 at 0.08 and 0.05 respectively.When the run time was considered, analyses longer than 80 min (B1) were put at disadvantage while analyses which exceeded 150 were automatically discarded (B0).As for the orthogonality coefficient, the bounds B0 and B1 were set to 50 and 80% respectively.Concerning the occupied space, B0 and B1 were set to 20 and 45% with raw data and to 30 and 55% with normalized data.
Then, the individual desirabilities were calculated.Figure 2 shows the individual desirability function of each criterion (blue line); the data of each analytical setup were plotted as red crosses.Data spreading is different for each criterion showing the complementarity of the selected criteria.Though data are clustered with the arithmetic mean, the use of the bounds defined prior to the study (cf.table 2) was sufficient to discriminate between analytical setups and make this criterion useful.With the Spearman correlation coefficient, the majority of data receives complete fitness value, and only small numbers of analytical setups receive 0.5 or some degrees between 0.5 and 1.These clusters show that a single criterion is not be sufficient to rank the analytical setups properly.However, most criteria showed good spreading of data.
Finally, the calculation of the global desirability was performed with and without the time constraint, leading to two different rankings.

2) Computation of the global desirability 2.1 Optimization for routine analyses with run time
Considering the run time, the calculation of occupied space with raw data was preferred to the calculation with normalized data in order to account for possibly empty places at the borders of the chromatograms.For instance, space can be lost at the end of the chromatogram with too slow ramps of temperature.Moreover, the use of a column with non-adapted polarities can lead to a loss of space covering which is not taken into account using normalized data.
The quality of the separation was also evaluated with the number of detected compounds and the number of coelutions.

Optimization regardless of run time
In this part, the objectives were to get the best separation regardless of run time (cf.table 2).Thus, we chose to work with normalized data -as defined in Statistical Analysis -in order not to consider empty space at the borders of chromatograms.Here, the quality of the separation was favored over the run time.In this way, a satisfying peak scattering -even if on a limited area of the chromatogram -was preferred.According to these choices, the number of detected compounds and the number of coelutions were also used to evaluate the performance of the separation.

3) Ranking of analytical setups
The exclusion of the run time criterion played a role but was shown not to be essential since the same column set DB-1MS×DB-1701 -even with different analytical setups -appeared 3 times in the top 5, whatever the objective (cf.table 3).The column set DB-1MS×DB-1701 emerged as the most appropriate choice for the separation of the mixture of 80 compounds (cf.chromatograms shown figures 3 and 4).
The column setup WAX×1701:3-6 ranked as fourth when run time was ignored.DB-WAX was the most polar column at our disposal but was quickly discarded.Combined with a DB-1MS or with a DB-5MS, it was expected to provide quite good results, because of the difference in polarities.But the bleeding proved to be a true limitation for its use as a first dimension column (cf.figure 5).When used as the second dimension column, an inacceptable echo phenomenon occurred which had a strong impact on several analytical setups (1MS×WAX:3-6, 5MS×WAX:3-6) evaluated in this study.The set DB-WAX×DB5 did not provide convincing results but one of its analytical setups (WAX×5:3-6) was kept to see if it could give interesting results anyway.
Prior to the experiments, only slight differences between the DB-1MS and the DB-5MS were expected.But it is interesting to notice that most of the setups with a DB-5MS in first dimension were discarded because of coelutions that were resolved using the DB-1MS.Thus, only four setups with the DB-5MS×DB-1701 set were evaluated.
The use of an ionic liquid column (SLB-IL60) was expected to provide an enhanced separation combined with a DB-1MS -or a DB-5MS -as its polarity is higher than DB-WAX's.However, the preliminary tests showed it was not relevant for this study because of the dual-jet cryomodulator.This column may be far too polar and the echo phenomenon was important all over the chromatogram, thus invalidating the assumption of a phase modification due to the cryomodulation.Moreover, even when the length was reduced from 1.5m to 1m, lots of compounds kept on wrapping around even with the largest modulation time, leading to broaden peaks.These two phenomena lead to eliminate this set because it was impossible to identify compounds properly.With another modulation system -flow modulator or nitrogen cryomodulator -the results might have been different.Another hypothesis is that the problem is related to the analyte elution temperature from the first dimension: using a more polar column might increase the analyte elution temperature, and, thereby, speed-up the elution in the second dimension, thus avoiding wrap around.Using desirability is a true asset in this case because the individual desirabilities of most criteria are acceptable for the 5MS×IL60:2-6 analytical setup.Considering that a lot of compounds were not found, the number of peaks was low.But in this case, they were well scattered, leading to good results -according to the desirability bounds -with the arithmetic mean, the harmonic mean, the correlation coefficients and the orthogonality coefficient.Only the calculation of the surface coverage is of particular interest here because the number of bins was chosen according to the number of expected compounds.It gave interesting information about clustering, peak spreading and took the number of peaks into account.
In the end, the same column set DB-1MS×DB-1701 with a gradient of 2.5°C/min -2°C/min if the run time is not considered -and a modulation time of 8 seconds appeared to be the best analytical setup for the separation of the synthetic mixture of 80 compounds representative of human hand odor.Moreover, this method was successfully applied to real samples and provided good separations meeting our expectations, results which are the topic of a future paper focusing on the sampling methods.

V) Conclusion
The use of comprehensive two-dimensional gas chromatography coupled with mass spectrometry would be a true asset for the analysis of human odor.The evaluation of multidimensional separation is not an easy task and various tools are available to assess the orthogonality of the separation and choose a proper column set.A desirability analysis allowed to consider more than one criterion and to rank the different column sets according to predefined objectives.In this paper, 27 different analytical setups were evaluated using nine criteria including six complementary orthogonality criteria: Spearman' correlation coefficient, the harmonic and arithmetic means described by Nowik et al., the coefficient of orthogonality described by Camenzuli et al. and the coverage of the separation space using raw and normalized data.The use of desirability functions enabled to consider additional simple but meaningful criteria such as the run time, the number of coelutions and the number of detected compounds.Two desirability calculations were performed, one with an objective of routine analysis and one without.Whatever the objectives, the same column set DB-1MS×DB-1701 was found to be the most appropriate for the analysis of human hand odor.This approach for the evaluation of orthogonality can be easily implemented with other criteria (convex hull, synentropy, etc.) according to the operator's choice, i.e. considering the targeted compounds and the application.The methods developed in this study are a solid background for further experimentation and sampling methods development.They will hopefully be used routinely with a large number of real samples for the analysis of human hand odor to support the information provided by dogs in courts of justice.

Figure 1 :
Figure 1: Example of a desirability plot

Table 2 :
Bounds used for individual desirability calculations