Multiscale biochemical mapping of the brain through deep-learning-enhanced high-throughput mass spectrometry.

Spatial omics technologies can reveal the molecular intricacy of the brain. While mass spectrometry imaging (MSI) provides spatial localization of compounds, comprehensive biochemical profiling at a brain-wide scale in three dimensions by MSI with single-cell resolution has not been achieved. We demonstrate complementary brain-wide and single-cell biochemical mapping using MEISTER, an integrative experimental and computational mass spectrometry (MS) framework. Our framework integrates a deep-learning-based reconstruction that accelerates high-mass-resolving MS by 15-fold, multimodal registration creating three-dimensional (3D) molecular distributions and a data integration method fitting cell-specific mass spectra to 3D datasets. We imaged detailed lipid profiles in tissues with millions of pixels and in large single-cell populations acquired from the rat brain. We identified region-specific lipid contents and cell-specific localizations of lipids depending on both cell subpopulations and anatomical origins of the cells. Our workflow establishes a blueprint for future development of multiscale technologies for biochemical characterization of the brain.

Advances in multimodal mass spectrometry for single-cell analysis and imaging enhancement.

Multimodal mass spectrometry (MMS) incorporates an imaging modality with probe-based mass spectrometry (MS) to enable precise, targeted data acquisition and provide additional biological and chemical data not available by MS alone. Two categories of MMS are covered; in the first, an imaging modality guides the MS probe to target individual cells and to reduce acquisition time by automatically defining regions of interest. In the second category, imaging and MS data are coupled in the data analysis pipeline to increase the effective spatial resolution using a higher resolution imaging method, correct for tissue deformation, and incorporate fine morphological features in an MS imaging dataset. Recent methodological and computational developments are covered along with their application to single-cell and imaging analyses.

Integrative Multiscale Biochemical Mapping of the Brain via Deep-Learning-Enhanced High-Throughput Mass Spectrometry.

Elucidating the spatial-biochemical organization of the brain across different scales produces invaluable insight into the molecular intricacy of the brain. While mass spectrometry imaging (MSI) provides spatial localization of compounds, comprehensive chemical profiling at a brain-wide scale in three dimensions by MSI with single-cell resolution has not been achieved. We demonstrate complementary brain-wide and single-cell biochemical mapping via MEISTER, an integrative experimental and computational mass spectrometry framework. MEISTER integrates a deep-learning-based reconstruction that accelerates high-mass-resolving MS by 15-fold, multimodal registration creating 3D molecular distributions, and a data integration method fitting cell-specific mass spectra to 3D data sets. We imaged detailed lipid profiles in tissues with data sets containing millions of pixels, and in large single-cell populations acquired from the rat brain. We identified region-specific lipid contents, and cell-specific localizations of lipids depending on both cell subpopulations and anatomical origins of the cells. Our workflow establishes a blueprint for future developments of multiscale technologies for biochemical characterization of the brain.

Optimizing column-to-column retention time alignment in high-speed gas chromatography by combining retention time locking and correlation optimized warping.

We examine and then optimize alignment of chromatograms collected on nominally identical columns using retention time locking (RTL), an instrumental alignment tool, and software-based alignment using correlation optimized warping (COW). For this purpose, three samples are constructed by spiking two sets of analytes into a base test mixture. The three samples are analyzed by high-speed gas chromatography with four nominally identical columns and identical separation conditions. The data is first analyzed without alignment, then using COW alone, then RTL alone, and finally with RTL followed by COW to correct the severe column-to-column misalignment. Principal component analysis (PCA) is used to investigate how well each alignment method clustered the chromatograms into the three sample classes via a scores plot without being compromised by the specific column(s) used. The degree-of-class separation (DCS) is used as a classification metric, measured as the Euclidian distance between the centroids of two clusters in PC space in the scores plot, normalized by their pooled variance. With no alignment, the average DCS between sample classes (DCSsam) was 3.0, while the average DCS between the four nominally identical columns, i.e., column classes (DCScol) was 76.1 (ideally the DCScol should be 0), indicating the chromatograms were initially classified by the columns used. Using either COW or RTL alone also produced unsatisfactory results, with COW alone incorrectly aligning many peaks, leading to a DCSsam of only 1.9 and DCScol of 1.7, while RTL alone provided a DCSsam of 4.7 and DCScol of 4.2. Finally, using RTL followed by COW alignment, DCSsam increased to 32.5, indicating successful classification by chemical differences between sample classes, while the DCScol decreased to 0.4, indicating virtually no classification due to column-to-column differences, as desired. Thus, RTL provided a "first-order" correction of the initial retention mismatch observed for the nominally identical columns, while additional alignment via COW was required to optimize sample classification by PCA.

Simulating comprehensive two-dimensional gas chromatography mass spectrometry data with realistic run-to-run shifting to evaluate the robustness of tile-based Fisher ratio analysis.

Untargeted analysis of comprehensive two-dimensional (2D) gas chromatography time-of-flight mass spectrometry (GC×GC-TOFMS) data has the potential to be hindered by run-to-run retention time shifting. To address this challenge, tile-based Fisher ratio (F-ratio) analysis (FRA) has been developed, which utilizes a supervised, untargeted approach involving a chromatographic segmentation routine termed "tiling" combined with the ANOVA F-ratio statistic to discover class-distinguishing analytes while minimizing false positives arising from shifting. The tiling algorithm is designed to account for retention shifting in both separation dimensions. Although applications of FRA have been reported, there remains a need to thoroughly evaluate the robustness of FRA for different levels of run-to-run retention shifting in order to broaden the scope of its application. To this end, a novel method of simulating GC×GC-TOFMS chromatograms with realistic run-to-run shifting is presented by random generation of low-frequency "shift functions". The dimensionless retention-time precision, <δr>, which is four times the standard deviation in retention time normalized to the peak width-at-base is used as a key modeling variable along with the 2D chromatographic saturation, αe,2D, and within-class relative standard deviation in peak area, RSDwc. We demonstrate that all three of these variables operate together to impact true positive discovery. To quantify the "success" of true positive discovery, GC×GC-TOFMS datasets for various combinations of <δr>, αe,2D, and RSDwc were simulated and then analyzed by FRA using a wide range of relative tile areas (RTA), which is a dimensionless measure of tile size. Since each hit in the FRA hit list was known a priori as either a true or false positive based on the simulation inputs, receiver operating characteristic (ROC) curves were readily constructed. Then, the area under the ROC curve (AUROC) was used as a metric for discovery "success" for various combinations of the modeling variables. Based on the results of this study, recommendations for tile size selection and experimental design are provided, and further supported by comparison to previous tile-based FRA applications. For instance, values for <δr>, αe,2D, and RSDwc obtained from a GC×GC-TOFMS dataset of yeast metabolites suggested an optimum RTA of 6.25, corresponding closely to the RTA of 4.00 employed in the study, implying the simulation results obtained here can be generalized to real datasets.

Profiling Olefins in Gasoline by Bromination Using GC×GC-TOFMS Followed by Discovery-Based Comparative Analysis.

An analytical workflow for the analysis of olefins in gasoline that combines selective bromination and comprehensive two-dimensional (2D) gas chromatography time-of-flight mass spectrometry (GC×GC-TOFMS) with discovery-based analysis is reported. First, a standard mix containing n-alkanes, 1-alkenes, and aromatic species was brominated and quantified using % reacted as a metric for each compound class, defined as the difference in the total peak area between the brominated and original samples normalized to the original sample. The average % reacted (1 s.d.) values were -1.45% (2.8%) for the alkanes, 99.5% (0.4%) for the alkenes, and 6.7% (11.6%) for the aromatics, demonstrating excellent selectivity toward the alkenes with only minor aromatic bromination. The bromination chemistry was then applied to gasoline, followed by GC×GC-TOFMS analysis of the original and brominated gasoline. This GC×GC-TOFMS data set was then submitted to the supervised discovery tool tile-based F-ratio analysis (FRA), which reduced the large data set to only the chromatographic regions which distinguish between the original and brominated gasoline samples. FRA discovered 314 hits, 56 of which were determined statistically significant using combinatorial null distribution analysis (CNDA), a permutation-based significance test. Since the brominated olefins elute in an uncrowded region of the 2D chromatogram and have no signal in the original sample, their discoverability was greatly increased relative to the original olefins. By combining the information gained from brominated olefin standards and the structured patterns of the GC×GC separations, the top hits were identified as the dibromoalkane products of mono-olefins, with five C5 mono-olefins identified on a species level. The analytical workflow has broad implications for using selective reaction chemistries to facilitate supervised discovery by targeting desired compound classes.

Tile-Based Pairwise Analysis of GC × GC-TOFMS Data to Facilitate Analyte Discovery and Mass Spectrum Purification.

A new tile-based pairwise analysis workflow, termed 1v1 analysis, is presented to discover and identify analytes that differentiate two chromatograms collected using comprehensive two-dimensional (2D) gas chromatography coupled with time-of-flight mass spectrometry (GC × GC-TOFMS). Tile-based 1v1 analysis easily discovered all 18 non-native analytes spiked in diesel fuel within the top 30 hits, outperforming standard pairwise chromatographic analyses. However, eight spiked analytes could not be identified with multivariate curve resolution-alternating least-squares (MCR-ALS) nor parallel factor analysis (PARAFAC) due to background contamination. Analyte identification was achieved with class comparison enabled-mass spectrum purification (CCE-MSP), which obtains a pure analyte spectrum by normalizing the spectra to an interferent mass channel (m/z) identified from 1v1 analysis and subtracting the two spectra. This report also details the development of CCE-MSP assisted MCR-ALS, which removes the identified interferent m/z from the data prior to decomposition. In total, 17 out of 18 spiked analytes had a match value (MV) > 800 with both versions of CCE-MSP. For example, MCR-ALS and PARAFAC were unable to decompose the pure spectrum of methyl decanoate (MVs < 200) due to its low 2D chromatographic resolution (∼0.34) and high interferent-to-analyte signal ratio (∼30:1). By leveraging information gained from 1v1 analysis, CCE-MSP and CCE-MSP assisted MCR-ALS obtained a pure spectrum with an average MV of 908 and 964, respectively. Furthermore, tile-based 1v1 analysis was applied to track moisture damage in cacao beans, where 86 analytes with at least a 2-fold concentration change were discovered between the unmolded and molded samples. This 1v1 analysis workflow is beneficial for studies where multiple replicates are either unavailable or undesirable to save analysis time.

Class comparison enabled mass spectrum purification for comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry.

Tile-based Fisher ratio (F-ratio) analysis is emerging as a versatile data analysis tool for supervised discovery-based experimentation using comprehensive two-dimensional (2D) gas chromatography coupled with time-of-flight mass spectrometry (GC × GC-TOFMS). None the less, analyte identification can often be marred by poor 2D resolution and low analyte abundance relative to overlapping compounds. Linear algebra-based chemometric methods, in particular multivariate curve resolution alternating least squares (MCR-ALS), parallel factor analysis (PARAFAC) and PARAFAC2, are often applied in an effort to address this situation. However, these chemometric methods can fail to produce an accurate spectrum when the analyte is at low 2D resolution and/or in low relative abundance. To address this challenge, we introduce class comparison enabled mass spectrum purification (CCE-MSP), a method that utilizes the underlying requirement for signal consistency of the background interference compounds between the two classes in the F-ratio analysis to purify the mass spectrum of the analyte hits. CCE-MSP is validated using a dataset obtained for a neat JP-8 jet fuel spiked with 14 sulfur containing compounds at two levels (15 ppm and 30 ppm), using the p-value and lack-of-fit (LOF) for each analyte hit as consistency metrics. A purified mass spectrum was produced for each spiked analyte hit and their mass spectrum match value (MV) was compared to the MV obtained by MCR-ALS, PARAFAC, and PARAFAC2. The resulting MV for CCE-MSP were found to be as good or better than these chemometric methods, eg., for 2-butyl-5-ethylthiophene with an analyte-to-interference relative signal abundance of 1:87 and a 2D resolution of 0.2, CCE-MSP produced a MV of 831, compared to 476 for MCR-ALS, 403 for PARAFAC, and 336 for PARAFAC2. CCE-MSP is also extended to obtain the purified spectrum for more than one analyte, eg., two analyte hits in overlapping hit locations. The spectra produced by CCE-MSP can also be utilized as estimates to facilitate quantitative signal decomposition using MCR-ALS.

Determination of the Signal-To-Noise Ratio Enhancement in Comprehensive Three-Dimensional Gas Chromatography.

We investigate the extent to which comprehensive three-dimensional gas chromatography (GC3) provides a signal enhancement (SE) and a signal-to-noise ratio enhancement (S/NRel) relative to one-dimensional (1D)-GC. Specifically, the SE is defined as the ratio of the tallest 3D peak height from the GC3 separation to the 1D peak height from the unmodulated 1D-GC separation. A model is proposed which allows the analyst to predict the theoretically attainable SE (SET) based upon the peak width and sampling density inputs. The model is validated via comparison of the SET to the experimentally measured SE (SEM) obtained using total-transfer GC3 (100% duty cycle for both modulators) with time-of-flight mass spectrometry detection. Two experimental conditions were studied using the same GC3 column set, differing principally in the modulation period from the 1D to 2D columns: 4 s versus 8 s. Under the first set of conditions, the average SEM was 97 (±22), in excellent agreement with the SET of 97 (±18). The second set of conditions improved the average SEM to 181 (±27), also in agreement with the average SET of 176 (±26). The average S/NRel following correction for the mass spectrum acquisition frequency was 38.8 (±11.2) and 59.0 (±27.2) for the two sets of conditions. The enhancement in S/N is largely attributed to moving the signal to a higher frequency domain where the impact of "low frequency" noise is less detrimental. The findings here provide strong evidence that GC3 separations can provide enhanced detectability relative to 1D-GC and comprehensive two-dimensional gas chromatography (GC×GC) separations.

Sequential injection analysis coupled to on-line benchtop proton NMR: Method development and application to the determination of synthetic cathinones in seized drug samples.

Synthetic cathinones are a class of new psychoactive substances (NPS), an emerging group of analogues to traditional illicit drugs which are functionalized to circumvent legal regulations. The analytical investigation of NPS by traditional methods, such as gas chromatography-mass spectrometry (GC-MS), is challenging because newly emerging NPS may not yet appear in spectral libraries and because of the inability to determine certain positional isomers. Low-field or "benchtop" proton nuclear magnetic resonance spectroscopy (NMR) is an alternative that provides significant qualitative information but is particularly susceptible to matrix interferences. To this end, the development of a Sequential Injection Analysis (SIA) method which uses solid-phase extraction (SPE) to remove interfering matrix components prior to NMR determination is described. Factors including the type of SPE sorbent, column dimensions, and sample loading and elution conditions were examined. Several cathinone simulants (primary, secondary, and tertiary amines), "DEA exempt" cathinone standards, as well as authentic case samples were studied. The selectivity of the SIA-NMR-UV method was investigated against a broad range of "cutting agents" and was found to successfully remove all compounds tested with the exception of other basic drugs (e.g., acetaminophen). The limit of detection and reproducibility of the method were optimized using a Plackett-Burman screening design and Sequential Simplex optimization. Using a UV detector for dual (in series) quantification, the multivariate-optimized method produced a method limit of detection (3σ) for the cathinone simulant Phenylpropanolamine (PPA) of 23 µmol L-1, and a calibration model, in terms of UV peak area, of Area = 0.19 [PPA, mmol L-1] - 0.04. The optimized method generated ~2 mL of waste per day, and had a footprint of ~1 m2 Finally, the multivariate-optimized SIA-NMR-UV method was successfully applied to several more case samples and the cathinones were definitively identified.

Total-transfer comprehensive three-dimensional gas chromatography with time-of-flight mass spectrometry.

Although comprehensive two-dimensional (2D) gas chromatography (GC × GC) is a powerful technique for complex samples, component overlap remains likely. An intriguing route to address this challenge is to utilize the additional peak capacity and chemical selectivity provided by comprehensive three-dimensional (3D) gas chromatography (GC3), especially with time-of-flight mass spectrometry detection (GC3-TOFMS). However, the GC3-TOFMS instrumentation reported to date has employed one or both modulators with a duty cycle < 100%, making the potential gain in detection sensitivity over GC × GC modest, or perhaps even worse. Herein, we describe instrumentation for GC3-TOFMS in which both modulators provide total-transfer (100% duty cycle). Specifically, the instrument is based on the facile modification of a commercial thermally modulated comprehensive GC × GC-TOFMS platform for modulation from the 1D column to the 2D column, with recently described dynamic pressure gradient modulation (DPGM) as the second modulator from the 2D column to the 3D column, which is a total-transfer flow modulation technique. Area measurements of 1D peaks are compared to the sum of 3D peak areas to validate the assumption that total-transfer from 1D to 3D is accomplished. Additionally, peak heights were amplified by as high as a factor of 177 (x̅ = 130, s = 47) via comparison of 1D peak heights to the maximum 3D peak heights. Column selection is explored, with emphasis on the resulting peak width-at-base on each dimension and usage of 3D space as evaluation metrics. Using a nonpolar × polar × ionic liquid column combination, an effective peak capacity which considers modulation-induced broadening as high as 32,300 for select analytes was achieved (x̅ = 19,900, s = 10,700). The analytical benefits of employing three selective phases, mass spectrometry detection, and total-transfer modulation are explored with separations of a metabolomics-type sample, i.e., derivatized porcine serum, and a jet fuel spiked with various sulfur-containing compounds.

A systematic investigation of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry with dynamic pressure gradient modulation for high peak capacity separations.

Dynamic pressure gradient modulation (DPGM) in full modulation mode is optimized for comprehensive two-dimensional (2D) gas chromatography (GC × GC) with time-of-fight mass spectrometry (TOFMS) detection to obtain high peak capacity separations and demonstrate broad applicability for complex samples. A pulse valve introduces an auxiliary carrier gas flow at a T-union connecting the first dimension (1D) column to the second dimension (2D) column. At a sufficiently high auxiliary pressure (Paux) the 1D flow is temporarily stopped. Then, during each modulation period (PM) the valve is turned off briefly, a period termed the pulse width (pw), allowing the 1D effluent to essentially be reinjected onto the 2D column for the modulated separations. Modifications to the modulator assembly are provided to improve performance. Method optimization is demonstrated for a 116-component test mixture by tuning the Paux and the pw. For a PM = 2 s and 1F of 0.10 ml/min, the optimal pw and initial Paux selected were 200 ms and 330.9 kPa (33 psig), respectively. The 30 min separation of the test mixture provided a 1D peak capacity of 1nc = 330 and a 2D peak capacity of 2nc = 15, hence an ideal 2D peak capacity nc,2D = 1nc × 2nc = 4950. Likewise, the 2D peak capacity corrected for undersampling of the 1D separation was 4500 and corrected for both undersampling and sampling variation via statistical overlap theory was 4090. These results provide a 2-fold improvement in peak capacity relative to the previous DPGM study in full modulation mode for GC × GC-TOFMS. The optimized conditions were applied for a variety of applications: diesel fuel, derivatized cow serum, solid phase microextraction (SPME) of coffee headspace, and SPME of river water headspace. Additionally, the fraction of 2D separation space utilized (fcoverage), as defined by the minimum convex hull method, ranged from 0.60 to 0.85. We observed that any fcoverage correction to 2D peak capacity is highly sample dependent, since all samples, except for the diesel sample, were run with the same separation conditions, and yet the fcoverage ranged from 0.60 to 0.80.

Discovery-based analysis and quantification for comprehensive three-dimensional gas chromatography flame ionization detection data.

Basic principles are introduced for implementing discovery-based analysis with automated quantification of data obtained using comprehensive three-dimensional gas chromatography with flame ionization detection (GC3-FID). The GC3-FID instrument employs dynamic pressure gradient modulation, providing full modulation (100% duty cycle) with a fast modulation period (PM) of 100 ms. Specifically, tile-based Fisher-ratio analysis, previously developed for comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GC×GC-TOFMS), is adapted and applied for GC3-FID where the third chromatographic dimension (3D) is treated as the "spectral" dimension. To evaluate the instrumental platform and software implementation, ten "non-native" compounds were spiked into a ninety-component base mixture to create two classes with a concentration ratio of two for the spiked analyte compounds. The Fisher ratio software identified 95 locations of potential interest (i.e., hits), with all ten spiked analytes discovered within the top fourteen hits. All 95 hits were quantified by a novel signal ratio (S-ratio) algorithm portion of the F-ratio software, which determines the time-dependent S-ratio of the 3D chromatograms from one class to another, thus providing relative quantification. The average S-ratio for spiked analytes was 1.94 ± 0.14 mean absolute error (close to the nominal concentration ratio of two), and 1.06 ± 0.16 mean absolute error for unspiked (i.e., matrix) components. The appearance of the S-ratio as a function of 3D retention time in the GC3 dataset, referred to as an S-ratiogram, provides indication of peak purity for each hit. The unique shape of the S-ratiogram for hit 1, α-pinene, suggested likely 3D overlap. Parallel factor analysis (PARAFAC) decomposition of the hit location confirmed that overlap was occurring and successfully decomposed α-pinene from a highly overlapped (3Rs = 0.1) matrix interferent.

Dynamic pressure gradient modulation for comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry detection.

Dynamic pressure gradient modulation (DPGM) is investigated for comprehensive two-dimensional gas chromatography (GC × GC) with time-of-flight mass spectrometry (TOFMS) detection. With DPGM, a commercial pneumatic "pulse" valve is opened to introduce a suitably high auxiliary gas pressure at a T-junction connecting the first dimension (1D) and second dimension (2D) columns during the modulation period (PM), temporarily stopping the 1D flow. The valve is then closed for the duration of a pulse width (pw) to "re-inject" temporally focused 1D eluate onto the 2D column for separation. This flow modulation technique is observed to be compatible with TOFMS detection using a 2D flow rate of 4 ml/min for the separation of a 90-component test mixture. A 25 min separation window using a PM = 1 s and pw = 200 ms for full modulation (and 100% duty cycle) provided an average 1Wb = 4.5 s and 2Wb = 130 ms for a 2D peak capacity of nc,2D = 2700 (100 peaks per min). The detector response enhancement factor (DREF) serves as a metric for the enhanced sensitivity of the modulated relative to the unmodulated 1D peaks, with DREFs ranging between 10 and 20 and about a 5-fold improvement in signal-to-noise ratio (S/N). The bilinear "quality" of the GC × GC data is studied using the chemometric method parallel factor analysis (PARAFAC). Since PARAFAC requires sufficiently trilinear data, the reproducibility of the 2D peak shape for a given analyte is confirmed using lack-of-fit (LOF) and percent variation (R2) metrics. The limit-of-detection (LOD) for the representative analyte hexadecane is determined using PARAFAC, providing an LOD of 0.7 ppb (±0.03 ppb) for three replicates. Seven heavily overlapped analytes are also fully resolved by PARAFAC down to the part-per-million (ppm) concentration level, producing reproducible spectra with a majority of spectral match values (MV) over 800 (RSD ≤ 7.1%). This study provides promising results for DPGM as a flow modulation technique compatible with GC × GC-TOFMS, providing high sensitivity data suitable for chemometric analysis.

Dynamic pressure gradient modulation for comprehensive two-dimensional gas chromatography.

We report the discovery, preliminary investigation, and demonstration of a novel form of differential flow modulation for comprehensive two-dimensional (2D) gas chromatography (GC×GC). Commercially available components are used to apply a flow of carrier gas with a suitable applied auxiliary gas pressure (Paux) to a T-junction joining the first (1D) and second (2D) dimension columns. The 1D eluate is confined at the T-junction, and introduced for 2D separation with a cyclic rhythm, dependent upon the relationship of the modulation period (PM) to the pulse width (pw), where pw is defined as the time interval when the auxiliary gas flow at the T-junction is off. We refer to this flow modulation technique as "dynamic pressure gradient modulation" (DPGM) since a pressure gradient oscillates with the PM along the 1D and 2D column ensemble providing temporary stop-flow conditions and fast 2D flow rates, resulting in 100% duty cycle and full modulation. A 90-component test mixture was used to evaluate the technique with a pw of 60 ms and a PM of 750 ms. The resulting peaks were narrow, with 2Wb ranging from about 20-180 ms. With an average 1Wb of 3 s and a 2nc of 10, a 2D peak capacity, nc,2D, for the 25 min separation was 5000. The detector response enhancement factor (DREF) is reported, defined as the peak height of the highest modulated 2D peak divided by the unmodulated 1D peak height (DREF = 2h/1h). The DREF ranged from about 7-87, depending on the 1Wb and 2Wb for a given analyte. A diesel sample was analyzed to demonstrate performance with a complex sample. Based upon the average 1Wb of 5 s and an average 2Wb of 168 ms, a nc,2D of 8640 was obtained for the 60 min diesel separation. Finally, the modulation principle was investigated as a function of PM, pw, and the volumetric flow rates, 1F and 2F. The measured 2Wb correlate well with the theoretical 2D injected width, given by 2Winj = (1F/2F) ·PM. However, the relevant 1F appears to be dictated by the 1D flow rate when no pressure is applied (during the pw interval), instead of 1F being the average flow rate on 1D (defined by the 1D dead time). The findings provide strong evidence for a differential flow modulation mechanism.