Patent Publication Number: US-8530828-B2

Title: Systems and methods for reducing noise from mass spectra

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation-in-part application of U.S. patent application Ser. No. 12/626,737, filed Nov. 27, 2009, now U.S. Pat. No. 8,148,678, which is a continuation application of U.S. patent application Ser. No. 12/023,873, filed Jan. 31, 2008, now U.S. Pat. No. 7,638,764, that claims priority to U.S. Provisional Patent Application No. 60/887,915 filed on Feb. 2, 2007, and this application claims priority to U.S. Provisional Patent Application No. 61/582,304 filed on Dec. 31, 2011. All of the above mentioned applications are incorporated by reference herein in their entireties. 
    
    
     INTRODUCTION 
     Periodic noise in mass spectrometry (presumably arising from clusters of ions and neutral molecules) is normally associated with very low flow rate electrospray ionization (ESI) (e.g., nanospray) and matrix-assisted laser desorption/ionization (MALDI). This noise is generally characterized by equally spaced peaks across a large mass range. The peaks have similar intensity, which may decrease with increasing mass, and are generally broader than expected for the given instrument and mass, suggesting the presence of unresolved components. 
     Periodic noise has been observed in data from separation coupled mass spectrometry. This noise affects both qualitative and quantitative measurements performed from this data. As a result, the removal of period noise from separation coupled mass spectrometry is desirable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The skilled artisan will understand that the drawings, described below, are for illustration purposes only. The drawings are not intended to limit the scope of the present teachings in any way. 
         FIG. 1  is a schematic diagram of a noise reducing system made in accordance with the present invention; 
         FIG. 2  is a graph illustrating an original mass spectrum as may be input into and manipulated by the system of  FIG. 1 ; 
         FIG. 3A  is a graph illustrating an original frequency spectrum determined by transforming the original mass spectrum of  FIG. 2  into the frequency domain; 
         FIG. 3B  is a magnified segment of the graph of  FIG. 3A ; 
         FIG. 3C  is a schematic diagram of a segment of a filter made and used in accordance with the present invention to filter the original frequency spectrum of  FIG. 3A , the segment corresponding to the original frequency segment illustrated in  FIG. 3B ; 
         FIG. 4  is a graph illustrating a noise frequency spectrum made in accordance with the present invention and determined by selectively filtering for dominant frequencies in the original frequency spectrum of  FIG. 3A ; 
         FIG. 5  is a graph illustrating a noise mass spectrum made in accordance with the present invention and determined by transforming the noise frequency spectrum of  FIG. 4  into the mass domain; 
         FIG. 6  is a graph illustrating a magnified portion of the noise mass spectrum of  FIG. 5  overlaid together with a corresponding magnified portion of the original mass spectrum of  FIG. 2 ; 
         FIG. 7A  is a graph illustrating the noise mass spectrum made in accordance with the present invention by determining the minimum value of each corresponding pair of intensity data points from the complete noise mass spectrum and original mass spectrum portions of which were illustrated in  FIG. 6 ; 
         FIG. 7B  is a graph illustrating a magnified portion of the noise mass spectrum of  FIG. 7A  corresponding to the magnified portions in  FIG. 6 ; 
         FIG. 8  is a graph illustrating a noise frequency spectrum determined by transforming the noise mass spectrum of  FIG. 7A  into the frequency domain; 
         FIG. 9  is a graph illustrating a noise frequency spectrum made in accordance with the present invention and determined by selectively filtering for dominant frequencies in the noise frequency spectrum of  FIG. 8 ; 
         FIG. 10  is a graph illustrating a noise mass spectrum made in accordance with the present invention and determined by transforming the noise frequency spectrum of  FIG. 9  into the mass domain; 
         FIG. 11  is a graph illustrating the noise mass spectrum made in accordance with the present invention by determining the minimum value of each corresponding pair of intensity data points from the complete noise mass spectrum of  FIG. 10  and the original mass spectrum of  FIG. 2 ; 
         FIG. 12  is a graph illustrating a corrected mass spectrum made in accordance with the present invention and determined by subtracting the noise frequency spectrum of  FIG. 11  from the original mass spectrum of  FIG. 2 ; and 
         FIG. 13  is a flow diagram illustrating the steps of a method of reducing noise in a mass spectrum, in accordance with the present invention. 
         FIG. 14  is a block diagram that illustrates a computer system, upon which embodiments of the present teachings may be implemented. 
         FIG. 15  is a schematic diagram showing a system for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. 
         FIG. 16  is an exemplary flowchart showing a method for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. 
         FIG. 17  is a schematic diagram of a system  1700  includes one or more distinct software modules that perform a method for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. 
         FIG. 18  is a schematic diagram showing a system for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. 
         FIG. 19  is an exemplary flowchart showing a method for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. 
         FIG. 20  is a schematic diagram of a system that includes one or more distinct software modules that perform a method for generating a background noise estimate for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. 
     
    
    
     Before one or more embodiments of the present teachings are described in detail, one skilled in the art will appreciate that the present teachings are not limited in their application to the details of construction, the arrangements of components, and the arrangement of steps set forth in the following detailed description or illustrated in the drawings. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. 
     DESCRIPTION OF VARIOUS EMBODIMENTS 
     Periodic Noise in Separation Coupled Mass Spectrometry 
     Referring to  FIG. 1 , illustrated therein is a noise reducing system, referred to generally as  10 , made in accordance with the present invention. The system  10  comprises a processor or central processing unit (CPU)  12  having a suitably programmed noise reduction engine  14 . The programming for the engine  14  may also be saved on storage media for example such as a computer disc or CD-ROM. An input/output (I/O) device  16  (typically including a data input component  16 .sup.A, and an output component such as a display  16 .sup.B) is also operatively coupled to the CPU  12 . As will be understood, preferably the data input component  16 .sup.A will be configured to receive mass spectrum and/or frequency domain data, and the display  16 .sup.B will similarly be configured to graphs corresponding to mass spectra and frequency domains. 
     Data storage  17  is also preferably provided in which may be stored mass spectrum and frequency domain data. 
     As will be understood, the system  10  may be a stand-alone analysis system for reducing noise in a mass spectrum (or frequency domain data). In the alternative, the system  10  may (but does not necessarily have to) comprise part of a spectrometer system having an ion source  20 , configured to emit a beam of ions, generated from a sample to be analyzed. 
     A detector  22  (having one or more anodes or channels) may also be provided as part of the spectrometer system, which can be positioned downstream of the ion source  20 , in the path of the emitted ions. Optics  24  or other focusing elements, such as an electrostatic lens can also be disposed in the path of the emitted ions, between the ion source  20  and the detector  22 , for focusing the ions onto the detector  22 . 
     Referring now to  FIG. 2 , illustrated therein is a graph  30  illustrating an original mass spectrum  40  as may be input into and analyzed by the system  10 . The vertical axis  42  corresponds to signal intensity, while the horizontal axis  44  corresponds to m/z (mass/charge). The graph displays the original mass spectrum  40 , which will typically comprise a real signal combined together with and obscured by a background noise or signal. As will be understood, the data corresponding to the original mass spectrum  40  is preferably input into and stored in the data storage  17 , and typically the graph  30  is displayed on the display  16 .sup.B. 
       FIG. 13  sets out the steps of the method, referred to generally as  200 , carried out by the noise reducing system  10 . Data corresponding to an original mass spectrum  40  (illustrated in  FIG. 2 ) is received (typically via the I/O device or determined by the system  10  if the system  10  comprises a spectrometer) and typically stored in data storage  17 , and the noise reduction engine  14  is programmed to initiate the noise reduction analysis (Block  202 ). A noise mass spectrum corresponding to the background signal component in the original mass spectrum  40  is then determined (Block  204 ). As set out in the discussion relating to Blocks  206  to  232  below, this step may itself comprise a number of steps. 
     The engine  14  can be programmed to effect a transformation of the original mass spectrum  40  into the frequency domain (typically by subjecting the original mass spectrum  40  data to a Fourier Transformation, sine/cosine transform or any mathematical or experimental method known in the art) to obtain an original frequency spectrum  50 , as illustrated in the graph  52  of  FIG. 3A  (a magnified segment of which is illustrated in the graph  52 ′ of  FIG. 3B ) (Block  206 ). In the graph  52 , the vertical axis  54  corresponds to intensity while the horizontal axis  56  corresponds to frequency. 
     The original frequency spectrum  50  comprises distinct peaks  58  corresponding to dominant frequencies. As will be understood, background noise is often periodic in nature, typically having a period of one atomic mass unit. Accordingly, a significant portion of the intensity of the dominant frequencies  58  may often be attributed to the noise component of the original mass spectrum  40 . These dominant frequencies  58  will often correspond to the background noise&#39;s base frequency and corresponding harmonics thereof. 
     The engine  14  preferably identifies at least one and preferably all of the dominant frequencies  58  in the original frequency spectrum  50  (although as will be understood, this step could be performed manually by a system  10  user) (Block  208 ). Next, the original frequency spectrum  50  is filtered for the identified dominant frequencies  58 , in order to generate a noise frequency spectrum  60 , as illustrated in the graph  61  of  FIG. 4  (Block  210 ). 
     To accomplish this, a filter  62 , such as that depicted for illustrative purposes in the schematic graph  64  of  FIG. 3C , may be created to selectively filter for the identified dominant frequencies  58 . Typically the data filter  62  will be implemented through software in the reduction engine  14 , and will often not be displayed to the end user. As can be seen, the vertical axis  66  represents the ratio (from 0 to 1) of the original frequency spectrum  50  to be retained or filtered for. The horizontal axis  68  corresponds to frequency. The filter  62  preferably comprises a plurality of tabs  70  corresponding to the number of dominant frequencies  58  identified in Block  208 . As can be seen from the juxtaposition of  FIGS. 3A and 3B , via the tabs  70 , the filter  62  is configured to preserve or filter for 100% of the identified dominant frequencies  58  data. Conversely, the filter  62  discards the frequency data in the original frequency spectrum  50  not forming part of the identified dominant frequencies data  58 , resulting in the noise frequency spectrum  60  data. 
     Subsequently, the engine  14  is preferably configured to determine a noise mass spectrum  72  illustrated in the graph  74  of  FIG. 5 , typically by affecting an inverse Fourier transformation of the noise frequency spectrum  60  data into the mass domain (Block  212 ). 
     As will be understood, the noise mass spectrum  72  data represents an estimate of the background noise signal component of the original mass spectrum  40 . 
     Referring to  FIG. 6 , illustrated therein is a graph  76  overlay of a close-up segment of the original mass spectrum  40  with a corresponding magnified segment of the noise mass spectrum  72 . As will be understood, the noise  72  and original  40  mass spectrums are formed of many thousands of data points. Data points in both mass spectrums  72  and  40  may be correlated as one data point should exist in each spectrum  40 ,  72  corresponding to each m/z value. 
     Referring to exemplary data points  74 A and  74 B (and  75 A and  75 B) of the original mass spectrum  40  and the noise mass spectrum  72 , respectively, each pair is correlated to the same m/z value (as indicated by the dotted lines). It can be seen that the noise mass spectrum  72  may have a higher intensity value at certain m/z values than the original mass spectrum  40 . However, as will be understood, this indicates an artifact in estimation of the background noise signal component, as the noise component should not exceed the combined background and real signals of the original mass spectrum  40  (at corresponding m/z values). This artifact is a result of the real peak(s) in the original mass spectrum  40 , for example at points  74 A,  75 A where the original mass spectrum  40  has a higher intensity value than the corresponding points  74 B,  75 B on the noise mass spectrum  72 . 
     Accordingly, to further refine the background signal estimate, the noise mass spectrum  72  data is revised such that for each correlated data point in the noise mass spectrum  72  and original mass spectrum  40  (having the same m/z value), the minimum intensity value of the two data points is determined (Block  214 ). In turn, the noise mass spectrum is preferably modified by making the noise intensity data point equal to the minimum value (Block  216 ). 
     For the sake of clarity, the steps of Blocks  214  and  216  may be implemented using the function set out in Equation 1, below:
 
 f ′( x )=min( f ( x ), g ( x ))  EQ. 1:
 
where x represents m/z and f(x) represents the intensity value of the noise mass spectrum  72  and g(x) represents the intensity value of the original mass spectrum  40 , and f′(x) represents the modified noise mass spectrum.
 
     Completion of Block  216  for all of the correlated data points in the original and noise mass spectrums  40 ,  72 , results in a modified noise mass spectrum  80 , as illustrated in the graph  82  of  FIGS. 7A  (and  7 B) (Block  218 ). 
     Next, a transformation of the modified noise mass spectrum  80  into the frequency domain is effected (again, typically by subjecting the noise mass spectrum  80  data to a Fourier Transformation) to obtain a noise frequency spectrum  90 , as illustrated in the graph  92  of  FIG. 8  (Block  220 ). 
     Next, at least one and preferably all of the dominant frequencies  94  in the noise frequency spectrum  90  are identified (Block  222 ). The noise frequency spectrum  90  is then filtered for the identified dominant frequencies  94 , in order to generate a filtered noise frequency spectrum  98 , a portion of which is illustrated in the graph  99  of  FIG. 9  (Block  224 ). 
     Typically, the filter  62  of  FIG. 3B  created in reference to Block  210 , may be reused to selectively filter for the identified dominant frequencies  94 , in creating the noise frequency spectrum  98 . 
     Subsequently, a noise mass spectrum  100  as illustrated in the graph  102  of  FIG. 10  is generated, typically by affecting an inverse Fourier Transformation of the noise frequency spectrum  98  data into the mass domain (Block  226 ). 
     To further refine the background signal estimate, in a manner similar to that discussed in relation to Block  216 , the noise mass spectrum  100  data is revised such that for each correlated data point in the noise mass spectrum  100  and original mass spectrum  40  (correlated by sharing the same m/z value), the minimum intensity value of the two data points is determined (Block  228 ). In turn, the noise mass spectrum  100  is preferably modified by making the noise intensity data point equal to the minimum value (Block  230 ). As will be understood, the steps of Blocks  228  and  230  may be implemented using Equation 1, above. 
     Completion of Block  230  for all of the correlated data points in the original and noise mass spectrums  40 ,  100 , results in a modified noise mass spectrum  102 , as illustrated in the graph  104  of  FIG. 11  (Block  232 ). 
     The steps of Blocks  220  to  232  will preferably (but not necessarily) be repeated multiple times (as indicated by the line  233  in  FIG. 13 ), each repetition further refining the background signal estimate (noise mass spectrum  102 ) and making it more closely approximate the actual background signal. The steps of Blocks  220  to  232  may be repeated a predetermined number of times (for example from 1 to 20 times, typically, but more repetitions may be necessary in some instances), or the engine  14  may be programmed to discontinue the repetitions automatically once the difference between the respective versions of the modified noise mass spectrum  102  data and the noise mass spectrum  100  data falls within a predetermined range. 
     Once the final version of the modified noise mass spectrum  102  has been determined, the noise mass spectrum  102  is subtracted from the original mass spectrum  40 , resulting in a corrected mass spectrum  110  as illustrated in graph  112  in  FIG. 12  (Block  250 ). As will be understood, the corrected mass spectrum  110  corresponds to the intended real signal of the sample to be analyzed, with a substantial portion of the background noise (present in the original mass spectrum  40 ) removed. 
     In an alternate embodiment  200 ′, it has been found that improved results may sometimes be obtained by segmenting the original mass spectrum  40  into a plurality of initial windows  120  (as illustrated in  FIG. 2  and separated by dotted lines) prior to Block  206  (Block  234 ). Typically, the windows  120  are of equal dimensions, although this is not required. Preferably, Blocks  206  through  212  inclusive are each completed separately for one initial window  120 , before Blocks  206  through  212  are commenced and completed for another (typically successive) initial window  120 , as indicated by dotted line  236 . 
     Of course, as will be understood, the description above of each of Blocks  206  through  212  refer to mass spectrums and corresponding frequency domains as a whole. However, if the original mass spectrum  40  is to be processed by initial windows  120  separately pursuant to Block  234 , as appropriate, references to whole mass spectrums and frequency domains in the descriptions for the Blocks  206  through  212  should be understood to refer to the mass spectrum and frequency domain segments corresponding to the initial window  120  being processed during the specific iteration of those Blocks. 
     Once the segmentation of the original mass spectrum  40  into initial windows  120  pursuant to Block  222  and the subsequent completion of Blocks  206  through  212  for each initial window  12  and the modified noise mass spectrum  80  has been generated pursuant to Blocks  214  through  218 , the noise mass spectrum  80  is segmented into a series of a plurality of subsequent windows  130  (as illustrated in  FIG. 7A ) prior to Block  220  (Block  238 ). Preferably, the subsequent windows  130  in the series are configured such that no subsequent window  130  is coextensive with any initial window  12  in the mass domain. It is also preferable if (other than at the beginning and end of the mass spectrums), the windows  130  do not share a leading or termination edge (indicated by the dotted lines in  FIG. 7A ) with any initial windows  12 . 
     Accordingly, if the subsequent windows  130  are configured to be generally of the same size as the initial windows  12 , the subsequent window segments  130  will be shifted in the mass domain such that the first  130 ′ and last  130 ″ subsequent window segments will typically be smaller than the remainder of the subsequent windows  130 . 
     Each of Blocks  220  through  226  inclusive is completed separately for one subsequent window  130  (including  130 ′,  130 ″), before Blocks  220  through  226  are completed for another (typically successive) subsequent window  130 , as indicated by dotted line  240 . As with the initial embodiment discussed above, Blocks  220  through  232 , may be repeated for each subsequent repetition (as indicated by dotted line  233 ′ instead of line  233 ) preferably a series of new subsequent windows is created in Block  238  such that no new subsequent window  130  is coextensive with any subsequent window  130  in any previous series. It is also preferable if (other than at the beginning and end of the mass spectrums), any new subsequent windows  130  do not share a leading or termination edge (indicated by the dotted lines in  FIG. 7A ) with any subsequent windows  120  in a previous series. 
     To avoid or minimize the overlap of leading or terminating edges, for each subsequent repetition, a series of new subsequent windows  130  may be configured to generally have the same size as previous series of windows  130 , but be shifted in location relative to m/z value. Alternatively, the size of the windows  130  may be changed for different series of windows  130  to minimize the overlapping of leading or terminating edges. 
     Computer-Implemented System 
       FIG. 14  is a block diagram that illustrates a computer system  1400 , upon which embodiments of the present teachings may be implemented. Computer system  1400  includes a bus  1402  or other communication mechanism for communicating information, and a processor  1404  coupled with bus  1402  for processing information. Computer system  1400  also includes a memory  1406 , which can be a random access memory (RAM) or other dynamic storage device, coupled to bus  1402  for storing instructions to be executed by processor  1404 . Memory  1406  also may be used for storing temporary variables or other intermediate information during execution of instructions to be executed by processor  1404 . Computer system  1400  further includes a read only memory (ROM)  1408  or other static storage device coupled to bus  1402  for storing static information and instructions for processor  1404 . A storage device  1410 , such as a magnetic disk or optical disk, is provided and coupled to bus  1402  for storing information and instructions. 
     Computer system  1400  may be coupled via bus  1402  to a display  1412 , such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. An input device  1414 , including alphanumeric and other keys, is coupled to bus  1402  for communicating information and command selections to processor  1404 . Another type of user input device is cursor control  1416 , such as a mouse, a trackball or cursor direction keys for communicating direction information and command selections to processor  1404  and for controlling cursor movement on display  1412 . This input device typically has two degrees of freedom in two axes, a first axis (i.e., x) and a second axis (i.e., y), that allows the device to specify positions in a plane. 
     A computer system  1400  can perform the present teachings. Consistent with certain implementations of the present teachings, results are provided by computer system  1400  in response to processor  1404  executing one or more sequences of one or more instructions contained in memory  1406 . Such instructions may be read into memory  1406  from another computer-readable medium, such as storage device  14140 . Execution of the sequences of instructions contained in memory  1406  causes processor  1404  to perform the process described herein. Alternatively hard-wired circuitry may be used in place of or in combination with software instructions to implement the present teachings. Thus implementations of the present teachings are not limited to any specific combination of hardware circuitry and software. 
     The term “computer-readable medium” as used herein refers to any media that participates in providing instructions to processor  1404  for execution. Such a medium may take many forms, including but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device  1410 . Volatile media includes dynamic memory, such as memory  1406 . Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus  1402 . 
     Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, or any other magnetic medium, a CD-ROM, digital video disc (DVD), a Blu-ray Disc, any other optical medium, a thumb drive, a memory card, a RAM, PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, or any other tangible medium from which a computer can read. 
     Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor  1404  for execution. For example, the instructions may initially be carried on the magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a network. The remote computer can receive data over the network and place the data on bus  1402 . Bus  1402  carries the data to memory  1406 , from which processor  1404  retrieves and executes the instructions. The instructions received by memory  1406  may optionally be stored on storage device  1410  either before or after execution by processor  1404 . 
     In accordance with various embodiments, instructions configured to be executed by a processor to perform a method are stored on a computer-readable medium. The computer-readable medium can be a device that stores digital information. For example, a computer-readable medium includes a compact disc read-only memory (CD-ROM) as is known in the art for storing software. The computer-readable medium is accessed by a processor suitable for executing instructions configured to be executed. 
     The following descriptions of various implementations of the present teachings have been presented for purposes of illustration and description. It is not exhaustive and does not limit the present teachings to the precise form disclosed. Modifications and variations are possible in light of the above teachings or may be acquired from practicing of the present teachings. Additionally, the described implementation includes software but the present teachings may be implemented as a combination of hardware and software or in hardware alone. The present teachings may be implemented with both object-oriented and non-object-oriented programming systems. 
     Periodic Noise in Separation Coupled Mass Spectrometry 
     As described above, periodic noise in mass spectrometry is normally associated with very low flow rate electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI). This noise is generally characterized by equally spaced peaks across a large mass range. 
     Periodic noise, however, has also been observed in data from separation coupled mass spectrometry. This noise affects both qualitative and quantitative measurements performed from this data. 
     For example, periodic noise is observed in liquid chromatography coupled mass spectrometry (LCMS). However, at higher flow rates periodic noise is generally not obvious in LCMS unless a number of spectra are combined, for example, by summing Even though the period noise is not obvious, the noise ions are still present in individual spectra and can overlap small peaks, causing mass assignment and isotope ratios inaccuracies. The periodic noise in LCMS can also impact the detection limit in quantitative experiments. An impact on the detection limit is obvious in mass spectrometry (MS) quantitation (e.g. selected ion monitoring (SIM) or selected reaction monitoring (SRM) quantitation). The presence of periodic noise is also observed in tandem mass spectrometry spectra, or mass spectrometry/mass spectrometry (MSMS) spectra. Periodic noise can, therefore, affect multiple reaction monitoring (MRM) quantitation at the highest sensitivities and lowest flow rates, for example. Low flow chromatography is common in peptide analysis, including quantitation, and is being explored for small molecule quantitation. Noise has been observed to increase as the flow rate is reduced. 
     The level of the periodic noise found in LCMS has been observed to track the total ion current (TIC). For example, it is dependent on the complexity and concentration of the species that are emerging from the column at any particular time. It also seems highly likely that the noise varies from sample to sample. For example, in drug metabolism and pharmacokinetics (DMPK) studies, the noise is probably different for different individuals, depends on the sample type (urine, bile, etc.), and changes over time for one individual. 
     Thus the periodic noise in LCMS and mass analyzers for tandem mass spectrometry (MSMS) data likely affects qualitative (mass accuracy, isotope ratios) and quantitative limit of detection and quantification (LOD/Q) measurements. Removing this periodic noise is, therefore, desirable. 
     In various embodiments, a periodic noise contribution is removed from LCMS data to improve the quality of the data and/or the detection limit. Periodic noise is removed from spectra by the iterative procedure described above. A Fourier transform (FT) of the data is obtained and the periodic frequencies are found. An inverse transform is performed on only these frequencies to generate an estimate of the background. Since the presence of peaks affects the initial FT, peaks that are above the background estimate are removed (set equal to the estimate). The process is repeated until only a small number of changes occur. 
     In various embodiments, periodic noise is removed from LCMS or MSMS data by combining several adjacent spectra in order to get an estimate of the noise. For LCMS data, for example, the spectra are processed in windows, since the noise changes during the analysis. For each window, the spectra are summed and processed to generate an estimate of the background, which can be used in two ways. 
     First, the estimate can be subtracted from the summed spectrum generating a single spectrum for the LC window. The filtered spectra from all windows can be combined to generate a single spectrum that represents the entire LCMS run. Also, the single spectra obtained here can be used in metabolomics to avoid the need for retention time alignment, while retaining the ability of the LC to reduce ion suppression. In addition, these single spectra can be used to detect the presence of metabolite masses, which can then be used to generate extracted ion chromatograms (XICs) to identify isomers. 
     Second, the estimate can be subtracted from the individual spectra in order to generate a filtered data set that contains the same number of spectra as the original run. These spectra can be further processed to generate XICs, etc. 
     MSMS periodic noise can also be estimated from the sum of several spectra if it is approximately constant over the range chosen, i.e. the spectra have similar retention times in LCMSMS, or was acquired from the same spot in a MALDI experiment. 
     Quantitation normally measures a single quantity (a mass or mass pair) during the course of a liquid chromatography (LC) run, so the experiment is modified to generate a spectrum (not necessarily of the entire mass range) that can be processed to determine the noise background. 
     In SIM mode, a single mass is monitored for the duration of the experiment. SIM is single ion monitoring, whereas the multiple ion equivalent is known as MIM. Since individual ions are normally monitored, the presence and extent of periodic noise cannot be determined. 
     In various embodiments for SIM or MIM mode, a narrow mass range spectrum (perhaps 5-10 amu) is acquired. The periodic noise in the region around the mass and retention time of interest is determined One or more adjacent spectra are combined to calculate or estimate the periodic noise, for example. The estimated or calculated periodic noise is then subtracted from each spectrum in the retention time range of interest. The processed signal is quantitated by generating an XIC from the processed spectra or, if the background offset is low, measuring the spectral peak height (single spectrum or sum). 
     Scanning reduces the amount of time spent looking at the ion of interest, and thus potentially the sensitivity, but can improve the signal to noise if the overall process reduces the noise more. This tradeoff is not true if the mass spectrometer inherently generates full scan data, i.e. a time-of-flight (TOF). 
     In an MRM experiment, periodic noise can also be observed in MSMS data. In various embodiments, the periodic noise is estimated from the sum of several product ion spectra. For example, a small mass range around the fragment ion of interest is scanned. Several scans are summed to generate and estimate the periodic noise. The periodic noise from the individual spectra. Finally, XICs are generated for quantitation. 
     Systems and Methods of Data Processing 
     Separation Coupled Mass Spectrometry Systems 
       FIG. 15  is a schematic diagram showing a system  1500  for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. System  1500  includes separation device  1510 , mass spectrometer  1520 , and processor  1530 . Separation device  1510  separates one or more compounds from a sample mixture. Separation device  1510  can include, but is not limited to, an electrophoretic device, a chromatographic device, or a mobility device. 
     Mass spectrometer  1520  is a tandem mass spectrometer, for example. Mass spectrometer  1520  can include one or more physical mass analyzers that perform two or more mass analyses. A mass analyzer of a tandem mass spectrometer can include, but is not limited to, a time-of-flight (TOF), quadrupole, an ion trap, a linear ion trap, an orbitrap, a magnetic four-sector mass analyzer, a hybrid quadrupole time-of-flight (Q-TOF) mass analyzer, or a Fourier transform mass analyzer. Mass spectrometer  1520  can include separate mass spectrometry stages or steps in space or time, respectively. Mass spectrometer  1520  scans the separating sample at a plurality of time intervals producing a collection of mass spectra. 
     Processor  1530  is in communication with tandem mass spectrometer  1520 . Processor  1530  can also be in communication with separation device  1510 . Processor  1530  can be, but is not limited to, a computer, microprocessor, or any device capable of sending and receiving control signals and data to and from tandem mass spectrometer  1520  and processing data. 
     Processor  1530  obtains the collection of mass spectra. Processor  1530  can obtain the collection of mass spectra directly from mass spectrometer  1520 , or it can get the collection of mass spectra from a file stored in a memory by mass spectrometer  1520 , for example. 
     Processor  1530  divides the collection of mass spectra into two or more time interval window widths. For each window width of the two or more time interval window widths, processor  1530  sums all spectra within each window width producing a summed spectrum for each of the two or more time interval window widths. For each summed spectrum of the two or more time interval window widths, processor  1530  (a) estimates a noise spectrum corresponding to background noise in each summed spectrum, and (b) repeats step (a) one or more additional times to generate a modified noise spectrum for each summed spectrum. 
     In various embodiments, processor  1530  further subtracts each modified noise spectrum for each summed spectrum from each summed spectrum, generating a filtered spectrum for each of the two or more time interval window widths. Processor  1530  assembles the plurality of filtered spectra of the two or more time interval window widths into a single spectrum for the plurality of time intervals. 
     In various embodiments, processor  1530  subtracts each modified noise spectrum for each summed spectrum from each spectra of the summed spectrum, generating a collection of filtered spectra. Each filtered spectrum of the collection of filtered spectra corresponds to a spectrum of the collection of mass spectra, for example. 
     In various embodiments, processor  1530  estimates the noise spectrum corresponding to background noise in each summed spectrum by performing a number of steps. In step (A), processor  1530  affects a transformation of each summed spectrum into the frequency domain to obtain an original frequency spectrum. In step (B), processor  1530  identifies at least one dominant frequency in the original frequency spectrum. In step (C), processor  1530  generates a noise frequency spectrum by selectively filtering for said at least one dominant frequency. In step (D), processor  1530  determines the modified noise spectrum by affecting a transformation of the noise frequency spectrum into the mass domain. 
     In various embodiments, each summed spectrum includes a plurality of original intensity data points and wherein the modified noise spectrum includes a plurality of noise intensity data points such that each noise intensity data point correlates to an original intensity data point. Processor  1530  then estimates the noise spectrum corresponding to background noise in each summed spectrum by performing the following additional steps. In step (E), for each correlated pair of original and noise intensity data points processor  1530 : (i) determines the minimum value; and (ii) modifies the modified noise spectrum by making the noise intensity data point equal to the minimum value. In step (F), processor  1530  affects a transformation of the modified noise spectrum modified in step (E) into the frequency domain to obtain a noise frequency spectrum. In step (G), processor  1530  identifies at least one dominant frequency in the noise frequency spectrum. In step (H), processor  1530  modifies the noise frequency spectrum by selectively filtering for said at least one dominant frequency. In step (I), processor  1530  determines the modified noise spectrum by affecting a transformation of the noise frequency spectrum into the mass domain. 
     In various embodiments, additional steps involve repeating previous steps. In step (J), processor  1530  repeats step (E) utilizing the modified noise spectrum determined in step (I). In step (K), processor  1530  repeats steps (F) through (J) inclusively. 
     In various embodiments, processor  1530  segments each summed spectrum into a plurality of initial windows prior to step (A), and separately affects steps (A) through (D) inclusive for each initial window. 
     In various embodiments, processor  1530  segments the modified noise spectrum into a plurality of subsequent windows prior to step (F), and separately affects steps (F) through (I) inclusive for each subsequent window. In various embodiments, the subsequent windows are configured such that no subsequent window is coextensive with any initial window. 
     In various embodiments, for each repeat of steps (G) through (J), processor  1530  segments the modified noise spectrum into a plurality of new windows prior to step (G), and separately affects steps (G) through (J) inclusive for each new window. The new windows are configured such that no new window is coextensive with any subsequent window. 
     Separation Coupled Mass Spectrometry Methods 
       FIG. 16  is an exemplary flowchart showing a method  1600  for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. 
     In step  1610  of method  1600 , a collection of mass spectra produced by a mass spectrometer that scans a sample at a plurality of time intervals as the sample is separating in a separation device is obtained. 
     In step  1620 , the collection of mass spectra is divided into two or more time interval window widths. 
     In step  1630 , for each window width of the two or more time interval window widths, all spectra within each window are summed. A summed spectrum for each of the two or more time interval window widths is produced. 
     In step  1640 , for each summed spectrum of the two or more time interval window widths, (a) a noise spectrum corresponding to background noise in each summed spectrum is estimated and (b) step (a) is repeated one or more additional times to generate a modified noise spectrum for each summed spectrum. 
     Separation Coupled Mass Spectrometry Computer Program Products 
     In various embodiments, a computer program product includes a non-transitory and tangible computer-readable storage medium whose contents include a program with instructions being executed on a processor so as to perform a method for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometer. This method is performed by a system that includes one or more distinct software modules. 
       FIG. 17  is a schematic diagram of a system  1700  that includes one or more distinct software modules that perform a method for generating a background noise estimate for a collection of mass spectra produced by separation coupled mass spectrometry, in accordance with various embodiments. System  1700  includes measurement module  1710  and analysis module  1720 . 
     Measurement module  1710  obtains a collection of mass spectra produced by a mass spectrometer that scans a sample at a plurality of time intervals as the sample is separating in a separation device. 
     Analysis module  1720  divides the collection of mass spectra into two or more time interval window widths. For each window width of the two or more time interval window widths, analysis module  1720  sums all spectra within each window. A summed spectrum for each of the two or more time interval window widths is produced. For each summed spectrum of the two or more time interval window widths, analysis module  1720  (a) estimates a noise spectrum corresponding to background noise in each summed spectrum and (b) repeats step (a) one or more additional times to generate a modified noise spectrum for each summed spectrum. 
     Filtered Data Mass Spectrometry Systems 
       FIG. 18  is a schematic diagram showing a system  1800  for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. System  1800  includes mass spectrometer  1820 , and processor  1830 . 
     Mass spectrometer  1820  is a tandem mass spectrometer, for example. Mass spectrometer  1820  can include one or more physical mass analyzers that perform two or more mass analyses. A mass analyzer of a tandem mass spectrometer can include, but is not limited to, a time-of-flight (TOF), quadrupole, an ion trap, a linear ion trap, an orbitrap, a magnetic four-sector mass analyzer, a hybrid quadrupole time-of-flight (Q-TOF) mass analyzer, or a Fourier transform mass analyzer. Mass spectrometer  1820  can include separate mass spectrometry stages or steps in space or time, respectively. Mass spectrometer  1820  performs a plurality of scans of a sample, producing a plurality of mass spectra. 
     Processor  1830  is in communication with tandem mass spectrometer  1820 . Processor  1830  can be, but is not limited to, a computer, microprocessor, or any device capable of sending and receiving control signals and data to and from mass spectrometer  1820  and processing data. 
     Processor  1830  obtains the plurality of mass spectra. Processor  1830  can obtain the plurality of mass spectra directly from mass spectrometer  1820 , or it can get the plurality of mass spectra from a file stored in a memory by mass spectrometer  1820 , for example. 
     Processor  1830  combines neighboring mass spectra of the plurality of mass spectra into a collection of mass spectra based on sample location, time, or mass. Neighboring mass spectra from an imaging experiment can be combined into a collection of mass spectra based on sample location, for example. Neighboring mass spectra from a separation or infusion experiment can be combined into a collection of mass spectra based on time, for example. Neighboring mass spectra from a tandem mass spectrometry experiment can be combined into a collection of mass spectra based on precursor mass, for example. 
     Processor  1830  calculates a background noise estimate for the collection of mass spectra. Processor  1830  filters the collection of mass spectra using the background noise estimate, producing a filtered collection of one or more mass spectra. 
     Finally, processor  1830  performs quantitative or qualitative analysis using the filtered collection of one or more mass spectra. Processor  1830  performs quantitative analysis by generating liquid chromatography (LC) peak areas using the filtered collection of one or more mass spectra from a complete LCMS run, for example. Processor  1830  performs qualitative analysis (library search, library creation, database search, elemental composition calculation, etc.) by using filtered collection of one or more mass spectra to provide spectral peak assignment (mass and intensity), for example. 
     In various embodiments, system  1800  further includes a separation device that separates one or more compounds of the sample. Mass spectrometer  1820  performs a plurality of scans of the separating sample, producing a plurality of mass spectra scans at different times. Processor  1830  combines neighboring mass spectra of the plurality of mass spectra into a collection of mass spectra based on time. 
     In various embodiments, processor combines neighboring mass spectra of the plurality of mass spectra into a collection of mass spectra based on sample location, time, or mass by combining neighboring precursor ion spectra. In other words, neighboring mass spectrometry (MS) spectra are combined using full scans or narrow windows. 
     In various embodiments, processor  1830  combines neighboring mass spectra of the plurality of mass spectra into a collection of mass spectra based on sample location, time, or mass by combining neighboring product ion spectra. In other words, neighboring mass spectrometry/mass spectrometry (MSMS) spectra are combined. For example, neighboring MSMS spectra are combined from the same precursor ion using full scans or narrow windows. Alternatively, neighboring MSMS spectra are combined from different precursor ions using full scans. 
     In various embodiments, a background noise estimate is generated when only a single data point is measured. 
     In various embodiments, processor  1830  calculates a background noise estimate for the collection of mass spectra using time-frequency analysis. 
     In various embodiments, processor  1830  divides the collection of mass spectra into two or more windows. The collection of mass spectra are divided into two or more windows based on sample location, time, or mass, for example. For each window of the two or more windows, processor  1830  combines all spectra within each window producing a combined spectrum for each of the two or more windows. Processor  1830  combines all spectra within each window by summing all spectra, for example. For each combined spectrum of the two or more windows, processor  1830  (a) estimates a noise spectrum corresponding to background noise in each combined spectrum, and (b) repeats step (a) one or more additional times to generate a modified noise spectrum for each combined spectrum. 
     In various embodiments, processor  1830  further subtracts each modified noise spectrum for each combined spectrum from each combined spectrum, generating a filtered spectrum for each of the two or more windows. Processor  1830  assembles the plurality of filtered spectra of the two or more windows into a single spectrum for the plurality of time intervals. 
     In various embodiments, processor  1830  subtracts each modified noise spectrum for each combined spectrum from each spectra of the combined spectrum, generating a collection of filtered spectra. Each filtered spectrum of the collection of filtered spectra corresponds to a spectrum of the collection of mass spectra, for example. 
     In various embodiments, processor  1830  estimates the noise spectrum corresponding to background noise in each combined spectrum by performing a number of steps. In step (A), processor  1830  affects a transformation of each combined spectrum into the frequency domain to obtain an original frequency spectrum. In step (B), processor  1830  identifies at least one dominant frequency in the original frequency spectrum. In step (C), processor  1830  generates a noise frequency spectrum by selectively filtering for said at least one dominant frequency. In step (D), processor  1830  determines the modified noise spectrum by affecting a transformation of the noise frequency spectrum into the mass domain. 
     In various embodiments, each combined spectrum includes a plurality of original intensity data points and wherein the modified noise spectrum includes a plurality of noise intensity data points such that each noise intensity data point correlates to an original intensity data point. Processor  1830  then estimates the noise spectrum corresponding to background noise in each combined spectrum by performing the following additional steps. In step (E), for each correlated pair of original and noise intensity data points processor  1830 : (i) determines the minimum value; and (ii) modifies the modified noise spectrum by making the noise intensity data point equal to the minimum value. In step (F), processor  1830  affects a transformation of the modified noise spectrum modified in step (E) into the frequency domain to obtain a noise frequency spectrum. In step (G), processor  1830  identifies at least one dominant frequency in the noise frequency spectrum. In step (H), processor  1830  modifies the noise frequency spectrum by selectively filtering for said at least one dominant frequency. In step (I), processor  1830  determines the modified noise spectrum by affecting a transformation of the noise frequency spectrum into the mass domain. 
     In various embodiments, additional steps involve repeating previous steps. In step (J), processor  1830  repeats step (E) utilizing the modified noise spectrum determined in step (I). In step (K), processor  1830  repeats steps (F) through (J) inclusively. 
     In various embodiments, processor  1830  segments each combined spectrum into a plurality of initial windows prior to step (A), and separately affects steps (A) through (D) inclusive for each initial window. 
     In various embodiments, processor  1830  segments the modified noise spectrum into a plurality of subsequent windows prior to step (F), and separately affects steps (F) through (I) inclusive for each subsequent window. In various embodiments, the subsequent windows are configured such that no subsequent window is coextensive with any initial window. 
     In various embodiments, for each repeat of steps (G) through (J), processor  1830  segments the modified noise spectrum into a plurality of new windows prior to step (G), and separately affects steps (G) through (J) inclusive for each new window. The new windows are configured such that no new window is coextensive with any subsequent window. 
     Filtered Data Mass Spectrometry Methods 
       FIG. 19  is an exemplary flowchart showing a method  1900  for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. 
     In step  1910  of method  1900 , a plurality of scans of a sample are performed, producing a plurality of mass spectra using a mass spectrometer. 
     In step  1920 , neighboring mass spectra of the plurality of mass spectra are combined into a collection of mass spectra based on sample location, time, or mass using a processor. 
     In step  1930 , a background noise estimate is calculated for the collection of mass spectra using the processor. 
     In step  1940 , the collection of mass spectra is filtered using the background noise estimate, producing a filtered collection of one or more mass spectra using the processor. 
     In step  1950 , quantitative or qualitative analysis is performed using the filtered collection of one or more mass spectra using the processor. 
     Filtered Data Mass Spectrometry Computer Program Products 
     In various embodiments, a computer program product includes a non-transitory and tangible computer-readable storage medium whose contents include a program with instructions being executed on a processor so as to perform a method for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data. This method is performed by a system that includes one or more distinct software modules. 
       FIG. 20  is a schematic diagram of a system  2000  that includes one or more distinct software modules that perform a method for generating a background noise estimate for quantitatively or qualitatively analyzing a sample based on filtered mass spectrometry data, in accordance with various embodiments. System  2000  includes measurement module  2010 , filtering module  2020 , and analysis module  2030 . 
     Measurement module  2010  receives a plurality of mass spectra produced by a mass spectrometer that performs a plurality of scans of a sample. Filtering module  2020  calculates a background noise estimate for the collection of mass spectra. Filtering module  2020  filters the collection of mass spectra using the background noise estimate, producing a filtered collection of one or more mass spectra. Analysis module  2030  performs quantitative or qualitative analysis using the filtered collection of one or more mass spectra. 
     While the present teachings are described in conjunction with various embodiments, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art. 
     Further, in describing various embodiments, the specification may have presented a method and/or process as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the various embodiments.