Extracted ion profile

An extracted ion profile plots selected mass-to-charge ratio signal across a time-ordered series of mass spectra. The selection can be one value or a set of values. When time follows a chromatographic separation, the result is an extracted ion chromatogram; the broader profile term also covers other time-dependent sampling.^[ref]

For recorded spectra $I_k(t_j)$, an explicit extracted ion mass window $W$ gives the reconstructed traceThis selects information already present in the spectra. It does not create missing mass measurements or turn the acquisition into a different instrumental measurement. Unlike a total ion current profile, it excludes signal outside the stated window.

An original three-scan example shows how the window changes the result. At mass coordinates $499.98$, $500.00$ and $500.03$, let the intensity vectors be $(0,1,0)$, $(3,8,5)$ and $(0,2,10)$ at successive times. A window $500.00\pm 0.01$ selects only the middle coordinate and gives $(1,8,2)$. Widening to $500.00\pm 0.04$ includes all three coordinates and gives $(1,16,12)$. The larger late signal in the broad trace comes from added spectral content; it is not evidence that the middle-coordinate signal remained high.

Choosing a window requires considering mass resolving power, mass-coordinate accuracy and what the instrument actually recorded. A narrow window can exclude a shifted target peak; a wide window can include neighbors. Even an isolated mass coordinate need not identify a unique chemical species, because different ions can share it. Preserve the raw spectra and state the window, summation rule and time axis so the profile can be reproduced and interpreted.

An extracted ion chromatogram is an extracted ion profile whose time axis follows a chromatographic separation. A mass spectrometer records successive mass spectra as separated material reaches the ion source; software follows a chosen mass-to-charge ratio interval through those spectra. It is a selected view of the recorded data rather than a direct picture of a single chemical species.^[ref]

The apparatus supplies two kinds of discrimination: chromatography changes when material reaches the detector, while mass analysis distinguishes ion coordinates at each time. An extracted ion mass window specifies which recorded coordinates contribute. A narrow window cannot separate two coeluting species whose relevant ions occupy the same mass coordinate.

An extracted-ion chromatogram peak area integrates selected signal over an explicitly chosen time range. For original sample points $(t,E)=(0,0),(1,4),(3,0)$, in minutes and arbitrary signal units, straight-line interpolation givesThe unweighted sum of ordinates is4, which ignores the unequal time intervals. These stipulated data illustrate numerical integration, not an experimental chromatogram.

Peak height and area also answer different questions. Triangular model peaks with height5 and full base widths2 and4 minutes have areas5 and10 signal-unit minutes. The same peak height does not imply the same integrated response. Converting area to amount requires an appropriate calibration and response model.

State the mass window, acquisition time spacing, baseline and time boundaries. Changes in baseline or overlap can change assigned area without changing analyte amount. Comparing retention behavior and other chemical evidence helps interpret a selected trace; its apparent isolation alone does not establish identity or freedom from analytical matrix effects.

An extracted-ion chromatogram peak area integrates selected ion signal over a stated chromatographic time interval, usually after estimating an extracted-ion chromatogram baseline. If $E_W(t)$ is an extracted ion chromatogram for mass window $W$ and $b(t)$ is its baseline,Both the extracted ion mass window and time boundaries are part of this definition. The selected-ion/time character follows the IUPAC extracted ion profile definition.^[ref]

An original nonuniform-sampling example uses times $(0,1,2,4)$ minutes and signals $(1,5,3,1)$. With baseline 1, corrected signals are $(0,4,2,0)$. Straight-line interpolation and the trapezoidal rule giveThe discrete corrected-signal sum is 6, which ignores the acquisition intervals. Neither number is an amount of analyte without a response calibration.

Baseline error accumulates across the integration interval. Over this four-minute interval, overestimating a constant baseline by 0.5 signal units reduces the assigned area by $0.5(4)=2$ signal-unit minutes, from 7 to 5. A broad weak feature can therefore be especially sensitive to its baseline convention.

Peak area can also include neighboring ions admitted by the mass window and coeluting compounds with the same recorded coordinate. More complete integration does not by itself make the assigned signal chemically specific. State boundaries, baseline, handling of negative corrected values and integration rule. Those choices can alter reported area even when the recorded spectra are unchanged, and differences in area need not mean proportional differences in analyte amount.

An extracted-ion chromatogram baseline is a model of the signal underlying a selected chromatographic peak in an extracted ion chromatogram. Subtracting it helps assign an extracted-ion chromatogram peak area to the feature of interest. The baseline need not be zero or constant, and it is not automatically the signal from a separate reagent blank.

Let $E_W(t)$ be the signal from an extracted ion mass window $W$ and let $b(t)$ be the baseline over $[t_1,t_2]$. The assigned extracted-ion chromatogram peak area isThe time-ordered mass selection follows the IUPAC extracted ion profile definition; the baseline is an additional integration-model choice.^[ref]

An original example takes $0\le t\le 4\min$ and a baseline rising linearly from 1 to 3 signal units. Its integrated area is $4(1+3)/2=8$ signal-unit minutes. If the recorded trace has total area 20, the corrected area is 12. Using a constant baseline 1 would subtract only 4 and assign area 16: a 33% overestimate relative to 12. No recorded ion signal changed; only its allocation between baseline and peak changed.

If a fitted baseline is $b(t)=a+kt$ over a duration $L$ starting at $t=0$, then the subtracted area is $B=aL+k{L}^2/2$. Chromatographic baseline-area uncertainty therefore includes the joint uncertainty of the fitted intercept and slope:This is a direct application of correlated-input uncertainty propagation.^[ref]

Candidate baseline regions should be inspected for neighboring peaks, broad tails and drifting background. Two overlapping compounds can generate one smooth trace; subtracting a convenient baseline cannot establish chemical specificity. Record the integration boundaries, baseline model and treatment of negative corrected values. Those choices are necessary to interpret or reproduce a reported extracted-ion chromatogram peak area.

Chromatographic baseline-area uncertainty quantifies uncertainty in the integrated baseline subtracted when assigning a chromatographic extracted-ion chromatogram peak area. For an extracted-ion chromatogram baseline $b(t)$ over fixed limits $t_1,t_2$, let $B={\int }_{t_1}^{t_2}b(t)dt$. The baseline's uncertainty is shared across time whenever fitted parameters or other common inputs are shared.

For sampled times with integration weights $w_i$ and baseline estimates $b_i$,The weights include the actual sampling intervals and chosen integration rule. This is correlated-input uncertainty propagation, not an assumption that each drawn baseline point is independently uncertain.^[ref]

An original constant-baseline example uses 100 equal intervals of $0.1\min$ and one common fitted baseline with standard uncertainty0.2 signal units. Its integrated uncertainty is $10(0.2)=2$ signal-unit minutes. Treating those 100 appearances of the same fitted quantity as independent would instead give $\sqrt{100}(0.1)(0.2)=0.2$, underestimating uncertainty tenfold. More sampling points do not average away a shared offset.

For total recorded area $P$ and assigned peak area $Q=P-B$,With stipulated $u_P=0.5$, $u_B=0.4$ and correlation coefficient0.6, the result is $u_Q=\sqrt{0.17}\approx 0.412$ area units, compared with 0.640 under independence. The appropriate covariance depends on how the trace and its baseline were estimated; it cannot be selected to obtain a preferred uncertainty.

Changing integration limits or choosing a different baseline form can create additional effects beyond parameter uncertainty within one fixed model. Inspect neighboring peaks and baseline regions, and record the fitted model and boundary choices. A precisely computed extracted-ion chromatogram peak area can still depend on an unsuitable baseline model.

An extracted ion mass window is the set of mass-to-charge ratio coordinates included when reconstructing an extracted ion profile or extracted ion chromatogram. A common choice is an interval centered at $m_0$ with half-width $w$: $|m-m_0|\le w$. The profile definition permits one value or a set of values; specifying the window makes that selection reproducible.^[ref]

A relative half-width can be stated in parts per million:where $p$ is the stipulated ppm half-tolerance and $m,m_0$ use the same displayed mass-coordinate scale. At $m_0=500$, a5ppm half-tolerance gives $w=0.0025$ and interval $499.9975\le m\le 500.0025$. At $m_0=1000$, the same relative tolerance gives $w=0.005$. Conversely, fixed $w=0.005$ corresponds to10ppm at500 and5ppm at1000. State whether a quoted width means half-width or full width.

Finite peak width makes window choice a signal-selection operation. A target whose measured center shifts from500.000 to500.003 moves outside the first window, although part of its broadened signal may remain inside. Widening the window can recover more target signal while admitting a neighboring ion. The extracted-ion window capture fraction depends on the peak shape, width and coordinate offset, not merely on the nominal target formula.

Mass resolving power describes separation of nearby ion peaks; coordinate accuracy and the chosen extraction tolerance are different properties. A narrow software window does not improve instrumental resolving power or recreate information that was not acquired. Nor does fitting the expected window establish a unique ion identity. The window should be interpreted together with acquisition conditions, reference measurements and the other evidence used for assignment.

An extracted-ion window capture fraction is the fraction of a particular ion peak's integrated mass-coordinate signal retained by an extracted ion mass window. For a nonnegative signal-density model $s(m)$ and window $W$,assuming the denominator is finite and positive. This is a fraction of the specified peak model, not necessarily a fraction of analyte molecules or of the entire total ion current. The extraction window selects which mass-coordinate signal enters a profile.^[ref]

An original Gaussian function model makes window-capture sensitivity to mass offset explicit. Let the peak center be displaced by $\delta$ from the nominal window center, with standard deviation $\sigma$ and symmetric half-width $w$. If $\Phi$ is the standard normal distribution's cumulative distribution function,At zero offset and $w=2\sigma$, the retained fraction is approximately $0.9545$. Shifting the peak center to the upper window boundary, $\delta =2\sigma$, reduces it to approximately $0.5000$. The model's total peak area has not changed; the selected fraction has.

A wider window admits more of this peak but can also admit another ion. The measured window sum can therefore increase for two different reasons: greater target capture or added interference. They cannot generally be distinguished from the summed trace alone.

The Gaussian shape is a stipulated teaching model, not a universal instrument response. Real peak asymmetry, finite recorded ranges, background and overlapping signals can change the fraction. Mass resolving power and mass-coordinate accuracy remain instrumental properties; a software window only selects from the information available.

Window-capture sensitivity to mass offset describes how the extracted-ion window capture fraction changes when an ion peak shifts relative to a fixed extracted ion mass window. The shift is in the reported mass coordinate; it can change the selected signal even if the target's total peak area is constant.

For a normalized peak shape $p(m-\delta )$ with offset $\delta$ and window boundaries $a,b$, writeDifferentiation givesThe first-order response is determined by the signal density at the two boundaries. A symmetric peak centered in a symmetric window has equal boundary densities and hence zero first derivative. Zero first derivative does not mean perfect immunity: finite offsets can still reduce capture.

For an original Gaussian function model with standard deviation $\sigma$ and half-width $w$, let $\varphi$ and $\Phi$ be the standard normal density and standard normal cumulative distribution function. ThenFor small offsets the leading loss is consequently quadratic:With $w=2\sigma$, the exact capture is 0.9545 at zero offset and 0.9270 at $\delta =0.5\sigma$. The quadratic approximation gives 0.9275, close for this stipulated displacement. At the boundary $\delta =2\sigma$, capture is about 0.5000 and a small-offset approximation is no longer appropriate.

An experimental check can re-extract the same recorded spectra with deliberately shifted windows while retaining the same time limits and extracted-ion chromatogram baseline. This isolates a software-selection effect. IUPAC's selected-mass profile definition supplies the measurement setting, rather than a claim that all instruments have Gaussian peaks.^[ref] Wider windows may reduce target losses but admit interfering ions; mass resolving power and instrument calibration remain separate instrumental considerations.