CIR Spreadsheet and Instructions

Our series on integration has been made possible with a spreadsheet by contributer Ali, which we have made available in the archive for download, inspection and use. Here is a description and instructions.

[MORE]

By Ali

Specifying Peaks and Background

The spreadsheet provides facilities for defining three peaks.

For each peak, the o/oo value, the peak response and the peak time can be controlled (rows 6 to 9). The time difference between m45 and m44 can also be defined (cell C9). Published material suggests that a suitable mean value for this would be 0.15 s. That can’t be accommodated as the time resolution is 0.1 s, so either use 0.1 or 0.2. It makes a difference! Our examples have been generated with the smaller value, while the larger one produces more pronounced effects, so we've erred on the conservative side.

The background noise level can be set (rows 29 to 31). The level, slope and o/oo parameters can be entered.

Generating Data

A template peak profile, conforming to a Normal (Gaussian) distribution is stored in the spreadsheet. Depending on the values entered against each peak, the template peak is scaled to produce a m44 peak which matches the defined peak height and time shifted to match the peak time. The entered o/oo values are then used to produce the m45 peaks which are vertically scaled down versions of their m44 counterparts so that the ratio of their area correspond exactly to the o/oo values. They are placed at the same points in time, then shifted by the m45 to m44 time difference (cell C9).

The m45, m44 and m45/m44 plots are generated from this tabular data. At each point in time, the background, peak1, peak2 and peak3 contributions are then summed to produce the net m44 and m45 responses.

The instantaneous m45/m44 plot is simply the ratio of net m45 divided by net m44 at each point in time.

Integration Limits

With the peaks defined, their integration limits can be set. Provision is made for t1 and t2 times for each peak. Integration occurs between these two times (rows 11 to 12).

Our understanding is that both human operators and software typically select integration points by looking at the 44/45 trace. The spreadsheet is completely manual for this operation.

Background Removal

Background removal in the spreadsheet is automatic, unless manualy overridden.

In automatic mode, for each integration interval, a straight line is fitted between the intersection of t1 and the m44 plot and the intersection of t2 and the m44 plot. The same happens for the m45 plot. Everything below this line and outside the integration interval is discarded. The display and methodology is consistent with what we've observed in various documented examples.

Automatic mode can be overidden by entering a value in cell C21. Clearing this cell returns to automatic mode.

Result Calculation

The calculated o/oo values (row 24) are generated by performing numerical integration over the selected t1-t2 interval on both the m44 and m45 plots (after the desired background has been removed). The ratio of m45 area to m44 area defines the C13/C12 ratio which in turn leads to a calculated o/oo value for the peak based on the relationship: o/oo=1000*((C13/C12)-PDB)/PDB (where PDB is an international standard).

Generating Plots

The plots shown in the Series on TBV have been generated by setting up the desired conditions in the spreadsheet, copying the Excel chart and pasting it into the standard Windows accessory MSPaint (any other equivalent application would be suitable). They are then sized, shaded and annotated as required.

That’s it really. No smoke and mirrors involved. Any observations on either the implementation or the assumptions made are welcome.