Dr. Brenna was an author on a 1994 paper that has been cited variously in the case, both for and against Landis, by the usual suspects. Contributor Ali has gotten a copy, and files this evaluation...
(Hereafter [Brenna 94])
The purpose of this review is to summarize their findings and highlight any aspects that may have relevance to the matter at hand – the Landis case.
The background of the paper is that overlapping peaks in IRMS analysis result in inaccurate calculation of o/oo values, which we've looked at before. It says,
The conventional algorithm resulted in systematic bias related to degree of overlap
And it attempts to offer a new algorithm involving curve fitting to get better results. It also offers some experimental results on the affects of overlaps, which are of interest to us.
The conventional algorithm is separating the peaks with a vertical line at the centre of the valley between their overlap and taking that line down to what is assumed to be the background level. This is then used as an integration limit.
It's what our spreadsheet does, and appears to have been employed on a number of Landis’s IRMS F3 chromatograms to separate the 5B and 5a peaks from either themselves, or more frequently from some unidentified small peak that appears to be between and overlapping both the 5B and 5a peaks.
The paper gives a brief description is presented on the GC/C/IRMS. An integration time of 0.25 s was specified, which we believe to be analogous to the sampling rate. Peak start and stop are detected using only the 44 plot (due to superior signal to noise ratio). This differs from the LNDD process described by Brenna, where the 45/44 ratio plot is used to determine the start and stop times. Peak maxima are detected on each plot (44, 45 and 46) to identify the time shifts between the three detectors and the previously determined integration interval is applied to all three plots. Background is identified by a straight line fitted between peak start and stop points (which may be at the same level for constant background or at different levels for sloping background).
Due to the extra plumbing involved in the GC/C/IRMS process, both chromatographic efficiency and peak shape are detrimentally affected. In other words, you tend to get more peak overlaps and the peaks are generally not Gaussian, but are skewed (exhibiting an extended tail). Therefore, fitting a pure Gaussian peak to real data would not yield the best results.
To compensate for the inaccuracies involved in the conventional algorithm, the paper proposes to assess the ability of four different curve-fitting algorithms to recover the true peak shape and o/oo values of the overlapping peaks. What these four functions are may be of interest to some but aren’t relevant to this review.
Two substances exhibiting near identical o/oo values were used to experimentally generate a series of overlapping peaks. With equal sized peaks, at varying degrees of overlap (between 0% and 70%), it was observed that the conventional algorithm exhibited a depleted C13 ratio for the leading peak (-8 o/oo at maximum overlap) and an enhanced C13 ratio for the lagging peak (+8 o/oo at maximum overlap). This result was described as “unexpected”. The degree of error was proportional to the degree of overlap.
Brenna's testimony at the hearing leaned heavily on these measurements.
Application of the proposed curve fitting functions to the peaks yielded an improvement in peak area and o/oo recovery.
Similar experiments were run with a 10:1 ratio of peaks (leading peak ten times bigger than lagging peak). Using the conventional algorithm, at 40% overlap, detection of the smaller, lagging peak became problematic due to interference from leading peak’s tail. Beyond 40% overlap it was not distinguished as an individual peak.
The general trend of the leading peak being depleted and lagging peak becoming enhanced was observed for those cases where the two peaks were distinguishable.
With the peaks reversed and the leading peak being the smaller, the conventional method detected the smaller, leading peak at all degrees of overlap and it reflected a similar depletion trend as had been previously been observed.
The larger lagging peak exhibited very little error at all degrees of overlap. Curve fitting in all cases appeared to offer some advantages and generally improved the ability to recover the true o/oo of the peaks.
The curve fitting aspect is not strictly relevant to the Landis case, as it would appear that this has not used by LNDD. The conventional method and the results obtained are of more interest.
The first observation is that these results confirm Dr Brenna’s testimony of the leading peak’s C13/C12 ratio becoming depleted and the lagging peak’s C13/C12 ratio becoming enhanced. This contradicts Dr Meier-Augunstein’s testimony.
A significant factor effecting this contradiction is the effect of the m45 signal leading the m44 signal by approximately 150 ms.
Uncorrected, if the left-hand integration limit for the lagging peak is taken as the minima of the valley between the peaks and that is applied directly to both the m44 and m45 plots (not time shifted), then one would expect the C13/C12 ratio of the lagging peak to become depleted, having had a relatively larger proportion of C13 (m45) chopped off, compared to the slightly retarded C12 (m44) signal.
It would appear that performing the correction described by Brenna would resolve this issue but clearly it doesn’t. If we assume identical but scaled down peaks between the m44 and m45 plots, with no time shift (or a corrected time shift), the instantaneous 45/44 ratio would be homogeneous, presenting a constant value across the integration interval. In that case, the overlap of two peaks having identical o/oo values should have little or no impact on the measured value.
So why did overlap have such a significant effect in Brenna’s study and why were the results both contradictory to Meier-Augunstein’s opinion and described as “unexpected” by Brenna?
One possible explanation may lie in the integration time of 0.25 s.
In sampling at 0.25s intervals, how accurately will the peak maxima times on the m45 and m44 plots be identified? That’s what determines the required time shift so that they line up exactly. Remember that the required time shift is approximately 0.15s and we’re sampling at 0.25 s. A degree of error appears unavoidable. What if this error resulted in overcompensation for the time shift, resulting in a correction that had the m44 plot leading the m45 plot by some small but significant amount? This would reverse the effects described by Dr Meier-Augenstein and result in the observations made by Dr Brenna . [un-UPDATE: incorrection removed, don't ask. ]
To this idiot, this seems the most likely reason.
In a later post, we'll look at a paper in the GDC collection, in which Brenna looks at quantization errors. These are ones where you have insufficient or mismatched sample times.