Progress in Bayesian DOSY and ROSY Transforms

by   aCarlos Cobas and bStanislav Sykora
aMestrelab Research, Santiago de Compostela, Spain     bExtra Byte, Castano Primo, Italy

presented at 51st ENC Conference, Daytona Beach, Florida (USA), April 18-23, 2010.

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At the 2008 edition of this meeting [ENC] we have presented a poster [1] which has introduced a Bayesian approach to the evaluation and graphic representation of multi-array NMR data sets characteristic of the diffusion (DOSY) and relaxation (ROSY) spectroscopies. At that time, the Bayesian algorithm was barely more than an interesting proposal and an alpha-tested piece of code. In the meantime, however, it has been released under the code-name BayDOSY as part of a commercial software package and proved to be very successful in everyday practice in terms of both qualitative performance (capability to distinguish various sample components, or z-resolution) and efficiency (fast execution times of just a handful of seconds). In view of this satisfactory beta-testing experience, it is now time to release the details of the algorithm, a step which is presently under way [2].

This presentation concentrates on aspects of the presently used algorithm which go beyond the original BDT core and which were added since the poster presentation two years ago. These include:

a) Refinement of what we call the LineSNAP algorithm which takes advantage of the fact that the 2D peaks should group into discreet lines of peaks (or ranges) corresponding to distinct sample components (different spectral peaks of the same molecule should exhibit the same diffusion constant). Incorporating this a-priori knowledge into the algorithm is not trivial and has been again done using a Bayesian approach. It is applicable preferentially to DOSY, while in ROSY the (line)alignment of relaxation times for various peaks of the same component is much less stringent. The LineSNAP algorithm takes these differences into account and allows a calibrated control of the line-alignment tendency.

b) Spectral [column] alignment of the arrayed spectra using several approaches, most notably the novel GSD (Global Spectrum Deconvolution) algorithm. It will be shown that, especially in DOSY where peaks positions and shapes are often affected by the settling magnetic field, proper spectral alignment plays wonders in terms of achievable z-resolution. In this context, spectral alignment must be sensitive enough to remove even misalignments substantially smaller than the peak width. For this reason, binning of any kind is not suitable, while GSD-based spectral alignment works very well.

c) The Bayesian algorithm has been now combined with a Bayesian handling of bi-exponentiality. Considering the very limited number of spectra available in typical arrayed data sets (anything beyond 32 is considered impractical and 16 is a very popular choice), a full multi-exponential analysis is hardly ever feasible, but a separation of two decay components in cases of overlapping spectral peaks can be done with profit. However, since it affects negatively the final z-resolution, it must be applied only to those spectral regions where it is really needed and this implies an algorithm capable of making such a decision automatically and using objective statistical criteria.

DOI of this document: 10.3247/SL3Nmr10.001
[1] C.Cobas, M.Sordo, N.Larin, S.Sykora, Novel Data Evaluation Algorithms: Bayesian DOSY and ROSY Transforms,
a poster presented at 49th ENC Conference, Asilomar, CA (USA), March 9-14, 2008 (DOI reference: 10.3247/SL2Nmr08.009).
[2] S.Sykora, C.Cobas, Bayesian DOSY and ROSY transforms, J.Magn.Reson., submitted

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