Optimal Sampling Strategies for the Measurement of Spin–Spin Relaxation Times

✍ Scribed by J.A. Jones; P. Hodgkinson; A.L. Barker; P.J. Hore

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 616 KB
• Volume: 113
• Category: Article
• ISSN: 1064-1866
• DOI: 10.1006/jmrb.1996.0151

✦ Synopsis

It is shown how Crame ´r-Rao theory may be used to determine

Here we use the theory of Crame ´r-Rao lower bounds (5the optimal sampling pattern for measuring the NMR spin-spin 8) to determine the optimum choice of sampling times for relaxation time, T 2 . The results may also be applied to the meameasuring T 2 in a spin-echo-type experiment. The results surement of any other exponential decay, including some pulse are not limited to T 2 measurements, but may also be applied sequences for measuring the spin-lattice relaxation time, T 1 . The to any experiment involving exponentially decaying signal optimal sampling pattern involves placing 22% of the sample intensity, including some sequences used to measure T 1 in points at zero time and the remaining 78% at 1.28 T 2 , or, more proteins. Unlike previous approaches, our optimal patterns practically and almost as accurately, one point at zero and four involve sampling at a small number of carefully chosen at 1.30 T 2 . These sampling patterns are very different from those times.

commonly used. The Crame ´r-Rao results are compared with ex-Crame ´r-Rao lower bounds (also known as ''minimumperimental measurements and computer simulations. Some limitations of the method are described, and its extension to the simulta-variance bounds'') provide a fundamental limit to the accuneous measurement of a range of T 2 values is addressed. ᭧ 1996 racy with which a parameter can be determined from any Academic Press, Inc.

given experimental data: for an unbiased data-processing method, the error in a parameter (as measured by its standard deviation) must be greater than or equal to the lower bound.