The Bloch Equations for an AB System and the Design of Spin-State-Selective RF Pulses for Coupled Spin Systems |
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| Institution: | 1. Institut für Organische Chemie and Institut für Biologische Grenzflächen 4 – Magnetische Resonanz, Karlsruher Institut für Technologie (KIT), Fritz-Haber-Weg 6, 76133 Karlsruhe, Germany;2. Eötvös Loránd University, Institute of Chemistry, Laboratory of Structural Chemistry and Biology, Pázmány Péter sétány 1/a, Budapest 1117, Hungary;1. UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Kalina Campus, Santacruz, Mumbai 400 098, India;2. Department of Chemical Sciences, Tata Institute of Fundamental Research (TIFR), 1-Homi Bhabha Road, Colaba, Mumbai 400 005, India;3. Department of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;1. Leibniz-Institut für Analytische Wissenschaften - ISAS - e.V., 44139 Dortmund, Germany;2. Experimental Physics III, TU Dortmund University, 44227 Dortmund, Germany |
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| Abstract: | Optimized AM/FM pulses are described which excite an arbitrary coherence of a coupled spin system with optimal intensity. These pulses may become important for creating maximum signal intensity in MQC-filtered and polarization-transfer experiments in HRNMR and in vivo spectroscopy. For an AB system, for example, a pure DQC or ZQC state is obtained (100%) compared to maximal 50% with a conventional π/2-π/2 MQC pulse sequence. The design and numerical optimization of these pulses, with pulse times of about 1/2J (J is the coupling constant), are described. Examples of three of these spin-state-selective pulses (SSSP) for an AB system are given; simulations and experiments confirm their expected performance. To get some insight in the relations between the expectation values of the several coherences under the influence of Zeeman, J-coupling, and RF terms, Bloch-like equations for a proton AB system are derived, with neglection of relaxation. A system of 15 first-order coupled differential equations is found. A solution to these equations is given for the evolution of the zero-quantum coherence and longitudinal magnetization. |
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