CPMG echo amplitudes with arbitrary refocusing angle: explicit expressions, asymptotic behavior, approximations.

Exact explicit analytical expression for echoes in the Carr-Purcell-Meiboom-Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T(1), T(2) and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.

The generating functions formalism for the analysis of spin response to the periodic trains of RF pulses. Echo sequences with arbitrary refocusing angles and resonance offsets.

The generating functions (GF) formalism was applied for calculation of spin density matrix evolution under the influence of periodic trains of RF pulses. It was shown that in a general case, closed expression for the generating function can be found that allows in many cases to derive analytical expressions for the generating function of spin density matrix (magnetization, coherences). This approach was shown to be particularly efficient for the analysis of multi-echo sequences, where one has to average over various frequency isochromats. The explicit analytical expressions for the generating function for echo amplitudes in a Carr-Purcell-Meiboom-Gill (CPMG) echo sequence, a multiecho sequence with incremental phase of refocusing pulse, a gradient echo sequence including transient period were obtained for an arbitrary flip angle and an arbitrary resonance offset. Comparison of the theory and the spin-echo experiments was done, demonstrating a good agreement.

Analysis of lipid peroxidation kinetics. 1. Role of recombination of alkyl and peroxyl radicals.

The kinetics of the lipid peroxidation reaction is only partly understood. Although the set of reactions constituting the overall reaction are believed to be known, it has not been possible to predict how the reaction will respond to a change of one or more of the parameters, e.g., initial concentrations of reactants or different ways of initiating the reaction, nor has it been possible to predict the time dependence of the products. The reason for these problems is the complicated structure of the kinetic scheme, which includes a chain reaction. In this work we perform an in-depth analysis of the importance of the individual reaction steps, and we introduce a new quasi-stationary concentration method based on the assumption that one or more concentrations vary much slower than the others. We show that it is justified to use a quasi-stationary concentration approximation for the alkyl radical L*, but not for the peroxyl radicals LO2 * as assumed in previous works. The method allows us to derive manageable analytical expressions. On the basis of literature values of the rate constants, we are able to introduce specific simplifications that allow us to obtain simple analytical expressions for the time dependence of all concentrations involved in the process.

Analytical derivation of multiple spin echo amplitudes with arbitrary refocusing angle.

Explicit non-recursive expressions for spin echo amplitudes have been derived for CPMG sequences with arbitrary refocusing flip angle.

Singlet and triplet products of the geminate recombination of a radical pair with a single magnetic nucleus (I = 1/2).

The double-channel recombination and separation of the photochemically created singlet radical pair is investigated, taking into account the spin conversion in a zero magnetic field and the arbitrary initial distance between the radicals. The quantum yields of the singlet and triplet products and the free radicals production are found analytically, assuming that the recombination of the diffusing radicals occurs at contact. All the yields are related to the singlet and triplet populations of the recombining radical pair, subjected to spin conversion and contact exchange interaction. The general analytical expressions for the quantum yields are specified for the particular limits of the weak and strong exchange. They are greatly simplified in the case of polar solvents, especially at the contact start. A close similarity is obtained with the results of a previously developed incoherent model of spin conversion, provided that the conversion rate is appropriately related to the hyperfine coupling constant.

Spin evolution of radical pair with radical containing two groups of equivalent magnetic nuclei.

Analytical solution is obtained for time-resolved magnetic field effects (TR-MFE) on recombination fluorescence of radical-ion pair (RIP) containing radical ion with two groups of magnetically equivalent nuclei. The present theoretical approach is applied to three experimental systems: RIPs containing radical cations of 2,3-dimethylbutane, 2,2,6,6-tetramethylpiperidine, or diisopropylamine and radical anion of p-terphenyl-d14 in nonpolar alkane solutions. Good agreement between theory and experiment is found for all the three systems, hyperfine coupling constants of radical cations are obtained by fitting the experimental TR-MFE traces. The potential of the TR-MFE technique for studying radical ions with nonequivalent nuclei is discussed in detail. The wide applicability of the theoretical model and the experimental technique make them useful for studying short-lived radical species that are often beyond the reach of the conventional electron paramagnetic resonance spectroscopy.

Electron self-exchange kinetics determined by MARY spectroscopy: theory and experiment.

The electron self-exchange between a neutral molecule and its charged radical, which is part of a spin-correlated radical ion pair, gives rise to line width effects in the fluorescence-detected MARY (magnetic field effect on reaction yield) spectrum similar to those observed in EPR spectroscopy. An increasing self-exchange rate (i.e., a higher concentration of the neutral molecule) leads to broadening and subsequent narrowing of the spectrum. Along with a series of MARY spectra recorded for several systems (the fluorophores pyrene, pyrene-d(10) and N-methylcarbazole in combination with 1,2- and 1,4-dicyanobenzene) in various solvents, a theoretical model is developed that describes the spin evolution and the diffusive recombination of the radical pair under the influence of the external magnetic field and electron self-exchange, thereby allowing the simulation of MARY spectra of the systems investigated experimentally. The spin evolution of the radicals in the pair is calculated separately using spin correlation tensors, thereby allowing rigorous quantum mechanical calculations for real spin systems. It is shown that the combination of these simulations with high resolution, low noise experimental spectra makes the MARY technique a novel, quantitative method for the determination of self-exchange rate constants. In comparison to a simple analytical formula which estimates the self-exchange rate constant from the slope of the linear part of a line width vs concentration plot, the simulation method yields more reliable and accurate results. The correctness of the results obtained by the MARY method is proved by a comparison with corresponding data from the well-established EPR line broadening technique. With its less stringent restrictions on radical lifetime and stability, the MARY technique provides an alternative to the classical EPR method, in particular for systems involving short-lived and unstable radicals.

Increased MR image contrast by correlation of tissue relaxation properties.

An image postprocessing technique that is based on the relaxation properties of tissues and that can produce MR images with increased contrast is proposed. The technique involves no a priori assumptions concerning the form of the relaxation decay. An arbitrary number of postprocessed images, each emphasizing a selected tissue type, is obtained from the original images of a multiecho acquisition. It is shown with examples that the technique allows more complete utilization of relaxation information for tissue differentiation.