Optimization of magnetic field sweep and field modulation amplitude for continuous-wave EPR oximetry

For continuous-wave electron paramagnetic resonance spectroscopy, what settings of magnetic field sweep width and field modulation amplitude yield the best accuracy in estimated linewidth? Statistical bounds on estimation error presented in this work provide practical guidance: set the sweep width and modulation amplitude to 8 and 4 times the half-width half-maximum linewidth, Γ, respectively. For unknown linewidths in the range [Γ(min),Γ(max)] the worst-case estimation error is minimized by using settings designed for Γ(max). The analysis assumes a Lorentzian lineshape and a constant modulation amplitude across the extent of the irradiated paramagnetic probe. The analytical guidelines are validated using L-band spectroscopy with a particulate LiNc-BuO probe.     

High Spatial Resolution Multi-Site EPR Oximetry: The Use of a Convolution-Based Fitting Method

We describe a new method to enhance the spatial resolution of multi-site electron paramagnetic resonance (EPR) oximetry. The method is suitable for any shape (density distribution function) of a solid paramagnetic material implanted in tissue. It corrects distortions of lineshapes caused by the gradient and thus overcomes limitations of previous multi-site EPR oximetry methods that restricted the ratio of the particle size to the distance between sites. The new method is based on consecutive applications of magnetic field gradients with the same direction but with a different magnitude and uses a convolution-based fitting algorithm to derive Lorentzian EPR linewidths of each individual peak of the EPR spectrum. The method is applicable for any particulate EPR oxygen sensitive materials whose EPR spectra can be approximated by a Lorentzian function or a superposition of Lorentzian functions. By incorporating this model of the lineshape in the data processing, we are able to decrease significantly the number of parameters needed for the calculations and to recover the oxygen concentration, even from quite noisy spectra. We (i) describe our method and the data-processing algorithm, (ii) demonstrate our approach in model and in vivo experiments, and (iii) discuss the limitations.     

EPR oximetry in three spatial dimensions using sparse spin distribution

A method is presented to use continuous wave electron paramagnetic resonance imaging for rapid measurement of oxygen partial pressure in three spatial dimensions. A particulate paramagnetic probe is employed to create a sparse distribution of spins in a volume of interest. Information encoding location and spectral linewidth is collected by varying the spatial orientation and strength of an applied magnetic gradient field. Data processing exploits the spatial sparseness of spins to detect voxels with nonzero spin and to estimate the spectral linewidth for those voxels. The parsimonious representation of spin locations and linewidths permits an order of magnitude reduction in data acquisition time, compared to four-dimensional tomographic reconstruction using traditional spectral-spatial imaging. The proposed oximetry method is experimentally demonstrated for a lithium octa-n-butoxy naphthalocyanine (LiNc–BuO) probe using an L-band EPR spectrometer.     

Evaluation of oxygen-response times of phthalocyanine-based crystalline paramagnetic spin probes for EPR oximetry

The goal of the present study was to evaluate the temporal response of particulate-based EPR oximetry probes to changes in partial pressure of oxygen (pO(2)). In order to accurately evaluate the oxygen-response time, we developed a method for rapid modulation of pO(2) in a chamber containing the probe using an oscillator-driven speaker-diaphragm setup. The apparatus was capable of producing sinusoidal changes in pO(2) at frequencies up to 300 Hz or more. The pressure-modulation setup was used to evaluate the temporal response of some of the most commonly used phthalocyanine-based particulate probes. For validation, the time-response of the probes was compared to that of a high sensitivity pressure sensor. The results revealed that some particulate probes could respond to changes in pO(2) with a temporal response of 3.3 ms (300 Hz). The observations were interpreted in the light of their crystalline packing in favor of oxygen diffusion. The results of the present study should enable the selection of probes for oximetry applications requiring high temporal resolution.     

Estimation of mean and median pO2 values for a composite EPR spectrum

Electron paramagnetic resonance (EPR)-based oximetry is capable of quantifying oxygen content in samples. However, for a heterogeneous environment with multiple pO2 values, peak-to-peak linewidth of the composite EPR lineshape does not provide a reliable estimate of the overall pO2 in the sample. The estimate, depending on the heterogeneity, can be severely biased towards narrow components. To address this issue, we suggest a postprocessing method to recover the linewidth histogram which can be used in estimating meaningful parameters, such as the mean and median pO2 values. This information, although not as comprehensive as obtained by EPR spectral-spatial imaging, goes beyond what can be generally achieved with conventional EPR spectroscopy. Substantially shorter acquisition times, in comparison to EPR imaging, may prompt its use in clinically relevant models. For validation, simulation and EPR experiment data are presented.     

Linewidth Analysis of Spin Labels in Liquids: I. Theory and Data Analysis

We present a method of simulating the EPR spectra of spin labels in liquids using direct convolution of hyperfine splitting with Lorentzian linewidths. The aim is to simulate the experimental lineshape by considering all spectrometer characteristics as well as inhomogeneous and homogeneous linewidth effects. A major advance in this method is the correction for the broadening produced by Zeeman modulation commonly used to obtain EPR signals; this allows experimenters much more freedom to optimize their experimental conditions for the best signal-to-noise ratio. Microwave power broadening (saturation) effects on the EPR lines are significant even at very low observer levels. Successful simulation requires that all contributions from unresolved hyperfine splittings be explicitly included. Inhomogeneous broadening is dealt with by including all spins that interact with the electron (as a set of superhyperfine interactions); there is no "effective Gaussian" to substitute for the correct superhyperfine interactions. The effects of spin exchange on the linewidth and lineshape can be observed and must be taken into account in order to extract the fundamental linewidths.     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.     

Effect of nitrogen dioxide on the EPR property of lithium octa-n-butoxy 2,3-naphthalocyanine (LiNc-BuO) microcrystals

Lithium octa-n-butoxy-naphthalocyanine (LiNc-BuO) is a stable free radical that can be detected by electron paramagnetic resonance (EPR) spectroscopy. Previously we have reported that microcrystals of LiNc-BuO exhibit a single sharp EPR peak, whose width varies linearly with the partial pressure of paramagnetic molecules such as oxygen and nitric oxide. In this report, we present the effect of nitrogen dioxide (NO2), which is also a paramagnetic molecule, on the EPR properties of LiNc-BuO. The gas-sensing property of LiNc-BuO is attributed to the open molecular framework of the crystal structure which is arranged with wide channels capable of accommodating large molecules such as NO2. The EPR linewidth of LiNc-BuO was highly sensitive to the partial pressure of NO2 in the gas mixture. The line-broadening was quick and reversible in the short-term for low concentration of NO2. However, the EPR signal intensity decreased with time of exposure, apparently due to a reaction of NO2 with LiNc-BuO crystals to give diamagnetic products. The results suggested that LiNc-BuO may be a useful probe for the determination of trace amounts of NO2 using EPR spectroscopy.     

Using of Digital Demodulation of Multiharmonic Overmodulated EPR Signals to Improve EPR Oximetry Reliability

Overmodulation of electron paramagnetic resonance (EPR) lines is routinely used in EPR oximetry in order to increase the signal-to-noise ratio and thus to improve the accuracy with which the line width of a spin probe can be measured. For a known probe type, the line width is easily translated into the oxygen partial pressure. A standard EPR spectrometer uses the analog phase-sensitive detection (PSD) to demodulate the EPR signal. PSD imposes the restriction that only one spectrum is measured at a time, which is normally the first-harmonic EPR line. Information about EPR signals centered at the other harmonics of the modulation frequency is irreversibly destroyed by PSD. The question is raised whether this information can be utilized for EPR oximetry, for overmodulation enhances the second- and the other harmonic spectra, so that they approach the first-harmonic spectrum in intensity. To find an answer, numerical simulation and experimental measurements have been conducted. The experiment required modification of the detection scheme, so that all EPR-related information in the overmodulated signal is preserved. This permits measuring of the multiharmonic EPR spectrum, which when fitted to a set of the corresponding theoretical lines produces more accurate results in comparison with the standard overmodulation method.     

High spatial resolution multi-site EPR oximetry. The use of convolution-based fitting method

We describe a new method to enhance the spatial resolution of multi-site electron paramagnetic resonance (EPR) oximetry. The method is suitable for any shape (density distribution function) of a solid paramagnetic material implanted in tissue. It corrects distortions of lineshapes caused by the gradient and thus overcomes limitations of previous multi-site EPR oximetry methods that restricted the ratio of the particle size to the distance between sites. The new method is based on consecutive applications of magnetic field gradients with the same direction but with a different magnitude and uses a convolution-based fitting algorithm to derive Lorentzian EPR linewidths of each individual peak of the EPR spectrum. The method is applicable for any particulate EPR oxygen sensitive materials whose EPR spectra can be approximated by a Lorentzian function or a superposition of Lorentzian functions. By incorporating this model of the lineshape in the data processing, we are able to decrease significantly the number of parameters needed for the calculations and to recover the oxygen concentration, even from quite noisy spectra. We (i) describe our method and the data-processing algorithm, (ii) demonstrate our approach in model and in vivo experiments, and (iii) discuss the limitations.     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

Absorption linewidth inversion with wavelength modulation spectroscopy

For absorption linewidth inversion with wavelength modulation spectroscopy(WMS), an optimized WMS spectral line fitting method was demonstrated to infer absorption linewidth effectively, and the analytical expressions for relationships between Lorentzian linewidth and the separations of first harmonic peak-to-valley and second harmonic zero-crossing were deduced. The transition of CO_2 centered at 4991.25 cm~(-1) was used to verify the optimized spectral fitting method and the analytical expressions. Results showed that the optimized spectra fitting method was able to infer absorption accurately and compute more than 10 times faster than the commonly used numerical fitting procedure. The second harmonic zero-crossing separation method calculated an even 6 orders faster than the spectra fitting without losing any accuracy for Lorentzian dominated cases. Additionally, linewidth calculated through second harmonic zero-crossing was preferred for much smaller error than the first harmonic peak-to-valley separation method. The presented analytical expressions can also be used in on-line optical sensing applications, electron paramagnetic resonance, and further theoretical characterization of absorption lineshape.     

Nonequivalent spectra of unpaired electrons in field and frequency modulation

We report a difference in the spectral lineshapes of continuous-wave (CW) electron paramagnetic resonance (EPR) spectroscopy between field and frequency modulation. This finding addresses the long-standing question of the effect of modulation in EPR absorption. We compared the first-derivative EPR spectra at 1.1 GHz for lithium phthalocyanine crystals, which have a single narrow linewidth in the EPR absorption spectrum, using field and frequency modulation. The experimental findings suggest that unpaired electrons have different behaviors under perturbation due to field and frequency modulation.     

Amplitude modulated transversal and longitudinal EPR spectroscopy

The amplitude modulated EPR spectroscopy is analyzed both in the time and the frequency domain. The results of numerical calculations and analytical approximate treatments indicate that the signal lineshape is differently affected by relaxation mechanisms when transversal or longitudinal detection is used in spectroscopies with variable frequencies of modulation. Measurements of longitudinally detected electron-spin double resonance obtained in dependence on the frequency of modulation confirm the lineshape expected by the theoretical analysis.     

Detection of electron paramagnetic resonance absorption using frequency modulation

A frequency modulation (FM) method was developed to measure electron paramagnetic resonance (EPR) absorption. The first-derivative spectrum of 1,1-diphenyl-2-picrylhydrazyl (DPPH) powder was measured with this FM method. Frequency modulation of up to 1.6 MHz (peak-to-peak) was achieved at a microwave carrier frequency of 1.1 GHz. This corresponds to a magnetic field modulation of 57microT (peak-to-peak) at 40.3 mT. By using a tunable microwave resonator and automatic control systems, we achieved a practical continuous-wave (CW) EPR spectrometer that incorporates the FM method. In the present experiments, the EPR signal intensity was proportional to the magnitude of frequency modulation. The background signal at the modulation frequency (1 kHz) for EPR detection was also proportional to the magnitude of frequency modulation. An automatic matching control (AMC) system reduced the amplitude of noise in microwave detection and improved the baseline stability. Distortion of the spectral lineshape was seen when the spectrometer settings were not appropriate, e.g., with a lack of the open-loop gain in automatic tuning control (ATC). FM is an alternative to field modulation when the side-effect of field modulation is detrimental for EPR detection. The present spectroscopic technique based on the FM scheme is useful for measuring the first derivative with respect to the microwave frequency in investigations of electron-spin-related phenomena.     

The continuous wave electron paramagnetic resonance experiment revisited

When the modulation frequency used in continuous wave electron paramagnetic resonance (cw EPR) spectroscopy exceeds the linewidth, modulation sidebands appear in the spectrum. It is shown theoretically and experimentally that these sidebands are actually multiple photon transitions, sigma(+)+kxpi, where one microwave (mw) sigma(+) photon is absorbed from the mw radiation field and an arbitrary number k of radio frequency (rf) pi photons are absorbed from or emitted to the modulation rf field. Furthermore, it is demonstrated that both the derivative shape of the lines in standard cw EPR spectra and the distortions due to overmodulation are caused by the unresolved sideband pattern of these lines. The single-photon transition does not even give a contribution to the first-harmonic cw EPR signal. Multiple photon transitions are described semiclassically in a toggling frame and their existence is proven using second quantization. With the toggling frame approach and perturbation theory an effective Hamiltonian for an arbitrary sideband transition is derived. Based on the effective Hamiltonians an expression for the steady-state density operator in the singly rotating frame is derived, completely describing all sidebands in all modulation frequency harmonics of the cw EPR signal. The relative intensities of the sidebands are found to depend in a very sensitive way on the actual rf amplitude and the saturation of single sidebands is shown to depend strongly on the effective field amplitude of the multiple photon transitions. By comparison with the analogous solutions for frequency-modulation EPR it is shown that the field-modulation and the frequency-modulation technique are not equivalent. The experimental data fully verify the theoretical predictions with respect to intensities and lineshapes.     

基于幅度相位联合校正算法的8-QAM自由空间相干光通信

提出了基于幅度相位联合校正算法的8阶正交幅度调制(8-QAM)自由空间相干光通信方案。与传统的自由空间光通信方案相比,本文提出的方案不仅无需信道状态信息(CSI)就可以实现对原信号的高精度还原,同时还具有较高的光谱效率。仿真实验表明,当接收端与发射端的频偏f 0=20 MHz、激光器联合线宽Δf=10 kHz、信噪比为20 dB时,该方案在归一化大气闪烁标准差σ=0.25、归一化相位噪声方差σΦ^2=0.07的对数正态湍流信道条件下,其误码率(BER)与未采用联合校正算法的8-QAM系统相比低4个量级。     

NMR spectral quantitation by principal component analysis. III. A generalized procedure for determination of lineshape variations

We present a general procedure for automatic quantitation of a series of spectral peaks based on principal component analysis (PCA). PCA has been previously used for spectral quantitation of a single resonant peak of constant shape but variable amplitude. Here we extend this procedure to estimate all of the peak parameters: amplitude, position (frequency), phase and linewidth. The procedure consists of a series of iterative steps in which the estimates of position and phase from one stage of iteration are used to correct the spectra prior to the next stage. The process is convergent to a stable result, typically in less than 5 iterations. If desired, remaining linewidth variations can then be corrected. Correction of (typically) unwanted variations of these types is important not only for direct peak quantitation, but also as a preprocessing step for spectral data prior to application of pattern recognition/classification techniques. The procedure is demonstrated on simulated data and on a set of 992 (31)P NMR in vivo spectra taken from a kinetic study of rat muscle energetics. The proposed procedure is robust, makes very limited assumptions about the lineshape, and performs well with data of low signal-to-noise ratio.     

A parametric approach to spectral-spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging for in vivo mapping of spin distribution and spectral shape requires rapid data acquisition. A spectral-spatial imaging technique is presented that provides an order of magnitude reduction in acquisition time, compared to iterative tomographic reprojection. The proposed approach assumes that spectral shapes in the sample are well-approximated by members from a parametric family of functions. A model is developed for the spectra measured with magnetic field modulation. Parameters defining the spin distribution and spectral shapes are then determined directly from the measurements using maximum a posteriori probability estimation. The approach does not suffer approximation error from limited sweep width of the main magnetic field and explicitly incorporates the variability in signal-to-noise ratio versus strength of magnetic field gradient. The processing technique is experimentally demonstrated on a one-dimensional phantom containing a nitroxide spin label with constant g-factor. Using an L-band EPR spectrometer, spectral shapes and spin distribution are accurately recovered from two projections and a spectral window which is comparable to the maximum linewidth of the sample.     

Anisotropic motion effects in CW non-linear EPR spectra: relaxation enhancement of lipid spin labels

Continuous-wave (CW) EPR measurements of enhancements in spin-lattice (T(1)-) relaxation rate find wide application for determining spin-label locations in biological systems. Often, especially in membranes, the spin-label rotational motion is anisotropic and subject to an orientational potential. We investigate here the effects of anisotropic diffusion and ordering on non-linear CW-EPR methods for determining T(1) of nitroxyl spin labels. Spectral simulations are performed for progressive saturation of the conventional in-phase, first-harmonic EPR signal, and for the first-harmonic absorption EPR signals detected 90 degrees -out-of-phase with respect to the Zeeman field modulation. Motional models used are either rapid rotational diffusion, or strong-jump diffusion of unrestricted frequency, within a cone of fixed maximum amplitude. Calculations of the T(1)-sensitive parameters are made for both classes of CW-experiment by using motional parameters (i.e., order parameters and correlation times), intrinsic homogeneous and inhomogeneous linewidth parameters, and spin-Hamiltonian hyperfine- and g-tensors, that are established from simulation of the linear CW-EPR spectra. Experimental examples are given for spin-labelled lipids in membranes.