A parametric approach to spectral-spatial EPR imaging

Accurate reconstruction of 4D spectral-spatial images from sparse-view data in continuous-wave EPRI

In continuous-wave electron paramagnetic resonance imaging (CW EPRI), data are collected generally at densely sampled views sufficient for achieving accurate reconstruction of a four dimensional spectral-spatial (4DSS) image by use of the conventional filtered-backprojection (FBP) algorithm. It is desirable to minimize the scan time by collection of data only at sparsely sampled views, referred to as sparse-view data. Interest thus remains in investigation of algorithms for accurate reconstruction of 4DSS images from sparse-view data collected for potentially enabling fast data acquisition in CW EPRI. In this study, we investigate and demonstrate optimization-based algorithms for accurate reconstruction of 4DSS images from sparse-view data. Numerical studies using simulated and real sparse-view data acquired in CW EPRI are conducted that reveal, in terms of image visualization and physical-parameter estimation, the potential of the algorithms developed for yielding accurate 4DSS images from sparse-view data in CW EPRI. The algorithms developed may be exploited for enabling sparse-view scans with minimized scan time in CW EPRI for yielding 4DSS images of quality comparable to, or better than, that of the FBP reconstruction from data collected at densely sampled views.

Ultrafast multiple paramagnetic species EPR imaging using a total variation based model

An EPR spectrum or an EPR sinogram for imaging contains information about all the paramagnetic species that are in the analyzed sample. When only one species is present, an image of its spatial repartition can be reconstructed from the sinogram by using the well-known Filtered Back-Projection (FBP). However, in the case of several species, the FBP does not allow the reconstruction of the images of each species from a standard acquisition. One has to use for this spectral-spatial imaging whose acquisition can be very long. A new approach, based on Total Variation minimization, is proposed in order to efficiently extract the spatial repartitions of all the species present in a sample from standard imaging data and therefore drastically reduce the acquisition time. Experiments have been carried out on Tetrathiatriarylmethyl, nitroxide and DPPH.

4D-image reconstruction directly from limited-angular-range data in continuous-wave electron paramagnetic resonance imaging

OBJECTIVE

We investigate and develop optimization-based algorithms for accurate reconstruction of four-dimensional (4D)-spectral-spatial (SS) images directly from data collected over limited angular ranges (LARs) in continuous-wave (CW) electron paramagnetic resonance imaging (EPRI).

METHODS

Basing on a discrete-to-discrete data model devised in CW EPRI employing the Zeeman-modulation (ZM) scheme for data acquisition, we first formulate the image reconstruction problem as a convex, constrained optimization program that includes a data fidelity term and also constraints on the individual directional total variations (DTVs) of the 4D-SS image. Subsequently, we develop a primal-dual-based DTV algorithm, simply referred to as the DTV algorithm, to solve the constrained optimization program for achieving image reconstruction from data collected in LAR scans in CW-ZM EPRI.

RESULTS

We evaluate the DTV algorithm in simulated- and real-data studies for a variety of LAR scans of interest in CW-ZM EPRI, and visual and quantitative results of the studies reveal that 4D-SS images can be reconstructed directly from LAR data, which are visually and quantitatively comparable to those obtained from data acquired in the standard, full-angular-range (FAR) scan in CW-ZM EPRI.

CONCLUSION

An optimization-based DTV algorithm is developed for accurately reconstructing 4D-SS images directly from LAR data in CW-ZM EPRI. Future work includes the development and application of the optimization-based DTV algorithm for reconstructions of 4D-SS images from FAR and LAR data acquired in CW EPRI employing schemes other than the ZM scheme.

SIGNIFICANCE

The DTV algorithm developed may be exploited potentially for enabling and optimizing CW EPRI with minimized imaging time and artifacts by acquiring data in LAR scans.

Fast backprojection-based reconstruction of spectral-spatial EPR images from projections with the constant sweep of a magnetic field

In this paper, we introduce a procedure for the reconstruction of spectral-spatial EPR images using projections acquired with the constant sweep of a magnetic field. The application of a constant field-sweep and a predetermined data sampling rate simplifies the requirements for EPR imaging instrumentation and facilitates the backprojection-based reconstruction of spectral-spatial images. The proposed approach was applied to the reconstruction of a four-dimensional numerical phantom and to actual spectral-spatial EPR measurements. Image reconstruction using projections with a constant field-sweep was three times faster than the conventional approach with the application of a pseudo-angle and a scan range that depends on the applied field gradient. Spectral-spatial EPR imaging with a constant field-sweep for data acquisition only slightly reduces the signal-to-noise ratio or functional resolution of the resultant images and can be applied together with any common backprojection-based reconstruction algorithm.

Nitroxide Spin-Labelling and Its Role in Elucidating Cuproprotein Structure and Function

Copper is one of the most abundant biological metals, and its chemical properties mean that organisms need sophisticated and multilayer mechanisms in place to maintain homoeostasis and avoid deleterious effects. Studying copper proteins requires multiple techniques, but electron paramagnetic resonance (EPR) plays a key role in understanding Cu(II) sites in proteins. When spin-labels such as aminoxyl radicals (commonly referred to as nitroxides) are introduced, then EPR becomes a powerful technique to monitor not only the coordination environment, but also to obtain structural information that is often not readily available from other techniques. This information can contribute to explaining how cuproproteins fold and misfold. The theory and practice of EPR can be daunting to the non-expert; therefore, in this mini review, we explore how nitroxide spin-labelling can be used to help the inorganic biochemist gain greater understanding of cuproprotein structure and function in vitro and how EPR imaging may help improve understanding of copper homoeostasis in vivo.

Implementation of GPU-accelerated back projection for EPR imaging

Electron paramagnetic resonance (EPR) Imaging (EPRI) is a robust method for measuring in vivo oxygen concentration (pO2). For 3D pulse EPRI, a commonly used reconstruction algorithm is the filtered backprojection (FBP) algorithm, in which the backprojection process is computationally intensive and may be time consuming when implemented on a CPU. A multistage implementation of the backprojection can be used for acceleration, however it is not flexible (requires equal linear angle projection distribution) and may still be time consuming. In this work, single-stage backprojection is implemented on a GPU (Graphics Processing Units) having 1152 cores to accelerate the process. The GPU implementation results in acceleration by over a factor of 200 overall and by over a factor of 3500 if only the computing time is considered. Some important experiences regarding the implementation of GPU-accelerated backprojection for EPRI are summarized. The resulting accelerated image reconstruction is useful for real-time image reconstruction monitoring and other time sensitive applications.

Comparison of parabolic filtration methods for 3D filtered back projection in pulsed EPR imaging

Pulse electron paramagnetic resonance imaging (Pulse EPRI) is a robust method for noninvasively measuring local oxygen concentrations in vivo. For 3D tomographic EPRI, the most commonly used reconstruction algorithm is filtered back projection (FBP), in which the parabolic filtration process strongly influences image quality. In this work, we designed and compared 7 parabolic filtration methods to reconstruct both simulated and real phantoms. To evaluate these methods, we designed 3 error criteria and 1 spatial resolution criterion. It was determined that the 2 point derivative filtration method and the two-ramp-filter method have unavoidable negative effects resulting in diminished spatial resolution and increased artifacts respectively. For the noiseless phantom the rectangular-window parabolic filtration method and sinc-window parabolic filtration method were found to be optimal, providing high spatial resolution and small errors. In the presence of noise, the 3 point derivative method and Hamming-window parabolic filtration method resulted in the best compromise between low image noise and high spatial resolution. The 3 point derivative method is faster than Hamming-window parabolic filtration method, so we conclude that the 3 point derivative method is optimal for 3D FBP.

Compressed sensing of spatial electron paramagnetic resonance imaging

PURPOSE

To improve image quality and reduce data requirements for spatial electron paramagnetic resonance imaging (EPRI) by developing a novel reconstruction approach using compressed sensing (CS).

METHODS

EPRI is posed as an optimization problem, which is solved using regularized least-squares with sparsity promoting penalty terms, consisting of the l1 norms of the image itself and the total variation of the image. Pseudo-random sampling was employed to facilitate recovery of the sparse signal. The reconstruction was compared with the traditional filtered back-projection reconstruction for simulations, phantoms, isolated rat hearts, and mouse gastrointestinal (GI) tracts labeled with paramagnetic probes.

RESULTS

A combination of pseudo-random sampling and CS was able to generate high-fidelity EPR images at high acceleration rates. For three-dimensional (3D) phantom imaging, CS-based EPRI showed little visual degradation at nine-fold acceleration. In rat heart datasets, CS-based EPRI produced high quality images with eight-fold acceleration. A high resolution mouse GI tract reconstruction demonstrated a visual improvement in spatial resolution and a doubling in signal-to-noise ratio (SNR).

CONCLUSION

A novel 3D EPRI reconstruction using compressed sensing was developed and offers superior SNR and reduced artifacts from highly undersampled data.

Statistical reconstruction algorithms for continuous wave electron spin resonance imaging

Electron spin resonance imaging (ESRI) is an important branch of ESR that deals with heterogeneous samples ranging from semiconductor materials to small live animals and even humans. ESRI can produce either spatial images (providing information about the spatially dependent radical concentration) or spectral-spatial images, where an extra dimension is added to describe the absorption spectrum of the sample (which can also be spatially dependent). The mapping of oxygen in biological samples, often referred to as oximetry, is a prime example of an ESRI application. ESRI suffers frequently from a low signal-to-noise ratio (SNR), which results in long acquisition times and poor image quality. A broader use of ESRI is hampered by this slow acquisition, which can also be an obstacle for many biological applications where conditions may change relatively quickly over time. The objective of this work is to develop an image reconstruction scheme for continuous wave (CW) ESRI that would make it possible to reduce the data acquisition time without degrading the reconstruction quality. This is achieved by adapting the so-called "statistical reconstruction" method, recently developed for other medical imaging modalities, to the specific case of CW ESRI. Our new algorithm accounts for unique ESRI aspects such as field modulation, spectral-spatial imaging, and possible limitation on the gradient magnitude (the so-called "limited angle" problem). The reconstruction method shows improved SNR and contrast recovery vs. commonly used back-projection-based methods, for a variety of simulated synthetic samples as well as in actual CW ESRI experiments.

Dual-scan acquisition for accelerated continuous-wave EPR oximetry

Statistical analysis reveals that, given a fixed acquisition time, linewidth (and thus pO(2)) can be more precisely determined from multiple scans with different modulation amplitudes and sweep widths than from a single-scan. For a Lorentzian lineshape and an unknown but spatially uniform modulation amplitude, the analysis suggests the use of two scans, each occupying half of the total acquisition time. We term this mode of scanning as dual-scan acquisition. For unknown linewidths in a range [Γ(min), Γ(max)], practical guidelines are provided for selecting the modulation amplitude and sweep width for each dual-scan component. Following these guidelines can allow for a 3-4 times reduction in spectroscopic acquisition time versus an optimized single-scan, without requiring hardware modifications. Findings are experimentally verified using L-band spectroscopy with an oxygen-sensitive particulate probe.

Spectral modeling for accelerated pH spectroscopy using EPR

A data modeling and processing method for electron paramagnetic resonance (EPR)-based pH spectroscopy is presented. The proposed method models the EPR spectrum of a pH-sensitive probe in both protonated and unprotonated forms. Under slow-exchange conditions, the EPR spectrum of a sample with an unknown pH value can be accurately represented by a weighted sum of the two models, with the pH value completely determined by their relative weights. Unlike traditional pH spectroscopy, which relies on locating resonance peaks, the proposed modeling-based approach utilizes the information from the entire scan and hence leads to more accurate estimation of pH for a given acquisition time. By employing the proposed methodology, we expect a reduction in the pH estimation error by more than a factor of three, which represents an order of magnitude reduction in acquisition time compared to the traditional method.

Multisite EPR oximetry from multiple quadrature harmonics

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported.

High-sensitivity Q-band electron spin resonance imaging system with submicron resolution

A pulsed electron spin resonance (ESR) microimaging system operating at the Q-band frequency range is presented. The system includes a pulsed ESR spectrometer, gradient drivers, and a unique high-sensitivity imaging probe. The pulsed gradient drivers are capable of producing peak currents ranging from ∼9 A for short 150 ns pulses up to more than 94 A for long 1400 ns gradient pulses. Under optimal conditions, the imaging probe provides spin sensitivity of ∼1.6 × 10(8) spins∕√Hz or ∼2.7 × 10(6) spins for 1 h of acquisition. This combination of high gradients and high spin sensitivity enables the acquisition of ESR images with a resolution down to ∼440 nm for a high spin concentration solid sample (∼10(8) spins∕μm(3)) and ∼6.7 μm for a low spin concentration liquid sample (∼6 × 10(5) spins/μm(3)). Potential applications of this system range from the imaging of point defects in crystals and semiconductors to measurements of oxygen concentration in biological samples.

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.

Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy

A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration.

In vivo multisite oximetry using EPR-NMR coimaging

Coimaging employing electron paramagnetic resonance (EPR) imaging and MRI is used for rapid in vivo oximetry conducted simultaneously across multiple organs of a mouse. A recently developed hybrid EPR-NMR coimaging instrument is used for both EPR and NMR measurements. Oxygen sensitive particulate EPR probe is implanted in small localized pockets, called sites, across multiple regions of a live mouse. Three dimensional MRI is used to generate anatomic visualization, providing precise locations of implant sites. The pO₂ values, one for every site, are then estimated from EPR measurements. To account for radio frequency (RF) phase inhomogeneities inside a large resonator carrying a lossy sample, a generalization of an existing EPR data model is proposed. Utilization of known spectral lineshape, sparse distribution, and known site locations reduce the EPR data collection by more than an order of magnitude over a conventional spectral-spatial imaging, enhancing the feasibility of in vivo EPR oximetry for clinically relevant models.

Regularized optimization (RO) reconstruction for oximetric EPR imaging

A new algorithm for EPR imaging oximetry is described and tested with experimental data for the case of one spatial and one spectral dimension. A single species with variable linewidth is assumed. Instead of creating a 2D image, two one-dimensional profiles are reconstructed: the concentration of the radical and the corresponding oxygen concentration, which reduces the dimensionality of the problem. The algorithm (i) seeks to minimize the discrepancy between experimental data and projections calculated from the profiles and (ii) uses Tikhonov regularization to constrain the smoothness of the results. This approach controllably smoothes profiles rather than the data, while preserving sharp features.

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.

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.