Regularized optimization (RO) reconstruction for oximetric EPR imaging

Direct Measurement and Imaging of Redox Status with Electron Paramagnetic Resonance

Significance: Fundamental to the application of tissue redox status to human health is the quantification and localization of tissue redox abnormalities and oxidative stress and their correlation with the severity and local extent of disease to inform therapy. The centrality of the low-molecular-weight thiol, glutathione, in physiological redox balance has long been appreciated, but direct measurement of tissue thiol status in vivo has not been possible hitherto. Recent advances in instrumentation and molecular probes suggest the feasibility of real-time redox assessment in humans. Recent Advances: Recent studies have demonstrated the feasibility of using low-frequency electron paramagnetic resonance (EPR) techniques for quantitative imaging of redox status in mammalian tissues in vivo. Rapid-scan (RS) EPR spectroscopy and imaging, new disulfide-dinitroxide spin probes, and novel analytic techniques have led to significant advances in direct, quantitative imaging of thiol redox status. Critical Issues: While novel RS EPR imaging coupled with first-generation molecular probes has demonstrated the feasibility of imaging thiol redox status in vivo, further technical advancements are desirable and ongoing. These include developing spin probes that are tailored for specific tissues with response kinetics tuned to the physiological environment. Equally critical are RS instrumentation with higher signal-to-noise ratio and minimal signal distortion, as well as optimized imaging protocols for image acquisition with sparsity adapted to image information content. Future Directions: Quantitative images of tissue glutathione promise to enable acquisition of a general image of mammalian and potentially human tissue health.

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.

Overmodulation of projections as signal-to-noise enhancement method in EPR imaging

A study concerning the image quality in electron paramagnetic resonance imaging in two-dimensional spatial experiments is presented. The aim of the measurements was to improve the signal-to-noise ratio (SNR) of the projections and the reconstructed image by applying modulation amplitude higher than the radical electron paramagnetic resonance linewidth. Data were gathered by applying four constant modulation amplitudes, where one was below 1/3 (Amod  = 0.04 mT) of the radical linewidth (ΔBpp  = 0.14 mT). Three other modulation amplitude values were used in this experiment, leading to undermodulated (Amod  < 1/3 ΔBpp), partially overmodulated (Amod  ~ 1/3 ΔBpp) and fully overmodulated (Amod  > > 1/3 ΔBpp) projections. The advantages of an applied overmodulation condition were demonstrated in the study performed on a phantom containing four shapes of 1.25 mM water solution of 2, 2, 6, 6-tetramethyl-1-piperidinyloxyl. It was shown that even when the overmodulated reference spectrum was used in the deconvolution procedure, as well as the projection itself, the phantom shapes reconstructed as images directly correspond to those obtained in undermodulation conditions. It was shown that the best SNR of the reconstructed images is expected for the modulation amplitude close to 1/3 of the projection linewidth, which is defined as the distance from the first maximum to the last minimum of the gradient-broadened spectrum. For higher modulation amplitude, the SNR of the reconstructed image is decreased, even if the SNR of the measured projection is increased.

Simultaneous iterative reconstruction technique software for spectral-spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging (EPRI) experiments often suffer from low signal to noise ratio. The increase in spectrometer time required to acquire data of sufficient quality to allow further analysis can be counteracted in part by more processing effort during the image reconstruction step. We suggest a simultaneous iterative reconstruction algorithm (SIRT) for reconstruction of continuous wave EPRI experimental data as an alternative to the widely applied filtered back projection algorithm (FBP). We show experimental and numerical test data of 2d spatial images and spectral-spatial images. We find that for low signal to noise ratio and spectral-spatial images that are limited by the maximum magnetic field gradient strength SIRT is more suitable than FBP.

Two-dimensional EPR imaging with the rapid scan and rotated magnetic field gradient

A new method for fast 2D Electron Paramagnetic Resonance Imaging (EPRI) is presented. To reduce the time of projections acquisition we propose to combine rapid scan of Zeeman magnetic field using high frequency sinusoidal modulation with simultaneously applied magnetic field gradient, whose orientation is changed at low frequency. The correctness of the method is confirmed by studies carried out on a phantom consisting of two LiPc samples. The images from the acquired data are reconstructed using iterative algorithms. The proposed method allows to reduce the image acquisition time up to 10 ms for 2D EPRI, and to detect the sinogram with infinitesimal angular step between projections.

New spectral-spatial imaging algorithm for full EPR spectra of multiline nitroxides and pH sensitive trityl radicals

An algorithm is derived and demonstrated that reconstructs an EPR spectral-spatial image from projections with arbitrarily selected gradients. This approach permits imaging wide spectra without the use of the very large sweep widths and gradients that would be required for spectral-spatial imaging with filtered back projection reconstruction. Each projection is defined as the sum of contributions at the set of locations in the object. At each location gradients shift the spectra in the magnetic field domain, which is equivalent to a phase change in the Fourier-conjugate frequency domain. This permits solution of the problem in the frequency domain. The method was demonstrated for 2D images of phantoms consisting of (i) two tubes containing (14)N and (15)N nitroxide and (ii) two tubes containing a pH sensitive trityl radical at pH 7.0 and 7.2. In each case spectral slices through the image agree well with the full spectra obtained in the absence of gradient.

Two-dimensional spectral-spatial EPR imaging with the rapid scan and modulated magnetic field gradient

A new method for fast spectral-spatial electron paramagnetic resonance imaging (EPRI) is presented. To reduce the time of projections acquisition we propose to combine rapid scan of Zeeman magnetic field using high frequency sinusoidal modulation with simultaneously applied magnetic field gradients, whose amplitude is modulated at low frequency. The correctness of the method is confirmed by studies carried out on a phantom consisting of two LiPc samples. The spectral-spatial images from the acquired data are reconstructed using iterative algorithms. The proposed method allows to acquire the spectral-spatial image with 800 projections at 200ms.

Use of rapid-scan EPR to improve detection sensitivity for spin-trapped radicals

The short lifetime of superoxide and the low rates of formation expected in vivo make detection by standard continuous wave (CW) electron paramagnetic resonance (EPR) challenging. The new rapid-scan EPR method offers improved sensitivity for these types of samples. In rapid-scan EPR, the magnetic field is scanned through resonance in a time that is short relative to electron spin relaxation times, and data are processed to obtain the absorption spectrum. To validate the application of rapid-scan EPR to spin trapping, superoxide was generated by the reaction of xanthine oxidase and hypoxanthine with rates of 0.1-6.0 μM/min and trapped with 5-tert-butoxycarbonyl-5-methyl-1-pyrroline-N-oxide (BMPO). Spin trapping with BMPO to form the BMPO-OOH adduct converts the very short-lived superoxide radical into a more stable spin adduct. There is good agreement between the hyperfine splitting parameters obtained for BMPO-OOH by CW and rapid-scan EPR. For the same signal acquisition time, the signal/noise ratio is >40 times higher for rapid-scan than for CW EPR. Rapid-scan EPR can detect superoxide produced by Enterococcus faecalis at rates that are too low for detection by CW EPR.

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.

The Instrument Set for Generating Fast Adiabatic Passage

The design and construction of a high-performance, low-cost, and easy to assemble adiabatic extension set for homebuilt and commercial spectrometers is described. Described apparatus set was designed for the fast adiabatic passage generation and is based on direct digital synthesizer DDS. This solution gives generator high signal to noise ratio, phase stability even during frequency change which is only possible in expansive commercial high-end hardware. Critical synchronization and timing issues are considered and solutions are discussed. Different experimental conditions and techniques for the measurements are briefly discussed. The proposed system is very flexible and might be used for the measurement of low-frequency nuclear magnetic resonance.

X-band rapid-scan EPR of nitroxyl radicals

X-band rapid-scan EPR spectra were obtained for dilute aqueous solutions of nitroxyl radicals (15)N-mHCTPO (4-hydro-3-carbamoyl-2,2,5,5-tetra-perdeuteromethyl-pyrrolin-1-(15)N-oxyl-d(12)) and (15)N-PDT (4-oxo-2,2,6,6-tetra-perdeuteromethyl-piperidinyl-(15)N-oxyl-d(16)). Simulations of spectra for (15)N-mHCTPO and (15)N-PDT agreed well with the experimental spectra. As the scan rate is increased in the rapid scan regime, the region in which signal amplitude increases linearly with B(1) extends to higher power and the maximum signal amplitude increases. In the rapid scan regime, the signal-to-noise for rapid-scan spectra was about a factor of 2 higher than for unbroadened CW EPR, even when the rapid scan spectra were obtained in a mode that had only 4% duty cycle for data acquisition. Further improvement in signal-to-noise per unit time is expected for higher duty cycles. Rapid scan spectra have higher bandwidth than CW spectra and therefore require higher detection bandwidths at faster scan rates. However, when the scan rate is increased by increasing the scan frequency, the increase in noise from the detection bandwidth is compensated by the decrease in noise due to increased number of averages per unit time. Because of the higher signal bandwidth, lower resonator Q is needed for rapid scan than for CW, so the rapid scan method is advantageous for lossy samples that inherently lower resonator Q.

Deconvolution of sinusoidal rapid EPR scans

In rapid scan EPR the magnetic field is scanned through the signal in a time that is short relative to electron spin relaxation times. Previously it was shown that the slow-scan lineshape could be recovered from triangular rapid scans by Fourier deconvolution. In this paper a general Fourier deconvolution method is described and demonstrated to recover the slow-scan lineshape from sinusoidal rapid scans. Since an analytical expression for the Fourier transform of the driving function for a sinusoidal scan was not readily apparent, a numerical method was developed to do the deconvolution. The slow scan EPR lineshapes recovered from rapid triangular and sinusoidal scans are in excellent agreement for lithium phthalocyanine, a trityl radical, and the nitroxyl radical, tempone. The availability of a method to deconvolute sinusoidal rapid scans makes it possible to scan faster than is feasible for triangular scans because of hardware limitations on triangular scans.

Combining absorption and dispersion signals to improve signal-to-noise for rapid-scan EPR imaging

Direct detection of the rapid-scan EPR signal with quadrature detection and without automatic frequency control provides both the absorption and dispersion components of the signal. The use of a cross-loop resonator results in similar signal-to-noise in the two channels. The dispersion signal can be converted to an equivalent absorption signal by means of Kramers-Kronig relations. The converted signal is added to the directly measured absorption signal. Since the noise in the two channels is not correlated, this procedure increases the signal-to-noise ratio of the resultant absorption signal by up to a factor of square root 2. The utility of this method was demonstrated for 2D spectral-spatial imaging of a phantom containing three tubes of LiPc with different oxygen concentrations and therefore different linewidths.