EPR imaging: the relationship between CW spectra acquired from an extended sample subjected to fixed stepped gradients and the Radon transform of the resonance density

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.

EPR Imaging of Metallic Lithium and its Application to Dendrite Localisation in Battery Separators

Conduction Electron Paramagnetic Resonance Imaging (CEPRI) is presented as a sensitive technique for mapping metallic lithium species. The method is demonstrated using different samples that are either thick or thin compared to the microwave skin depth. As a thin sample, microstructured metallic lithium deposits in a lithium-ion battery (LIB) separator were analysed, illustrating the capabilities of CEPRI by obtaining a high-resolution image with an image resolution in the micrometre range. Limitations and intricacies of the method due to non-linear effects caused by the skin effect are discussed based on images of surface patterns on thick metallic lithium samples. The lineshape of the EPR spectrum is introduced as a proxy to determine the suitability of CEPRI for the quantitative visualisation of metallic lithium deposits. The results suggest that CEPRI is particularly suited to analyse the spatial distribution of microstructured Li that forms during charging and discharging of LIB cells, including the localization of the point of failure in the case of an internal cell short circuit caused by dendrites.

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.

How in vivo EPR measures and images oxygen

The partial pressure of oxygen (pO₂) in tissues plays an important role in the pathophysiology of many diseases and influences outcome of cancer therapy, ischemic heart and cerebrovascular disease treatments and wound healing. Over the years a suite of EPR techniques for reliable oxygen measurements has been developed. This is a mini-review of pulse EPR in vivo oxygen imaging methods that utilize soluble spin probes. Recent developments in pulse EPR imaging technology have brought an order of magnitude increase in image acquisition speed, enhancement of sensitivity and considerable improvement in the precision and accuracy of oxygen measurements.

Electron paramagnetic resonance oxygen imaging in vivo

This review covers the last 15 years of the development of EPR in vivo oxygen imaging. During this time, a number of major technological and methodological advances have taken place. Narrow line width, long relaxation time, and non-toxic triaryl methyl radicals were introduced in the late 1990s. These not only improved continuous wave (CW) imaging, but also enabled the application of pulse EPR imaging to animals. Recent developments in pulse technology have brought an order of magnitude increase in image acquisition speed, enhancement of sensitivity, and considerable improvement in the precision and accuracy of oxygen measurements. Consequently, pulse methods take up a significant part of this review.

Where it's at really matters: in situ in vivo vascular endothelial growth factor spatially correlates with electron paramagnetic resonance pO2 images in tumors of living mice

Purpose

Tumor microenvironments show remarkable tumor pO₂ heterogeneity, as seen in prior EPR pO₂ images (EPROI). pO₂ correlation with hypoxia response proteins is frustrated by large rapid pO₂ changes with position.

Procedures

To overcome this limitation, biopsies stereotactically located in the EPROI were used to explore the relationship between vascular endothelial growth factor A (VEGF) concentrations in living mouse tumors and the local EPROI pO₂.

Results

Quantitative ELISA VEGF concentrations correlated (p = 0.0068 to 0.019) with mean pO₂, median pO₂, and the fraction of voxels in the biopsy volume with pO₂ less than 3, 6, and 10 Torr.

Conclusions

This validates EPROI hypoxic fractions at the molecular level and provides a new paradigm for the assessment of the relationship, in vivo, between hypoxia and hypoxia response proteins. When translated to human subjects, this will enhance understanding of human tumor pathophysiology and cancer response to therapy.

Oxidative stress imaging in live animals with techniques based on electron paramagnetic resonance

Oxidative stress has been the object of considerable biological and biochemical investigation. Quantification has been difficult although the quantitative level of products of biological oxidations in tissues and tissue products has emerged as a widely used technique. The relationship between these products and the amount of oxidative stress is less clear. Imaging oxidative stress with electron paramagnetic resonance related magnetic resonance imaging, while not addressing the specific issue of quantification of initiating events, focuses on the anatomic specific location of the oxidative stress. Moreover, the relative quantification of oxidative stress of one location against another is possible, sharpening our understanding of oxidative stress. This promises to improve our understanding of oxidative stress and its deleterious consequences and enhance our understanding of the effectiveness of interventions to modulate oxidative stress and its consequences.

Multiple-stepped Zeeman field offset method applied in acquiring enhanced resolution spin-echo electron paramagnetic resonance images

PURPOSE

Electron paramagnetic resonance (EPR) imaging techniques provide quantitative in vivo oxygen distribution images. Time-domain techniques including electron spin echo (ESE) imaging have been under study in recent years for their robustness and promising new features. One of the limitations of ESE imaging addressed here is the finite acquisition frequency bandwidth, which imposes limits on applied magnetic field gradients and the resulting image spatial resolution. In order to improve the image spatial resolution, we have extended the effective frequency bandwidth of the imaging system by acquiring projections at multiple Zeeman magnetic field offsets and combining them to restore complete projections obtained with more uniform frequency response, resulting in higher quality images.

METHODS

In multiple-stepped magnetic field or multi-B scheme, every projection of the three dimensional object is acquired at different main or Zeeman magnetic field (B) offset values. The data from field offset steps are combined, normalizing to the imaging system frequency acquisition window function, a sensitivity profile, to restore the complete projection. A multipurpose pulse EPR imager and phantoms containing the same type of spin probe (OX063H) used in routine animal imaging were also used in this study.

RESULTS

Using the multi-B method, we were able to acquire images of our phantoms with enhanced spatial resolution compared to the conventional ESE approach. Compared to standard single-B ESE images, the T2 resolutions of multi-B images were superior using a high spatial-resolution regime. Image artifacts present in high-gradient single-B ESE images are also substantially reduced using in the multi-B scheme.

CONCLUSIONS

The multi-B method is less susceptible to instrumental limitations for larger gradient fields and acquiring images with higher spatial resolution better overall quality, without the need to alter the existing pulse ESE image acquisition hardware.

Scaling of EPR spectral-spatial images with size of sample: images of a sample greater than 5 cm in linear dimension

The authors have obtained spectral-spatial EPR images of a phantom significantly larger than those previously obtained. Images of a homogeneous phantom 4.2 cm in diameter and 6.5 cm in length with B1 equivalent to that used for smaller samples give a similar linewidth resolution both with linewidth population distributions of width 0.1 microT. Spatial resolution appeared to have modest degradation. Images of the large homogeneous phantom provide maps of the magnetic field of a partially shimmed magnet.

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.

Electron paramagnetic resonance oxygen image hypoxic fraction plus radiation dose strongly correlates with tumor cure in FSa fibrosarcomas

PURPOSE

Tumor hypoxia has long been known to produce resistance to radiation. In this study, electron paramagnetic resonance (EPR) oxygen imaging was investigated for its power to predict the success of tumor control according to tumor oxygenation level and radiation dose.

METHODS AND MATERIALS

A total of 34 EPR oxygen images were obtained from the legs of C3H mice bearing 0.5-cm(3) FSa fibrosarcomas under both normal (air breathing) and clamped tumor conditions. Under the same conditions as those during which the images were obtained, the tumors were irradiated to a variety of doses near the FSa dose at which 50% of tumors were cured. Tumor tissue was distinguished from normal tissue using co-registration of the EPR oxygen images with spin-echo magnetic resonance imaging of the tumor and/or stereotactic localization. The tumor voxel statistics in the EPR oxygen image included the mean and median partial pressure of oxygen and the fraction of tumor voxels below the specified partial pressure of oxygen values of 3, 6, and 10 mm Hg. Bivariate logistic regression analysis using the radiation dose and each of the EPR oxygen image statistics to determine which best separated treatment failure from success.

RESULTS

The measurements of the dose at which 50% of tumors were cured were similar to those found in published data for this syngeneic tumor. Bivariate analysis of 34 tumors demonstrated that tumor cure correlated with dose (p = 0.004) and with a <10 mm Hg hypoxic fraction (p = 0.023).

CONCLUSION

Our results have shown that, together, radiation dose and EPR image hypoxic fraction separate the population of FSa fibrosarcomas that are cured from those that fail, thus predicting curability.

High spatial resolution multisite EPR oximetry of transient focal cerebral ischemia in the rat

In vivo electron paramagnetic resonance (EPR) spectroscopy can provide direct noninvasive, continuous, and repeatable measurements of oxygen in tissues. High-spatial-resolution multisite (HSRMS) oximetry is an EPR technique that uses applied magnetic field gradients to extend this capability to multiple implanted probes within the sample and accurately to estimate their respective local pO(2) values. These capabilities are crucial in experiments in which pO(2) varies across space and time and in which information about these variations is needed to describe physiologic and pathophysiologic phenomena and evaluate their responses to interventions such as therapy. One important application is the investigation of transient focal ischemia in the rat brain and the effects of treatment with hyperoxygenation. We used HSRMS oximetry with overmodulation to measure brain tissue oxygenation in a rat stroke model using lithium phthalocyanine as the oxygen probe. Oxygen measurements were made in a small cohort of rats at four implant sites during ischemia and reperfusion after transient focal ischemia initiated by occlusion of the middle cerebral artery. These measurements demonstrate the capabilities of the HSRMS oximetry technique and set the stage for more extensive physiologic studies.

Targeted-ROI imaging in electron paramagnetic resonance imaging

Electron paramagnetic resonance imaging (EPRI) is a technique that has been used for in vivo oxygen imaging of small animals. In continuous wave (CW) EPRI, the measurement can be interpreted as a sampled 4D Radon transform of the image function. The conventional filtered-backprojection (FBP) algorithm has been used widely for reconstructing images from full knowledge of the Radon transform acquired in CW EPRI. In practical applications of CW EPRI, one often is interested in information only in a region of interest (ROI) within the imaged subject. It is desirable to accurately reconstruct an ROI image only from partial knowledge of the Radon transform because acquisition of the partial data set can lead to considerable reduction of imaging time. The conventional FBP algorithm cannot, however, reconstruct accurate ROI images from partial knowledge of the Radon transform of even dimension. In this work, we describe two new algorithms, which are referred to as the backprojection filtration (BPF) and minimum-data filtered-backprojection (MDFBP) algorithms, for accurate ROI-image reconstruction from a partial Radon transform (or, truncated Radon transform) in CW EPRI. We have also performed numerical studies in the context of ROI-image reconstruction of a synthetic 2D image with density similar to that found in a small animal EPRI. This demonstrates both the inadequacy of the conventional FBP algorithm and the success of BPF and MDFBP algorithms in ROI reconstruction. The proposed ROI imaging approach promises a means to substantially reduce image acquisition time in CW EPRI.

Simulation of 4D spectral-spatial EPR images

Electron paramagnetic resonance imaging (EPRI) can be modeled by the forward projection of a 4D synthetic spectral-spatial phantom. We developed a simulation tool for EPRI and carried out a quantitative comparison between simulation and experiment, focusing on the signal and noise characteristics. The signal height in the simulation was compared to that in the experimental projections at gradients of different magnitudes and directions. We investigated the noise power spectrum of an EPR imager and incorporated it into the simulation. The signal and noise modeling of the simulation achieved the same performance as the EPR imager. Using this simulation, various sampling schemes were tried to find an optimized parameter set under the customized noise model of this EPR imager.

Comparison of local and global angular interpolation applied to spectral-spatial EPR image reconstruction

Spectral-spatial images reconstructed from a small number of projections suffer from streak artifacts that are seen as noise, particularly in the spectral dimension. Interpolation in projection space can reduce artifacts in the reconstructed images. The reduction of background artifacts improves lineshape fitting. In this work, we compared the performances of angular interpolation implemented using linear, cubic B-spline, and sinc methods. Line width maps were extracted from 4-D EPR images of phantoms using spectral fitting to evaluate each interpolation method and its robustness to noise. Results from experiment and simulation showed that the cubic B-spline, angular interpolation was preferable to either sinc or linear interpolation methods.

Object dependent sweep width reduction with spectral-spatial EPR imaging

For spectral-spatial EPR imaging, prior knowledge about the spatial support of an imaged object can be exploited in two ways. We can shrink the spatial field of view (FOV) to closely wrap the object in a sphere or reduce the sweep width in a projection dependent fashion. Use of a smaller spatial FOV with the same number of samples enhances spatial resolution by reducing voxel volume at the expense of signal-to-noise and a consequent degraded line-width resolution. We have developed another approach to define sweep width that prunes away the portions of the projection sweep with no signal. This reduces data acquisition time for the continuous wave (CW) EPR image proportional to the sweep width reduction. This method also avoids voxel volume reduction. Using the reduced-sweep method, we decreased the data acquisition time by 20% maintaining spatial and linewidth resolution.

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.

Spatially uniform sampling in 4-D EPR spectral-spatial imaging

Four-dimensional EPR imaging involves a computationally intensive inversion of the sampled Radon transform. Conventionally, N-dimensional reconstructions have been carried out with N-1 stages of 2-D backprojection to exploit a dimension-dependent reduction in execution time. The huge data size of 4-D EPR imaging demands the use of a 3-stage reconstruction each consisting of 2-D backprojections. This gives three orders of magnitude reduction in computation relative to a single stage 4-D filtered backprojection. The multi-stage reconstruction, however, requires a uniform angular sampling that yields an inefficient distribution of gradient directions. We introduce a solution that involves acquisition of projections uniformly distributed in solid angle and reconstructs in three 2-D stages with the spatial uniform solid angle data set converted to uniform linear angular projections using 2-D interpolation. Images were taken from the two sampling schemes to compare the spatial resolution and the line width resolution. The degradation in the image quality due to the additional interpolation was small, and we achieved approximately 30% reduction in data acquisition time.

Spin echo spectroscopic electron paramagnetic resonance imaging

The use of spin echoes to obtain spectroscopic EPR images (spectral-spatial images) at 250 MHz is described. The advantages of spin echoes-larger signals than the free induction decay, better phase characteristics for Fourier transformation, and decay shapes undistorted by instrumental dead time-are clearly shown. An advantage is gained from using a crossed loop resonator that isolates the 250-W pump power by greater than 50 dB from the observer arm preamplifiers. The echo decay rates can be used to determine the oxygen content in solutions containing 1 mM trityl concentrations. Two- and three-dimensional images of oxygen concentration are presented.

Electron Paramagnetic Resonance Oxygen Images Correlate Spatially and Quantitatively with Oxylite Oxygen Measurements

Tumor oxygenation predicts cancer therapy response and malignant phenotype. This has spawned a number of oxymetries. Comparison of different oxymetries is crucial for the validation and understanding of these techniques. Electron paramagnetic resonance (EPR) imaging is a novel technique for providing quantitative high-resolution images of tumor and tissue oxygenation. This work compares sequences of tumor pO2 values from EPR oxygen images with sequences of oxygen measurements made along a track with an Oxylite oxygen probe. Four-dimensional (three spatial and one spectral) EPR oxygen images used spectroscopic imaging techniques to measure the width of a spectral line in each image voxel from a trityl spin probe (OX063, Amersham Health R&D) in the tissues and tumor of mice after spin probe injection. A simple calibration allows direct, quantitative translation of each line width to an oxygen concentration. These four-dimensional EPR images, obtained in 45 minutes from FSa fibrosarcomas grown in the legs of C3H mice, have a spatial resolution of approximately 1 mm and oxygen resolution of approximately 3 Torr. The position of the Oxylite track was measured within a 2-mm accuracy using a custom stereotactic positioning device. A total of nine images that involve 17 tracks were obtained. Of these, most showed good correlation between the Oxylite measured pO2 and a track located in the tumor within the uncertainties of the Oxylite localizability. The correlation was good both in terms of spatial distribution pattern and pO2 magnitude. The strong correlation of the two modalities corroborates EPR imaging as a useful tool for the study of tumor oxygenation.