Spectral fitting: the extraction of crucial information from a spectrum and a spectral image

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.

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.

Going Low in a World Going High: The Physiologic Use of Lower Frequency Electron Paramagnetic Resonance

Yakov Sergeevich Lebedev was a pioneer in high frequency EPR, taking advantage of the separation of g-factor anisotropy effects from nuclear hyperfine splitting and the higher frequency molecular motion sensitivity from higher frequency measurements⁸. This article celebrates a second EPR subfield in which Prof. Lebedev pioneered, EPR imaging. ⁹ We celebrate the clinical enhancements that are suggested in this low frequency work and imaging application to animal physiology at lower-than-standard EPR frequencies.

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.

In Vivo pO2 Imaging of Tumors: Oxymetry with Very Low-Frequency Electron Paramagnetic Resonance

For over a century, it has been known that tumor hypoxia, regions of a tumor with low levels of oxygenation, are important contributors to tumor resistance to radiation therapy and failure of radiation treatment of cancer. Recently, using novel pulse electron paramagnetic resonance (EPR) oxygen imaging, near absolute images of the partial pressure of oxygen (pO2) in tumors of living animals have been obtained. We discuss here the means by which EPR signals can be obtained in living tissues and tumors. We review development of EPR methods to image the pO2 in tumors and the potential for the pO2 image acquisition in human subjects.

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.

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.

Comparison of 250 MHz electron spin echo and continuous wave oxygen EPR imaging methods for in vivo applications

PURPOSE

The authors compare two electron paramagnetic resonance imaging modalities at 250 MHz to determine advantages and disadvantages of those modalities for in vivo oxygen imaging.

METHODS

Electron spin echo (ESE) and continuous wave (CW) methodologies were used to obtain three-dimensional images of a narrow linewidth, water soluble, nontoxic oxygen-sensitive trityl molecule OX063 in vitro and in vivo. The authors also examined sequential images obtained from the same animal injected intravenously with trityl spin probe to determine temporal stability of methodologies.

RESULTS

A study of phantoms with different oxygen concentrations revealed a threefold advantage of the ESE methodology in terms of reduced imaging time and more precise oxygen resolution for samples with less than 70 torr oxygen partial pressure. Above 100 torr, CW performed better. The images produced by both methodologies showed pO2 distributions with similar mean values. However, ESE images demonstrated superior performance in low pO2 regions while missing voxels in high pO2 regions.

CONCLUSIONS

ESE and CW have different areas of applicability. ESE is superior for hypoxia studies in tumors.

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.

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.

Electron paramagnetic resonance oxygen imaging of a rabbit tumor using localized spin probe delivery

PURPOSE

Application of in vivo electron paramagnetic resonance (EPR) oxygen imaging (EPROI) to tumors larger than those of mice requires development of both instrumental and medical aspects of imaging.

METHODS

250 MHz EPR oxygen imaging was performed using a loop-gap resonator with a volume exceeding 100 cm3. The paramagnetic spin probe was injected directly into the femoral artery feeding the rabbit leg/tumor.

RESULTS

The authors present continuous wave and electron spin echo EPR oxygen images of a large size (4 cm) VX-2 tumor located on the leg of a New Zealand white rabbit.

CONCLUSIONS

This study demonstrates the feasibility of continuous wave and electron spin echo oxygen imaging modalities for investigation of volumes of tumor and normal tissue relevant to large animals. The injection of the spin probe directly into the artery feeding a rabbit leg will allow one to reduce, by over one order of magnitude, the amount of spin probe used as compared to whole animal i.v. injection.

DANCING WITH THE ELECTRONS: TIME-DOMAIN AND CW IN VIVO EPR IMAGING

The progress in the development of imaging the distribution of unpaired electrons in living systems and the functional and the potential diagnostic dimensions of such an imaging process, using Electron Paramagnetic Resonance Imaging (EPRI), is traced from its origins with emphasis on our own work. The importance of EPR imaging stems from the fact that many paramagnetic probes show oxygen dependent spectral broadening. Assessment of in vivo oxygen concentration is an important factor in radiation oncology in treatment-planning and monitoring treatment-outcome. The emergence of narrow-line trairylmethyl based, bio-compatible spin probes has enabled the development of radiofrequency time-domain EPRI. Spectral information in time-domain EPRI can be achieved by generating a time sequence of T(2)* or T(2) weighted images. Progress in CW imaging has led to the use of rotating gradients, more recently rapid scan with direct detection, and a combination of all the three. Very low field MRI employing Dynamic Nuclear polarization (Overhauser effect) is also employed for monitoring tumor hypoxia, and re-oxygenation in vivo. We have also been working on the co-registration of MRI and time domain EPRI on mouse tumor models at 300 MHz using a specially designed resonator assembly. The mapping of the unpaired electron distribution and unraveling the spectral characteristics by using magnetic resonance in presence of stationary and rotating gradients in indeed 'dancing with the (unpaired) electrons', metaphorically speaking.

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.

A Versatile High Speed 250 MHz Pulse Imager for Biomedical Applications

A versatile 250 MHz pulse electron paramagnetic resonance (EPR) instrument for imaging of small animals is presented. Flexible design of the imager hardware and software makes it possible to use virtually any pulse EPR imaging modality. A fast pulse generation and data acquisition system based on general purpose PCI boards performs measurements with minimal additional delays. Careful design of receiver protection circuitry allowed us to achieve very high sensitivity of the instrument. In this article we demonstrate the ability of the instrument to obtain three dimensional images using the electron spin echo (ESE) and single point imaging (SPI) methods. In a phantom that contains a 1 mM solution of narrow line (16 μT, peak-to-peak) paramagnetic spin probe we achieved an acquisition time of 32 seconds per image with a fast 3D ESE imaging protocol. Using an 18 minute 3D phase relaxation (T(2e)) ESE imaging protocol in a homogeneous sample a spatial resolution of 1.4 mm and a standard deviation of T(2e) of 8.5% were achieved. When applied to in vivo imaging this precision of T(2e) determination would be equivalent to 2 torr resolution of oxygen partial pressure in animal tissues.

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.

Post-processing of EPR spectra by convolution filtering: calculation of a harmonics' series and automatic separation of fast-motion components from spin-label EPR spectra

This communication reports on post-processing of continuous wave EPR spectra by a digital convolution with filter functions that are subjected to differentiation or the Kramers-Krönig transform analytically. In case of differentiation, such a procedure improves spectral resolution in the higher harmonics enhancing the relative amplitude of sharp spectral features over the broad lines. At the same time high-frequency noise is suppressed through filtering. These features are illustrated on an example of a Lorentzian filter function that has a principal advantage of adding a known magnitude of homogeneous broadening to the spectral shapes. Such spectral distortion could be easily and accurately accounted for in the consequent least-squares data modeling. Application examples include calculation of higher harmonics from pure absorption echo-detected EPR spectra and resolving small hyperfine coupling that are unnoticeable in conventional first derivative EPR spectra. Another example involves speedy and automatic separation of fast and broad slow-motion components from spin-label EPR spectra without explicit simulation of the slow motion spectrum. The method is illustrated on examples of X-band EPR spectra of partially aggregated membrane peptides.

Continuous wave EPR oximetric imaging at 300 MHz using radiofrequency power saturation effects

A novel continuous wave (CW), radiofrequency (RF), electron paramagnetic resonance (EPR) oximetric imaging technique is proposed, based on the influence of oxygen concentration on the RF power saturation of the EPR resonance. A linear relationship is demonstrated between the partial oxygen pressure (pO(2)) and the normalized signal intensity (I(N)), defined as, I(N) = (I(HP) - I(LP))/I(LP), where I(LP) and I(HP) refer to signal intensities at low (P(L)) and high (P(H)) RF power levels, respectively. A formula for the determination of pO(2), derived on the basis of the experimental results, reliably estimated various oxygen concentrations in a five-tube phantom. This new technique was time-efficient and also avoided the missing angle problem associated with conventional spectral-spatial CW EPR oximetric imaging. In vivo power saturation oximetric imaging in a tumor bearing mouse clearly depicted the hypoxic foci within the tumor.

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.

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.

A new strategy for fast radiofrequency CW EPR imaging: direct detection with rapid scan and rotating gradients

Rapid field scan on the order of T/s using high frequency sinusoidal or triangular sweep fields superimposed on the main Zeeman field, was used for direct detection of signals without low-frequency field modulation. Simultaneous application of space-encoding rotating field gradients have been employed to perform fast CW EPR imaging using direct detection that could, in principle, approach the speed of pulsed FT EPR imaging. The method takes advantage of the well-known rapid-scan strategy in CW NMR and EPR that allows arbitrarily fast field sweep and the simultaneous application of spinning gradients that allows fast spatial encoding. This leads to fast functional EPR imaging and, depending on the spin concentration, spectrometer sensitivity and detection band width, can provide improved temporal resolution that is important to interrogate dynamics of spin perfusion, pharmacokinetics, spectral spatial imaging, dynamic oxymetry, etc.

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.

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.

Application of magnetic field over-modulation for improved EPR linewidth measurements using probes with Lorentzian lineshape

Magnetic field modulation in CW electron paramagnetic resonance (EPR) is used for signal detection. However, it can also distort signal lineshape. In experiments where the linewidth information is of particular importance, small modulation amplitude is usually used to limit the lineshape distortion. The use of small modulation amplitude, however, results in low signal-to-noise ratio and therefore affects the precision of linewidth measurements. Recently, a new spectral simulation model has been developed enabling accurate fitting of modulation-broadened EPR spectra in liquids. Since the use of large modulation amplitude (over-modulation) can significantly enhance the EPR signal, the precision of linewidth measurements is therefore greatly improved. We investigated the over-modulation technique in EPR oximetry experiments using the oxygen-sensing probe lithium octa-n-butoxy-substitued naphthalocyanine (LiNc-BuO). Modulation amplitudes 2-18 times the intrinsic linewidth of the probe were applied to increase the spectral signal-to-noise ratio. The intrinsic linewidth of the probe at different oxygen concentrations was accurately extracted through curve fitting from the enhanced spectra. Thus, we demonstrated that the over-modulation model is also applicable to particulate oxygen-sensing probes such as LiNc-BuO and that the lineshape broadening induced by oxygen is separable from that induced by over-modulation. Therefore, the over-modulation technique can be used to enhance sensitivity and improve linewidth measurements for EPR oximetry with particulate oxygen-sensing probes with Lorentzian lineshape. It should be particularly useful for in vivo oxygen measurements, in which direct linewidth measurements may not be feasible due to inadequate signal-to-noise ratio.

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.

Near-field microwave microscope and electron-spin-resonance detection: ruby crystal surface

Microwave photons can image a surface by using near-field geometry with spatial resolution close to the nanometer-length scale. We detected electron-spin resonance (ESR) on ruby surfaces by using microwave photons at the S-band frequency (3.73 GHz). The spatial locations of the electron-spin centers were pinpointed with localized incident microwave photons generated by using evanescent microwave microscopy (EMM). We show that the EMM probe is capable of resolving 20,000 spin transitions, compared with the approximately 10(10) minimum detectable spins of the conventional continuous-wave ESR spectrometer. This represents roughly a 6-order-of-magnitude enhancement in sensitivity. Our ultimate goal is to achieve the minimum detectable spin transition of a single electron and nanometer-level spatial resolution by using microfabricated atomic force microscopy-EMM probes.

Progressive EPR imaging with adaptive projection acquisition

Continuous wave electron paramagnetic resonance imaging (EPRI) of living biological systems requires rapid acquisition and visualization of free radical images. In the commonly used multiple-stage back-projection image reconstruction algorithm, the EPR image cannot be reconstructed until a complete set of projections is collected. If the data acquisition is incomplete, the previously acquired incomplete data set is no longer useful. In this work, a 3-dimensional progressive EPRI technique was implemented based on inverse Radon transform in which a 3-dimensional EPR image is acquired and reconstructed gradually from low resolution to high resolution. An adaptive data acquisition strategy is proposed to determine the significance of projections and acquire them in an order from the most significant to the least significant. The image acquisition can be terminated at any time if further collection of projections does not improve the image resolution distinctly, providing flexibility to trade image quality with imaging time. The progressive imaging technique was validated using computer simulations as well as imaging experiments. The adaptive acquisition uses 50-70% less projections as compared to the regular acquisition. In conclusion, adaptive data acquisition with progressive image reconstruction should be very useful for the accelerated acquisition and visualization of free radical distribution.

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

EPR spectroscopy can be extended to a spectroscopic imaging modality by applying magnetic field gradients across the sample to encode spatial information in the measured spectra. In this work, we present a mathematical model of the EPR imaging process in terms of the Radon transform. We describe a model for electron paramagnetic resonance imaging, derive its explicit relationship to the Radon transform, and discuss several options for reconstructing the sample absorption and dispersion densities. An important extension to previous descriptions is the incorporation of large amplitude magnetic field modulation, which can be used to improve the signal-to-noise ratio for continuous wave signal acquisition. Magnetic field modulation is shown to cause well understood changes in the shapes of spectra in the reconstructed images, but does not affect the spatial resolution achieved in these images. Since many of the novel image reconstruction strategies and noise filtering algorithms that have been developed for other modalities start from this formalism, this work allows for their direct application to EPR imaging. This promises to lead to further improvements in EPR imaging techniques.

The solution conformation of triarylmethyl radicals

Hyperfine coupling tensors to 1H, 2H, and natural abundance 13C were measured using X-band pulsed electron nuclear double resonance (ENDOR) spectroscopy for two triarylmethyl (trityl) radicals used in electron paramagnetic resonance imaging and oximetry: methyl tris(8-carboxy-2,2,6,6-tetramethyl-benzo[1,2d:4,5-d']bis(1,3)dithiol-4-yl) and methyl tris(8-carboxy-2,2,6,6-tetramethyl(-d3)-benzo[1,2d:4,5-d']bis(1,3)dithiol-4-yl). Quantum chemical calculations using density functional theory predict a structure that reproduces the experimentally determined hyperfine tensors. The radicals are propeller-shaped with the three aryl rings nearly mutually orthogonal. The central carbon atom carrying most of the unpaired electron spin density is surrounded by the sulfur atoms in the radical and is completely shielded from solvent. This structure explains features of the electron spin relaxation of these radicals and suggests ways in which the radicals can be chemically modified to improve their characteristics for imaging and oximetry.

Esters of 5-carboxyl-5-methyl-1-pyrroline N-oxide: a family of spin traps for superoxide

Apparent rate constants, at acidic pH and neutral pH for the reaction of a family of ester-containing 5-carboxyl-5-methyl-1-pyrroline N-oxides with superoxide (O2*-) were estimated, using ferricytochrome c as a competitive inhibitor. It was of interest to note that the rate constants were similar among the different nitrones and not that significantly different from that found for 5-(diethoxyphosphoryl)-5-dimethyl-1-pyrroline N-oxide. At acidic pH, the rate constant for spin trapping O2*- was 3-fold greater than that at physiological pH. Subsequent experiments determined the half-life of aminoxyls, derived from the reaction of these nitrones with O2*-. The EPR spectra were modeled by using a global analysis method. The results clearly demonstrated that EPR spectra of all the aminoxyls were inconsistent with a model that included a single gamma-hydrogen splitting. A better interpretation modeled them as two diastereomers with identical nitrogen splittings and slightly different beta-hydrogen splittings. Detailed line width analyses slightly favored an equal line width-unequal population ratio for the two diastereomers.

Influence of Conformation on the EPR Spectrum of 5,5-Dimethyl-1-hydroperoxy-1-pyrrolidinyloxyl: A Spin Trapped Adduct of Superoxide

Spin trapping, a technique used to characterize short-lived free radicals, consists of using a nitrone or nitroso compound to "trap" an unstable free radical as a long-lived aminoxyl that can be characterized by EPR spectroscopy. The resultant aminoxyl exhibits hyperfine splitting constants that are dependent on the spin trap and the free radical. Such is the case with 2,2-dimethyl-5-hydroxy-1-pyrrolidinyloxyl (DMPO-OH) and 2,2-dimethyl-5-hydroperoxy-1-pyrrodinyloxyl (DMPO-OOH) whose hyperfine splitting constants, A(N) = A(H) = 14.9 G and A(N) = 14.3 G, A(H)(beta) = 11.7 G, and A(H)(gamma) = 1.25 G, respectively, have been used to demonstrate the generation of HO(*) and O(2)(*)(-). However, to date, the source of the apparent A(H)(gamma) hyperfine splitting in DMPO-OOH is not known. We consider three possible explanations to account for the unique EPR spectrum of DMPO-OOH. The first is that the gamma-splitting arises from one of the hydrogen atoms at either carbon 3 or carbon 4 of DMPO-OOH. The second is that the gamma-splitting originates from the hydrogen atom of DMPO-OOH. The third is that the conformational properties of DMPO-R change upon going from DMPO-OH to DMPO-OOH. Experimental and theoretical chemical approaches as well as EPR spectral modeling were used to investigate which of these hypotheses may explain the asymmetric EPR spectrum of DMPO-OOH. From these studies it is shown that the 12-line EPR spectrum of DMPO-OOH results not from any proximal hydrogen, but from additional conformers of DMPO-OOH. Thus, the 1.25 G hyperfine splitting, which has been assigned as a gamma-splitting, is actually from two individual EPR spectra associated with different conformers of DMPO-OOH.