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ABSTRACT: To develop and evaluate a two-dimensional (2D) fast spin echo (FSE) pulse sequence for enhancing temporal resolution and reducing tissue heating for in vivo proton electron double resonance imaging (PEDRI) of mice.
A four-compartment phantom containing 2 mM TEMPONE was imaged at 20.1 mT using 2D FSE-PEDRI and regular gradient echo (GRE)-PEDRI pulse sequences. Control mice were infused with TEMPONE over ~1 min followed by time-course imaging using the 2D FSE-PEDRI sequence at intervals of 10-30 s between image acquisitions. The average signal intensity from the time-course images was analyzed using a first-order kinetics model.
Phantom experiments demonstrated that EPR power deposition can be greatly reduced using the FSE-PEDRI pulse sequence compared with the conventional gradient echo pulse sequence. High temporal resolution was achieved at ~4 s per image acquisition using the FSE-PEDRI sequence with a good image SNR in the range of 233-266 in the phantom study. The TEMPONE half-life measured in vivo was ~72 s.
Thus, the FSE-PEDRI pulse sequence enables fast in vivo functional imaging of free radical probes in small animals greatly reducing EPR irradiation time with decreased power deposition and provides increased temporal resolution.
Journal of Magnetic Resonance Imaging 12/2011; 35(2):471-5. · 2.70 Impact Factor
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Andrey A Bobko,
Timothy D Eubank,
Jeffrey L Voorhees,
Olga V Efimova,
Igor A Kirilyuk, Sergey Petryakov,
Dmitrii G Trofimiov,
Clay B Marsh,
Jay L Zweier,
Igor A Grigor'ev,
Alexandre Samouilov,
Valery V Khramtsov
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ABSTRACT: Approach for in vivo real-time assessment of tumor tissue extracellular pH (pH(e)), redox, and intracellular glutathione based on L-band EPR spectroscopy using dual function pH and redox nitroxide probe and disulfide nitroxide biradical, is described. These parameters were monitored in PyMT mice bearing breast cancer tumors during treatment with granulocyte macrophage colony-stimulating factor. It was observed that tumor pH(e) is about 0.4 pH units lower than that in normal mammary gland tissue. Treatment with granulocyte macrophage colony-stimulating factor decreased the value of pH(e) by 0.3 units compared with PBS control treatment. Tumor tissue reducing capacity and intracellular glutathione were elevated compared with normal mammary gland tissue. Granulocyte macrophage colony-stimulating factor treatment resulted in a decrease of the tumor tissue reducing capacity and intracellular glutathione content. In addition to spectroscopic studies, pH(e) mapping was performed using recently proposed variable frequency proton-electron double-resonance imaging. The pH mapping superimposed with MRI image supports probe localization in mammary gland/tumor tissue, shows high heterogeneity of tumor tissue pH(e) and a difference of about 0.4 pH units between average pH(e) values in tumor and normal mammary gland. In summary, the developed multifunctional approach allows for in vivo, noninvasive pH(e), extracellular redox, and intracellular glutathione content monitoring during investigation of various therapeutic strategies for solid tumors.
Magnetic Resonance in Medicine 11/2011; 67(6):1827-36. · 2.96 Impact Factor
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ABSTRACT: In vivo mapping of alterations in redox status is important for understanding organ specific pathology and disease. While electron paramagnetic resonance imaging (EPRI) enables spatial mapping of free radicals, it does not provide anatomic visualization of the body. Proton MRI is well suited to provide anatomical visualization. We applied EPR/NMR co-imaging instrumentation to map and monitor the redox state of living mice under normal or oxidative stress conditions induced by secondhand cigarette smoke (SHS) exposure. A hybrid co-imaging instrument, EPRI (1.2 GHz)/proton MRI (16.18 MHz), suitable for whole-body co-imaging of mice was utilized with common magnet and gradients along with dual EPR/NMR resonators that enable co-imaging without sample movement. The metabolism of the nitroxide probe, 3-carbamoyl-proxyl (3-CP), was used to map the redox state of control and SHS-exposed mice. Co-imaging allowed precise 3D mapping of radical distribution and reduction in major organs such as the heart, lungs, liver, bladder and kidneys. Reductive metabolism was markedly decreased in SHS-exposed mice and EPR/NMR co-imaging allowed quantitative assessment of this throughout the body. Thus, in vivo EPR/NMR co-imaging enables in vivo organ specific mapping of free radical metabolism and redox stress and the alterations that occur in the pathogenesis of disease.
Journal of Magnetic Resonance 11/2011; 216:21-7. · 2.14 Impact Factor
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ABSTRACT: Proton-electron double resonance imaging (PEDRI) has been utilized for indirect determination of oxygen concentrations in aqueous samples and living systems. Due to the complexity of the problem, there are seven oxygen related parameters that need to be measured to determine the distribution of oxygen. We present an improved approach in which image intensities from only two PEDRI acquisitions with different EPR irradiation powers are required to determine the distribution of a paramagnetic probe and oxygen in an analyzed sample. This is achieved using three reference samples with known concentrations of a paramagnetic probe and oxygen placed inside the resonator together with the measurement sample. An EPR-off image, which has low signal intensity at low magnetic field (0.02 T) is not required for the calculations, significantly reducing the total time of the experiments and the noise while enhancing the accuracy of these oxygen measurements. The Finland trityl radical was used as the paramagnetic probe and oxygen concentrations could be accurately measured and imaged over the physiological range from 0 to 240 μM.
Journal of Magnetic Resonance 07/2011; 212(1):197-203. · 2.14 Impact Factor
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ABSTRACT: Proton-electron double-resonance imaging (PEDRI) offers rapid image data collection and high resolution for spatial distribution of paramagnetic probes. Recently we developed the concept of variable field (VF) PEDRI which enables extracting a functional map from a limited number of images acquired at pre-selected EPR excitation fields using specific paramagnetic probes (Khramtsov et al., J. Magn. Reson. 202 (2010) 267-273). In this work, we propose and evaluate a new modality of PEDRI-based functional imaging with enhanced temporal resolution which we term variable radio frequency (VRF) PEDRI. The approach allows for functional mapping (e.g., pH mapping) using specifically designed paramagnetic probes with high quality spatial resolution and short acquisition times. This approach uses a stationary magnetic field but different EPR RFs. The ratio of Overhauser enhancements measured at each pixel at two different excitation frequencies corresponding to the resonances of protonated and deprotonated forms of a pH-sensitive nitroxide is converted to a pH map using a corresponding calibration curve. Elimination of field cycling decreased the acquisition time by exclusion periods of ramping and stabilization of the magnetic field. Improved magnetic field homogeneity and stability allowed for the fast MRI acquisition modalities such as fast spin echo. In total, about 30-fold decrease in EPR irradiation time was achieved for VRF PEDRI (2.4s) compared with VF PEDRI (70s). This is particularly important for in vivo applications enabling one to overcome the limiting stability of paramagnetic probes and sample overheating by reducing RF power deposition.
Journal of Magnetic Resonance 01/2011; 209(2):227-32. · 2.14 Impact Factor
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ABSTRACT: Dynamic nuclear polarization (DNP) is an NMR-based technique which enables detection and spectral characterization of endogenous and exogenous paramagnetic substances measured via transfer of polarization from the saturated unpaired electron spin system to the NMR active nuclei. A variable field system capable of performing DNP spectroscopy with NMR detection at any magnetic field in the range 0-0.38 T is described. The system is built around a clinical open-MRI system. To obtain EPR spectra via DNP, partial cancellation of the detection field B(0)(NMR) is required to alter the evolution field B(0)(EPR) at which the EPR excitation is achieved. The addition of resistive actively shielded field cancellation coils in the gap of the primary magnet provides this field offset in the range of 0-100 mT. A description of the primary magnet, cancellation coils, power supplies, interfacing hardware, RF electronics and console are included. Performance of the instrument has been evaluated by acquiring DNP spectra of phantoms with aqueous nitroxide solutions (TEMPOL) at three NMR detection fields of 97 G, 200 G and 587 G corresponding to 413 kHz, 851.6 kHz and 2.5 MHz respectively and fixed EPR evolution field of 100 G corresponding to an irradiation frequency of 282.3 MHz. This variable-field DNP system offers great flexibility for the performance of DNP spectroscopy with independent optimum choice of EPR excitation and NMR detection fields.
Journal of Magnetic Resonance 08/2010; 205(2):202-8. · 2.14 Impact Factor
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ABSTRACT: The development of a dual frequency resonator that enables both EPR and proton NMR imaging within the same resonator, magnet and gradient system is described. A novel design allows the same resonator to perform both EPR and proton NMR operation without moving resonator cables or switches. The resonator is capable of working at frequencies of 16.18 MHz for proton NMR and 1.2 GHz for EPR and is optimized for isolated rat heart experiments, measuring 22 mm in inner diameter and 19 mm in length. In EPR mode, the resonator functions as a one-loop-two gap resonator, electrically coupled through a half wavelength inverter. In NMR mode, it functions a single turn coil. Using the same loop for both modalities maximizes filling factor at both frequencies. Placing the tuning and switching controls away from the resonator prevents any inadvertent movement that would cause errors of EPR and NMR co-imaging registration. The resonator enabled good quality EPR and proton MRI of isolated rat hearts with precise registration.
Journal of Magnetic Resonance 07/2010; 205(1):1-8. · 2.14 Impact Factor
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ABSTRACT: A new concept of Variable Field Proton-Electron Double-Resonance Imaging (VF PEDRI) is proposed. This allows for functional mapping using specifically designed paramagnetic probes (e.g. oxygen or pH mapping) with MRI high quality spatial resolution and short acquisition time. Studies performed at 200 G field MRI with phantoms show that a pH map of the sample can be extracted using only two PEDRI images acquired in 140 s at pre-selected EPR excitation fields providing pH resolution of 0.1 pH units and a spatial resolution of 1.25mm. Note that while concept of functional VF PEDRI was demonstrated using the pH probe, it can be applied for studies of other biologically relevant parameters of the medium such as redox state, concentrations of oxygen or glutathione using specifically designed EPR probes.
Journal of Magnetic Resonance 11/2009; 202(2):267-73. · 2.14 Impact Factor
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ABSTRACT: A four-loop segmented surface coil resonator (SSCR) with electronic frequency and coupling adjustments was constructed with 18mm aperture and loading capability suitable for in vivo Electron Paramagnetic Resonance (EPR) spectroscopy and imaging applications at L-band. Increased sample volume and loading capability were achieved by employing a multi-loop three-dimensional surface coil structure. Symmetrical design of the resonator with coupling to each loop resulted in high homogeneity of RF magnetic field. Parallel loops were coupled to the feeder cable via balancing circuitry containing varactor diodes for electronic coupling and tuning over a wide range of loading conditions. Manually adjusted high Q trimmer capacitors were used for initial tuning with subsequent tuning electronically controlled using varactor diodes. This design provides transparency and homogeneity of magnetic field modulation in the sample volume, while matching components are shielded to minimize interference with modulation and ambient RF fields. It can accommodate lossy samples up to 90% of its aperture with high homogeneity of RF and modulation magnetic fields and can function as a surface loop or a slice volume resonator. Along with an outer coaxial NMR surface coil, the SSCR enabled EPR/NMR co-imaging of paramagnetic probes in living rats to a depth of 20mm.
Journal of Magnetic Resonance 06/2009; 198(1):8-14. · 2.14 Impact Factor
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ABSTRACT: The goal of the present study was to evaluate the temporal response of particulate-based EPR oximetry probes to changes in partial pressure of oxygen (pO(2)). In order to accurately evaluate the oxygen-response time, we developed a method for rapid modulation of pO(2) in a chamber containing the probe using an oscillator-driven speaker-diaphragm setup. The apparatus was capable of producing sinusoidal changes in pO(2) at frequencies up to 300 Hz or more. The pressure-modulation setup was used to evaluate the temporal response of some of the most commonly used phthalocyanine-based particulate probes. For validation, the time-response of the probes was compared to that of a high sensitivity pressure sensor. The results revealed that some particulate probes could respond to changes in pO(2) with a temporal response of 3.3 ms (300 Hz). The observations were interpreted in the light of their crystalline packing in favor of oxygen diffusion. The results of the present study should enable the selection of probes for oximetry applications requiring high temporal resolution.
Journal of Magnetic Resonance 08/2008; 193(1):127-32. · 2.14 Impact Factor
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ABSTRACT: A loop resonator was developed for 300 MHz continuous-wave electron paramagnetic resonance (CW-EPR) spectroscopy and imaging in live rats. A single-turn loop (55 mm in diameter) was used to provide sufficient space for the rat body. Efficiency for generating a radiofrequency magnetic field of 38 microT/W(1/2) was achieved at the center of the loop. For the resonator itself, an unloaded quality factor of 430 was obtained. When a 350 g rat was placed in the resonator at the level of the lower abdomen, the quality factor decreased to 18. The sensitive volume in the loop was visualized with a bottle filled with an aqueous solution of the nitroxide spin probe 3-carbamoyl-2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy (3-CP). The resonator was shown to enable EPR imaging in live rats. Imaging was performed for 3-CP that had been infused intravenously into the rat and its distribution was visualized within the lower abdomen.
Journal of Magnetic Resonance 02/2008; 190(1):124-34. · 2.14 Impact Factor
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ABSTRACT: For whole body EPR imaging of small animals, typically low frequencies of 250-750 MHz have been used due to the microwave losses at higher frequencies and the challenges in designing suitable resonators to accommodate these large lossy samples. However, low microwave frequency limits the obtainable sensitivity. L-band frequencies can provide higher sensitivity, and have been commonly used for localized in vivo EPR spectroscopy. Therefore, it would be highly desirable to develop an L-band microwave resonator suitable for in vivo whole body EPR imaging of small animals such as living mice. A 1.2 GHz 16-gap resonator with inner diameter of 42 mm and 48 mm length was designed and constructed for whole body EPR imaging of small animals. The resonator has good field homogeneity and stability to animal-induced motional noise. Resonator stability was achieved with electrical and mechanical design utilizing a fixed position double coupling loop of novel geometry, thus minimizing the number of moving parts. Using this resonator, high quality EPR images of lossy phantoms and living mice were obtained. This design provides good sensitivity, ease of sample access, excellent stability and uniform B(1) field homogeneity for in vivo whole body EPR imaging of mice at 1.2 GHz.
Journal of Magnetic Resonance 10/2007; 188(1):68-73. · 2.14 Impact Factor
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ABSTRACT: Electron paramagnetic resonance imaging (EPRI) is a powerful technique that enables spatial mapping of free radicals or other paramagnetic compounds; however, it does not in itself provide anatomic visualization of the body. Proton magnetic resonance imaging (MRI) is well suited to provide anatomical visualization. A hybrid EPR/NMR coimaging instrument was constructed that utilizes the complementary capabilities of both techniques, superimposing EPR and proton-MR images to provide the distribution of paramagnetic species in the body. A common magnet and field gradient system is utilized along with a dual EPR and proton-NMR resonator assembly, enabling coimaging without the need to move the sample. EPRI is performed at approximately 1.2 GHz/ approximately 40 mT and proton MRI is performed at 16.18 MHz/ approximately 380 mT; hence the method is suitable for whole-body coimaging of living mice. The gradient system used is calibrated and controlled in such a manner that the spatial geometry of the two acquired images is matched, enabling their superposition without additional postprocessing or marker registration. The performance of the system was tested in a series of phantoms and in vivo applications by mapping the location of a paramagnetic probe in the gastrointestinal (GI) tract of mice. This hybrid EPR/NMR coimaging instrument enables imaging of paramagnetic molecules along with their anatomic localization in the body.
Magnetic Resonance in Medicine 08/2007; 58(1):156-66. · 2.96 Impact Factor
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ABSTRACT: Sample motion, particularly that of a beating heart, induces baseline noise and spectral distortion on an EPR spectrum. In order to quench motional noise and restore the EPR signal amplitude and line-width, an L-band transverse oriented electric field re-entrant resonator (TERR) was designed and constructed with provisions for automatic tuning control (ATC) and automatic coupling control (ACC) suited for studies of isolated beating rat hearts. Two sets of electronic circuits providing DC biased voltage to two varactor diodes were implemented to electronically adjust coupling and tuning. The resonator has a rectangular cross-sectional sample arm of 25 mm diameter with a Q value of 1100 without sample. Once inserted with lossy aqueous samples of 0.45% NaCl, Q value drops to 400 with a volume of 0.5 ml and 150 with 5 ml. The ATC/ACC functions were tested with a moving phantom and isolated beating rat hearts with the improvement of signal to noise ratio (S/N, peak amplitude of signal over peak amplitude of baseline noise) of 6.7-, and 4 to 6-fold, respectively. With these improvements, EPR imaging could be performed on an isolated beating rat heart. Thus, this TERR resonator with ATC/ACC enables application of EPR spectroscopy and imaging for the measurement and imaging of radical metabolism, redox state, and oxygenation in the isolated beating rat heart.
Journal of Magnetic Resonance 08/2007; 187(1):57-65. · 2.14 Impact Factor
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ABSTRACT: A novel procedure for in vivo imaging of the oxygen partial pressure (pO2) in implanted tumors is reported. The procedure uses electron paramagnetic resonance imaging (EPRI) of oxygen-sensing nanoprobes embedded in the tumor cells. Unlike existing methods of pO2 quantification, wherein the probes are physically inserted at the time of measurement, the new approach uses cells that are preinternalized (labeled) with the oxygen-sensing probes, which become permanently embedded in the developed tumor. Radiation-induced fibrosarcoma (RIF-1) cells, internalized with nanoprobes of lithium octa-n-butoxy-naphthalocyanine (LiNc-BuO), were allowed to grow as a solid tumor. In vivo imaging of the growing tumor showed a heterogeneous distribution of the spin probe, as well as oxygenation in the tumor volume. The pO2 images obtained after the tumors were exposed to a single dose of 30-Gy X-radiation showed marked redistribution as well as an overall increase in tissue oxygenation, with a maximum increase 6 hr after irradiation. However, larger tumors with a poorly perfused core showed no significant changes in oxygenation. In summary, the use of in vivo EPR technology with embedded oxygen-sensitive nanoprobes enabled noninvasive visualization of dynamic changes in the intracellular pO2 of growing and irradiated tumors.
Magnetic Resonance in Medicine 06/2007; 57(5):950-9. · 2.96 Impact Factor
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ABSTRACT: Proton-electron double resonance imaging (PEDRI) requires a dual EPR/NMR resonator. In order to saturate electron spins, long high-power RF EPR pulses are needed. Dissipated power causes resonator and sample heating, resulting in instability of the resonator frequency and coupling, which in turn causes a reduction in sensitivity. To overcome this problem, we designed, built, and tested a modified Alderman-Grant (MAG) resonator for in vivo and in vitro applications. We improved the temperature stability by using fused quartz in critical structural components of the resonator and employing a design that minimized moving parts. All of the components of the resonator and matching circuit, including coupling capacitors, were rigidly positioned on the surface of the quartz tube. Electrical coupling circuitry between the feeding cable and resonator was employed to provide independent coupling and tuning adjustments, which improved the ease and speed of operation. The equivalent schematic of the matching circuit is presented along with calculations of critical parameters. The resonator exhibits no frequency shift with 20 W of continuous power irradiation, and can handle intermittent power of 60 W for up to 3 min without detuning, enabling stable and reliable data acquisition for PEDRI of biological samples.
Magnetic Resonance in Medicine 10/2006; 56(3):654-9. · 2.96 Impact Factor
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ABSTRACT: Fast and reliable data acquisition is a major requirement for successful and useful biological electron paramagnetic resonance imaging (EPRI) experiments. Even a technologically advanced and professionally supervised EPRI system can exhibit instabilities initiated by perturbations such as animal motion, microphonics, and temperature changes. As a result, part of an acquired data set may become corrupted with excessive noise and distortions, which in turn may degrade the quality of the reconstructed image. In this work an automated scheme to monitor the system performance and stability over the course of an experiment is demonstrated. This method ensures that the quality of the acquired data is maintained during the experiment. For this purpose, four parameters including noise content and integration of each acquired projection are quantified and measured against those of the zero-gradient (ZG) projection, which is set as a quality benchmark. Projections with parameter values that differ substantially from the expected values are identified as damaged and consequently are reacquired. Therefore, the proposed technique not only effectively monitors the quality of acquisition, it also saves a substantial amount of acquisition time because it eliminates the necessity of repeating the entire experiment in cases in which only a small fraction of the data are corrupted.
Magnetic Resonance in Medicine 10/2006; 56(3):644-53. · 2.96 Impact Factor
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ABSTRACT: Electron paramagnetic resonance imaging (EPRI) enables noninvasive spatial mapping of free radical metabolism and has recently been shown to provide in vivo physiologic information regarding alterations in the redox state of tumors and neoplastic tissues. With the use of nitroxide spin probes, it has been shown that certain tumors possess a highly reduced state. To determine whether EPRI can be used for early detection and visualization of gastric carcinoma based on its altered redox metabolism, studies were performed in a rat gastric cancer model induced by 1-methyl-3-nitro-1-nitrosoguanidine. Using a specialized 750 MHz resonator and EPRI instrument, a technique was developed for imaging nitroxide radicals in the whole stomach. In vivo three-dimensional EPRI of the stomach of rats with continuous intravenous administration of nitroxide 3-carboxamido-2,2,5,5-tetramethylpyrrolidine-N-oxyl (3-carbamoyl-proxyl) [3-CP] was performed. Whereas electron paramagnetic resonance images from untreated controls provide a uniform visualization of the stomach mucosa and wall, in the treated rats with gastric cancer, holes were present in the image at the locations of tumors. With localized spectroscopy, it was confirmed that the tumor regions were devoid of signal, and this was largely due to the presence of a more reduced state with rapid reduction of nitroxide. Pharmacokinetic studies indicated that 3-CP in tumors was rapidly reduced to an undetectable level, whereas the 3-CP levels in normal stomach tissue persisted. Near-infrared reflectance measurements of indocyanine green dye uptake indicated that there were no significant differences in tumor versus normal mucosal perfusion. From these results, we concluded that gastric cancer tumors could be distinguished from normal tissue based primarily on the marked difference in their rate of radical metabolism. Because alterations in cellular redox state and radical metabolism are of critical importance in tumor biology and treatment, this methodology should provide an important new tool for the study and visualization of gastric carcinoma and may also be of use in other cancer models.
Cancer Research 10/2004; 64(18):6495-502. · 7.86 Impact Factor
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ABSTRACT: Oxygen plays a critical role in the pathophysiology of myocardial injury during both ischemia and subsequent reperfusion (I/R). Thus, oxygen concentration is an important variable to measure during I/R. In the present work, electron paramagnetic resonance (EPR)-based oximetry was used to measure the oxygen concentration during a series of I/R episodes and oxygenation levels were correlated with the contractile and hemodynamic functions of the heart. A custom-developed electronically tunable surface coil resonator working at 1.1 GHz was used to determine tissue pO(2) in the beating heart. Microcrystalline particulate of lithium phthalocyanine was used as an EPR oximetry probe. Isolated and perfused rat hearts were subjected to 1 or 3 hr durations of preischemic perfusion, followed by 15-min I/R cycles. In hearts perfused for 3 hr prior to 15-min I/R cycles, the myocardial pO(2) decreased gradually on subsequent reperfusions of three successive I/R cycles. However, in hearts perfused for 1 hr there was almost 100% recovery of myocardial pO(2) in all three I/R cycles. The extent of oxygenation recovered in each reperfusion cycle correlated with the recovery of hemodynamic and contractile function. The results also showed that the oxygen consumption rate of the heart at the end of each I/R episode decreased in direct proportion to the functional recovery. In summary, it was observed that the amount of myocardial oxygen consumption during I/R could provide a reliable index of functional impairment in the heart.
Magnetic Resonance in Medicine 05/2004; 51(4):835-42. · 2.96 Impact Factor
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ABSTRACT: Surface coil resonators have been widely used to perform topical EPR spectroscopy. They are usually positioned adjacent to or implanted within the body. For EPR applications these resonators have a number of important advantages over other resonator designs due to their ease of sample accessibility, mechanical fabrication, implementation of electronic tuning and coupling functions, and low susceptibility to sample motions. However, a disadvantage is their B(1) field inhomogeneity, which limits their usefulness for 3D imaging applications. We show that this problem can be addressed by mapping and correcting the B(1) field distribution. We report the use of EPR imaging (EPRI) to map the B(1) distribution of a surface coil resonator. We show that EPRI provides a fast, accurate, and reliable technique to evaluate the B(1) distribution. 3D EPRI was performed on phantoms, prepared using three different saline concentrations, to obtain the B(1) distribution. The information obtained from the phantoms was used to correct the images of living animals. With the use of this B(1) correction technique, surface coil resonators can be applied to perform 3D mapping of the distribution of free radicals in biological samples and living systems.
Magnetic Resonance in Medicine 01/2003; 48(6):1057-62. · 2.96 Impact Factor
