Research article Received: 4 November 2014
Revised: 8 July 2015
Accepted: 4 August 2015
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI 10.1002/mrc.4330
Overmodulation of projections as signal-tonoise enhancement method in EPR imaging Krzysztof Tadyszak,a Agnieszka Boś-Liedke,a,g* Jan Jurga,b,f Mikołaj Baranowski,c,f Radosław Mrówczyński,a Wojciech Chlewicki,d,f Stefan Jurgaa,e and Tomasz Czechowskia,b,f 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. Copyright © 2015 John Wiley & Sons, Ltd. Keywords: electron paramagnetic resonance; electron paramagnetic resonance imaging; overmodulation; image reconstruction; signal-tonoise ratio; image quality
Introduction Thirty-five years after the discovery of electron paramagnetic resonance (EPR) by Zavoisky, Hoche and Day demonstrated the phenomenon that can be used to reveal spatial distribution of paramagnetic centers in diamond,[1] which initiated the field of electron paramagnetic resonance imaging (EPRI). Over the years, considerable progress has been made in the methodology and research equipment used in EPRI. There are three main techniques widely used to perform imaging experiments, namely, continuous wave (CW), pulse, and rapid scan techniques. The conventional CW technique with low-frequency modulation and phase-sensitive detection is most often used in EPRI, because the EPR lines of common spin probes are relatively broad. The spatial information is contained within the EPR spectrum, which is called a projection. A set of projections is recorded by applying a linear magnetic field gradient across the sample while sweeping with the homogenous magnetic field. Each projection is recorded for a fixed angle between external magnetic field and gradient direction. By making stepwise changes in the direction of the magnetic field gradient, a two-dimensional (2D) EPR image of the spin density can be calculated by filtered back projection.[2,3] Furthermore, threedimensional (3D) image data can be obtained by an extension to this procedure.[4,5] A comprehensive introduction about the implementation of EPRI can be found in the literature.[6–8] One of the most important problems in CW-EPRI that needs to be solved is the relatively long image acquisition time. As acquisition of each projection takes typically 500 ms–10 s,[9] the data collection
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time for the 2D image can range from several minutes to hours depending on the signal-to-noise ratio (SNR) of the projections. A straightforward solution is to use fast scanning of the magnetic field, so each projection is acquired more quickly. This approach was used in the past in a 300 MHz CW-EPRI experiment on small animals.[10] Special magnet’s current control hardware was used,
* Correspondence to: Agnieszka Boś-Liedke, Department of Medical Physics, Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61614 Poznań, Poland. E-mail:
[email protected] a NanoBioMedical Centre, Adam Mickiewicz University, ul. Umultowska 85, 61614 Poznań, Poland b Laboratory of EPR Tomography, Poznań University of Technology, ul. Piotrowo 3, 60965 Poznań, Poland c Department of Physics, Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61614 Poznań, Poland d Faculty of Electrical Engineering, West Pomeranian University of Technology, al. Piastów 17, 70-310 Szczecin, Poland e Department of Macromolecular Physics, Faculty of Physics, Adam Mickiewicz University, ul. Romana Maya 1, 61371 Poznań, Poland f noviLET, ul. Naramowicka 232, 61611 Poznań, Poland g Department of Medical Physics, Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61614 Poznań, Poland
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K. Tadyszak et al. which allowed a 5 mT field sweep to be completed in 4 s, with no detectable spectral distortion. It was found that a scan time of 8 s caused minimal spectral distortion and allowed a 2D image to be collected in less than 2 min, using 16 projections of 1024 points each. Likewise, a 3D data set was collected in less than 9 min, using 64 projections. The minimum time to measure a single projection is mainly determined by the gradient setting (about 50 ms). It has been reported that by decreasing the setup time of gradients and the sweeping time, the acquisition of a single projection may take from 78 to 500 ms and up to 4 s for 3D image acquisition.[11–14] In order to speed up the data acquisition by an order of magnitude, compared with conventional CW-EPRI, a method using spinning magnetic field gradients was proposed.[15] Instead of collecting multiple and separate projections at different angles through the sample, a continuously rotating magnetic field gradient was used. In this technique, only one magnetic field sweep is required, applied in a stepwise fashion. By using 64 steps of field sweep and a spinning frequency of 24 Hz, the 2D images with 203 projections were acquired in 2.6 s.[16] A more recent method involved direct detection of resonances, without conventional low-frequency field modulation and phase-sensitive detection, which extended the imaging time.[17–22] The approaches based on the rapid scan strategy employed the fast triangular or sinusoidal modulation of the main magnetic field.[23] Alternatively, rapid frequency scans may be use.[24] As a result, an absorption spectrum is observed instead of its first derivative. By eliminating the phase-sensitive detection, the measurement time for a single projection can be reduced to 6.6 μs (in the 250 MHz range) for rapid scan of the magnetic field.[25] Another approach for fast radiofrequency EPR imaging has been presented by Subramanian et al.[26] The advantages of rapid scan relative to CW and pulse EPR are improvements in SNR per unit time as high as 250.[27] In the EPRI experiment, when a magnetic field gradient is applied, the amplitude of EPR signal decreases depending on the gradient strength. The strong dependence of the SNR for the projections measured in CW mode on the gradient strength in practice limits the use of the highest gradients. Thus, an optimal magnitude for the gradient should be chosen on the basis of SNR and spectral overlap considerations. To overcome SNR limitations, the modulation amplitude higher than the linewidth (referred to as overmodulation) has been proposed. Generally, to obtain accurate information about signal linewidth, the modulation amplitude should be between 1/3 and 1/10 of the linewidth.[28] Modulation amplitudes that are of the same order of magnitude or larger than the EPR linewidth will distort the shape of the detected signal. The problem of evaluating signal distortion due to sinusoidal modulation amplitude has been investigated by several authors since 1962.[29] An advantage of using a large amplitude of square-wave modulation instead of a small amplitude of sinusoidal wave is a significantly higher output after phase sensitive detection.[30] Larger modulation amplitudes produce stronger signals and therefore lead to better SNR. Such high modulation amplitude can be used because the broadening effect can be modeled accurately, allowing the extraction of spin packet linewidths, as has been demonstrated previously.[31,32] It was shown that an appropriate fitting procedure could be used to reverse any broadening effects even for a modulation amplitude that is 12.5 times higher than the radical linewidth,[33] and it significantly increases the SNR. Moreover, overmodulation can be used to increase the SNR of spectra for spectral–spatial EPR imaging and to increase the precision of oximetry measurements.[33,34,37] The linewidth
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information of radicals at different oxygen concentrations can be accurately extracted, and the line shape broadening induced by oxygen can be separated from the line broadening induced by overmodulation.[35,36] In most EPR spectrometers, the first harmonic spectrum is obtained as an output of a phase-sensitive detector (100 kHz modulation, and 100 kHz detection). In the limit of low modulation amplitude, the first harmonic is a good approximation of the first derivative of an EPR signal. For modulation amplitudes lower than the linewidth, the SNR of the nth harmonic decreases rapidly with n. Yet, for strongly overmodulated signals, the higher harmonics have much higher SNR.[41] Further improvement of SNR could be carried out by combining up information from first ten harmonics of the field-modulated signal. The first derivative spectrum reconstructed in such a way that it not only has better SNR but is not broadened by overmodulation.[42] This work presents a systematic analysis of the influence of different levels of overmodulation on SNR of the measured projections for 2D spatial EPRI.
Experiment and equipment The measurements were carried out using an Bruker ELEXSYS E540 L-Band Spectrometer equipped with E 540R23 resonator, a 3D gradient unit and image reconstruction software. The 2D EPR images of the phantom were reconstructed using spatial encoding under constant gradients at different orientations to generate projections. This procedure was followed by two stage filtered back projection. The influence of modulation amplitude on the SNR of measured projections was evaluated on the basis of experimental tests. For each of the four subsequent amplitude modulations, namely, 0.04, 0.2, 0.4, and 0.9 mT, 60 projections of a 2D plane were measured. Finally, the influence of different levels of overmodulation on the SNR of the measured projection for 2D spatial EPRI was analyzed.
Figure 1. Photograph of the printed phantom. Marked diameter and edge lengths in mm.
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EPR imaging with overmodulation In order to validate the proposed method, we performed a 2D imaging measurement using a homemade cylindrical phantom that is shown in Fig. 1. The measured EPR phantom was designed using the Autodesk Inventor® program and consists of two phases, namely, solid made out of polylactic acid, produced using 3D printing technology, and liquid that fills the hollow space and produces the EPR signal. The total volume of the phantom free space designated for signal production (2.71 ml) was shared among four different solids with a base shape of a regular pentagon, hexagon, equilateral triangle, and square. They were filled up by a solution of 1.25 mM of 2, 2, 6, 6-tetramethyl-1-piperidinyloxyl in water solvent (linewidth of 0.12 mT) giving a total number of spins of 2 × 1018 (Table 1). Freshly prepared single crystals of copper sulfate pentahydrate (CuSO4 · 5H2O) were used as the spin concentration standard.[28,38–40] Before the experiment, the mass of monocrystals was weighed and the absolute spin concentration was gained by experimental, simultaneous method. The integral intensity was measured by means of double numerical integration.
Results Recording CW-EPR spectra using a modulation amplitude similar to or higher than the linewidth causes an artificial line broadening. Generally, one should set the modulation amplitude to at least 3–10 times lower than the linewidth to avoid this effect. The same rule should apply when recording projections for an image
Table 1. Volume and number of spins related to different polyhedrons of the phantom Polygonal base
3
Volume (ml)
Volume (mm )
Spin number
0.81 0.61 0.64 0.65
806.04 613.07 645.96 640.22
6 × 10 17 4.6 × 10 17 4.8 × 10 17 4.9 × 10
Hexagon Regular pentagon Square Equilateral triangle
17
reconstruction. In an EPRI experiment, when the magnetic field gradient is applied, the amplitude of EPR signal is diminished and decreases with the square of the gradient strength. For a high gradient, the signal can be much lower than the noise amplitude, and as a result, large numbers of accumulations are needed to detect it. To increase the SNR of the measured projections and to accelerate the 2D EPR experiment, we propose to use modulation amplitude up to an order of magnitude higher than the radical linewidth. To show the usefulness of the presented method from all recorded sinograms, a few projections were chosen to compare their quality as shown in Fig. 2. To simplify the comparison, all projections were recorded for the same angle of the gradient to external magnetic field (0°). Projections were collected for specified conditions, namely, modulation amplitudes of 0.04, 0.2, 0.4, and 0.9 mT; 1 or 40 accumulations (Acc); and 0.36 or 5.1 mW of microwave power. Other parameters during an experiment were set as follows: microwave frequency 1.09 GHz, central field 39.1 mT, sweep width 1.8 mT, modulation frequency 10 kHz, number of points 2048, magnetic field gradient 4 mT/cm, field of view 25 mm, number of projections 60, and sweep time 20 s. Decrease of the SNR is clearly visible in Fig. 2a, for spectra from 2 to 5. Concomitantly with the decrease of modulation amplitude, the signal is less visible and is finally dominated by noise. The reference spectrum taken with 40 accumulations, 0.04 mT modulation amplitude, and microwave power of 5.1 mW (Fig. 2a, 1) exhibits the highest information level that is possible to gain, and the highest SNR. The same spectrum is repeated again and presented in Fig. 2b with the rest of the spectra taken with a microwave power of 5.1 mW and with four accumulations. Higher power and additional accumulations enhanced spectral quality providing at the same time more detailed information. Examples 2–4 in Fig. 2b show that the details in the spectra disappear with increase in modulation amplitude. The loss of information starts from 0.4 mT modulation amplitude and is caused by the overmodulation effect. By adjusting the modulation amplitude to the width of the gradient-broadened spectra (projection linewidth), the overmodulation can be avoided. The projection linewidth is defined as the distance from the first maximum to the last
Figure 2. EPR spectra of the TEMPO phantom recorded with gradient strength of 4mT/cm: (a) 1 accumulation, 0.39 mW of microwave power and different modulation amplitudes, and reference spectrum recorded with 0.04 G of modulation amplitude, 40 accumulations, and 5.1 mW of microwave power (b) repeated reference spectrum, and spectra recorded with 5.1 mW, 4 accumulations and different modulation amplitudes.
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K. Tadyszak et al. minimum of the gradient-broadened spectra. This situation is also depicted in Fig. 2b. Spectra recorded using 0.2 mT amplitude modulation and a reference spectrum acquired with 0.04 mT amplitude modulation with a 10 times higher number of accumulations show no significant difference. This proves that there is no difference between spectra recorded with a modulation amplitude of 0.04 mT (Fig. 2b, 1) and 0.2 mT (Fig. 2b, 4) for gradientbroadened spectra, respectively. The only difference is that SNR and acquisition time favors the latter. Signal quality analysis was performed by comparison of the SNR at various stages of image reconstruction. The SNR is a quantitative marker of how external parameters, e.g. modulation amplitude, influence the quality of the recorded signal. Figure 3 presents the change in this parameter during measurements. The precise
Figure 3. Signal-to-noise ratio (SNR) for spectra with a gradient of 4 mT/cm ((1), multiplied by 10), from reconstructed images ((2), multiplied by 10), and without gradient (3). Dotted lines are described in the text.
analyses of SNR were taken from 50 spectra each time, for the spectra without gradient (black), spectra with gradient (4 mT/cm, red), and from the reconstructed image, with modulation amplitudes in the range of 0.02 up to 1 mT with step 0.02 mT. The red line, gained from spectra recorded with gradient switched on (projection), shows the decreases in SNR and the movement of the maximum point to higher modulation amplitudes. The overmodulation for the spectra recorded with magnetic field gradient switched off (ΔBpp = 0.14 mT) is the most apparent. Projections recorded with gradient switched on gave a peak-topeak width of about 0.4 mT (signal at approximately 0.375 mT). This explains an absence of an overmodulation effect here. All plots can be approximated by a tangent for small modulation amplitudes. The bifurcation appears for the black curve in the region of approximately 0.04 mT, and at 0.4 mT for the projection (red line). The blue line in Fig. 3 presents the fitted SNR of the reconstructed images obtained for modulation amplitudes of 0.04, 0.2, 0.4, and 0.9 mT. All images reconstructed from projections and references were recorded using the same modulation amplitude. The fast increase in SNR for small modulation amplitudes is caused by the decrease in image noise. However, an increase of the modulation amplitude up to 0.9 mT caused a strong overmodulation effect in the reference spectrum that was used in the deconvolution procedure.[43–45] Therefore, it led to an increase of the SNR in the final image. The images were reconstructed from a set of projections of the radical density distribution obtained at different modulation amplitudes. Data obtained after the deconvolution procedure [43–45] from measured projections and reference spectra served as a starting point for further analysis. Figure 4 presents images reconstructed from spectra measured without accumulation and with different modulation amplitudes, as previously presented. By using the lowest modulation amplitude (0.04 mT), overmodulation of the EPR signal for the non-gradient conditions is not observed, but the SNR of the image decreases to 3.6 (Fig. 4a). For such a low SNR, the image reconstructed from a sinogram consisting of 60 projections does not provide useful
Figure 4. Four reconstructed images obtained with use of different modulation amplitudes: (a) 0.04 mT, (b) 0.2 mT, (c) 0.4 mT, and (d) 0.9 mT.
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EPR imaging with overmodulation information. The SNRs of images reconstructed using modulation amplitudes of 0.2, 0.4, and 0.9 mT were 14.8, 17.2, and 11.7, respectively. To compare reconstructed images, two reference images were reconstructed by using 0.04 mT modulation amplitude, 5.1 mW of microwave power, and 40 accumulations with a magnetic field gradient of 4 mT/cm and 4 accumulations with a magnetic field gradient of 1 mT/cm. Reconstructed images are presented in Fig. 5. To verify the influence of the applied modulation amplitude on the quality of reconstructed images, four corresponding cross sections were provided from images shown in Fig. 4 and presented in Fig. 6a. The position of the sections was chosen in the center of the images, which means that the sectional plane intersects the square and hexagonal forms. The influence of the modulation amplitude on the sharpness of the right edge of the square phantom was investigated (Fig. 6b). In order to analyze the imaging procedure more precisely, the first derivatives from smaller ranges of the slices presented in Fig. 6b were
obtained and plotted in Fig. 6c. The edge thickness was determined in the first derivative (Fig. 6c, f) of the curves showed in the magnified images of the edge (Fig. 6b, e). It was defined as the distance between two central minima as it is depicted for the red curve. The thicknesses of the square-shaped phantom edge obtained from the image, which was reconstructed using projections measured with modulation amplitude from 0.2 to 0.9 mT, were presented in Table 2. From these data, one could suspect that the high overmodulation condition completely destroys the resolution of the reconstructed image. However, this is not true. The images presented in Fig. 4 were obtained for the best image quality, which leads to the use of different low-pass filter levels in the deconvolution procedure (for high modulation amplitude, a low-pass filter was lower than the low modulation amplitude). By using the same parameters for deconvolution procedures, the lowest value in the low-pass filter has to be chosen; otherwise, the SNR of the image reconstructed from the projection measured for high overmodulation condition
Figure 5. Images recorded at (a) 4 mT/cm and (b) 1 mT/cm.
Figure 6. Normalized horizontal cross sections of images from Fig. 4 and first derivatives of the left rising curve of the square-shaped element of the phantom.
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K. Tadyszak et al. Table 2. The thickness of the right edge of the square phantom obtained from the first derivative of the horizontal cross section (Fig. 6) estimated for two cut-off frequencies of low-pass filter used for deconvolution. Modulation amplitude (mT)
0.2 0.4 0.9 0.04a
Thickness (mm) 7.5 Hz
10 Hz
1.08 1.00 1.80 (5.5 Hz) 1.00
0.65 0.58 0.70 0.70 (0.50 for 15 Hz)
a
Recorded with Amod = 0.04 mT, 40 accumulations, and 5.1 mW of microwave power.
will be too low for future analysis. To overcome this problem, the measurements of the phantom were repeated by using higher microwave power (5.1 mW) and four accumulations. The analyses from these data are presented in Fig. 6d–f and in Table 2. To improve the SNR of the projections, a higher cutoff frequency for the low-pass filter was chosen. This operation allowed a more precise slope analysis of the square-shaped phantom to be performed. The result of this analysis has shown no effect of the chosen modulation amplitude on the sharpness of the phantom wall. Application of higher modulation amplitude than the radical linewidth allows the sharpness of the phantom to be well reconstructed, and blurring effects should not be observed. Therefore, it is possible to overmodulate the reference spectrum and projection even a few times and still obtain a satisfactory reconstruction.
Conclusions It is possible to use overmodulated spectra and still reconstruct images of a good quality. By using a magnetic field gradient of 4 mT/cm (radical linewidth was 0.14 mT), the resolution of the reconstructed images was determined as 0.35 mm, which is two times smaller than the thickness of the phantom wall. The observed image resolution is the ultimate determinant in EPR imaging, which is the result of SNR and the number of projections. The minimum-sized voxel that can be resolved is the one that contains enough spins to be detected with adequate SNR. For a sufficiently high SNR, the resolution should be close to the theoretical value, although for low SNR, the resolution could be much lower. Figure 2 shows the effect of modulation amplitude on the measured projections. For modulation amplitude that is higher than the radical linewidth, but still lower than 1/3 of the projection linewidth, the SNR of the projection is improved without visible distortions. However, if the modulation amplitude reaches 1/3 of the projection linewidth or is higher, a smoothing effect is observed. It was shown that even when reference spectra used in the deconvolution procedure were overmodulated, as well as the projection itself, the reconstructed images directly correspond to those obtained in undermodulated conditions. It was shown that the best SNR of the reconstructed images is expected for modulation amplitude close to 1/3 of the projection linewidth. For higher modulation amplitude, the SNR of the reconstructed image is decreased even if the SNR of the measured projections is increased. In conclusion, the results of this work have
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shown an overmodulation condition that leads to decrease in SNR after a deconvolution process. Acknowledgements Financial support from The National Science Centre (UMO-2014/15/ B/ST4/04946), the National Centre for Research and Development (PBS1/A9/13/2012), and the National Cohesion Strategy from Innovative Economy (POIG.01.03.01-30-150/09) was gratefully acknowledged. Authors are thankful for the kind support of Benjamin B. Williams from Dartmouth College, Sandra S. Eaton from Denver University, and Emerson Coy from Adam Mickiewicz University.
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