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August 20, 2017 | Autor: Set Eaton | Categoria: Image Processing, Image Reconstruction, Magnetic Resonance, Prior Knowledge
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Descrição do Produto

JOURNAL

OF MAGNETIC

RESONANCE

77, 75-83 (1988)

Reconstruction of Spectral-Spatial Two-Dimensional EPR Images from Incomplete Sets of Projections without Prior Knowledge of the Component Spectra MARTINM.MALTEMPO Department

of Physics,

University

of Colorado,

Denver,

Colorado

80204

SANDRAS.EATON Department

of Chemistry,

University

of Colorado,

Denver,

Colorado

80204

AND GARETH Department

of Chemistry,

R.EATON of Denver,

University

Denver,

Colorado

80208

Received May 5, 1987; revised September 9, 1987 Spectral-spatial EPR imaging gives the EPR spectrum as a function of position in the sample. Spectra were obtained at a series of magnetic field gradients that correspond to projections in a spectral-spatial plane. For a given maximum magnetic field gradient, the spatial resolution of the image can be improved by collection 6f data for less than a full 180” angular range. An iterative algorithm was used to estimate the “missing” information. The algorithm does not require prior knowledge of the signals that contribute to the spectra. Images have been obtained that show variations in nitroxyl lineshape due to collisional broadening and variations in motional averaging of the hyperIine interaction at different locations in the sample. Images have also been obtained that distinguish a weak TCNE signal and a strong galvinoxyl signal in adjacent tubes from a surrounding solution of nitrOxy1 radical. 0 1988 Academic Press, 1~. Magnetic resonance imaging, both NMR and EPR, focused first on the problem of obtaining maps of spin density as a function of position in the sample (1-3). Both techniques are now being extended to obtain spectral information as a function of location in the sample. Modulated magnetic field gradients have been used to separate spectral and spatial information in EPR imaging by selectively examining a small region within a sample (4, 5). However, problems in image reconstruction from the data obtained by this technique have been noted (6). We have recently shown that EPR imaging with one spectral dimension and one spatial dimension can be obtained from spectra taken at a series of magnetic field gradients (3, 7, 8). An analogous approach was developed independently by Lauterbur et al. for NMR imaging (9-1 I) and applied to EPR imaging by Ewert and Herrling (6). In this paper we report implementation of an iterative 75

0022-2364/88 $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.

76

MALTEMPO,

EATON,

AND

EATON

algorithm (12) for spectral-spatial EPR imaging that does not require prior knowledge of the paramagnetic species in the sample. SPECTRAL-SPATIAL

IMAGE

RECONSTRUCTION

The spectral-spatial imaging experiment examines a pseudo-object with length AH in the spectral dimension and L in the spatial dimension (o-8). The angle cxdefines the orientation of a projection relative to the spectral axis. The maximum gradient, Gmax, is related to L and AH by G max= tan(a,,,)A

H/L.

[II

The magnetic field sweep for each projection is given by sweep width = ~~AH/cos a.

PI

Equations [l] and [2] impose constraints on the imaging experiment. For given values of Gmaxand spectral width, AH, the ratio of tan(ol,,,)/L is fixed. The resolution of the image depends on the dimensions of the pseudo-object and the number of projections. If L is greater than the dimension of the resonator, part of the spatial axis is experimentally inaccessible, and the resolution over the usable region of space is degraded. It is therefore desirable to maintain L as close as possible to the dimension of the sample. For experiments performed in a Varian E231 cavity, this would be limited by the dimensions of the cavity. Most image reconstruction algorithms require projections obtained over 180” with equal angular increments. If a complete set of projections is used for spectral-spatial imaging, as in Ref. (6), the number of projections determines the value of LY,,, , which determines the value of G,,, (Eq. [I]) and the maximum sweep width (Eq. [2]). For example, a complete set of 64 projections would require CY,~~= 88.59”, and if L = 0.8 cm and AH = 32 G, G,,,,, = 1625 G/cm, and the maximum sweep width is 1839 G. However, if accurate image reconstruction could be obtained with experimental data for 60 of the 64 projections and with estimates for the 4 “missing” projections (at the largest positive and negative angles), (Y,, would be 82.97”. Then if L = 0.8 cm and AH = 32 G, G,,, would be 324 G/cm and the maximum sweep width would be 370 G. Thus both the gradient and sweep width requirements can be reduced by about a factor of five if about 6% “missing” information can be accepted. Since both maximum gradient and maximum sweep width are directly proportional to AH, the,advantage of using an incomplete set of projections is significant for any value of AH. The large heat dissipation from the magnetic field gradient coils required for large gradients presents a major problem. The large difference in sweep widths is also a concern. If the widest sweep is 40 times greater than the narrowest sweep and the full digitizer accuracy is used to generate the voltage ramp for the wide sweep, there is about 5 bits less accuracy available for the narrow sweep than for the wide sweep. Thus from the perspective both of the gradient and of the sweep widths it is advantageous to examine methods to handle even a modest amount of “missing” information. In Ref. (8) the estimates of the projections for the “missing” angles were obtained by extrapolation of the peak positions and linewidths in the spectra at the largest

SPECTRAL-SPATIAL

2D EPR IMAGES

77

positive and negative gradients followed by convolution with a Gaussian lineshape. This procedure worked well for the samples in Ref. (8) with two spatially localized signals, but is not appropriate as a general solution. Procedures have been developed to obtain images from projections at equal angular increments that do not span a full 180” by extrapolation of the experimental data to obtain estimates for the “missing” projections (12-17). An extrapolation based on a harmonic series expansion has been applied in NMR spectral-spatial imaging, but was of limited utility due to its sensitivity to the amount of “missing” information and the number of terms in the expansion (9). We have implemented an iterative convoluted back projection algorithm for estimation of the “missing” projections (12, 17). This approach was selected because it gives accurate image reconstruction with moderate computational requirements (12). The steps in the image reconstruction can be summarized as follows. (a) Input experimental data for an incomplete set of projections. (b) Make initial estimates for the “missing projections” by setting the elements of these projections to zero. (c) Take the Fourier transform of each projection and use filtering in Fourier space to remove noise and condition the data for back-projection, (d) Obtain the reverse Fourier transform of each projection. (e) Use back-projection to obtain an estimate of the image. (f) Set image elements to zero outside of the known boundary and set all negative elements within the image to zero. (g) Obtain new estimates for the “missing” projections by taking projections of the estimated image at appropriate angles. (h) Repeat steps (c) to (g) until there is no further improvement in the image. Three to five iterations gave an image that exhibited no visible change with further iteration. Images reported in this paper were obtained with 60 known and 4 “missing” projections. Images of the same samples obtained with 58 known and 6 “missing” projections contained significantly greater artifacts. A similar algorithm has been applied to NMR spectral-spatial imaging by Stillman et al. (1 I), with the fundamental difference that they assumed that the chemical shifts for the signals in the spectrum were known. This information was used to do a nonlinear least-squares fit to each spatial slice in the image, thereby removing artifacts from the image. For a sample with N signals there were 2N + 1 variables in the least-squares fit (N concentrations, N linewidths, and a local magnetic field parameter). Our approach does not require that the signals in the EPR spectra are known in advance. It might be argued that the contributing spectra could be obtained from a spectrum in the absence of gradient. However, this could cause a weak or broad signal to be overlooked in the presence of stronger or sharper signals. Also, nuclear hyperhne splitting and/or linewidth can vary as a function of environment so the spectrum of a single paramagnetic species may vary with position in the sample. In addition, least-squares fitting becomes cumbersome for samples with multiple signals. The angular iteration method (AIM) of Ref. (12) was also used in conjuction with iterative convoluted back-projection. The resulting images showed no improvement, and in some cases were degraded, compared with images obtained by convoluted back-projection alone. DATA

COLLECTION

Data collection, including control of the gradient and magnetic field scans, was performed with a VAXstation II interfaced to a Varian E9 (8). The gradient coils have

78

MALTEMPO,

EATON,

AND

EATON

been described previously (8). A current of 3.0 A provided a gradient of 300 G/cm. Experimental data were obtained for 60 projections out of a complete set of 64 projections. For each projection, 128 data points were collected in 30 s scans. The firstderivative EPR spectra were numerically integrated to obtain the corresponding absorption spectra. The image was obtained by the iterative procedure described above. RESULTS

One incentive for spectral-spatial imaging is to be able to monitor changes in lineshape of a spin probe as a function of molecular environment such as viscosity or oxygen concentration. To model this type of experiment, a sample was constructed with five solutions of “N-tempone (4-oxo-2,2,6,6-tetramethylpiperidin-I-oxyl) in solvents with viscosities ranging from about 1 to 100 CS-toluene; 1: 1 toluene:di-o-xylylethane; 1:4 toluenedi-a-xylylethane; and Apiezon C oil. The samples were not degassed, so the lineshapes of the nitroxyl signals reflect changes in collision broadening by

g.2c

fly. 1. Spectral-spatial EPR image of “N-tempone in five solvents with were contained in flat microslides with internal dimensions of 0.04 cm. The the first and last microslides was 0.56 cm. The five solvents were (A) toluene, (C) I:4 toluene:di-o-xylylethane, (D) di-o-xylylethane, and (E) Apiezon C were 0.5 to 2.0 mM. The image was obtained from 60 experimental projections The locations of the slices shown in Fig. 2 are marked.

different viscosities. The samples center-to-center spacing between (B) 1: 1 toluene:di-o-xylylethane, oil. The nitroxyl concentrations out of a total of 64 projections.

SPECTRAL-SPATIAL

2D EPR IMAGES

79

oxygen and molecular tumbling as a function of solvent viscosity. The solutions were put into microslides (18) with 0.04 cm path length. Five microslides were positioned such that the spacing between the centers of the first and last samples was 0.56 cm and the separations between samples were equal. Data were obtained with a maximum magnetic field gradient of 300 G/cm. The resulting image after five iterations is shown in Fig. 1. The locations of the five samples are clearly resolved and the lineshapes vary as expected with increasing solvent viscosity. The lineshape changes can be seen more clearly in the three rows from the image, which are shown in Figs. 2a-2c. Each row corresponds to the spectrum at a particular location along the spatial axis. In toluene solution (Fig. 2a) the signal is broadened by collisions with oxygen. In 1:4 toluene:di-

FIG. 2. Slices from the image shown in Fig. 1. The rows show the spectral changes as a function of viscosity in (a) toluene, (b) 1:4 toluene:di-o-xylylethane, and (c) Apiezon C oil. The column displayed in (d) shows the spatial variation in the intensity of the signal at the magnetic field that corresponds to the low-field nitroxyl peak.

80

MALTEMPO,

EATON, AND EATON

o-xylylethane solution (Fig. 2b) the viscosity is sufficiently high to reduce the collisional broadening, but the two peaks of the nitroxyl signal are of approximately equal amplitude, which indicates that molecular tumbling is rapid on the EPR time scale. In the Apiezon C solution (Fig. 2c) the high viscosity reduces the rate of molecular tumbling enough that the two peaks of the nitroxyl signal are of unequal amplitude. The 13C sidebands are resolved on the sharp lines shown in Figs. 2b and 2c. Figure 2d is a slice through the image at constant magnetic field that shows the variation in the amplitude of the nitroxyl signal as a function of location in the sample. The signals from the five solutions are approximately equally spaced as expected for this sample. The width at half-height is in good agreement with the dimensions of the sample. A second incentive for spectral-spatial imaging is to examine samples in which the

731.5

GI

Fig.5c Fig.5b

I Fig.5a

RG. 3. Spectral-spatial EPR image of two 3 mm o.d. tubes surrounded by a 1 mA4 solution of 15Ntempone in 1:1 toluene:di-a-xylylethane solution in a 0.3 cm X 0.7 cm quartz tube. Tube A was a standard Varian sample of TCNE. Tube C contained about 3 mM galvinoxyl in degassed toluene. The image was obtained from 60 experimental projections out of a total of 64 projections. The locations of the slices shown in Figs. 4 and 5 are marked.

SPECTRAL-SPATIAL

2D EPR IMAGES

81

type of paramagnetic center varies across the sample. One question that arises in this context is whether weak signals can be detected in the presence of strong signals. A sample was constructed from a 3 mm o.d. Varian standard sample of TCNE (tetracyanoethylene anion radical) and a 3 mm o.d. sample of a concentrated solution (about 3 m&I) of galvinoxyl radical (2,6-di-tevt-butyl-cy-(3,5-di-tevt-butyl-4-oxo-2,5cyclohexadien- 1-ylidene)-@olyloxy). The two tubes were placed in a 0.30 X 0.70 cm i.d. quartz tube and surrounded by a 1 m&I solution of “N-tempone in 1: 1 toluene: di-a-xylylethane. The spectrum in the absence of gradient was dominated by the signals from the galvinoxyl and nitroxyl radicals and the signal from the TCNE was sufficiently weak that it was difficult to detect. Projections were obtained with a maximum gradient of 270 G/cm. The resulting image after five iterations is shown in Fig. 3. The TCNE signal is readily observed. Three rows from the image show the TCNE signal plus small contributions from the surrounding nitroxyl solution (Fig. 4a), the nitroxyl signal from the central portion of the sample (Fig. 4b), and the galvinoxyl signal that is broadened due to collisional interaction (Fig. 4~). These spectra are of sufficient quality

FIG. 4. Slices from the image in Fig. 3: (a) row that corresponds to the center of the tube containing TCNE; (b) row at a location between tubes A and C; and (c) row that corresponds to the center of the tube containing the galvinoxyl radical.

82

MALTEMPO,

EATON, AND EATON

FIG. 5. Slices from the image in Fig. 3: (a) column at a magnetic field that shows the spatial distribution of both the TCNE and the galvinoxyl signals; (b) column at a magnetic field that shows the spatial distribution of the galvinoxyl signal; and (c) column at a magnetic field that shows the spatial distribution of the nitroxyl signal.

that species could be identified from the slices through the image. Three columns from the image show the spatial distribution of the signal amplitude at a particular magnetic field as a function of location in the sample (Fig. 5). These accurately reflect the distribution of species. CONCLUSION

Spectral-spatial EPR images can be reconstructed accurately with an iterative algorithm from incomplete sets of projections without prior knowledge of the signals present in the sample. The spectral information is of sufficient quality to permit identification of species in the sample and to monitor changes in lineshape that reflect the molecular environment.

SPECTRAL-SPATIAL

2D

EPR

83

IMAGES

ACKNOWLEDGMENTS This work was supported in part by NSF Grant CHE842 128 1. Dr. Hayner generously provided copies of his subroutines for image reconstruction with convoluted back-projection and angular iteration (12). Richard W. Qume assisted with the design of the power supplies for the imaging experiments. Linda E. Gully contributed to the computer programming at an early stage of this work. REFERENCES

1. P. G. MORRIS, “NMR in Biology and Medicine,” Oxford Univ. 2. K. OHNO, Appl. Spectrosc. Rev. 22, 1 (1986). 3. S. S. EATON AND G. R. EATON, Spectroscopy 1, 32 (1986). 4. 5. 6. 7. 8. 9.

10. 11.

T. U. U. M. M. P. M. A.

12. 13. 14. 15.

D. K. T. A. 16. R. 17. M. 18. S.

Press, Oxford,

1986.

HERRLING, N. KLIMES, W. KARTHE, U. EWERT, AND B. EBERT, J. Magn. Reson. 49,203 (1982). EWERT AND T. HERRLING, J. Magn. Reson. 61, 1 I (1985). EWERT AND T. HERRLING, Chem. Phys. Lett. 129,516 (1986). M. MALTEMPO, J. Magn. Reson. 69, 156 (1986). M. MALTEMPO, S. S. EATON, AND G. R. EATON, J. Magn. Reson. 72,449 (1987). C. LAUTERBUR, D. N. LEVIN, AND R. B. MARR, J. Magn. Reson. 59, 536 (1984). L. BERNARDO, JR., P. C. LAUTERBUR, AND L. K. HEDGES, J. Magn. Reson. 61, 168 (1985). E. STILLMAN, D. H. LEVIN, D. B. YANG, R. B. MARR, AND P. C. LAUTERBUR, J. Magn. Reson. 69, 168 (1986). A. HAYNER AND W. K. JENKINS, Adv. Comput. Vision Image Proc. 1, 83 (1984). C. TAM, V. PEREZ-MENDEZ, AND B. MACDONALD, IEEE Trans. Nucl. Sci. NS-26,279l (1979). INOUYE, IEEE Trans. Nucl. Sci. NS-26,2666 (1979). LENT, J. Math. Anal. Appl. 83, 554 (1981). RANGAYYAN, A. P. DHAWAN, AND R. GORDON, Appl. Opt. 24,400O (1985). NASSI, W. R. BRODY, B. P. MEDOFF, AND A. MACOVSKI, IEEE Trans. Biomed. Eng. BME-29, 333 (1982). S. EATON AND G. R. EATON, Anal. Chem. 49, 1277 (1977).

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