Automated On-the-Fly Detection and CorrectionProcedure for EPR Imaging Data Acquisition

Rizwan Ahmad,1 Deepti S. Vikram,2 Sergey Petryakov,2 Yuanmu Deng,2 Jay L. Zweier,2

Periannan Kuppusamy,2* and Bradley Clymer1,3

Fast and reliable data acquisition is a major requirement forsuccessful and useful biological electron paramagnetic reso-nance imaging (EPRI) experiments. Even a technologically ad-vanced and professionally supervised EPRI system can exhibitinstabilities initiated by perturbations such as animal motion,microphonics, and temperature changes. As a result, part of anacquired data set may become corrupted with excessive noiseand distortions, which in turn may degrade the quality of thereconstructed image. In this work an automated scheme tomonitor the system performance and stability over the courseof an experiment is demonstrated. This method ensures thatthe quality of the acquired data is maintained during the exper-iment. For this purpose, four parameters including noise con-tent and integration of each acquired projection are quantifiedand measured against those of the zero-gradient (ZG) projec-tion, which is set as a quality benchmark. Projections withparameter values that differ substantially from the expectedvalues are identified as damaged and consequently are reac-quired. Therefore, the proposed technique not only effectivelymonitors the quality of acquisition, it also saves a substantialamount of acquisition time because it eliminates the necessityof repeating the entire experiment in cases in which only a smallfraction of the data are corrupted. Magn Reson Med 56:644–653, 2006. © 2006 Wiley-Liss, Inc.

Key words: noise; system stability; microphonics; motion arti-facts

Electron paramagnetic resonance imaging (EPRI) is a non-invasive technique that is capable of mapping the distri-bution of unpaired electrons (1,2). It has a distinct advan-tage for many medical applications (3–5) in which it canbe used to directly measure both endogenous and intro-duced free radicals that carry unpaired electrons. In thepast few years, the potential applications of EPRI to stud-ies of living biological systems have been recognized (6–9). However, despite all of the progress made in the lasttwo decades, the acquisition of high-quality images ofbiological samples has been limited by several technicalfactors, including gradient strength and accuracy, sensitiv-ity, reliability, and speed of data acquisition (10,11).

In the past decade, advances in hardware (12–14), suchas lumped circuit resonator designs and optimized auto-matic frequency control systems, have led to more stableand efficient EPRI systems, but system stability (15,16) stillremains a serious issue that may limit the reproducibilityand quality of the acquired data. In addition, electromag-netic interference, microphonics, temperature fluctua-tions, and animal motion may introduce unwanted noiseor distortions to the data, which may leave the entire dataset unusable even if only a small fraction of the data areaffected. Testing the performance of the system hardwarein advance does improve the chances of attaining sus-tained performance during the acquisition, but because ofthe complex nature of the system, there is no guaranteethat it would behave as expected over the course of anexperiment. Therefore, it would be extremely useful toconstantly monitor the performance of a system to ensurethe quality of data acquired during the experiment. In thiswork we present a procedure to identify any damagedprojections. For this purpose we first quantify four param-eters: the noise intensity, spike amplitude, and first andsecond integrations of the acquired projections. We thencompare the monitored parameters (MPs) of each projec-tion with the corresponding values of the zero-gradient(ZG) projection, which is set as a quality benchmark. In theabsence of any distortion or noise, the values of MPs foreach projection would be consistent with those of the ZGprojection. In the presence of noise or system instabilities,however, these values deviate from projection to projec-tion. By developing an effective noise model, we can sug-gest reasonable bounds for the MP values. Thus, any pro-jection with values of MPs outside the suggested bounds isdeclared damaged. Consequently, by ensuring the qualityof just one standard projection (the ZG in this case), we canenhance the fidelity and reproducibility of the entire dataset.

A potential reduction in the acquisition time is anothermajor advantage of using this scheme. In situations whereonly a fraction of the data are damaged, one simple solutionwould be to reacquire the entire data set; however, this is notan efficient or convenient solution because data acquisitionfor EPRI can be a time-consuming process. For example, ittypically takes several minutes for a conventional EPRI sys-tem to acquire a 2D image, and more than an hour for a 3Dimage (14). Another commonly used procedure is to visuallyinspect the data (projection by projection) and identify theprojections that do not “look” correct. These projections areeither reacquired or partially corrected using basic signalprocessing techniques. Again, this approach is not preciseand is subject to judgment errors by the user. The proposedscheme would enable us to identify the damaged projectionsmore effectively. Once identified, these projections can be

1Department of Electrical and Computer Engineering, Ohio State University,College of Engineering, Columbus, Ohio, USA.2Center for Biomedical EPR Spectroscopy and Imaging, Davis Heart andLung Research Institute, Department of Internal Medicine, Ohio State Univer-sity, College of Medicine, Columbus, Ohio, USA.3Department of Biomedical Engineering, Ohio State University, College ofEngineering, Columbus, Ohio, USA.Grant sponsor: NIH; Grant numbers: EB000591; EB005004.*Correspondence to: Periannan Kuppusamy, Ph.D., Davis Heart and LungResearch Institute, Ohio State University, 420 West 12th Ave., Room 114,Columbus, OH 43210. E-mail: kuppusamy.1@osu.eduReceived 1 February 2006; revised 12 April 2006; accepted 17 April 2006.DOI 10.1002/mrm.20967Published online 28 July 2006 in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 56:644–653 (2006)

© 2006 Wiley-Liss, Inc. 644

corrected by using basic signal processing techniques, suchas median filtering. If the damage is extensive, the affectedprojections can be reacquired while the sample is still inplace without repeating the whole experiment. Another sub-sequent advantage of the suggested scheme is its potential toevaluate hardware performance and identify discrepanciesin the system configuration. We tested the proposed schemeon data from EPRI experiments for both phantom and in vivoimaging.

THEORY

Internal electrical resistance is an inherent source of noisein any electronic circuitry, and hence such noise is un-avoidable for any nontrivial electric system. Fortunately,contributions from such noise source can be efficientlyquantified once the related parameters, such as tempera-ture and resistance values, are known. On the other hand,contributions from some other noise sources, such as mi-crophonics, temperature fluctuations, electromagnetic in-terference, and animal motion, are extremely difficult toquantify. Since it is not possible to estimate and henceavoid the contribution of intermittent noise or distortionsfrom such sources, it is intuitive to monitor the perfor-mance of acquisition from the output (acquired projec-tions) of the system and to identify any projections thatexhibit excessive noise or distortion as compared to the ZGprojection. Since the quality of all of the acquired projec-tions is compared with that of the ZG projection, ensuringthe quality of the ZG projection is a fundamental require-ment for this scheme. Therefore, the user is required toensure that the ZG projection is not damaged. The selec-tion of the ZG projection (as opposed to any other projec-tion) as a quality reference, therefore, is an intuitive choicebecause its simple and relatively well-known shape makesit easier for the user to judge its quality. In this research thequality of the ZG projection was judged visually. Thedevelopment of a more robust and automated procedure tojudge the quality of the ZG projection is left for furtherinvestigation.

In this research we selected four parameters to monitorsystem performance. Each of these MPs is discussed indetail in this section. It should be noted that these fourMPs constitute only a subset of a complete list of variablesthat could possibly be related to the system performance.Moreover, information provided by the selected MPs is nottotally independent, which means that a damaged projec-tion is likely to be identified by more than one MP. Re-dundancy among MPs, nevertheless, reduces the chancesof missing a damaged projection. Although it is possible touse a different set of parameters to monitor system perfor-mance, the experimental data verify that for a regular EPRIsetup, the four MPs selected in this work are effective foridentifying projections affected with excessive noise ordistortions.

Noise Intensity

In a typical EPRI experiment, a projection pi(r) measuredin the presence of a magnetic field gradient is a convolu-tion of the spatial profile of the paramagnetic materials,

yi(r), and its lineshape function, which is also called theZG projection p0(r) (17,18):

pi �r� � p0 �r� � yi �r� i � 1,2,. . .,M [1]

where r is the spatial coordinate, V stands for convolution,and M is the total number of projections acquired. The ZGprojection does not contain information regarding the spa-tial distribution of the paramagnetic material under study,but it provides the lineshape function that is later used fordeconvolution.

In order to improve the signal-to-noise ratio (SNR), it isa common practice to observe the first derivative of theEPR absorption by modulating the magnetic field (19).From now onwards, ZG would refer to the first derivativeof the EPR absorption signal. To reflect the effect of fieldmodulation, Eq. [1] can be rewritten in the form of

�i �r� � �0 �r� � yi �r� [2]

where �i(r) represents the first derivative of pi(r) and �0(r)represents the first derivative of p0(r). In the Fourier do-main, Eq. [2] transforms into

�i�k� � �0�k�Yi �k� [3]

where �i(k), �0(k), and Yi (k) are the Fourier transforms of�i(r), �0(r), and yi(r), respectively.

The cutoff frequency kc for �0(k) is selected so that mostof the EPR signal energy lies in the region �k��kc, andanything in �k��kc is primarily noise. A number of tech-niques to find kc have been proposed (10,20,21). In thisresearch we adopt a similar approach to find kc. A two-stepprocedure to find kc is as performed as follows:

The acquired ZG projection �0(r) is curve-fitted with thefirst derivative of the Lorentzian function �0(r) to generatea noise-free lineshape. If the lineshape of the paramagneticspecies under study is known to be non-Lorentzian, or ifthere is not enough information available about the line-shape, then it is safe to curve-fit the observed ZG projec-tion with a mixture (sum) of first derivatives of Lorentzianand Gaussian functions (22).

After fitting the measured lineshape �0(r) with �0(r), wetake the Fourier transform of �0(r) that is denoted by �0(k).Now, kc is selected to be the value of k beyond which thesignal strength (��0(k)�) falls below a threshold that is se-lected to be a small fraction of ��0(k)�max as it is describedby

��0�k�� � ��0�k��max for �k� � kc [4]

In this work we use 0.005, which corresponds to theintegration (in the region �k��kc) that is 0.2% of the totalintegration of ��0(k)�. Once the kc is calculated, the noiseintensity of each projection, including the ZG projection,can be estimated by

N�i � �kkc

ks/2

��i�k��2 i � 0,1,2,. . .,M [5]

EPR Imaging 645

where ks is the sampling frequency of the projections, andN�i

represents the noise intensity of the ith projection.For a stable system we assume that noise is additive

(independent of signal strength) and wide-sense stationary(23), which implies that first and second moments (themean and correlation, respectively) do not vary with re-spect to time. Therefore, the measurement of noise powerfor each projection relative to the base value N�0

withintolerance is a test of system stability. We empirically chose1.5N�0

for the acceptance range for this study (50% safetymargin):

N�i � 1.5N�0 i � 1,2,3,. . .,M [6]

More conservative or tighter bounds can be applied de-pending on the system setup and applications. It should benoted that we are not taking into account the fraction ofnoise that lies in the low-frequency region (�k��kc). In fact,the direct estimation of low-frequency noise, where it co-exists with the EPR signal, is not straightforward and re-mains to be studied further. In this noise estimation tech-nique, we expect that the fraction of noise that lies in theregion �k��kc provides an estimate of the overall noisestrength. This technique, however, does not guard againstsituations where noise is strictly confined to low frequen-cies, but generally contributions from the majority of noisesources are broadband.

Spikes

EPR data can become corrupted with a burst of spikes thatmay come from externally introduced mechanical vibra-tions, a brief lapse in system stability, or even abruptanimal motion. Such interferences, even when limited to asingle projection, may have extreme degrading effects onthe quality of the reconstructed image, as is illustrated in

Fig. 1, in which only one of the 128 projections is cor-rupted with additive spikes. Although a higher value ofsignal energy in the region �k��kc suggests the presence ofexcessive noise, it cannot differentiate between regularnoise and spikes. On the other hand, the finite forwarddifference of a projection is more effective in identifyingthe presence of spikes, given that the spikes are narrowerthan the linewidth of the paramagnetic species understudy. Once the presence of spikes is detected, medianfilters (24,25) can be effectively used to suppress this typeof distortion without significantly affecting the image res-olution. Figure 1f indicates that a median filter of width3 has effectively removed the unwanted spikes, which as aresult has eliminated the artifacts from the reconstructedimage shown in Fig. 1c.

The suggested procedure to identify spikes is also validin the situations where the first derivative of EPR absorp-tion �(r) (instead of p(r)) is observed. For a projection oflength L, the first-order finite forward difference for the ith

projection (�i(r)) can be written as

��i � �i�r � 1� � �i�r� r � 0,1,2,. . .,L � 1 [7]

S�i � ���i�max [8]

where ��i is the first-order finite forward difference of anith projection, and S�i

is the maximum difference betweentwo adjacent data points of the projection. For i 0, Eqs.[7] and [8] give the maximum difference between twoadjacent data points of the ZG projection.

Intuitively, �0(r) can be defined as a convolution of thefirst derivative of the lineshape and a Dirac delta function,while �i(r) can be defined as a convolution of the firstderivative of the lineshape and the spatial profile of para-magnetic species yi(r) (Eq. [2]). We can think of yi(r) as a

FIG. 1. Reconstruction artifacts due to spikes added to one of the projections, and the effectiveness of the median filtering in suppressingsuch distortion. a: A 256 � 256 Shepp-Logan phantom simulated in MATLAB. b: The Shepp-Logan phantom in image a, reconstructedusing filtered back-projection with one of the 128 projections corrupted with spikes (in this case projection number 32). To simulate actualexperimental conditions, each projection is convolved with a Lorentzian function before adding the white Gaussian noise (with mean 0and standard deviation (SD) 4% of the peak signal strength of the projection with maximum amplitude). c: The Shepp-Logan phantomof image a, reconstructed using filtered back-projection from the same set of 128 projections after the corrupted projection was treated witha single scan of median filtering. d: Projection number 32 p32(r) and its corrupted version q32(r), which was generated by adding spikes top32(r). e: First-order finite forward difference (Eq. [7]) of the corrupted projection q32(r). f: Projection q32(r) after it was treated with a medianfilter of width 3.

646 Ahmad et al.

non-negative weighted average filtering kernel (or aspreading function) that is convolved with an object func-tion �0(r). Therefore, for a given peak-to-peak projectionamplitude, S�0

S�ifor all values of i, it is expressed in Eq.

[9].

S�0

�0�r�pp�

S�i

�i�r�ppfS�i � S�0

�i�r�pp

�0�r�pp[9]

where �0(r)pp is the peak-to-peak amplitude of �0(r), and�i(r)pp is the peak-to-peak amplitude of �i(r). It is worthmentioning that the bounds suggested in Eq. [9] are afunction of �i(r)pp, which may not be accurately known fora damaged projection. For example, a projection withstrong additive spikes may exhibit an exaggerated value of�i(r)pp, which would result in unnecessarily loose boundsfor that projection. However, in such cases a reasonableestimate can be achieved by first suppressing the spikesusing a median filter and then measuring �i(r)pp.

An accurate model is required to take the effects of noiseinto consideration. We developed a simple noise modelwith the assumptions that noise is additive, wide-sensestationary, and zero-mean Gaussian. However, we madeno assumption that the noise is white, because data fromEPRI experiments suggest that observed noise may beheavily colored (26), especially for the large values of themodulation amplitude and the time constant of a lock-inamplifier.

We denote the additive noise in �(r) by �(r), and later wewill use notation n(r) to denote the additive noise in p(r).Here n(r) is calculated by integrating �(r) over r. We collecta noise sample �(r) of length l (l�L) from the marginalareas (24) of �0(r), where the signal strength is negligibleand hence the data in that region are essentially noise. Thevariance ���

2 of the first-order finite difference of the ob-served noise sample �(r) can be calculated using Eqs.[10]–[14]:

���2 � E����r � 1� � ��r��2� r � 0,1,2,. . .,l � 1 [10]

���2 � E���r � 1�2� � E���r�2� � 2E���r���r � 1�� [11]

where E[�] is the expectation value operator.Under the assumption of stationarity, the first two terms

in Eq. [11] are essentially identical and represent the vari-ance ��

2 of the observed noise sample �(r), and the last termmeasures the autocorrelation ��(r) between the adjacentpoints of �(r). Therefore,

���2 � 2��

2 � 2���1� [12]

For a sufficiently large value of l, the values of ��2 and ��(1)

can be approximated using Eqs. [13] and [14], respectively:

��2 � E���r�2� �

1l �

r0

l�1

�(r)2 [13]

���j� � E���r���r � j�� �1

l � j �r0

l�j�1

��r���r � j� [14]

Once ��� is calculated from Eq. [12], we can suggestbounds on the value of difference between two adjacentpoints of a noise sample �(r). For example, bounds corre-sponding to 5��� have more than 99.9999% confidencethat the value of difference between adjacent points of �(r)stays within bounds. Therefore, in the presence of noise,Eq. [9] can be modified as follows:

S�i � �S�0

�i�r�pp

�0�r�pp� 5���� [15]

Any projection with an S� lying outside the suggestedbounds (Eq. [15]) is declared damaged. A moderate extentof damage can be reversed by applying median filtering;otherwise, that projection is reacquired. Generally, thewidth of the median filter is kept smaller than the observedlinewidth of the sample to avoid rounding-off the sharpedges of the projection.

First and Second Integrations of Projection

In the absence of noise or distortions, the integration ofeach projection with respect to spatial coordinate r isconserved, and is equal to a constant that is proportional tothe total spins present in the paramagnetic sample. In adiscrete domain, integration can be approximated by thesummation:

�r0

L�1

pi�r� � Api � Ap0 i � 1,2,. . .,M [16]

where Apirepresents the area under pi(r), and Ap0

repre-sents the area under p0(r).

Furthermore, it can be shown that the integration of thefirst derivative (and all of the subsequent derivatives) ofeach projection with respect to the spatial coordinate r isalso conserved:

�r0

L�1

�i�r� � A�i � A�0 i � 1,2,. . .,M [17]

where A�idenotes the area under �i(r) and A�0

representsthe area under �0(r).

As mentioned above, the ZG projection �0(r) is assumedto be distortion-free and is selected as a quality bench-mark. Deviation of the values of Api

and A�ifrom Ap0

andA�0

, respectively, is a measure of the amount of noise ordistortion present in the ith projection. This distortion mayarise due to baseline errors, unintended change in tuningor coupling, change in receiver gain, or animal motion.Monitoring both Ap and A� (as opposed to just one ofthem) is more effective for identifying the damaged pro-jections. For example, a baseline distortion that is a linearfunction of r may not affect both Ap and A�, but it isguaranteed to affect at least one of these two parameters.

EPR Imaging 647

In the presence of noise, the values of Ap and A� deviatefrom those of Ap0

and A�0, respectively, and the extent of

deviation depends on the strength and statistical charac-teristics of the noise. To quantify the effects of noise, weuse the same noise model that was developed in the pre-vious section for the estimation of spike strength S�. Weassume that noise is additive, wide-sense stationary, andzero-mean Gaussian, but not necessarily white. We collectnoise sample �(r) of length l (l L) from the marginal areasof �0(r). We then have

A� � ��0� � ��1� � ��2� � . . .��l � 1� [18]

where A� represents the area under �(r). In vector form:

A� � 1t� [19]

where � stands for the column vector of the collected noisesample, 1 is a column vector of all ones, and the super-script t stands for transpose. The variance �A�

2 of A� can becalculated using

�A�

2 � E��A��2� � E�1t��t1� � 1tR�1 [20]

where R� is the autocorrelation matrix of � for which eachelement can be calculated using

R��i,i � j� � E���i���i � j�� � ���j� for j � m

R��i,i � j� � E���i���i � j�� � 0 for j � m [21]

where ��(j) can be calculated using Eq. [14].Equation [21] essentially displays the procedure of ap-

proximating the random noise by a moving average (MA)model (27) of the order m (m�0). For white noise, R� is adiagonal matrix and the value of m is 0, while for colorednoise the autocorrelation matrix R� has nonzero off-diag-onal entries, but generally the value of R�(i,i�j) becomessmaller and hence less influential as j increases. We canselect a threshold � such that all entries of R� that liebelow that threshold (��(j)����(0)) are set to zero. Conse-quently, R� is converted to a banded matrix with m equalto its half-bandwidth. In this research we used � 0.20.Once �A�

is calculated, we can propose bounds on thevalue of A� using Eq. [22].

�A�0 � 5�A�� � A�i � �A�0 � 5�A�

� i � 1,2,3,. . .,M [22]

For Ap we repeat the same procedure as for A� with n (firstintegral of ��) as the noise sample.

Here n � ���0�,��0� � ��1�,��0� � ��1� � ��2�,. . .��0�

� ��1� � . . . � ��l � 1��t [23]

By following the same procedure, the variance (�An

2 of An

can be calculated using

�An

2 � E��A��2� � E�lt��tl�ltR�l [24]

where l[l, l�1, l�2, . . ., 1]t

Once �Anis calculated, we can suggest bounds on the

value of Ap as follows:

�Ap0 � 5�An� � Api � �Ap0 � 5�An� i � 1,2,3,. . .,M [25]

Hence, if there is a projection for which the values of A�

and Ap are not within the suggested bounds (Eqs. [22] and[25]), it is declared damaged. This unacceptably large vari-ation in A� and Ap may result from an unintended changein the experimental setup, such as a change in receivergain, a frequency shift of the resonator, baseline errors,animal motion, etc.

After the noise intensity (N�), spike amplitude (S�), andfirst and second integrations (A� and Ap) of each projectionare quantified, we can make a more knowledgeable andaccurate decision regarding the quality of each and everyprojection as it is acquired. Once the damaged projectionshave been marked out, we can reacquire them withoutrepeating the entire experiment.

MATERIALS AND METHODS

Phantom Imaging

2D EPRI experiments were conducted on an in-house-builtL-band (1.2 GHz) conventional EPRI system (10). A totalof two data sets were considered in this study. Each dataset consisted of 128 projections with each projectionhaving a fixed length of 1024 points. A ZG projectionwas acquired before each data set, and the quality of theZG projection was used as a reference for the entire dataset. The acquisition time for each projection was 8 s, andthe total acquisition time for each data set was approx-imately 24 min. The time constant of the lock-in ampli-fier was fixed to 30 ms. The field modulation was ap-plied at 100 kHz, and the first derivative EPR absorptionline was detected with a lock-in amplifier. A volumeloop-gap (one loop and four gaps) resonator with a di-ameter of 22 mm and length of 25 mm was used with astandard reflection-type EPR bridge. No correction for anonuniform microwave field or sensitivity was appliedin this work.

An imaged phantom was made of 1 mM Tempone (4-oxo-2,2,2,6-tetramethyl-1-piperidinyloxy) solution. Thecenter field and sweep width were selected such that theobserved signal was due solely to one of the three lines ofthe Tempone spectrum, while the other two lines were putsafely outside the range of the magnetic field sweep.Hence, we were not required to perform a hyperfine cor-rection. The structure of the phantom is shown in Fig. 2.The length and diameter of the sample were 16.8 mm and15 mm, respectively. The SNR, defined as the ratio of peaksignal amplitude to the peak noise amplitude of the ZGprojection, was measured to be 250. The measured line-width of Tempone was 780 mG, and the gradient strengthwas 4.5 G/cm. Before deconvolution, the image resolutionwas approximately 1 mm (28), and after deconvolution itcould be enhanced by a factor of 2–3 (29). The strength offield modulation was 700 mG. The field of view (FOV) wasselected to be 40 mm � 40 mm.

648 Ahmad et al.

In Vivo Imaging

Animal studies were done using the approved protocol ofthe Institutional Laboratory Animal Care and Use Commit-tee of Ohio State University. Mice bearing RIF-1 (radiation-induced fibrosarcoma) tumor in their upper hind legs wereused in this study. The tumors were approximately 300 �25 mm3 in size at the time of experiment. A Xylazine/Ketamine (90 mg/kg b.w.) anesthetic was given intraperi-toneally before imaging. A widely used particulate probe,lithium phthalocyanine (LiPc), which is nontoxic and sta-ble, was used for this in vivo imaging experiment. Theprocedure for implanting LiPc crystals was performed ac-cording to Ilangovan et al. (30). About 10 �g of microcrys-talline powder of LiPc were placed into a 22-gauge needle,and after the needle was inserted into the tumor on theright hind limb of the mouse, a thin wire was used to pushcrystals into the tumor. Implantation of the crystals wascarried out in three locations of the tumor. At the end ofthe experiments the animals were killed by cervical dislo-cation.

A total of two data sets were considered in this study.Each data set consisted of 32 projections, with each pro-jection having a fixed length of 1024 points. A ZG projec-tion was acquired before each data set and the quality ofthe ZG projection was used as a reference for the entiredata set. The acquisition time for each projection was set to6.5 s and the total acquisition time for each data set wasapproximately 5 min. The time constant of the lock-inamplifier was fixed to 40 ms. A surface loop-gap (one loopand one gap) resonator with a 9.5-mm inner diameter,

12-mm outer diameter, and 28-mm length was used with astandard reflection type EPR bridge. The SNR was deter-mined to be 50. The measured linewidth was 450 mG, andthe gradient strength was 5 G/cm. The strength of fieldmodulation was 400 mG. The FOV was selected to be10 mm � 10 mm.

RESULTS

Summary of Phantom Imaging Results

Two phantom imaging data sets (PDS-1 and PDS-2) wereacquired back to back using the same experimentalsetup and parameter values described in the PhantomImaging section. PDS-1 was acquired without disturbingthe system after the initial setup. Figure 3 shows theMPs (i.e., noise intensity (N�), maximum spike ampli-tude (S�), and first and second integration of the projec-tions (A� and Ap)) for PDS-1 measured against those ofthe ZG projection (N�0

, S�0, A�0

, and Ap0). All of the

projections were considered undamaged because thevariations in N�, S�, A�, and Ap, were within the sug-gested bounds. For PDS-2, system instability was artifi-cially triggered by generating microphonics by clappingin the vicinity of the cavity after acquiring 85 (out of128) projections. Figure 4 shows the values of the MPsFIG. 2. Phantom used in the EPRI experiment. The black color

represents plastic walls of the tubes containing 1 mM Temponesolution, which is shown in gray. The overall length of the sample is15 mm and outer diameter is 20 mm. 2D images of XY orientationwere obtained using an L-band EPRI system.

FIG. 3. Examination of the data acquisition quality of the first phan-tom imaging data set (PDS-1). a: Noise intensity N� of each projec-tion (calculated using Eq. [5]) compared to that of the ZG projection.The value of N� for each projection is within the suggested bounds(calculated using Eq. [6]). b: Maximum spike amplitude S� (calcu-lated using Eq. [8]) for each projection. Again, all of the projectionshave an S� that is within the suggested bounds (calculated usingEq. [15]). c: Integration A� of each projection compared with that ofthe ZG projection. A� is again within the suggested bounds (calcu-lated using Eq. [22]) for all acquired projections. d: Second integra-tion Ap of each projection compared with that of the ZG projection.Ap is also within the suggested bounds (calculated using Eq. [25]) forall acquired projections.

EPR Imaging 649

for each projection measured against those of the ZGprojection for PDS-2. It is shown that PDS-2 has a frac-tion of data (42 projections) that were identified as dam-aged because one or more MP values for these projec-tions were not within the suggested bounds. For illus-tration, two of these 42 projections (projections 100 and107), along with the corresponding undamaged projec-tions from PDS-1, are shown in Fig. 4e and f. Thisdistortion in data is also reflected in the reconstructedimage shown in Fig. 5a. Figure 4b indicates that only

one projection (#119) may have been affected by spikes.This projection was treated with median filtering, butthe single scan of median filtering could not bring all theMPs for this projection back within bounds. Therefore,all 42 projections identified as damaged were reac-quired. Figure 5b displays the reconstructed image afterall of the damaged projections were reacquired. It isimportant to mention that the quality of these reac-quired projections was again tested using the suggestedprocedure as it was done for the originally acquired datasets (PDS-1 and PDS-2). Figure 5 illustrates that reac-quiring the damaged projections substantially improvedthe reconstruction quality.

Summary of In Vivo Imaging Results

Two in vivo imaging data sets (IDS-1 and IDS-2) wereacquired using identical parameter values as described inthe In Vivo Imaging section. IDS-1 was acquired 15 minafter injection of the anesthesia. There was no noticeableanimal motion during the acquisition for this data set. ForIDS-1, all of the MPs were within the suggested bounds.Figure 6 shows the MPs for IDS-1 measured against thoseof the ZG projection. All of the projections were consid-ered undamaged since the variations in N�, S�, A�, and Ap

were within the suggested bounds. IDS-2 was acquired55 min after administration of the anesthesia, and therewas some visible animal motion during the acquisition ofIDS-2 because the animal was coming out of the anestheticeffects of the Xylazine/Ketamine. Figure 7 shows the val-ues of MPs for each projection for IDS-2 measured againstthose of ZG projection. It is shown that IDS-2 has a fractionof data (five projections) that were corrupted. Two of thesefive projections (#13 and #29) along with the correspond-ing undamaged projections from IDS-1 are shown in Fig.7e and f. This distortion in data due to animal motion isalso reflected in the reconstructed image shown in Fig. 8a.The analysis shown in Fig. 7b suggests that three projec-tions (projections 27, 28, and 29) may have been affectedby spikes. After a single scan of median filtering, two out ofthree projections were successfully repaired as their MPvalues moved back within bounds. However, there werestill three projections with one or more MPs out of bounds.More Xylazine/Ketamine (90 mg/kg b.w.) was given to themouse without removing it from the instrument, and15 min later when the animal motion was subdued visibly,

FIG. 4. Examination of the data acquisition quality of the secondphantom imaging data set (PDS-2). a: Noise intensity N� of eachprojection (calculated using Eq. [5]) compared with that of the ZGprojection. The value of N� for a fraction of projections is not withinthe suggested bounds (calculated using Eq. [6]). b: Maximum spikeamplitude S� (calculated using Eq. [8]) for each projection. All of theprojections have an S� that is within the suggested bounds (calcu-lated using Eq. [15]), except for one projection (#119). c: IntegrationA� of each projection compared with that of the ZG projection. Acouple of projections have an A� that is not within the suggestedbounds (calculated using Eq. [22]). d: Second integration Ap of eachprojection compared with that of the ZG projection. There is aconsiderable fraction of projections for which Ap is not within thesuggested bounds (calculated using Eq. [25]). e: An example of adamaged projection (#100) from PDS-2 along with the correspond-ing undamaged projection from PDS-1. f: Another example of adamaged projection (#107) from PDS-2 along with the correspond-ing undamaged projection from PDS-1.

FIG. 5. Images from the first phantom imaging data set (PDS-1) andsecond phantom imaging data set (PDS-2) reconstructed usingfiltered back-projection. a: Image reconstructed from PDS-2, inwhich 42 of 128 projections are identified as damaged. There isvisible distortion in the reconstructed image. b: Image recon-structed from PDS-2 after all of the 42 damaged projections werereacquired. c: Image based on PDS-1, in which all of the projectionsare identified as undamaged.

650 Ahmad et al.

the three remaining damaged projections were reacquired.Figure 8 illustrates that repairing and reacquiring the dam-aged projections considerably improved the reconstruc-tion quality.

DISCUSSION

We have demonstrated a new procedure to monitor theperformance of the acquisition process quantitatively. Theeffectiveness of the suggested scheme was demonstratedwith the help of two EPR experiments (one for phantomimaging and one for in vivo imaging). Two data sets (oneundamaged and one damaged) were acquired in each ex-periment. The results indicate that the suggested qualityinspection scheme is effective in identifying the projec-tions damaged due to a variety of noise or distortionsources, such as animal motion or a lapse in system sta-bility. For example, the suggested scheme successfullyidentified damaged projections 100 and 107 from PDS-2(the former was the victim of baseline error, and the latterexhibited a significant loss in SNR).

In addition to monitoring system performance, the pro-posed method eliminates the requirement to reacquire thewhole data set when only a fraction of the data set isaffected. For example, we reacquired only 42 (out of 128)

projections for PDS-2 and only three (out of 32) projectionsfor IDS-2, and thus saved 67% and 91% of the data acqui-sition time, respectively. In addition, the suggested proce-dure is computationally straightforward. For example, thetotal time required to analyze a data set with 128 projec-tions was less than 8 s in MATLAB.

The technique presented in this paper is intendedmainly for samples in which the observed signal intensitystays constant over the course of an experiment. In tem-

FIG. 6. Examination of the data acquisition quality of the first in vivoimaging data set (IDS-1). a: Noise intensity N� of each projection(calculated using Eq. [5]) compared with that of the ZG projection.The value of N� for each projection is within the suggested bounds(calculated using Eq. [6]). b: Maximum spike amplitude S� (calcu-lated using Eq. [8]) for each projection. Again, all of the projectionshave an S� that is within the suggested bounds (calculated usingEq. [15]). c: Integration A� of each projection compared with that ofthe ZG projection. A� is again within the suggested bounds (calcu-lated using Eq. [22]) for all acquired projections. d: Second integra-tion Ap of each projection compared with that of the ZG projection.Ap is also within the suggested bounds (calculated using Eq. [25]) forall acquired projections.

FIG. 7. Examination of the data acquisition quality of the second invivo imaging data set (IDS-2). a: The noise intensity N� of eachprojection (calculated using Eq. [5]) compared with that of the ZGprojection. The value of N� for a fraction of the projections is notwithin the suggested bounds (calculated using Eq. [6]). b: Maximumspike amplitude S� (calculated using Eq. [8]) for each projection. Allof the projections have an S� that is within the suggested bounds(calculated using Eq. [15]), except for three projections (#27, #28,and #29). c: Integration A� of each projection compared with that ofthe ZG projection. A couple of projections have an A� that is notwithin the suggested bounds (calculated using Eq. [22]). d: Secondintegration Ap of each projection compared with that of the ZGprojection. Again, there are a couple of projections for which Ap isnot within the suggested bounds (calculated using Eq. [25]). e: Anexample of a damaged projection (#13) from IDS-2 along with thecorresponding undamaged projection from IDS-1. f: Another exam-ple of a damaged projection (#29) from IDS-2 along with the corre-sponding undamaged projection from IDS-1.

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poral EPRI (31), which is used mainly to study the kineticsof free radicals, the intensity of the observed signalchanges over time, which violates one of the assumptionsmade in this work. Therefore, modifications are requiredto extend this scheme to temporal EPRI. One possiblesolution is to repeatedly acquire a ZG projection at regularintervals. This way the ZG projection acquired at the startof the interval can be used as a reference to calculatebounds for all of the projections acquired during that in-terval. The quality of each subsequently acquired projec-tion can be tested using the suggested scheme as soon as itis acquired. If a damaged projection is identified by thescheme, it can be immediately reacquired before the radi-cal has decayed considerably. However, this is only pos-sible if the rate of radical decay is somewhat moderate sothat the observed signal statistics do not change substan-tially within the interval selected to repeat the ZG mea-surements. The suggested technique has limited applica-tions for cases in which signal decay is rapid.

CONCLUSIONS

We have proposed a new procedure to monitor the dataquality of EPRI by quantitatively inspecting the projec-tions as they are acquired. It is an automated procedure,which implies that it is not necessary to visually inspecteach acquired projection to judge its acquisition quality.First, we discussed a procedure for estimating the noiseintensity, maximum spike amplitude, and first and secondintegrations of each acquired projection. Then, by devel-oping a simple but effective noise model, we suggestedreasonable bounds on the values of these MPs. The exper-imental results suggest that the estimated noise intensity,maximum spike amplitude, and first and second integra-tions of each acquired projection are effective criteria formonitoring the system performance over the course of anexperiment. The suggested scheme was tested using datafrom EPRI experiments for both phantom and in vivoimaging. The results indicate that the use of the demon-strated scheme ensures a more reliable and improved qual-ity of data acquisition, along with a potential reduction inacquisition time. Although the procedure is demonstratedonly for 2D imaging, it can readily be extended to 3D cases.The technique is also applicable to spectral-spatial imag-ing.

ACKNOWLEDGMENTS

We thank Guanglong He and Nancy Trigg for technicalassistance.

REFERENCES

1. Ferrari M, Quaresima V, Sotgiu A. Present status of electron paramag-netic resonance (EPR) spectroscopy/imaging for free radical detection.Pflugers Arch 1996;431(6 Suppl 2):R267–R268.

2. Fujii H, Berliner LJ. One- and two-dimensional EPR imaging studies onphantoms and plant specimens. Magn Reson Med 1985;2:275–282.

3. Fuchs J, Freisleben HJ, Groth N, Herrling T, Zimmer G, Milbradt R,Packer L. One- and two-dimensional electron paramagnetic resonanceimaging in skin. Free Radic Res Commun 1991;15:245–253.

4. Hochi A, Furusawa M, Ikeya M. Applications of microwave scanningESR microscope: human tooth with metal. Appl Radiat Isot 1993;44:401–405.

5. Kuppusamy P. EPR spectroscopy in biology and medicine. AntioxidRedox Signal 2004;6:583–585.

6. Matsumoto A, Matsumoto S, Sowers AL, Koscielniak JW, Trigg NJ,Kuppusamy P, Mitchell JB, Subramanian S, Krishna MC, MatsumotoKI. Absolute oxygen tension (pO) in murine fatty and muscle tissue asdetermined by EPR. Magn Reson Med 2005;54:1530–1535.

7. Rolett EL, Azzawi A, Liu KJ, Yongbi MN, Swartz HM, Dunn JF.Critical oxygen tension in rat brain: a combined (31)P-NMR and EPRoximetry study. Am J Physiol Regul Integr Comp Physiol 2000;279:R9 –R16.

8. Velayutham M, Li H, Kuppusamy P, Zweier JL. Mapping ischemic riskregion and necrosis in the isolated heart using EPR imaging. MagnReson Med 2003;49:1181–1187.

9. Kuppusamy P, Shankar RA, Roubaud VM, Zweier JL. Whole bodydetection and imaging of nitric oxide generation in mice followingcardiopulmonary arrest: detection of intrinsic nitrosoheme complexes.Magn Reson Med 2001;45:700–707.

10. Deng Y, He G, Petryakov S, Kuppusamy P, Zweier JL. Fast EPR imagingat 300 MHz using spinning magnetic field gradients. J Magn Reson2004;168:220–227.

11. Joshi JP, Ballard JR, Rinard GA, Quine RW, Eaton SS, Eaton GR. Rapid-scan EPR with triangular scans and Fourier deconvolution to recoverthe slow-scan spectrum. J Magn Reson 2005;175:44–51.

12. Diodato R, Alecci M, Brivati JA, Varoli V, Sotgiu A. Optimization ofaxial RF field distribution in low-frequency EPR loop-gap resonators.Phys Med Biol 1999;44:N69–N75.

13. Hirata H, Walczak T, Swartz HM. Electronically tunable surface-coil-type resonator for L-band EPR spectroscopy. J Magn Reson 2000;142:159–167.

14. Kuppusamy P, Chzhan M, Zweier JL. Development and optimization ofthree-dimensional spatial EPR imaging for biological organs and tis-sues. J Magn Reson 1995;106:122–130.

15. Hirata H, Luo ZW. Stability analysis and design of automatic frequencycontrol system for in vivo EPR spectroscopy. Magn Reson Med 2001;46:1209–1215.

16. Hirata H, Watanabe H, Kumada M, Itoh K, Fujii H. Decoupling ofautomatic control systems in a continuous-wave electron paramagneticresonance spectrometer for biomedical applications. NMR Biomed2004;17:295–302.

17. Ohno K. ESR imaging: a deconvolution method for hyperfine patterns.J Magn Reson 1982;50:145–150.

18. Sotgiu A, Gazzillo D, Momo F. ESR imaging: spatial deconvolution inthe presence of an asymmertic hyperfine structure. J Phys C: Solid StatePhys 1987;20:1297–6304.

19. Poole Jr CP. Electron spin resonance: a comprehensive treatise onexperimental techniques. New York: Dover Publications; 1983. 229 p.

20. Deng Y, He G, Kuppusamy P, Zweier JL. Deconvolution algorithmbased on automatic cutoff frequency selection for EPR imaging. MagnReson Med 2003;50:444–448.

FIG. 8. Images from IDS-1 and IDS-2 using filteredback-projection a: Image reconstructed from IDS-2,in which five of 32 projections are identified as dam-aged. There are visible artifacts in the marked sec-tion. b: Image reconstructed from IDS-2 after all ofthe five damaged projections were either repaired orreacquired. c: Image based on IDS-1, in which all ofthe projections are declared undamaged.

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21. Hirata H, Itoh T, Hosokawa K, Deng Y, Susaki H. Systematic approachto cutoff frequency selection in continuous-wave electron paramag-netic resonance imaging. J Magn Reson 2005;175:177–184.

22. Bales BL, Peric M, Lamy-Freund MT. Contributions to the Gaussianline broadening of the proxyl spin probe EPR spectrum due to magnet-ic-field modulation and unresolved proton hyperfine structure. J MagnReson 1998;132:279–286.

23. Barry JR, Lee EA, Messerschmitt DG. Digital communication. Boston:Kluwer Academic Publishers; 2003. 67–68 p.

24. Gallagher NC, Wise GL. A theoretical analysis of the properties ofmedian filters. IEEE Trans Acoust Speech Signal Process 1981;ASSP-29:1136–1141.

25. Tukey JW. Nonlinear (nonsuperposable) methods for smoothing data.IEEE EASCON 1974:673.

26. Li XR. Probability, random signals, and statistics. Boca Raton: CRCPress; 1999. 327 p.

27. Crespo J, Maojo V. Medical data analysis. Berlin: Springer; 2001. 82 p.28. Hoch MJR, Ewert U. Resolution in EPR imaging. In: Eaton GR, Eaton SS,

Ohno K, editors. EPR imaging and in vivo EPR. Boca Raton: CRC Press; 1991.29. Blass WE, Halsey GW. Deconvolution of absorption spectra. New York:

Academic Press; 1981.30. Ilangovan G, Zweier JL, Kuppusamy P. Mechanism of oxygen-induced

EPR line broadening in lithium phthalocyanine microcrystals. J MagnReson 2004;170:42–48.

31. Ueda A, Yokoyama H, Nagase S, Hirayama A, Koyama A, Ohya H. Invivo temporal EPR imaging for estimating the kinetics of a nitroxideradical in the renal parenchyma and pelvis in rats. Magn Reson Imaging2002;20:77–82.

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