EPR-based oximetric imaging: a combination of single point-based spatial encoding and T₁ weighting

Abstract

Purpose:

Spin-lattice relaxation rate (R₁)-based time-domain EPR oximetry is reported for in vivo applications using a paramagnetic probe, a trityl-based Oxo71.

Methods:

The R₁ dependence of the trityl probe Oxo71 on partial oxygen pressure (pO₂) was assessed using single-point imaging mode of spatial encoding combined with rapid repetition, similar to T₁-weighted MRI, for which R₁ was determined from 22 repetition times ranging from 2.1 to 40.0 μs at 300 MHz. The pO₂ maps of a phantom with 3 tubes containing 2 mM Oxo71 solutions equilibrated at 0%, 2%, and 5% oxygen were determined by R₁ and apparent spin–spin relaxation rate $\left({\text{R}}_2^{*}\right)$ simultaneously.

Results:

The pO₂ maps derived from R₁ and ${\text{R}}_2^{*}$ agreed with the known pO₂ levels in the tubes of Oxo71. However, the histograms of pO₂ revealed that R₁ offers better pO₂ resolution than ${\text{R}}_2^{*}$ in low pO₂ regions. The SDs of pixels at 2% pO₂ (15.2 mmHg) were about 5 times lower in R₁-based estimation than ${\text{R}}_2^{*}$-based estimation (mean±SD: 13.9±1.77 mmHg and 18.3±8.70 mmHg, respectively). The in vivo pO₂ map obtained from R₁-based assessment displayed a homogeneous profile in low pO₂ regions in tumor xenografts, consistent with previous reports on ${\text{R}}_2^{*}$-based oximetric imaging. The scan time to obtain the R₁ map can be significantly reduced using 3 repetition times ranging from 4.0 to 12.0 μs.

Conclusion:

Using the single-point imaging modality, R₁-based oximetry imaging with useful spatial and oxygen resolutions for small animals was demonstrated.

1 |. INTRODUCTION

The importance of EPR imaging (EPRI) stems from the fact that it can be used to quantitatively determine tissue oxygenation because both the spin-lattice relaxation time (T₁ = 1/R₁) and spin-spin relaxation time (T₂ = 1/R₂) of paramagnetic electrons are shortened in the presence of oxygen. EPRI can be performed in vivo either in the continuous wave mode or in the time domain using pulsed Fourier transform techniques with exogenous paramagnetic probes.^1–4 The observed EPR spectral line widths of many paramagnetic systems, such as lithium phthalocyanine^5,6 and triphenylmethyl (trityl) radicals,^7–9 linearly depend on the partial oxygen pressure (pO₂). In fact, the time domain approach to EPR imaging became feasible for in vivo applications after the availability of narrow-line spin probes based on the trityl radical.^7–9

Recently developed trityl derivatives^8,9 with T₁ and T₂ of several microseconds are nontoxic at the concentrations required for imaging and have pharmacologic half-lives suffi-cient for 3D imaging. Using excitation pulses ~50 nanosec-onds and low Q resonators, in vivo EPR images were generated using a strategy known as single-point imaging (SPI), involving pure phase encoding in the presence of static gradients and subsequent Fourier transformation.^10–20 In order to perform EPR oximetry, the apparent spin–spin relaxation time (T*-), T₂-, or T₁-weighted maps can be obtained as in MRI to generate oxygen-dependent quantitative contrast in the images.^10,21–23 The MRI approaches require no exogenous contrast agent but provide indications of oxygenation,^21–23 whereas quantitative oximetry is accomplished by EPRI.

EPR oximetry based on measuring the spectral line width (LW), for which LW= R₂/γ_e and γ_e is the gyromagnetic ratio of the electron, needs correction for self-broadening of the probe due to its own spin–spin interactions, which manifest at concentrations greater than 5 mM.^18,24 This self-broadening of the probe cannot be easily deconvolved from the oxygen-dependent broadening in vivo because it requires quantitative estimation of the spin probe’s accumulation in specific tissues, for example, in kidneys and tumors. Halpern et al. reported R₁-based EPR oximetry by an inversion recovery electron spin echo sequence and discovered negligible dependence of self-broadening of the spin probe Oxo63 on its concentration,²⁴ providing a means to map in vivo pO₂ at greater accuracy for the first time. An analogous technique in MRI using ¹⁹F-labeled tracers has been developed and validated in studying tumor oxygenation.^25–28 In this study, we present another strategy for R₁-based EPR oximetry that combines the high-resolution capability of SPI by a single pulse sequence¹⁸ and the effect of interpulse delays and R₁ on the steady state magnetization for rapid signal averaging.^29–34 This approach is applicable to a wide range of R₁ values, is independent of differences in the concentration of the contrast agent as originally demonstrated by Epel and Halpern, and has a lower specific absorption rate (SAR).³⁴ Oxo71, a deuterated Oxo63 probe, was assessed for: 1) the linear relationship between R₁ and pO₂, 2) R₁ mapping of a phantom by EPR imaging, and 3) in vivo oximetry of a mouse tumor based on a R₁ map.

2 |. THEORY

Methods for R₁ mapping, such as inversion recovery,³⁵ saturation recovery,³⁶ and variable nutation angle,³⁷ are unsuitable for EPR in vivo studies due to high SARs and long scan times. Approaches to the estimation of R₁ by the steady-state free precession sequences at short repetition times, and their relative merits and shortcomings, are well documented in the NMR literature.^29,30,32 R₁-dependent magnetization recovery, that is, T₁-weighted signal intensity, is defined as a function of the TR to estimate R₁ by these sequences.

The saturation by fast repetition (SFR) sequence³⁴ for R₁-weighted in vivo imaging offers a high scan speed at low SAR. The SFR sequence consists of a train of phase-coherent RF pulses of a specific flip angle. In this scheme, when TR is small (TR<3T₂), the signal behavior becomes complex due to the refocusing of the residual transverse magnetization M_xy from one pulse by its succeeding pulses, resulting in spin and stimulated echoes.^32,33 MRI sequences such as steady-state free precession and gradient recalled echo use this scheme, interleaved with spoiler gradient pulses to destroy the residual transverse magnetization before the next pulse is applied. Such spoiler gradient sequences are not practical for EPRI due to the microsecond time scales required for the gradient settling times, which are in the same time range as the FIDs. In this study, we examined the signal intensities using an SFR sequence of π/2 pulses by varying TR values from 2.1 to 40 μs. The time-domain signal intensity S(t_p) at a delay time t_p from the π/2 pulse is approximated to:

$$\text{S}\left(t_p\right)={\text{M}}_0\left[1-\exp \left(-{\text{R}}_1\text{TR}\right)\right]\exp \left(-t_p{\text{R}}_2^{*}\right),$$ (1)

for which M₀ is equilibrium magnetization. In SPI, image reconstruction is done by monitoring the phase of a single point in the FID at a chosen delay time (t_p) following the excitation pulse. The image pixel intensities reflect both R₁ and ${\text{R}}_2^{*}$ effects. Hence, it is possible to obtain pO₂ maps based on both R₁ and ${\text{R}}_2^{*}$ effects from the same data set.

3 |. METHODS

3.1 |. Chemicals

The trityl probe Oxo71, which is the deuterated form of Oxo63 at the methylene moieties indicated by asterisks in Figure 1A, was obtained from GE Health Care (Milwaukee, WI). Gas tanks of argon, air, and mixtures of 2% (±0.1%), 5% (±0.1%), 10% (±0.1%) oxygen with nitrogen were procured from local suppliers (Roberts Oxygen, Rockville, MD). Argon and medical air were used for 0% oxygen and 21% oxygen, respectively. The pressure of 21% O₂ after equilibration is 760 mmHg×0.21=160 mmHg, which is approximately 0.25mM O₂ at 25 °C.

FIGURE 1.

(A) The structure of triarylmethyl probe Oxo71. The asterisks indicate deuterated methylene moieties. (B) Schematic (left) and cross-section (right) of the 3-tube phantom showing the tubes filled with spin probe solution as filled circles

3.2 |. Animals

Female C3H Hen MTV mice, supplied by the Frederick Cancer Research Center’s Animal Production unit (Frederick, MD), were housed in a climate-controlled and circadian rhythm-adjusted room and allowed food and water ad libitum. Squamous cell carcinoma SCCVII cells were implanted (0.2–0.3 million cells/mouse were injected subcutaneously as 10⁶ cells suspension) in the right thigh. Approximate tumor size during experimentation was about 10 mm. Experiments were conducted in compliance with the Guide for the Care and Use of Laboratory Animal Resources (National Research Council, 1996) and were approved by the National Cancer Institute’s Animal Care and Use Committee.

3.3 |. Acquisition of calibration data

The spectral and imaging data were scanned on a home-built time-domain EPR imager described previously (NIH, Bethesda, MD)³⁸ and operating at 300 MHz. The power amplifier used in this study (BT0250-EF-RBB, Tomco Technologies, Norwood SA 5067, Australia) had a rise time and fall time of<20 ns, with a duty cycle of 5%. This allowed a repetition time TR of ~ 2 microseconds using pulse widths of 110 nanoseconds for a π/2 pulse. The pO₂ calibration experiments were performed using aqueous solutions of 2mM Oxo71 equilibrated at 5 oxygen levels (0%, 2%, 5%, 10%, and 21%) and 1, 5, and 10mM Oxo71 solutions equilibrated at 0% oxygen in separate glass tubes. Oxygen levels were achieved by bubbling the appropriate gas into the sample for about 45 min and were maintained by sealing with epoxy. Time-domain EPR signals were recorded by a series of π/2 pulses, separated by TR ranging from 2.1 to 40 μs at ambient temperature.

3.4 |. Phantom 2D imaging

Three tubes containing 2mM Oxo71 solution equilibrated at 0%, 2%, and 5% oxygen were mounted parallel to the magnetic field y axis in an equilateral triangular geometry in a plastic holder placed in a resonator of 25-mm diameter (Figure 1B). The phantom 2D data were acquired in the xz-plane (cross-section of the tubes) at ambient temperature using a 31×31 Cartesian grid; G_max =10 mT/m; 5,000 signal averages; a sampling dwell time of 5 ns; a flip angle of 90°; TR=3 to 40 μs; and dead time of 0.25 μs. Calculations and image reconstruction were done by MatLab (MathWorks, Natick, MA) scripts developed in-house.

3.5 |. In vivo imaging

A mouse was anesthetized by 2% isoflurane in medical air, mounted prone on a custom-designed holder, and maintained at a breathing rate of 60 per min and a core body temperature of 37±1 °C by a flow of warm air. The mouse body temperature was monitored by a nonmagnetic probe (FISO technologies, Quebec, Canada) inserted into the rectum. The urethra was cannulated using size 10 polyethylene tubing. The urine was drained during the experiment. A 30-G needle extended using size 10 polyethylene tubing was cannulated into the tail vein. The mouse thigh having the squamous cell carcinoma tumor was positioned in a 19-mm diameter resonator. Oxo71 solution at 75mM concentration was administered through tail vein cannulation by giving an initial bolus of 1.125 μmol/g body weight and continuous administration of 0.06 μmol/g/min subsequently to maintain a steady signal level. Images were acquired in the yz-plane, which corresponds to the sagittal plane on the mouse leg, at 21×21 phase encodings in the Cartesian grid by varying the TR from 2.3 to 40 μs.

3.6 |. Scan times

The data acquisition time for a single scan=TR×N_av×(N_k+1)+dT, for which N_av is the number of averages, N_k is number of all phase encodings, and dT is about 1 s—the sum of instrument delays before acquisition after changing the configuration or gradient. Background signals were acquired under identical conditions before the data acquisition. For phantom imaging, N_av=5,000 and N_k=31²; and scan times at TR=3.4, 8, 12, and 40 μs were 18, 40, 59 and 194 s, respectively. Approximate ${\text{R}}_2^{*}$ may be assessed by a single scan at a specific TR, whereas 3 scans at different gradient maxima are necessary to minimize edge artifacts. The scan time for ${\text{R}}_2^{*}$ mapping at TR=40 μs was 194 s and at TR=12 μs was 59 s. The scan time for 3 gradient scans performed at TR=8 μs was 120 s. The scan time for the estimation of R₁ from 22 TR values was 24 min, and from 3 TR values at 5, 8, and 12 μs was 125 s. For mice, N_k=21²; and single scan times at TR=3.4, 8, 12, and 40 μs were 9, 19, 28, and 90 s, respectively. The R₁ estimation from 23 TR values was 11 min.

4 |. RESULTS

4.1 |. Calibration parameters

The relationships 1) LW versus pO₂, for which LW $(\mathrm{\mu }\text{T})={\text{R}}_2^{*}/(28025\pi );2)$ LW versus [Oxo71]; and 3) pO₂ versus longitudinal relaxation rate R₁ were calculated from Oxo71 calibration spectral data. The apparent transverse relaxation rate ${\text{R}}_2^{*}$ was considered as the asymptotic ${\text{R}}_2^{*}$ value at a long TR (Figure 2A) to avoid echo contributions observed at short TR (Figure 2B). The linear fit of ${\text{R}}_2^{*}$-based LW to pO₂ in the range of 0% to 21% (Figure 2C) indicated the following relationship:

$$\text{LW}(\mathrm{\mu }\text{T})=0.1257{\text{pO}}_2(\text{mmHg})+\mathrm{8.786.}$$ (2)

FIGURE 2.

Dependence of R₁ on pO₂ for Oxo71. (A) Phantom imaging FID signals acquired at TR=12 μs. (B) Steady-state free precession FID profiles observed in phantom imaging at TR=2.1 μs. Note the beginning of echoes at the short TR. The echo is truncated by the TR. (C) Linear dependence of line width calculated from ${\text{R}}_2^{*}$ on pO₂. (D) The spectral peak heights normalized to M₀=1 as a function of TR in the range 2.1 to 40 μs at 0%, 2%, 5%, and 10% pO₂ of a 2mM Oxo71 solution. Observed data are shown by the symbol×, and continuous lines indicate the fit to Equation 5. Note the larger deviations at low TR values. (E) The deviations are reduced at low TR if the echo contributions are included in the fit. (F) Linear dependence of pO₂ on R₁. Standard errors of R₁ and R₂ are in the range of 0.0021 to 0.0165. LW, line width; PO₂, partial oxygen pressure.

Equation 2 was used directly to calculate a pO₂ map of the phantom from the LW. However, in vivo studies require correction for the self-broadening of [Oxo71]. The linear fit of LW to [Oxo71] in the range of 1 to 10mM at 0% pO₂ indicated that:

$$\text{LW}(\mathrm{\mu }\text{T})=0.5745[\text{Oxo}71](\text{mM})+\mathrm{6.733.}$$ (3)

Therefore, the following equation was used for pO₂ estimations from LW in vivo.

$$\text{LW}(\mathrm{\mu }\text{T})=0.1257{\text{pO}}_2(\text{mmHg})+0.5745[\text{Oxo71}](\text{mM})+\mathrm{7.637.}$$ (4)

Next, the R₁ value at each pO₂ was calculated by fitting the observed spectral peak height S_p as a function of TR (Figure 2D) according to Equation 5 below:

$${\text{S}}_{\text{p}}={\text{M}}_0\left[1-\exp \left(-{\text{R}}_1\text{TR}\right)\right].$$ (5)

S_p depends on the FID profile covered. The peak heights of the observed spectra $\left({\text{S}}_{\text{p}}^{\text{obs}}\right)$ were obtained by fast Fourier transform of the FID within a constant t_p range beginning right after the dead time and ending just before the intensity rise due to echo. The calculated peak heights $\left({\text{S}}_{\text{p}}^{\text{calc}}\right)$ were obtained by fast Fourier transform of simulated time-domain signals according to Equation 1 for given R₁, ${\text{R}}_2^{*}$, TR values, and a scaling factor to account for M₀ within the same t_p range. The Nelder-Mead simplex direct-search algorithm³⁹ was used by varying R₁ and the scaling factor. The R₁ values resulting in the smallest sum of squares of errors between ${\text{S}}_{\text{p}}^{\text{obs}}$ and ${\text{S}}_{\text{p}}^{\text{calc}}$ were determined. The S_p values shown in Figure 2D were scaled to a maximum of ~1 for each pO₂ separately because the peak heights decrease with increasing pO₂ levels. This fitting indicated larger deviations at low TR values (< 3 μs) owing to echo contributions. Furthermore, the intensity variation of 21% pO₂ was too small to determine R₁ accurately with a 300 MHz EPRI scanner. Therefore, we explored the peak height calculation, including the spin and stimulated echo contributions according to the procedure described by Gyngell.³² The fitting improved at low TR values, as expected (Figure 2E), but the R₁ value at 21% pO₂ remained approximately the same as previously estimated by Equation 1. It is likely a limitation of the SFR sequence for R₁ estimation that a significant fraction of the the signal is lost in dead time. The relationship between pO₂ and R₁ was found to be linear for pO₂≤10% (Figure 2F) according to Equation 1, as follows:

$${\text{pO}}_2(\text{mmHg})=122.22{\text{R}}_1(\text{MHz})-\mathrm{20.36.}$$ (6)

The advantage of Equation 1 over the procedure described by Gyngell³² is its ability to implement the SPI method when the interference from echo signals is negligible.

4.2 |. Phantom T₁-weighted imaging

2D images of the phantom were scanned by an SFR sequence in the TR range of 3.0 to 40.0 μs. At low TR values, the echoes led to ghosts at different scales and orientations, superimposed on the original image depicted in Figure 3A. This is in analogy to Nyquist N/2 ghosts in MR echo planar imaging.⁴⁰ The FOV, orientation, and intensity of a ghost depend on its phase and the time passed since its originating pulse at the current delay time (Figures 3A–3F). For example, at TR=3 μs and t_p=1.5, 1.75, and 2.25 μs, the image of original 3-tube phantom appears 4 times, twice in normal orientation and twice in inverted orientation (Figures 3B 3D). However, only 1 of those follows the expected intensity decay and phase evolution profile after a π/2 pulse, and the others are removed by fitting. Specific delay times for which the interference distorts the image, as shown in Figure 3C, are to be avoided by suitable choice of delay times (t_p). The early delay times were found to have fewer echo signals.

FIGURE 3.

The effect of spin and stimulated echoes at short repetition times for a phantom containing 3 tubes. (A–C) TR=3 μs and delay times of 1.0, 1.5, and 2.25 μs, respectively. (D–F) Delay time=1.75 μs and TR values of 3, 5, and 12 μs, respectively. The crosshairs are not part of the map. Notice multiple ghost 3-tube shapes of different sizes and orientations at TR=3 μs in C and D, for which 2 overlapping images are in normal orientation and 2 more are in inverted orientation of phantom in F at lower scales. These begin to disappear at TR=5 μs and are fully absent at TR=12 μs

Initially, the ${\text{R}}_2^{*}$ map was calculated from the pixel intensities of images at 5 delay times equally spaced from 1.0 to 1.4 μs because ${\text{R}}_2^{*}$ is required to estimate R₁ according to Equation 1. The k-space data were preprocessed prior to image reconstruction to correct for any zero shifts and weighted by a tapered cosine window to minimize ringing artifact from the tubes. All the images were reconstructed by scaling to the smallest FOV via chirp-z transformation. Any marginal FOV mismatches arising from inaccurate estimate of dead time were adjusted by recalculating the scaling factors to minimize the errors. Further reduction of ringing artifacts was accomplished by re-gridding of k-space, as previously described.¹⁷ The pixel intensities S(t_p) were normalized to account for the change in FOV and the spin density (S₀, pixel intensity at t_p=0), and ${\text{R}}_2^{*}$ maps were calculated by fitting to Equation 7, as described previously.¹⁸

$$\text{S}\left(t_p\right)={\text{S}}_0\exp \left(-t_p{\text{R}}_2*\right).$$ (7)

The R₁ estimation, however, needs only 1 delay point at different TR values. If the intensities at a specific delay are normalized to the longest delay by which the intensities reach a constant value asymptotically, the graphs of intensity as a function of TR will coincide for all the images at different single-point time delays and decay due to ${\text{R}}_2^{*}$ will be eliminated.

The intensities at the first delay time (t_p=1.0 μs) as a function of TR were chosen to estimate R₁ to take advantage of the higher SNR. R₁ and M₀ values were calculated for each pixel separately by fitting to Equation 1 because S(t_p) and ${\text{R}}_2^{*}$ are known. This M₀ map is merely a map of scaling factors obtained from the fitting that may have a complex relationship to the equilibrium magnetization, depending on the pO₂ map. The background regions containing essentially noise were masked prior to fitting to optimize the computation. The pixels at<5% of the maximum intensity were included in the mask.

The pO₂ estimation from LW and R₁ using Equations 6 and 2 is shown in Figure 4. The M₀ and R₁ maps were calculated including 22 TR values ranging from 3.4 to 40.0 μs at t_p=1.0 μs, and S₀ and ${\text{R}}_2^{*}$ were calculated at TR=40 μs from 5 t_p values equally spaced from 1.0 to 1.4 μs. In the M₀ map (Figure 4A), the intensities of 0% and 5% pO₂ tubes appear to be distinctly different, whereas this difference is smaller in the S₀ (TR=40 μs) map (Figure 4D). The contrast between the 3 tubes appears relatively more distinct in the R₁ map than in ${\text{R}}_2^{*}$ (Figures 4B and 4E). The contrast-to-noise ratios calculated from 0% and 5% pO₂ regions, considering the noise as RMS deviation, were 10.7 and 3.8 for R₁ and ${\text{R}}_2^{*}$ methods, respectively. However, the pO₂ maps obtained from both R₁ and ${\text{R}}_2^{*}$ are in agreement (Figures 4C and 4F), despite a better SNR of the pO₂ map derived from R₁. The calculation of the M₀ and R₁ maps was repeated, including only 3 TR values—5, 8, and 12 μs (Figure 5)—in order to check the feasibility of increasing the scan speed. These images are in good agreement with those calculated from 22 TR values (difference of means=0.65 mmHg and 1.96 SD=5.7 mmHg) (Supporting Information Figure S3), indicating the possibility of fast R₁ scans using 3 low TR values approximately in the range of 5 to 12 μs.

FIGURE 4.

Phantom images calculated using data acquired at 22 TR values (3.4, 3.8, 4.2, 4.6, 5, 5.5, 6, 6.5, 7, 7.5, 8, 9, 10, 11, 12, 14, 16, 20, 25, 30, 35, and 40 μs). Scan time=23 min. (A–C) M₀, R₁, and pO₂ maps, respectively. (D–F) S₀, ${\text{R}}_2^{*}$, and pO₂ maps calculated from 5 delay times from 1.0 to 1.4 μs at TR=40 μs. Scan time=3.2 m.M₀, equilibrium magnetization.

FIGURE 5.

Phantom images calculated from signal intensities at 3 TR values (5, 8, and 12 μs). Scan time=2 min. (A–C) M₀, R₁, and pO₂ maps, respectively. (D–F) S₀, ${\text{R}}_2^{*}$, and pO₂ maps calculated from 5 delay times from 1.0 to 1.4 μs at TR=12 μs. Scan time=1 min

The pixel histograms of 0%, 2%, and 5% oxygenated Oxo71 solutions (Figure 6) indicate better resolution of pO₂ in the maps derived from R₁ than from ${\text{R}}_2^{*}$. The pO₂ values calculated from the R₁ map are more uniform whether 3 or 22 repetition times were used (Figures 6A and 6B). pO₂ values of pixels (mean±SD) in the regions of 0%, 2%, and 5% pO₂ tubes were 0.68±0.20, 1.83±0.23, and 4.95±0.5%, respectively. In contrast, the ${\text{R}}_2^{*}$ map gave broader ranges of pO₂ values in all 3 regions, leading to higher overlap of histograms (Figures 6C and 6D). The mean±SD of pO₂ values for pixels in the regions of 0%, 2%, and 5% pO₂ were 1.58±1.02, 2.41±1.14, and 4.72±0.54%, respectively. The phantom study suggests that oximetry by R₁ yields not only more reliable pO₂ estimates but also better pO₂ resolution than the ${\text{R}}_2^{*}$ method, despite the linearity of ${\text{R}}_2^{*}$ with pO₂ over a wider range.

FIGURE 6.

Histograms of pO₂ maps in the regions of tubes at pO₂=0%, 2%, and 5%. (A) Calculated using R₁ derived from 22 TR values. (B) Calculated using R₁ derived from 3 TR values. (C) Calculated using ${\text{R}}_2^{*}$ derived from 5 points at TR=40 μs. (D) Calculated using ${\text{R}}_2^{*}$ derived from 5 points at TR=12 μs

4.3 |. In vivo imaging of mouse tumor

The mouse 2D projection image data were acquired by phase encoding in 21×21 Cartesian grid, and the images were reconstructed at a 256×256 matrix size. A steady infusion of Oxo71 was maintained to provide an adequate signal throughout the data acquisition. The ${\text{R}}_2^{*}$ and S₀ maps were calculated using 5 equally spaced delay times from 0.85 to 1.25 μs for 23 TR values ranging from 2.3 to 40 μs. Initially the M₀, R₁, and pO₂ maps were calculated at t_p=0.85 μs from these data, without correction for the variations in the infused Oxo71 probe. Comparison of the pixel intensity versus TR profiles of the phantom with those of the mice revealed differences. In the case of the phantom experiment, smooth profiles asymptotically reached a maximum, as expected (Supporting Information Figure S1A). In the case of the mouse experiment, the profiles were noisy, and the pixel intensity continued to increase up to the longest TR due to continuous infusion of the spin probe (Supporting Information Figure S1B). The intensity change due to the infused probe appeared to be linearly correlated with TR because the scan time is directly proportional to the local amount of probe in this case. The rate of increase in the signal due to probe infusion was estimated from TR=16 to 40 μs, for which the signal is expected to reach an asymptotic maximum level (99.8% for T₁=2.5 μs). Each profile was corrected for this variation, and M₀, R₁, and pO₂ maps were recalculated (Figure 7). Despite the correction, no appreciable improvement was observed in the R₁ maps, indicating the robustness of this method for a large number of TR values. A calculation using only 3 TR values (4.2, 6, and 12 μs) without applying this correction produced almost identical M₀ maps (Figures 7A and 7D), but the R₁ map differed in some regions (Figures 7B and 7E). However, the pO₂ maps obtained from R₁ measurement were homogeneous.

FIGURE 7.

In vivo R₁-based mapping of a mouse bearing a squamous cell carcinoma tumor. (A–C) M₀, R₁, and pO₂ maps calculated from signal intensities measured at 23 TR values (2.3, 3.2, 3.4, 3.8, 4.2, 5, 5.5, 6, 6.5, 7, 7.5, 8, 9, 10, 11, 12, 14, 16, 20, 25, 30, 35, and 40 μs). Scan time=10.8 min. (D–F) M₀, R₁, and pO₂ maps calculated using 3 TR values (4.2, 6, and 12 μs). Scan time=52 s. The background is masked in all maps. A region of interest covering high M₀ is indicated by the dashed contour line in all the maps to allow comparisons

5 |. DISCUSSION

This study provides an approach to calculate pO₂ from both R₁ and ${\text{R}}_2^{*}$ methods for the deuterated trityl probe Oxo71, which has a longer ${\text{T}}_2^{*}$ than Oxo63. The calibration graph shown in Figure 2F indicates a linear relationship between pO₂ and R₁ for pO₂≤10%. Because the linearity below 10% pO₂ is adequate for in vivo studies, extension to higher pO₂ levels is not addressed in this study.

Equilibration of 10% oxygen in water yields approximately 0.12mM oxygen dissolved at 25 °C. In vivo pO₂ in muscle tissues are reported to be around 40 mmHg,⁴¹ corresponding to 0.05mM oxygen at 37 °C. Most tissues have lower pO₂ than muscle, except for lung and arterial blood. Therefore, the linear range of pO₂ versus R₁ in this phantom study is adequate for most in vivo studies measuring pathophysiological tissue pO₂. The data for SPI-based R₁ estimation inherently contain data for ${\text{R}}_2^{*}$-based pO₂ mapping, which can estimate higher pO₂ ranges if desired.

Phantom imaging experiments suggest that the pixel intensities follow Equation 5 for a wide range of TR values fairly well at a constant delay time (t_p) (Supporting Information Figure S1A). Three TR values defining the intensity curve were found to be sufficient to produce a reliable pO₂ map in vitro, for which probe concentrations remain constant with time. Interestingly, the quality of both phantom and mouse images was unaffected by the echoes when suitable delay times and TR values were chosen. The choices of TR and t_p are not critical except for avoiding the overlap of ghosts, as shown in Figure 3C, for which the FOVs and phases of the original and ghost images are almost equal (which happens in special cases of TR <5 μs for Oxo71).

The estimation of R₁ in vivo by EPRI was previously reported by Epel et al. using the inversion recovery electron spin echo sequence π-T-π/2-τ-π-τ-echo.²⁴ Subsequently a comparison of various pulse schemes to measure R₁ by EPRI was reported by these authors,³⁴ for which an inversion recovery sequence was recommended for reliable spin probe concentration-independent pO₂ mapping. An SFR sequence can provide T₁-weighted maps from which pO₂ can be determined. Although the R₁ is not as accurate as the inversion recovery electron spin echo sequence, it offers faster scan speeds and high spatial resolution at low SAR. This single-pulse experiment is widely used in MRI to estimate R₁.^29,30,32 We chose rectangular hard pulses at a flip angle of 90° for this study, for which transverse magnetization did not completely decay at TR<3 μs. Optimization of this method using fewer TR values will reduce the scan times to acceptable levels for in vivo imaging, similar to ${\text{R}}_2^{*}$-based SPI oximetry. The phantom studies revealed that the ratio of SDs in ${\text{R}}_2^{*}$ versus R₁ methods for pO₂<2% is about 5, indicating the possibility of higher resolution by R₁ at pO₂ values below 2%. In SPI, the 1D spatial resolution Δ is given by FOV/N=2π/(γ_eG^maxt_p), for which N is the number of phase encodings; γ_e is the gyromagnetic ratio of the electron; G^max is the maximum gradient; and t_p is the delay time.²⁰ The ${\text{R}}_2^{*}$ computation involves FOV scaling while the t_p value is varied. The spatial resolution is 2mm for the mouse data at t_p=0.85 μs (1.7mm for the phantom at t_p=1 μs). However, a spatial resolution of 1.4mm (1.25mm for phantom) was realized in the pO₂ maps due to extension of k-space dimensions by the regridding necessary for ${\text{R}}_2^{*}$ estimation.

Experiments in this study were done with a single maximum-field-gradient configuration, although the multiple maximum-field-gradient configuration was proposed in a previous study¹⁸ to avoid the edge artifacts. The single maximum-field-gradient configuration causes alteration of SPI resolution, along with t_p.¹⁷ Due to edge artifacts in ${\text{R}}_2^{*}$ and S₀, some artificially high values unnaturally distributed on the edge of the object can be obtained. On the other hand, the R₁ and the M₀ estimations, along with TR, did not give such edge artifacts because a set of SPIs obtained at the identical t_p has the same resolution. The R₁ map was computed at shortest t_p value but at the same resolution applied to ${\text{R}}_2^{*}$. The images were reconstructed at a single t_p value with the best S/N ratio, reducing the uncertainties.

The mouse and phantom images at 5 delay times (t_p=0.85–1.25 μs) and 3 TR values (TR=4.2, 6, and 12 μs) are shown respectively in Figure 8 and Supporting Information Figure S2 in matrix form for better insights into the data. The M₀ and R₁ maps calculated at early t_p (0.85 μs in Figure 9 and 1.0 μs in Supporting Information Figure S2) are shown on the right, and the S₀ and ${\text{R}}_2^{*}$ calculated for each column are shown in the top 2 rows. Because the FOV changes with t_p but not by TR, the M₀ map resembles the images at shortest t_p. In contrast, the S₀ map depends on the intensity variations with t_p at each TR. The FID signal in some regions, for example, those having high pO₂ or low intensities, decays to noise faster than in the other regions, which leads to stronger contrasts in S₀ and ${\text{R}}_2^{*}$ maps. Further, the relaxation of transverse magnetization varies with TR, leading to differences in the S₀ and ${\text{R}}_2^{*}$ maps with TR. As a result, the SDs observed in pO₂ values based on ${\text{R}}_2^{*}$ are inherently higher. In addition, the accuracy of pO₂ estimates from ${\text{R}}_2^{*}$ depend on the ability to correct for self-broadening accurately. Although this is not obvious in the phantom in which which the concentrations are uniform, it is apparent in mouse imaging when a highly concentrated bolus of the spin probe distributes inhomogeneously in the body via systemic circulation, yielding a wide range of concentrations. This suggests that the use of R₁ is superior to ${\text{R}}_2^{*}$ for in vivo pO₂ studies. The advantage of SPI using an SFP sequence is fast data acquisition at the equivalent scan time of the multigradient approach previously reported for ${\text{R}}_2^{*}$-based oximetry.¹⁸

FIGURE 8.

Overview of R₁ and ${\text{R}}_2^{*}$ determination methods. Single-point images S(t_p) of a mouse leg bearing a squamous cell carcinoma tumor calculated at TR=4.2, 6, and 12 μs; and t_p=0.85, 0.95, 1.05, 1.15, and 1.25 μs are shown as a matrix. The images in the columns are used to calculate ${\text{R}}_2^{*}$ and S₀ maps. The images in the rows are used to calculate R₁ and M₀ maps. The images at longest TR (column at 12 μs) and shortest t_p (row at 0.85 μs) provide relatively better SNR

FIGURE 9.

Left: ${\text{R}}_2^{*}$ and S₀ calculated from single-point image intensities S(t_p) at TR=4.2, 6, and 12 μs; and t_p=0.85, 0.95, 1.05, 1.15, and 1.25 μs of a mouse leg bearing a squamous cell carcinoma tumor. Bottom right: M₀ and R₁ calculated at t_p=0.85 μs. Top right: The pO₂ maps calculated from ${\text{R}}_2^{*}$ at TR=12 μs and from R₁ calculated at t_p=0.85 μs. The relationship between ${\text{R}}_2^{*}$ and pO₂ is: pO₂ (mmHg)=7.957 LW (μT) − 4.571 [oxo71](mM) − 60.765, for which $\text{LW}(\mathrm{\mu }\text{T})={\text{R}}_2^{*}/(28025\pi )$ and the relationship between R₁ and pO₂ is pO₂ (mmHg)=122.21R₁(MHz) − 20.36

It has been shown by inversion recovery methods that R₁ is linearly proportional to pO₂ in the range of 0% to 21% for Oxo63.²⁴ In this work, although the range of pO₂ assessed by ${\text{R}}_2^{*}$ includes 0% to 21%, the R₁-based method limits the pO₂ range to 0% to 10% (Figure 2). This limitation arises from the availability of the FID signal after the dead time at a flip angle of π/2. Recall that the smaller flip angle limits the change in z-magnetization (M_z), and hence the accuracy of R₁ assessment. The best R₁ assessment is accomplished when pO₂ is close to 0% and scans include both low and high TR values to define the intensity versus TR profile adequately. About 12 TR values from 4.2 to 40 μs were found to be adequate for accurate pO₂ estimation by the R₁ method. Calibration experiments on individual Oxo71 solutions suggest that it is possible to attain a linear relationship between pO₂ and R₁ for pO₂<10%. The slope and intercept of Equation 6 are 122.22 and −20.35, with standard errors of±1.96, and±0.96, respectively. These values indicate that pO₂ can be determined at a resolution of 0.6 mmHg at 0% and ~3 mmHg at 10%. The sensitivities of both R₁ and ${\text{R}}_2^{*}$ methods were compared with the pO₂ levels estimated from phantom images. The R₁ and ${\text{R}}_2^{*}$ methods estimated 0% pO₂ as 5 and 12 mmHg, respectively. At 2% and 5%, the pO₂ estimations are closer to the expected values. The slope of observed versus expected pO₂ in the 0% to 5% range is closer to 1 for R₁ (slope=0.88) than ${\text{R}}_2^{*}$ (slope=0.71), indicating that pO₂ estimated by R₁ is more specific and more sensitive than the estimate by ${\text{R}}_2^{*}$. R₁ values estimated by 3 TR points indicated a lower slope of 0.84, pointing to a loss of sensitivity. Although SDs of histograms are expected to decrease with increasing the number of TR points, no apparent improvement was observed by increasing to 5 TR points. About 12 TR points (phantom scan time=14 min) (Supporting Information Figure S5) were found to be adequate to obtain SDs similar to those of Figure 6A. In order to perform 3D imaging in vivo, the scan time is to be reduced to under 10 minutes by constraining several parameters such as N_av=1,250; matrix size=19×19×19; partial k-space acquisition, and by excluding long TR (> 25 μs) values.

6 |. CONCLUSION

This study demonstrated the feasibility of mapping spin-lattice relaxation times based on SPI data collection and their use to determine spatially resolved oxygen levels in vivo. The scan time can be reduced to match conventional ${\text{R}}_2^{*}$ measurements by using a combination of relatively short TR data sets and further optimization. The single pulse sequence with variable TR is an attractive approach to evaluate R₁ for in vivo oximetry due its low SAR. The R₁ estimation by SPI simultaneously determines ${\text{R}}_2^{*}$. The fact that the R₁ method offers a more accurate pO₂ estimation with very little dependence on spin probe concentration, coupled with the intrinsic line width-independent high resolution and the relatively large effective uniform excitation band width, make this a highly practical approach for small animal EPR oximetric imaging.

Supplementary Material

Supplemental figures

FIGURE S1. The pixel intensity profiles as a function of TR. A. Phantom data in the 0% pO₂ region. B and C. In vivo data of a mouse tumor for the top 1000 pixels, before and after probe abundance correction, respectively.

FIGURE S2. Overview of R₁ and ${\text{R}}_2^{*}$ determination methods. Single point images of a three-tube phantom calculated at TR=5, 8, and 12 μs and t_p=1.0, 1.1, 1.2, 1.3 and 1.4 μs are shown in the black box. The rows above the box are the ${\text{R}}_2^{*}$ and S₀ maps calculated at the corresponding TR. Right, top row: The pO₂ map calculated from ${\text{R}}_2^{*}$ at TR=12 μs and the pO₂ map calculated from R₁. Right, bottom row: M₀ and R₁ maps calculated at t_p=1.0 μs are indicated by the red arrow.

FIGURE S3. Bland-Altman plot comparing pixel to pixel pO₂ values of the phantom calculated using (a) 22 TR values and (b) 3 TR values. The ordinate is (a) – (b) and the abscissa is their mean.

FIGURE S4. Relationship between R₁ determined by SFR sequence and ${\text{R}}_2^{*}$ of Oxo71 for pO₂ in the range of 0 – 10%.

FIGURE S5. A. Phantom pO₂ map calculated using data acquired at 12 TR values (4.2, 4.6, 5, 6, 7, 8, 10, 14, 20, 25, 30 and 35 μs). B. Histograms of pO₂ in the regions of tubes at 0%, 2%, and 5%. Scan time=14 min.