The ability to image the distribution of alveolar partial pressure of oxygen (pAO2) in the lung is an important development for the pulmonary physiology community as it provides a window through which regional gas exchange can be assessed in each of the functional units of the lung. Indirect techniques have been used to measure pAO2 in the whole lung (globally), using either fundamental relationships between mixed expired partial pressures of CO2, O2, and their arterial concentrations (1) or helium washout (2). Global pAO2 measurements, however, are insensitive to small and regional changes in the ventilation to perfusion ratio (VA/Q). Invasive regional measurements tested in animals (3, 4) are impractical in clinical applications. To monitor conditions such as cystic fibrosis and emphysema and to evaluate emerging treatment strategies, achieving a robust, noninvasive, high-resolution pAO2 imaging modality covering the entire human lung becomes increasingly desirable (5).
Hyperpolarized (HP) gas magnetic resonance imaging (MRI) has emerged over the past decade as a sensitive technique permitting direct visualization of gas in the airways and parenchyma (6). HP 3He, specifically, with an attractive safety profile and negligible blood uptake, has demonstrated unique potential to probe functional and structural aspects of the lung at the acinar level, including ventilation (7), diffusion (8), and most notably oxygen tension (9). Several pAO2 imaging schemes have been implemented in animals and humans (10–12). All of these techniques are based on the linear relationship between the O2-induced 1/T1 decay rate of 3He spin polarization and the local oxygen concentration reported by Saam et al. (13).
Assuming that depolarization of 3He in a living lung is entirely due to imaging-associated radiofrequency (RF) pulses (14) and interactions with oxygen, the pAO2 can be computed by measuring the combined relaxation rate. Decoupling these two dominant decay mechanisms is the challenge in this approach. pAO2 measurement techniques generally require a time-series of images during a 10–25 s breath-hold after the inhalation of a mixture of HP 3He and other gases (typically N2 and O2). Timing and ordering of the images may be chosen to maximize accuracy. Deninger et al. (15) originally differentiated O2-induced decay from that of RF-pulses by using two separate breath-holds with two different interscan time-delays. This double-acquisition approach was later replaced with an improved single acquisition scheme (Fischer et al. (10)), albeit on a single-slice basis. Yu et al. extended Fischer's scheme to multiple slices and optimized the RF-pulse flip-angle to minimize pAO2 uncertainty using a nonlinear timing pattern (16). However, only three slices (dorsal, middle and ventral) were imaged due to breath-hold time constraints and the chosen timing scheme. More recently, Miller et al. proposed a variable flip-angle pAO2 acquisition scheme over a shorter breath-hold (∼ 6 s) with a substantially reduced coupling between O2-induced and RF-decay mechanisms. This implementation was limited to projection images, largely to eliminate interslice diffusion effects (17). Spatial resolution in all three directions, however, is important in clinical and research applications, especially in heterogeneous lung disease where a projection or single-slice pAO2 map can mask important localized gas-exchange defects. To address this limitation, three-dimensional volume-localized measurements were introduced to minimize the effect of interslice diffusion (18, 19). These are especially useful if high resolution is sought in the slice direction but are nevertheless subject to ringing artifacts.
All of these techniques, including the present work, require proper coregistration of each voxel's gas content in the time-series of images. Lung motion (especially near the heart and diaphragm), gas flow, and intervoxel diffusion are not taken into account in the modeled signal dynamics and thus introduce errors into the derived pAO2.
Here, we present a robust, multislice imaging technique to measure the regional alveolar oxygen tension over the entire human lung with a satisfactory three-dimensional spatial resolution during a 12-s breath-hold, tolerable for most patients. The proposed technique is based on an interleaved slice ordering pattern and utilizes the interslice time-delays to acquire multiple slices within a given breath-hold, without sacrificing the O2-induced contrast. While acquisition of 12 stacked pAO2 maps (48 × 36) of the entire human lung is demonstrated here, the scheme can easily be adapted to attain the best possible resolution on a desired uncertainty. Given the length-scale of motion and diffusion artifacts, we limit spatial resolution to ∼1 cm, duplicate flip-angle measurements in the same breath-hold, and introduce a flip-angle fitting procedure to reduce residual coregistration errors. Furthermore, the effect of interslice and in-plane diffusion is simulated and minimized by introducing an interslice gap. It should be kept in mind that some deviations from the expected smooth pAO2 distribution may be attributable to intervoxel gas motion on the time-scale of oxygen-induced depolarization, particularly in disease. These deviations may be of diagnostic value even if their strict interpretation as alveolar oxygen tension is uncertain.
3He Spin-Relaxation Dynamics in vivo
The longitudinal relaxation rate (1/T1) of HP 3He gas in the presence of molecular oxygen at a given temperature T has been shown (13) to depend linearly on the oxygen concentration [O2]:
where T1, T, and [O2] are measured in s, K, and amagat, respectively. At body temperature, Eq. 1 yields:
with ξ = 1.95 × 103 Torr·s.
Assuming a slowly varying pAO2, and that 3He depolarization in the lung is dominated (20) by: (i) the dipole–dipole interaction of 3He nuclei with the magnetic moments of O2 molecules (Eq. 2), and (ii) tipping by RF-pulses used in imaging (with flip-angle α), 3He magnetization available to the nth acquired image in the series can be expressed as (16):
where M0 and Mn are the 3He magnetization levels in the initial and nth images, respectively, and tn(k) is the start time of the nth acquisition of the kth slice, α is the flip-angle due to the applied RF-pulse at the location of the voxel, and NPE is the number of the phase-encode gradients applied to the voxel per imaged slice. In the case of a time-varying pAO2, the value in Eq. 3 represents the average alveolar oxygen tension between t0(k) and tn(k).
pAO2 Acquisition Scheme
The choice of the time-delays separating the images acquired during a breath-hold is crucial to distinguishing the effects of the oxygen and RF-pulses, directly impacting the accuracy of pAO2 estimation. As can be seen from signal dynamics time dependence, the general approach is to utilize both short and long time-delays during a single breath-hold in order to constrain both depolarization mechanisms. A minimum of three images with different interscan time-delays is theoretically necessary to decouple the two effects successfully. Though not attempted here, a fourth measurement is required to constrain oxygen uptake in a single image series (9, 21).
Figure 1 compares our acquisition scheme (Fig. 1e) to earlier techniques. The single acquisition scheme (Fig. 1a), on which most pAO2 measurements in large species (pig, rabbit, and human) were based, is described in Ref. 10. The first two images are used to obtain an initial map of α, whereas the O2-induced relaxation rate is determined from the remaining images. This was generalized to multislice imaging (Fig. 1b) by acquiring entire slice stacks according to the single-acquisition scheme of Fig. 1a. The number of slices was limited to three (9), primarily because the α estimation becomes compromised as the initial delay between the same-slice scans is extended to accommodate additional slices. A different multislice implementation used a partially interleaved sequence (11), where each slice was first imaged twice (Fig. 1c) then ordered sequentially, similar to Fig. 1b. This made the quality of α estimates independent of the number of slices. In contrast, we apply the paired acquisition scheme not only to the initial pass but also to all of the following acquisitions in the breath-hold. This scheme can be implemented with or without a time-delay between each group of paired multislice acquisitions (Fig. 1d and e). In this study, time-delay is eliminated to enable comparisons with other techniques: two paired sets of interleaved 12-slice images are acquired; corresponding to four scans of each slice, during a 12-s acquisition time (Fig. 1e).
Imperfect registration of the image time-series dominates pAO2 estimation errors. This could be addressed through explicit image coregistration before extraction of the local pAO2 and flip-angle. Instead, we make use of the relatively large length scale of spatial variations in B1 field at the 3He frequencies at 1.5 T. This justifies spatial smoothing of the flip-angle map and reapplication of the corrected map to enhance accuracy.
In our case, the transmit coil is a rigid saddle coil. The intensity map of the saddle coil geometry has been well studied and parameterized; Hanssum (22) gives an analytic formulation in terms of a series expansion of the form:
where , and X, Y, Z are the voxel's Cartesian positions and R0 is the coil radius, and the coefficients are presented in Ref. 22. For flip-angle smoothing, we use Eq. 4 as an efficient basis-set in which geometrically plausible low-order coefficients can be extracted using polynomial regression, while high-order terms arising from noise and coregistration artifacts are rejected.
Imaging Parameter Optimization Through Simulation
In order to balance the signal-to-noise gains of a large flip-angle with the associated, undesirable depolarization, the acquired signal intensity S at a given voxel was simulated in terms of the available magnetization M and the RF-pulse flip-angle α, as described earlier (7), but with the image timing, localization, and resolution specific to this work (Fig. 1e). Signal intensity of the nth image was taken to be,
where Mn is as given in Eq. 3, flip-angles ranged over α =3°–7°, and nominal pAO2 values were 50–150 Torr.
First, the effect of an incorrect estimation of α on the resulting pAO2 value was modeled in the absence of noise. The simulated α value was varied ±30% away from nominal to generate four values of magnetization M, which were then fit to Eq. 3 with the nominal α to estimate pAO2. The relative error in estimated pAO2 was defined as δ pAO2 = (pAO2esimated - pAO2nominal) / pAO2nominal.
In the second simulation, the accuracy of pAO2 estimation as a function of signal-to-noise ratio (SNR) of the first time-point was assessed. Normally distributed noise (23) with a zero mean and a variance calculated from the nominal SNR value was added to the magnetization values M, which were then fit to Eq. 3 to estimate both pAO2 and α. This was repeated 1000 times for nominal α = 5° with pAO2 values of 50, 100, and 150 Torr. The relative average error in pAO2 was defined as δ pAO2 = (standard deviation of pAO2esimated)/pAO2nominal.
Finally, the effect of imperfect slice excitation profiles and interslice diffusion was assessed. These calculations were performed in the manner of Ref. 11, utilizing the asymmetric truncated sinc excitation waveform employed in the imaging studies and assuming a uniform initial magnetization and underlying pAO2. The imaging sequence of Fig. 1e was then applied using the same flip-angle and slice thickness (ST; 3.5° and 1.3 cm) used in the imaging studies. The interslice 3He magnetization diffusion was numerically computed as a function of the 3He diffusion coefficient, the interslice gap, and the pAO2 value.
A fourth set of simulations was pursued in order to compare the performance of the proposed acquisition scheme (Fig. 1e) to the other multislice methods (Fig. 1b,c). pAO2 estimation error of each technique was assessed as a function of the SNR in the first image of each sequence under identical imaging time and spatial resolution conditions. The imaging time was constant and equal to 12 s for all schemes. As a basis for comparison, the acquisition was designed to span 12 slices with 48 × 36 pixels in each, resulting in whole-lung acquisition-time of approximately 11.5 s (based on TR = 6.69 ms and NPE = 36). The sequentially acquired single acquisition scheme (Fig. 1b) requires a nonuniform interscan time-delay for convergence of the iterative reconstruction algorithm, meaning only three time points can be used with a 3-s delay between the second and third acquisitions. The interleaved slice ordering eliminated the need for the interscan time-delay, thus allowing four time points to be acquired in the breath-hold with an additional time-delay between the slice groups. In order to ensure a fair comparison between the schemes with different total number of RF-pulses and/or time-delays, for each strategy, α was optimized in each case. The signal intensity was then calculated for each according to Eq. 4 with identical initial magnetization. Simulations were performed for a nominal pAO2 = 100 Torr, as in the noise sensitivity analysis.
HP 3He Production
The imaging gas (3He:N2 = 99.19:0.81, Linde, Branchburg, NJ) was HP through spin-exchange collisions with optically pumped rubidium atoms (24) using a commercial polarizer (IGI 9600.He, GE Healthcare, Durham, NC). Polarization levels of 25–35% were achieved after ∼15 h of optical pumping. For each study, HP 3He gas was diluted based on the subject's total lung capacity using medical-grade nitrogen gas. The gas mixture was then dispensed into a Tedlar plastic bag (Jensen Inert Products, Coral Springs, FL) and transferred to the MRI scanner for administration.
All imaging studies were performed on a whole-body 1.5-T MRI scanner (MAGNETOM Sonata, Siemens Medical Solutions, Malvern, PA), using an 8-channel chest coil (Stark Contrast, Erlangen, Germany) tuned to the 3He resonance frequency of 48.48 MHz. In human experiments, 12 coronal slices were acquired using a gradient-echo imaging pulse-sequence with the field of view (FOV) = 40 × 30 cm2, ST = 13 mm, interslice gap = 20% ST, αnominal = 5°, matrix size = 48 × 36 pixels, NPE = 36, TR/TE = 6.69/3.1 ms. Using the interleaved acquisition scheme of Fig. 1e, four images of each of the 12 coronal slices (A to L) were acquired continuously in an “AABBCC…KKLLAABBCC…KKLL” pattern. With 8.3 × 8.3 × 15.6 mm3 voxel-size resolution, acquiring this pattern of 48 raw images took ∼ 12 s. Phantom projection images were acquired with the same pulse sequence except for the following imaging parameters: FOV = 35 × 26.3 cm2, ST = 250 mm, 7.3 × 7.3 mm2 planar resolution.
To demonstrate and validate the proposed pAO2 imaging technique, two phantom studies were performed. The first study used a pair of Tedlar plastic bags that were initially filled with known volumes of HP 3He and N2 mixtures, transferred to the scanner, and placed inside the imaging coil. Prior to imaging, variable quantities of O2 (shown in Table 1) were simultaneously injected into the bags using two graduated syringes connected to the input ports of the bags. The second study used a 50-mL glass syringe (BD Yale, Franklin Lakes, NJ). A custom-designed MRI-compatible automatic gas mixing and delivery device (7) was used to push a total of 40 mL of the gas mixture into the syringe. HP 3He used in the mixture was polarized in batches shared among the repeated measurements with the same gas concentrations. Following each measurement, the concentration of oxygen in the syringe was measured using a respiratory gas analyzer (GEMINI Respiratory Monitor, CWE, Inc., Ardmore, PA).
Table 1. The Summary of Phantom Studies in Tedlar Bags
Gas mixture (ml)
Measured and imaged PO2 values in Tedlar bags with different oxygen concentrations. Actual values refer to gas analysis results, whereas estimated values are based on PO2 imaging as described in the Data Analysis section.
The proposed pAO2 imaging technique was implemented and tested on four human subjects: one healthy nonsmoker (female, 53 years), one former smoker (male, 57 years), one asymptomatic long-time smoker (male, 47 years), and one heavy smoker patient with COPD (male, 64 years). On three separate days within a 2-week period, two pAO2 measurements were performed 10 min apart, resulting in a total of six separate pAO2 image series of each subject's lungs. On the first measurement of each day, anterior-to-posterior ordering of slices according to the scheme of Fig. 1e was used; in the second measurement, temporal ordering was reversed. However, in the data presented, slice numbers always refer to the physical ordering from anterior (#1) to posterior (#12). Subjects were in supine position in all experiments.
All experiments were conducted under a protocol approved by the Institutional Review Board at the University of Pennsylvania, and with informed subject consent. The subject's vital signs were continuously monitored throughout the imaging session, and a physician supervised the entire procedure. Prior to each pAO2 imaging session, 1H MRI was performed using the 3He administration protocol described below, with the HP gas mixture substituted by air.
3He imaging was performed during a breath-hold after inhaling a mixture of HP 3He, N2, and O2 at a prescribed ratio with FiO2 ∼ 21%. The volume of administered gas was adjusted to functional residual capacity (FRC) + 12% total lung capacity that was measured prior to each MRI session by plethysmography. The gas mixture was initially dispensed into a Tedlar bag, transferred to the bore of the MRI scanner, and connected to a three-way pneumatic valve that was also connected to the bag with O2 gas. Prior to the inhalation of the HP gas mixture, the subject was instructed to breathe normally over three breath cycles (inhale:exhale ∼ 3:4) at a uniform rate. The three-way valve was then actuated and the subject was allowed to inhale the entire contents of both bags simultaneously. In order to ensure adequate postinspiratory mixing of the gases and to minimize gas redistribution and flow artifacts in the measurements, imaging began ∼ 3 s after the beginning of breath-hold (total breath-hold ∼ 15 s). Upon completion of the imaging, the subject was instructed to exhale forcefully into the bag, from which end-tidal O2 and CO2 concentrations were measured using the respiratory gas analyzer.
The data analysis was performed using custom software developed by the MATLAB environment (MathWorks, Inc., Natick, MA). In human studies, analysis was done on a slice-by-slice basis. The signal in the acquired images was bias-corrected for the background noise according to: , where is the inherent noise in the MR image and is the average background signal intensity corresponding to a 10 × 10-pixel region far away from the lung in the acquired image. An SNR threshold was selected based on the first raw 3He image in the four-image time series in order to mask the background voxels.
Each voxel's signal-intensity drop in the consecutive four images was used in a least-square fit to Eq. 3 in order to extract the M0, α, and pAO2. After decoupling the flip-angle and pAO2 maps in the whole lung, the flip-angle values located in a predefined cube covering the heart were excluded from data. The remaining data were fit to the regression model described in the methods section. The maximum order of four (l + m + n ≤ 4, 30 terms in all) was used for the polynomial model in accordance with Hanssum's observations (22). This smoothed α was used again in a least-square fit of the four images to Eq. 3 to re-evaluate pAO2. After these computations, all voxels with pAO2 values outside the range of 0 < pAO2 < 200 Torr and flip-angles outside 0 < α < 10° were excluded.
To estimate and correct for the effect of oxygen uptake during the breath-hold, two otherwise identical image sets were acquired sequentially with anterior-first (A→P) slice ordering in the first set and posterior-first (P→A) in the second. A corrected image was generated by averaging these two pAO2 image sets. Oxygen uptake was estimated by calculating the difference r(z) between the median pAO2 values on a slice-by-slice basis, and fitting a line to r(z) as a function of slice position z, weighed by , where standard errors of the means (SEM) for each slice were estimated as , where σ and n are the standard deviation of pAO2 values and the number of valid voxels in the given slice, respectively. The slope of r(z) is related to the oxygen uptake rate R (assumed to be constant) as
Model Sensitivity and Noise Analysis
The relative error of pAO2 estimation as a function of the relative error in the assumed α value is plotted in Fig. 2a for three representative α values in the absence of noise. For the case of α = 5°, a 25% error in α leads to a 50% error in pAO2 estimation, assuming a nominal pAO2 = 100 Torr. Smaller α values reduce the sensitivity of pAO2 estimation to α errors, while larger values of α exacerbate that sensitivity, making the decoupling of the two signal-loss mechanisms more challenging. Figure 2b shows the pAO2 estimation sensitivity to α errors at a fixed nominal α = 5° for three representative pAO2 values. Lower pAO2 values are more susceptible to α estimation errors than higher ones.
The dependency of pAO2 estimation on noise, parameterized by SNR of the first image in the time series, is shown in Fig. 2c for three representative pAO2 values and a nominal α = 5°. The relative estimation error δPO2 with respect to true values of 50 < PO2 < 150 Torr with an SNR > 100 is less than 20% using the proposed interleaved pAO2 imaging technique. Within this range, sensitivity to noise increases monotonically with pAO2.
Technique Comparison and Optimal Flip-Angle
The average noise-induced relative errors of pAO2 estimations of the three acquisition schemes of Fig. 1b,c,e are compared in Fig. 2d as a function of SNR in the first image of each time series. The pAO2 estimation error was minimized as a function of α to yield the optimal flip-angle value (αopt) specific to each scheme. As shown in Fig. 3 for the four-point interleaved scheme (Fig. 1e), the optimal flip-angle is a function of the nominal pAO2 value. For the range of physiological pAO2 values (50–100 Torr), however, αopt = 5 ± 0.25°. Using this flip-angle, the four-point acquisition demonstrated a substantially better estimation error than the classic sequential three-point technique (using αopt = 6.3°) based on Fig. 1b, e.g. 20% versus 60% relative error for SNR = 60. The difference between the two four-point methods based on Fig. 1c and e was smaller. The interleaved scheme (using αopt = 5°), however, exhibited a somewhat better performance, especially for low SNR values, e.g., 32% versus 40% error for SNR = 40. Using three rather than four points in the interleaved scheme allows for a longer delay between acquisitions and improves the approximation (using αopt = 6°).
Interslice Diffusion Effects
Simulation of diffusion effects was performed throughout the physiologically expected range of diffusion coefficients, D = 0.02-0.8 cm2/s, an interslice gap between -25 and 25%, and a nominal pAO2 value of 100 Torr. As shown in Fig. 4, we find that interslice 3He diffusion can significantly bias the extracted pAO2 values, although a judicious choice of interslice gap is expected to limit the error to <1% over the range of diffusion coefficients typical of the healthy lung, and <10% in all but large airways and the most emphysematous regions of the lung. Simulations performed at different nominal values of pAO2 (not shown) indicate a qualitatively similar behavior, with near-zero error introduced for a 20% interslice gap and a D = 0.02 cm2/s typical of healthy lungs, although lower pAO2 values are more susceptible to the effects of interslice diffusion in the case of elevated D (e.g., 12, 9, and 4% error is introduced for D = 0.5 cm2/s and nominal pAO2 = 50, 100, and 150 Torr, respectively).
Representative PO2 maps measured in the Tedlar-bag phantoms are shown in Fig. 5a, corresponding to 28% (217.6 Torr) and 5% (38.1 Torr) O2 concentrations in the left and right bags, respectively. Table 1 summarizes the PO2 measurements in each bag for the six different O2 concentrations in comparison with the prepared O2 concentration in each bag. Results are expressed as the mean and standard deviation of the measured PO2 for all enclosed voxels in the bag. Neglecting wall relaxation effects, the average deviation between the actual and estimated PO2 values in the bags was 9.3 ± 5.7%, with a maximum discrepancy of 25.3 Torr. The estimated and actual PO2 values corresponded to a correlation coefficient of R = 0.993.
The PO2 measurements in the glass syringe phantom are summarized in Table 2 and compared with the averaged O2 concentration measurements using the respiratory gas analyzer. The variation in the actual O2 concentrations originates from the gas mixing and delivery device. The average deviation between the measured and estimated PO2 values in the glass syringe was 4.7 ± 4.1%, with a maximum discrepancy of 7.1 Torr. Figure 5b depicts the correlation plot between the estimated and actual PO2 values, indicating a significant correlation coefficient of R = 0.9993.
Table 2. Summary of Phantom Studies in Syringe
Number of Repeats
Actual values refer to the gas analysis results, whereas estimated values are based on PO2 imaging as described in the Data Analysis section. STD values are standard deviations calculated from the number of repeated measurements given in the first column.
Performing the measurements on a multislice basis resulted in a dataset consisting of twelve coronal slices of the human lung. Figure 6 shows a representative set of these measurements for the healthy subject using the four-point interleaved pAO2 imaging technique. The pAO2 maps for the odd-numbered slices are shown in the column from anterior to posterior. Figure 6a shows the SNR map for the first image in the series along with the decoupled α and pAO2 maps in Fig. 6b–c, respectively. The last row shows the pAO2 histograms for all 12 slices. Figure 6d shows the smoothed flip-angle maps after regression. The smoothing decreases the patchiness of the maps but leaves the overall mean almost unchanged, as shown in the histograms. The last column displays the recalculated pAO2 maps using corrected flip-angle maps. The whole-lung pAO2 means before and after the flip-angle correction differ by less than 1 Torr, though the latter is more symmetric.
The combined results for six pAO2 measurements in this healthy subject on three different days (two scans per day separated by at least 4 days) are shown in Fig. 7; only four middle slice images (## 5–8) are shown, while pAO2 distributions as a function of slice position are summarized using boxplots. Except for the most anterior and posterior slices, which are most affected by lung boundary motion artifacts and lower SNR, the slice position (i.e., gravity) and time (i.e., oxygen uptake) dependence of the pAO2 distribution is highly reproducible; visual differences between the boxplots are entirely due to the reversed slice ordering of every other acquisition.
All measurements were performed with the same total administered volume of 820 mL according to subject's 12% total lung capacity, and an identical mixture of 3He:N2:O2 = 440:200:180 with one exception; the subject did not make adequate effort on the last day's experiments to inhale the entire contents of both the 3He/N2 and O2 bags, which, judging by the exhaled residual gas volume in the bags, resulted in an FiO2> 21% as listed in Table 3. This effect is evidenced by a higher than normal pAO2 in the last measurement (129.3 ± 23.9 Torr over the entire lung), and also by the expiratory gas analysis results, ETO2 = 21.6%. Excluding this anomaly, the remaining measurements showed mean pAO2 values ranging within 100–120 Torr, in agreement with the corresponding gas analysis results, ETO2 = 16.6–19.4%. Excluding the last experiment, the same-day difference between corresponding slice averages never exceeded more than 4 Torr.
Table 3. Summary of Human Subjects pAO2 Measurements
Imaged whole lung pAO2(mean ± STD, Torr) for six repeated measurements in each human subject and exhaled end tidal gas analysis results.
Table 3 summarizes the pAO2 measurement results expressed as the mean and standard deviation of the whole lung in addition to the end-tidal expiratory gas sample analysis results in all experiments for each subject.
Figure 8 illustrates one representative slice (slice#7) of each subject from all six measurements in 3 days. The last row shows the whole lung histograms in all experiments for each subject. The nonsmoker shows the highest mean pAO2 values, although the subject with COPD shows higher regional values in specific areas and shows a broader distribution; this trend is seen to a lesser extent in the healthy smokers. Another trend, likely attributable to the subjects' increasing familiarity with the protocol, can be observed quantitatively in the increasing pAO2 values of a few percent each day. This was also observed qualitatively during the experiment as a more steady and complete inhalation of the bag contents.
Figure 9a shows pAO2 trends in all the experiments with respect to gravity-dependent slice position; bold-lines represent anterior-first and dashed-lines show the posterior-first acquisitions. Each subject had a reproducible overall trend of decreasing pAO2 in both anterior-first and posterior-first acquisitions along the physical anterior–posterior direction. The subject with COPD and the current smoker showed a more pronounced pAO2 drop in posterior slices. Figure 9b shows the difference between the anterior-first and posterior-first map medians for corresponding slice images along the lungs and a linear fit to these values. The slope can be decoded as a measure of oxygen uptake. The negative slope in most of the cases shows the oxygen uptake during the breath-hold time. The average among all of the subjects is (–1.20 ± 1.91) Torr/s, with a noticeably higher and more consistent value in the subject with COPD. Figure 9c shows the average of posterior-to-anterior and anterior-to-posterior pAO2 maps from same-day corresponding slices and a linear fit to the slice-averaged values. These averages correct for slice timing and oxygen uptake and display gravity-dependent effects. The figure shows a negative slope for all experiments with an average of (–1.65 ± 1.01) Torr/cm.
Accuracy of Measurements
The accuracy of the proposed pAO2 imaging scheme was validated in glass syringe phantoms, where the measured PO2 values were compared with the post-imaging gas analysis. Projection imaging was used to avoid diffusional coupling between slices (11). As shown in Fig. 5b and Table 2, the image-averaged mean PO2 values were within 7.1 Torr of the average O2 concentrations obtained from gas analysis data, over the broad 40–460 Torr range. This demonstrated excellent agreement between the two independent O2 concentration measurements and supports the use of the model given in Eq. 3, as well as the end-expiratory gas analysis. A more realistic phantom set-up consisting of two Tedlar bags allowed us to compare the results of PO2 imaging to the O2 concentrations determined from the amounts of gases used to fill the bags. As shown in Table 1, the differences between the imaged and the actual concentrations were within 15% over the range of 0–218 Torr, not exceeding 12 Torr for physiologically relevant concentrations.
As simulation results showed in Fig. 2a,b, the accuracy of the pAO2 measurements was very sensitive to the quality of the flip-angle estimation. This sensitivity, enhanced by the NPE exponent in Eq. 3, stems from the need to decouple the signal loss mechanisms due to O2 and the RF-pulses used in the imaging, as the flip-angle maps are determined from the same raw images that are used for pAO2 estimation. As the comparative simulations demonstrated in Fig. 2d, the proposed interleaved pAO2 measurement scheme maintains a more effective decoupling of these two signal loss mechanisms over a wide range of available SNR ratios and, as a result, exhibits a robustness in the presence of noise superior to previous reports (9, 11). This improvement is attained by making limited breath-hold time more efficient: by securing maximal disparity between short and long time intervals between same-slice images and by eliminating dead time-delays. In this scheme, the two adjacent back-to-back time points at the beginning and end of each image series are employed to enhance the effect of flip-angle and improve the decoupling quality. Moreover, this scheme mitigates the effect of early gas redistribution in the breath-hold and lung motion. The latter consideration, given extremely high errors associated with α estimation, justifies the use of this scheme with its repeated α estimate over the three-point interleaved acquisition, despite their similar relative error estimation shown in simulation (while in the absence of motion or gas flow).
As human images show (Figs. 6–8), the proposed interleaved pAO2 measurement technique is capable of approximating the pAO2 distribution over the entire human lung in a less than 15-s breath-hold. Repeated measurements, depicting similar histograms as well as distinguishable visual features (e.g., repeated areas of high or low pAO2 in the same region of the lung), suggest that the technique is robust and repeatable.
Other Possible Sources of Uncertainty
The quality of pAO2 images in the first and last slices can be markedly lower, as shown in Figs. 7 and 9. We attribute this phenomenon to partial volume effects, where subvoxel motion of the lung boundary in the slice direction can lead to inconsistent 3He signal intensities during the four acquisitions of a given slice, thereby reducing the fit quality. The errors due to the continuing gas redistribution in the lung during the breath-hold have been recently quantified in the rat model (25). However, that study required averaging over multiple breath-holds and would not be practical in humans. To diminish the measurement errors due to early gas redistribution and oxygen uptake in the lung, a 3-s delay between the beginning of the breath-hold and the start of the 12-s scan was introduced, and the second set of closely spaced image pairs was acquired at the end of the breath-hold.
Interslice diffusion of gas (primarily 3He, due to its large diffusion coefficient, but potentially also O2) can induce error in measurements because the gas in a given slice is partially substituted by gas from the neighboring slices through diffusion or pressure gradients. Using an interslice gap generally tends to skew pAO2 measurements toward lower values because the RF-depolarized gas is replaced with the gas in the gap compartment during the waiting period. Imperfect slice profiles, on the other hand, skew pAO2 values in the opposite direction; additional depolarization due to the excitation of neighboring slices makes the apparent relaxation greater, indicating a higher-than-actual pAO2. To minimize this uncertainty, a 20% gap was introduced between the slices as a balance between these two counteracting effects (i.e., slice centers offset from each other by 15.6 mm, with the ST reduced to 13 mm), in accordance with earlier studies (11, 26) and the simulation results presented here; the resulting error is likely negligible in the healthy lung parenchyma and small in any case (D = 0.02–0.5 cm2/s). Restricted diffusion length in human lungs (27) for this case was calculated to be 7 mm, less than the planar pixel size of 8.3 mm. Nonetheless, non-negligible in-plane diffusion is to be expected, which would either smooth the resulting pAO2 maps if the initial magnetization is uniform or introduce coupled errors in neighboring voxels if not. Notably, gradients in inhaled gas concentration, which are to be expected especially in diseased lungs, may locally skew the apparent pAO2 values because diffusion between regions then correspond to a gas (and the corresponding magnetization) flow. Neighboring regions will therefore exhibit skewed pAO2 values proportional to the 3He concentration gradient, which in turn leads to a wider dispersion. In either case, signal evolution alone cannot resolve the ambiguity, whether multislice or 3D imaging is performed; additional measurements that are directly sensitive to gas redistribution are required.
With no comparable techniques in the human lung available, the error introduced by lung and gas motion is not yet knowable. However, it is clear from a qualitative viewing of the oxygen maps that the local pAO2 is not always accurately represented. The subject with COPD, in particular, displays regions of elevated and depressed pAO2 that are near each other, a greatly broadened pAO2 histogram, and a non-negligible number of voxels with a derived pAO2 = 0. Such values are non-physical, likely indicating gas flow effects, and are seen to a lesser extent in the current and former smokers as well. While these observations highlight the need for care if the results are to be interpreted strictly as a locally accurate pAO2 map, features arising from air-trapping and other effects are indicative of anomaly and may therefore be diagnostically useful.
Gravity-Dependent Effects and Oxygen Uptake
An additional complication arises from oxygen uptake during the breath-hold. Oxygen uptake and concentrations in the lung are usually assumed to be near-constant during normal tidal breathing (9), although values can be different among individuals, especially when comparing healthy and diseased lungs. In breath-hold pAO2 measurements, however, the measured pAO2 value is affected by the physiological oxygen uptake uncompensated by breathing (28). It has been previously shown that the pAO2 level drops off fairly linearly during the first 12–15 s of a long breath-hold, after which it approaches equilibrium (18). The range of oxygen uptake rates reported in the literature is 1–5 Torr/s (11, 18). As described in Ref. 25, the lung-averaged uptake rate R may be estimated in terms of steady-state pAO2, tidal volume (TV), functional residual capacity (FRC), and breathing rate (BR) as:
The maps presented here should be regarded as representing the pAO2 at the middle of the period during which the four images of the corresponding slice were taken. This ranges from approximately 6 s after the beginning of the breath-hold for the first slice to 12 s for the last. We therefore expect a slice-dependent pAO2 gradient of ∼ 1.0 Torr/cm, resulting from slice timing, independent of any real gravity-dependent effects.
In order to verify and correct for this effect, two separate image sets were acquired with anterior-first and posterior-first slice ordering. The average of the pAO2 maps is expected to correct for oxygen uptake, with the derived maps corresponding to the pAO2 at ∼ 9 s into the breath-hold. The difference between these maps can be interpreted as a measure of oxygen uptake during the time span between the corresponding slice images. This time span ranges from ∼ 6 s for peripheral slices to 0 s for the central slice.
A summary of this analysis appears as Fig. 9. Notably, each subject displays a repeatable and characteristic pattern of pAO2 in the anterior–posterior direction (Fig. 9a). With the effect of slice ordering removed (Fig. 9c), each repetition for each subject shows a marked pAO2 gradient, averaging to (−1.65 ± 1.01) Torr/cm. Subtracting the two pAO2 maps (Fig. 9b) yields an average derived oxygen uptake rate of (−1.12 ± 1.91) Torr/s, consistent with the estimated 1.3 Torr/s of Eq. 6, although insensitivity to uptake in the central regions of the lung leads to a large uncertainty. The accuracy of the above analysis is limited by the coregistration of corresponding slice positions, the potential for variability in gas delivery, and the potential for different O2 uptake rates between the two measurements. We note that the subject with COPD showed a uniquely consistent and large oxygen uptake rate; we do not yet know the reason for this finding.
Before applying this technique to in vivo mapping of pAO2 in human lungs for clinical studies, the following challenges must be resolved: (i) maintaining the inhaled oxygen fraction (FiO2) at a standard 21%, (ii) quantifying the physiological uptake of oxygen by the lung during the imaging, and (iii) image coregistration errors due to heart and diaphragm motion. Keeping FiO2 close to the nominal 21% of room air is vital for a pAO2 measurement that correlates with the physiological state of tidal breathing. In our study, subjects practiced the breathing pattern several times. They were asked to deflate both 3He mixture and O2 bags completely to attain the prescribed gas concentrations. In three cases (nonsmoker, day 3, and former smoker, day 1, first repetition), the inhaled O2 concentration was affected by partial inhalation, which resulted in FiO2 deviating from 21% and led to erroneous pAO2 estimates. This was confirmed by the gas analysis of end-expiratory gas samples as shown in Table 3. We included these data as an additional demonstration of the sensitivity of the proposed technique to the overall O2 level and to emphasize the need for a reproducible inhalation protocol. It is also worth noting that deviations from the average physiological pAO2 level result in an exceptionally skewed histogram of the localized pAO2 values over the whole lung, which could be similar to the claims reported earlier by invasive regional pAO2 measurements in rabbit lungs (3).
A characteristic distortion pattern in pAO2 maps was seen around the heart as well as above the diaphragm in Fig. 7. Because local pAO2 value is the result of a fit to the raw signal amplitudes acquired at four interleaved time points over 6 s, even subvoxel motion contributes to errors in the resulting pAO2 and α values. In cases of the most severe coregistration errors, the affected voxels resulted in failed fits and were excluded by incorporating them into the mask. In less extreme cases, the fit quality estimated from the χ2 of the last iteration's nonlinear regression signified a markedly higher error around the heart and the diaphragm.
These limitations and potential inaccuracies aside, six experiments on each of four subjects displayed a strong correlation between the measured oxygen concentration of end-expiratory gas and the mean imaged pAO2 value over the subject's lung (correlation coefficient R = 0.805 with a P < 0.0001). It should be noted that a significant fraction of the end-expiratory gas comes from the dead space in the conductive airways and gas delivery apparatus, with little or no oxygen uptake (29), limiting direct comparison to the average intrinsic pAO2 value measured by our imaging technique. We therefore expect the end-expiratory values to be biased toward higher observed pAO2 values. Nevertheless, the strong correlation provides confirmation that the imaging technique is sensitive to small variations of global pAO2 in the human lung.
The proposed multislice interleaved pAO2 imaging scheme is a practical, robust method for the imaging of the pAO2 in human lungs with several demonstrated advantages over prior methods. By shortening the required breath-hold time while maintaining a strong decoupling of the effects of RF-pulses and the O2-induced relaxation, the four-point interleaved timing scheme improves both the SNR of the raw images and the intrinsic quality of the postprocessing analysis. The spatial resolution of the technique is near the limit of what is practical given expected intervoxel diffusive transport rates. Despite potential difficulty with strict interpretation of the resulting maps as pAO2 on a voxel-by-voxel basis, especially in disease, the scheme is sensitive to global alterations in pAO2 and has the potential to serve as a marker for the functional assessment of lung diseases that affect regional pulmonary gas exchange.