Measurement of Pulmonary Partial Pressure of Oxygen and Oxygen Depletion Rate with Hyperpolarized Helium-3 MRI A Preliminary Reproducibility Study on Pig Model

Rational and Objectives

Pulmonary partial pressure of oxygen ( p O 2 ) and oxygen depletion rate ( R ) are two important parameters of lung function. The dependence of hyperpolarized 3 He (HP 3 He) T 1 on local oxygen concentration provides the basis for high-resolution mapping of the regional distributions of p O 2 and R in the lung. Although the oxygen-sensitive HP 3 He magnetic resonance imaging technique has been applied in human subjects and several animal species, reproducibility studies are rarely reported in the literature. This work presents a preliminary reproducibility study on a pig model. In this study, important scan parameters, such as measurement timing and flip angle, are optimized to minimize the noise-induced measurement uncertainty.

Materials and Methods

In the in vivo study, five normal pigs and one diseased pig with simulated pulmonary emboli were scanned with a small flip angle gradient echo sequence. The pulmonary oxygen measurement was repeated two to four times in each pig. In each measurement, a series of six images were acquired with optimal timing and flip angle. The parametric maps were generated using a bin-based data processing procedure that applied the multiple regression fitting method to extract the p O 2 and R . Variations of global mean, percentiles, and regions of interest were calculated from the maps to analyze reproducibility.

Results

The global statistical analyses show that average variation of global mean is 10.7% for p O 2 and 23.8% for R , and that the average variation of percentiles (10th, 25th, 50th, 75th, and 90th) and interquartile range is 14.8% for p O 2 and 30.4% for R . The region-of-interest analysis on the manually selected regions shows that the average variation of mean is 12.6% for p O 2 and 21.9% for R .

Conclusion

In this work, a preliminary study on the reproducibility of measuring p O 2 and R with HP 3 He magnetic resonance imaging on a pig model is presented.

Pulmonary partial pressure of oxygen ( p O 2 ) and oxygen depletion rate ( R ) are important parameters of lung function. The measurements of p O 2 and R give quantitative information on the efficiency of gas exchange within the lungs. Chronic obstructive pulmonary disease, pulmonary embolism, and most of the other diseases that affect regional ventilation-perfusion ratios disturb p O 2 and R ( ). Therefore, the accurate measurement of these parameters has the potential to serve as a sensitive marker for the early detection and diagnosis of lung diseases.

Traditionally, p O 2 could only be measured globally from the inspired and mixed expiratory gas, assuming a simple model of lung physiology ( ). In recent years, hyperpolarized 3 He (HP 3 He) magnetic resonance imaging (MRI) has been developed as a promising tool for the regional, sensitive, and noninvasive assessment of pulmonary parameters ( ). The application of this technique to pulmonary oxygen measurement has generated considerable interest because high-resolution mapping of regional p O 2 and R distributions not only enhances detection of lung pathologies, but also provides fundamental insights into the pathophysiologic mechanisms of disease ( ).

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Materials and methods

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Single-acquisition Technique Based on the Multiple Regression Method

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Sn=S0⋅(cosα)Nn⋅exp[−1ξ∫t(n)0pO2(t)dt], S

⋅

(

cos

⁡

)

⋅

exp

⁡

[

−

∫

(

)

(

)

]

where S 0 and S n represent the signal intensities of the initial and n th images, N is the number of phase encoding steps of an image, α is the flip angle, t(n) is the time at which the acquisition of n th image is completed, ξ = 1976.0 Torr/sec represents the 3 He relaxation coefficient at body temperature, and p O 2 ( t ) is the time-dependent oxygen partial pressure. It can be assumed that during the initial period of breathhold when the measurement takes place, p O 2 ( t ) can be approximated as a linear function of time ( ):

pO2(t)=p0−Rt, p

(

)

−

where p 0 is the initial oxygen partial pressure and R is the oxygen depletion rate, the speed at which oxygen diffuses from the alveoli into the blood. Substituting Eq 2 into Eq 1 and normalizing S n with respect to the initial signal S 0 yields:

En=ln(Sn/S0)=ε⋅n−1ξp0⋅t(n)+12ξR⋅t2(n), E

⁡

(

)

⋅

−

⋅

(

)

⋅

(

)

where ε=N1n(cosα). ε

(

cos

⁡

)

. In Eq 3 , the normalized signal intensity, E n , is a linear sum of the three parameters, ε , p 0 , and R , weighted by the associated functions n , t(n) , and t 2 (n) , respectively. Therefore, the multiple regression method can be used to extract the values of ε , p 0 , and R from a single series of acquired images ( ). The analytic uncertainty expression of each parameter in the presence of measurement noise can also be obtained. These expressions provide the basis for comparing the noise performances between different measurement schemes; an optimal scheme that yields minimal measurement uncertainties for p 0 and R can be found from a variety of possible choices.

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Polarized 3 He Production and Administration

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Animal Model

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Table 1

Global Partial Pressure of Oxygen Values for Repeated Measurements in the Hyperpolarized 3 He Pulmonary Oxygen Reproducibility Study in the Pig Model

Pig # Slice # Measurement # Variation of Mean (%) 1st 2nd 3rd 4th 1 1 127 ± 21 125 ± 19 — — 1.6 2 127 ± 18 125 ± 28 — — 1.6 3 114 ± 18 105 ± 23 — — 8.2 2 1 109 ± 14 105 ± 15 — — 3.7 2 94 ± 16 95 ± 17 — — 1.1 3 85 ± 15 87 ± 13 Expectation maximization Expectation maximization 2.3 3 1 67 ± 16 62 ± 18 59 ± 21 69 ± 23 15.6 2 76 ± 27 64 ± 28 60 ± 24 69 ± 30 23.8 3 59 ± 16 54 ± 13 62 ± 25 62 ± 23 13.5 4 ⁎ 1 182 ± 28 178 ± 26 156 ± 21 — 15.1 5 1 90 ± 11 94 ± 16 114 ± 12 — 24.2 2 89 ± 12 87 ± 14 103 ± 20 — 17.2 3 78 ± 7 81 ± 11 79 ± 14 — 3.8 6 † 1 109 ± 20 127 ± 19 — — 15.3 2 116 ± 22 128 ± 18 — — 9.8 3 100 ± 28 115 ± 30 — — 14.0

Values are listed in mean ± standard deviation (Torr) form. The last column is the variation of the global mean.

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Imaging

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Data Processing

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Sn=S¯¯2n−2π−−−−−−√σ¯2, S

−

where S n and Sn− S

− respectively denote the signal intensities before and after the correction; and σ¯ σ

¯ is the background noise, calculated as an average from a 5 × 5 region at the right-bottom corner of the image where no signal is contained. The second threshold was the pixel inhomogeneity inside a bin. The inhomogeneity was calculated as the ratio of standard deviation of pixel intensities over the average. A bin with an inhomogeneity greater than 0.4 was discarded for fitting. Such bins usually occurred at the edge of the lung, where only a portion of the pixels contained signal and a large signal variation existed.

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Reproducibility Analysis

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δ=max−minmean. δ

max

⁡

−

min

⁡

mean

Here max, min, and mean, respectively, stand for the maximum, minimum, and mean values of the repeated measurements.

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Results

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Table 2

Global R Values for Repeated Measurements in the Hyperpolarized 3 He Pulmonary Oxygen Reproducibility Study in the Pig Model

Pig # Slice # Measurement # Variation of Mean (%) 1st 2nd 3rd 4th 1 1 1.50 ± 1.00 2.22 ± 1.16 — — 38.7 2 2.19 ± 1.00 2.68 ± 1.44 — — 20.1 3 2.27 ± 0.98 3.26 ± 1.46 — — 35.8 2 1 1.64 ± 1.13 1.32 ± 0.90 — — 21.6 2 2.58 ± 1.03 2.43 ± 0.99 — — 6.0 3 2.38 ± 0.91 2.51 ± 0.94 — — 5.3 3 1 1.43 ± 0.94 1.45 ± 0.90 1.75 ± 1.19 1.99 ± 1.21 33.8 2 1.84 ± 1.51 1.54 ± 1.25 1.77 ± 1.31 2.07 ± 1.53 29.4 3 1.53 ± 0.93 1.41 ± 0.90 2.24 ± 1.47 2.31 ± 1.31 48.1 4 ⁎ 1 3.77 ± 1.77 1.29 ± 1.00 1.00 ± 0.70 — 137.1 5 1 0.72 ± 0.42 0.49 ± 0.41 0.89 ± 0.45 — 57.1 2 1.56 ± 0.55 1.08 ± 0.53 1.59 ± 0.77 — 36.2 3 1.61 ± 0.39 1.39 ± 0.55 1.39 ± 0.52 — 15.0 6 † 1 2.05 ± 0.70 1.98 ± 0.69 — — 3.5 2 2.41 ± 0.80 2.24 ± 0.93 — — 7.3 3 2.34 ± 0.57 2.34 ± 0.83 — — 0.0

Values are listed in mean ± standard deviation (Torr) form. The last column is the variation of the global mean.

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Table 3

Statistical Results of the Percentile Analysis on the Reproducibility of Partial Pressure of Oxygen

Pig # Slice # Variation of Percentile of p 0 Interquartile Range 10th 25th 50th 75th 90th 1 1 5.1 4.4 0.9 2.5 2.7 31.8 2 13.6 6.3 2.9 5.1 7.9 52.9 3 15.3 17.1 15.1 4.4 1.8 40.0 2 1 1.9 7.1 5.2 0.5 2.3 28.4 2 0.8 1.4 2.0 0.9 0.5 1.4 3 11.0 4.8 2.9 3.5 0.9 2.6 3 1 41.9 20.9 17.2 15.9 16.3 28.9 2 52.2 30.4 22.8 18.5 19.0 22.9 3 27.8 7.6 15.9 16.3 26.8 42.3 4 ⁎ 1 12.7 13.3 16.0 17.1 17.6 39.8 5 1 27.4 24.9 23.2 22.1 21.4 8.8 2 17.2 15.9 14.1 15.6 21.9 27.5 3 10.0 4.1 3.4 5.6 10.5 54.2 6 † 1 20.3 15.8 13.4 16.3 8.4 18.5 2 15.2 11.5 11.6 6.4 5.5 12.1 3 13.3 16.8 18.0 11.4 9.6 2.7 Average of variations_17.9_12.6__11.5__10.1__10.8__25.9

The variations of five percentiles (10th, 25th, 50th, 75th, and 90th) and interquartile range (25–75%) are calculated.

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Table 4

Statistical Results of the Percentile Analysis on the Reproducibility of R

Pig # Slice # Variation of Percentile of R Interquartile Range 10th 25th 50th 75th 90th 1 1 48.7 33.5 56.2 51.1 30.8 62.4 2 3.3 8.5 14.4 25.8 29.7 42.6 3 27.7 33.0 31.6 43.3 29.9 54.0 2 1 138.4 30.3 9.5 0.3 32.9 16.6 2 19.5 4.4 5.5 0.4 2.6 7.9 3 13.8 12.3 2.8 1.8 2.1 16.3 3 1 83.8 26.6 37.1 34.7 36.6 39.9 2 53.0 34.9 30.2 38.1 24.6 40.0 3 88.9 44.6 57.3 42.6 49.1 48.9 4 ⁎ 1 187.7 160.0 152.6 139.4 121.1 124.5 5 1 127.8 108.1 76.1 50.4 37.8 11.5 2 69.3 47.0 38.0 29.9 39.2 3.8 3 47.6 26.7 16.2 17.8 6.7 6.3 6 † 1 1.9 5.5 10.4 1.3 7.6 5.1 2 32.6 23.6 9.7 0.5 4.7 36.4 3 20.9 10.5 1.5 4.2 11.9 33.1 Average of variations_51.8_30.0__26.4__22.8__23.1__28.3

The variations of five percentiles (10th, 25th, 50th, 75th, and 90th) and interquartile range (25–75%) are calculated. The hyperventilated case is excluded when calculating average of variations.

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Discussion

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Conclusions

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References

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Measurement of Pulmonary Partial Pressure of Oxygen and Oxygen Depletion Rate with Hyperpolarized Helium-3 MRI A Preliminary Reproducibility Study on Pig Model

Rational and Objectives

Materials and Methods

Results

Conclusion

Materials and methods

Single-acquisition Technique Based on the Multiple Regression Method

Polarized 3 He Production and Administration

Animal Model

Imaging

Data Processing

Reproducibility Analysis

Results

Discussion

Conclusions

References

Further Reading

A Robust Method for Estimating Regional Pulmonary Parameters in Presence of Noise

Abstracts of Funded National Institutes of Health Grants

Advances in Physiologic, Metabolic, and Molecular Lung Imaging