Investigating 3He diffusion NMR in the lungs using finite difference simulations and in vivo PGSE experiments

An overview of Helium-3 NMR: Recent developments and applications

The present review is focused on experimental and theoretical methods together with applications of helium NMR in chemistry and biochemistry. It comprises two main sections, the first dealing with standardization and instrumentation for 3He NMR spectroscopy and the second dealing with its practical applications, mainly those in general and organic chemistry with a special emphasis on the rapidly developing and exciting area of fullerenes encapsulating helium atoms. Several general applications of 3He NMR spectroscopy in physical chemistry and biomedicine are also briefly discussed.

In vivo methods and applications of xenon-129 magnetic resonance

Hyperpolarised gas lung MRI using xenon-129 can provide detailed 3D images of the ventilated lung airspaces, and can be applied to quantify lung microstructure and detailed aspects of lung function such as gas exchange. It is sensitive to functional and structural changes in early lung disease and can be used in longitudinal studies of disease progression and therapy response. The ability of 129Xe to dissolve into the blood stream and its chemical shift sensitivity to its local environment allow monitoring of gas exchange in the lungs, perfusion of the brain and kidneys, and blood oxygenation. This article reviews the methods and applications of in vivo129Xe MR in humans, with a focus on the physics of polarisation by optical pumping, radiofrequency coil and pulse sequence design, and the in vivo applications of 129Xe MRI and MRS to examine lung ventilation, microstructure and gas exchange, blood oxygenation, and perfusion of the brain and kidneys.

Comparison of 3 He and 129 Xe MRI for evaluation of lung microstructure and ventilation at 1.5T

BACKGROUND

To support translational lung MRI research with hyperpolarized 129 Xe gas, comprehensive evaluation of derived quantitative lung function measures against established measures from 3 He MRI is required. Few comparative studies have been performed to date, only at 3T, and multisession repeatability of 129 Xe functional metrics have not been reported.

PURPOSE/HYPOTHESIS

To compare hyperpolarized 129 Xe and 3 He MRI-derived quantitative metrics of lung ventilation and microstructure, and their repeatability, at 1.5T.

STUDY TYPE

Retrospective.

POPULATION

Fourteen healthy nonsmokers (HN), five exsmokers (ES), five patients with chronic obstructive pulmonary disease (COPD), and 16 patients with nonsmall-cell lung cancer (NSCLC).

FIELD STRENGTH/SEQUENCE

1.5T. NSCLC, COPD patients and selected HN subjects underwent 3D balanced steady-state free-precession lung ventilation MRI using both 3 He and 129 Xe. Selected HN, all ES, and COPD patients underwent 2D multislice spoiled gradient-echo diffusion-weighted lung MRI using both hyperpolarized gas nuclei.

ASSESSMENT

Ventilated volume percentages (VV%) and mean apparent diffusion coefficients (ADC) were derived from imaging. COPD patients performed the whole MR protocol in four separate scan sessions to assess repeatability. Same-day pulmonary function tests were performed.

STATISTICAL TESTS

Intermetric correlations: Spearman's coefficient. Intergroup/internuclei differences: analysis of variance / Wilcoxon's signed rank. Repeatability: coefficient of variation (CV), intraclass correlation (ICC) coefficient.

RESULTS

A significant positive correlation between 3 He and 129 Xe VV% was observed (r = 0.860, P < 0.001). VV% was larger for 3 He than 129 Xe (P = 0.001); average bias, 8.79%. A strong correlation between mean 3 He and 129 Xe ADC was obtained (r = 0.922, P < 0.001). MR parameters exhibited good correlations with pulmonary function tests. In COPD patients, mean CV of 3 He and 129 Xe VV% was 4.08% and 13.01%, respectively, with ICC coefficients of 0.541 (P = 0.061) and 0.458 (P = 0.095). Mean 3 He and 129 Xe ADC values were highly repeatable (mean CV: 2.98%, 2.77%, respectively; ICC: 0.995, P < 0.001; 0.936, P < 0.001). DATA CONCLUSION: 129 Xe lung MRI provides near-equivalent information to 3 He for quantitative lung ventilation and microstructural MRI at 1.5T.

LEVEL OF EVIDENCE

3 Technical Efficacy Stage 2 J. Magn. Reson. Imaging 2018.

3D diffusion-weighted 129 Xe MRI for whole lung morphometry

Purpose

To obtain whole lung morphometry measurements from ¹²⁹Xe in a single breath‐hold with 3D multiple b‐value ¹²⁹Xe diffusion‐weighted MRI (DW‐MRI) with an empirically optimized diffusion time and compressed sensing for scan acceleration.

Methods

Prospective three‐fold undersampled 3D multiple b‐value hyperpolarized ¹²⁹Xe DW‐MRI datasets were acquired, and the diffusion time (Δ) was iterated so as to provide diffusive length scale (Lm_D) estimates from the stretched exponential model (SEM) that are comparable to those from ³He. The empirically optimized ¹²⁹Xe diffusion time was then implemented with a four‐fold undersampling scheme and was prospectively benchmarked against ³He measurements in a cohort of five healthy volunteers, six ex‐smokers, and two chronic obstructive pulmonary disease patients using both SEM‐derived Lm_D and cylinder model (CM)‐derived mean chord length (Lm).

Results

Good agreement between the mean ¹²⁹Xe and ³He Lm_D (mean difference, 2.2%) and Lm (mean difference, 1.1%) values was obtained in all subjects at an empirically optimized ¹²⁹Xe Δ = 8.5 ms.

Conclusion

Compressed sensing has facilitated single‐breath 3D multiple b‐value ¹²⁹Xe DW‐MRI acquisitions, and results at ¹²⁹Xe Δ = 8.5 ms indicate that ¹²⁹Xe provides a viable alternative to ³He for whole lung morphometry mapping with either the SEM or CM. Magn Reson Med 79:2986–2995, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Diffusion lung imaging with hyperpolarized gas MRI

Lung imaging using conventional 1 H MRI presents great challenges because of the low density of lung tissue, lung motion and very fast lung tissue transverse relaxation (typical T2 * is about 1-2 ms). MRI with hyperpolarized gases (3 He and 129 Xe) provides a valuable alternative because of the very strong signal originating from inhaled gas residing in the lung airspaces and relatively slow gas T2 * relaxation (typical T2 * is about 20-30 ms). However, in vivo human experiments should be performed very rapidly - usually during a single breath-hold. In this review, we describe the recent developments in diffusion lung MRI with hyperpolarized gases. We show that a combination of the results of modeling of gas diffusion in lung airspaces and diffusion measurements with variable diffusion-sensitizing gradients allows the extraction of quantitative information on the lung microstructure at the alveolar level. From an MRI scan of less than 15 s, this approach, called in vivo lung morphometry, allows the provision of quantitative values and spatial distributions of the same physiological parameters as measured by means of 'standard' invasive stereology (mean linear intercept, surface-to-volume ratio, density of alveoli, etc.). In addition, the approach makes it possible to evaluate some advanced Weibel parameters characterizing lung microstructure: average radii of alveolar sacs and ducts, as well as the depth of their alveolar sleeves. Such measurements, providing in vivo information on the integrity of pulmonary acinar airways and their changes in different diseases, are of great importance and interest to a broad range of physiologists and clinicians. We also discuss a new type of experiment based on the in vivo lung morphometry technique combined with quantitative computed tomography measurements, as well as with gradient echo MRI measurements of hyperpolarized gas transverse relaxation in the lung airspaces. Such experiments provide additional information on the blood vessel volume fraction, specific gas volume and length of the acinar airways, and allow the evaluation of lung parenchymal and non-parenchymal tissue. Copyright © 2015 John Wiley & Sons, Ltd.

Dephasing and diffusion on the alveolar surface

We propose a surface model of spin dephasing in lung tissue that includes both susceptibility and diffusion effects to provide a closed-form solution of the Bloch-Torrey equation on the alveolar surface. The nonlocal susceptibility effects of the model are validated against numerical simulations of spin dephasing in a realistic lung tissue geometry acquired from synchotron-based μCT data sets of mouse lung tissue, and against simulations in the well-known Wigner-Seitz model geometry. The free induction decay is obtained in dependence on microscopic tissue parameters and agrees very well with in vivo lung measurements at 1.5 Tesla to allow a quantification of the local mean alveolar radius. Our results are therefore potentially relevant for the clinical diagnosis and therapy of pulmonary diseases.

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.

Finite element modeling of (129)Xe diffusive gas exchange NMR in the human alveoli

Existing models of (129)Xe diffusive exchange for lung microstructural modeling with time-resolved MR spectroscopy data have considered analytical solutions to one-dimensional, homogeneous models of the lungs with specific assumptions about the alveolar geometry. In order to establish a model system for simulating the effects of physiologically-realistic changes in physical and microstructural parameters on (129)Xe exchange NMR, we have developed a 3D alveolar capillary model for finite element analysis. To account for the heterogeneity of the alveolar geometry across the lungs, we have derived realistic geometries for finite element analysis based on 2D histological samples and 3D micro-CT image volumes obtained from ex vivo biopsies of lung tissue from normal subjects and patients with interstitial lung disease. The 3D alveolar capillary model permits investigation of the impact of alveolar geometrical parameters and diffusion and perfusion coefficients on the in vivo measured (129)Xe CSSR signal response. The heterogeneity of alveolar microstructure that is accounted for in image-based models resulted in considerable alterations to the shape of the (129)Xe diffusive uptake curve when compared to 1D models. Our findings have important implications for the future design and optimization of (129)Xe MR experiments and in the interpretation of lung microstructural changes from this data.

Probing lung microstructure with hyperpolarized noble gas diffusion MRI: theoretical models and experimental results

The introduction of hyperpolarized gases ((3)He and (129)Xe) has opened the door to applications for which gaseous agents are uniquely suited-lung MRI. One of the pulmonary applications, diffusion MRI, relies on measuring Brownian motion of inhaled hyperpolarized gas atoms diffusing in lung airspaces. In this article we provide an overview of the theoretical ideas behind hyperpolarized gas diffusion MRI and the results obtained over the decade-long research. We describe a simple technique based on measuring gas apparent diffusion coefficient (ADC) and an advanced technique, in vivo lung morphometry, that quantifies lung microstructure both in terms of Weibel parameters (acinar airways radii and alveolar depth) and standard metrics (mean linear intercept, surface-to-volume ratio, and alveolar density) that are widely used by lung researchers but were previously available only from invasive lung biopsy. This technique has the ability to provide unique three-dimensional tomographic information on lung microstructure from a less than 15 s MRI scan with results that are in good agreement with direct histological measurements. These safe and sensitive diffusion measurements improve our understanding of lung structure and functioning in health and disease, providing a platform for monitoring the efficacy of therapeutic interventions in clinical trials.

Response to Commentary on "The influence of lung airways branching structure and diffusion time on measurements and models of short-range 3He gas MR diffusion"

Our extensive investigation of the cylinder model theory through numerical modelling and purpose-designed experiments has demonstrated that it does produce inaccurate estimates of airway dimensions at all diffusion times currently used. This is due to a variety of effects: incomplete treatment of non-Gaussian effects, finite airway size, branching geometry, background susceptibility gradients and diffusion time dependence of the (3)He MR diffusion behaviour in acinar airways. The cylinder model is a good starting point for the development of a lung morphometry technique from (3)He diffusion MR but its limitations need to be understood and documented in the interest of reliable clinical interpretation.

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.

Achieving high spatial resolution and high SNR in low-field MRI of hyperpolarised gases with Slow Low Angle SHot

MRI of hyperpolarised gases is usually performed with fast data acquisition to achieve high spatial resolutions despite rapid diffusion-induced signal attenuation. We describe a double-cross k-space sampling scheme suitable for Slow Low Angle SHot (SLASH) acquisition and yielding an increased SNR. It consists of a series of anisotropic partial acquisitions with a reduced resolution in the read direction, which alleviates signal attenuation and still provides a high isotropic resolution. The advantages of SLASH imaging over conventional FLASH imaging are evaluated analytically, using numerical lattice calculations, and experimentally in phantom cells filled with hyperpolarised (3)He-N(2) gas mixtures. Low-field MRI is performed (here 2.7 mT), a necessary condition to obtain long T(2)(∗) values in lungs for slow acquisition. Two additional benefits of the SLASH scheme over FLASH imaging have been demonstrated: it is less sensitive to the artefacts due to concomitant gradients and it allows measuring apparent diffusion coefficients for an extended range of times.

The influence of lung airways branching structure and diffusion time on measurements and models of short-range 3He gas MR diffusion

Hyperpolarized (3)He diffusion experiments have been shown to be sensitive to changes in acinar structure due to emphysematous lung disease. Extracting quantitative information about lung microstructure from the diffusion signal is complicated due its dependence on a number of factors including diffusion time and the complex branching acinar geometry. A theoretical model (cylinder model) has been proposed as a means of estimating acinar airway dimensions from measured diffusivities. This model assumes that the effects of acinar branching geometry and finite airway length upon (3)He diffusion behaviour are negligible. In this work, we use finite element simulations of diffusion in a model of branching alveolar ducts to investigate in detail the effects of acinar branching structure and finite airway length on short-range (3)He diffusion measurements. The results show that branching effects have a significant influence upon (3)He diffusivity, even at short diffusion times. The expressions of the cylinder model theory do not account for significant dependences upon diffusion time, branching geometry and airway length, as a consequence of the oversimplified geometrical model used. The effect of diffusion time on (3)He ADC was also investigated through experiments with healthy human volunteers. The results demonstrate that the cylinder model can produce inaccurate estimates of the airway dimensions as a consequence of incompletely accounting for the diffusion-time dependence in the model equations and confirmed the predicted limitations of the cylinder model for reliable lung morphometry measurements. The results and models presented in this work may help in the development of a more realistic theoretical framework for 'in vivo lung morphometry' using (3)He diffusion MR.

Measurement of 129Xe gas apparent diffusion coefficient anisotropy in an elastase-instilled rat model of emphysema

Hyperpolarized noble gas ((3)He and (129)Xe) apparent diffusion coefficient (ADC) measurements have shown remarkable sensitivity to microstructural (i.e., alveolar) changes in the lung, particularly emphysema. The ADC of hyperpolarized noble gases depends strongly on the diffusion time (Δ), and (3)He ADC has been shown to be anisotropic for Δ ranging from a few milliseconds down to a few hundred microseconds. In this study, the anisotropic nature of (129)Xe diffusion and its dependence on Δ were investigated both numerically, in a budded cylinder model, and in vivo, in an elastase-instilled rat model of emphysema. Whole lung longitudinal ADC (D(L)) and transverse ADC (D(T)) were measured for Δ = 6, 50, and 100 ms at 73.5 mT, and correlated with measurements of the mean linear intercept (L(m)) obtained from lung histology. A significant increase (P = 0.0021) in D(T) was measured for Δ = 6 ms between the sham (0.0021 ± 0.0005 cm(2)/s) and elastase-instilled (0.005 ± 0.001 cm(2)/s) cohorts, and a strong correlation was measured between D(T) (Δ = 6 ms) and L(m), with a Pearson's correlation coefficient of 0.90. This study confirms that (129)Xe D(T) increases correlate with alveolar space enlargement due to elastase instillation in rats.

Acquisition of ³He ventilation images, ADC, T₂* and B₁ maps in a single scan with compressed sensing

In imaging of human lungs with hyperpolarised noble gases, measurements of apparent diffusion coefficient (ADC) and relaxation time provide valuable information for the assessment of lung microstructure. In this work, a sequence was developed for interleaved acquisition of ventilation images, ADC, T(2)* and flip angle maps in a single scan from the human lungs with a single dose of inhaled (3)He at 3 T. Spatially registered ventilation images with parametric maps were obtained. The total acquisition time was reduced by random undersampling of the k-space and reconstruction using compressed sensing (CS). The gain in speed was used for an increase in spatial resolution. Mean ADC values from the fully sampled and undersampled CS data exhibit no statistically significant difference in a given subject. The mean T(2)* values, however, were found to differ significantly, which is attributed to the combined effect of low signal-to-noise ratio (SNR) of the fully sampled data and the smoothing effect inherent in CS reconstruction.

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs.

Random walk simulation of the MRI apparent diffusion coefficient in a geometrical model of the acinar tree

Apparent diffusion coefficient (ADC) measurement in the lung using gas magnetic resonance imaging is a promising technique with potential for reflecting changes in lung microstructure. Despite some recent impressive human applications, full interpretation of ADC measures remains an elusive goal, due to a lack of detailed knowledge about the structure dependency of ADC. In an attempt to fill this gap we have performed random walk simulations in a three-dimensional geometrical model of the lung acinus, the distal alveolated sections of the lung tree accounting for approximately 90% of the total lung volume. Simulations were carried out adjusting model parameters after published morphological data for the rat peripheral airway system, which predict an ADC behavior as microstructure changes with lung inflation in partial agreement with measured ADCs at different airway pressures. The approach used to relate experimental ADCs to lung microstructural changes does not make any assumption about the cause of the changes, so it could be applied to other scenarios such as chronic obstructive pulmonary disease, lung development, etc. The work presented here predicts numerically for the first time ADC values measured in the lung from independent morphological measures of lung microstructure taken at different inflation stages during the breath cycle.

Quantification of lung microstructure with hyperpolarized 3He diffusion MRI

The structure and integrity of pulmonary acinar airways and their changes in different diseases are of great importance and interest to a broad range of physiologists and clinicians. The introduction of hyperpolarized gases has opened a door to in vivo studies of lungs with MRI. In this study we demonstrate that MRI-based measurements of hyperpolarized (3)He diffusivity in human lungs yield quantitative information on the value and spatial distribution of lung parenchyma surface-to-volume ratio, number of alveoli per unit lung volume, mean linear intercept, and acinar airway radii-parameters that have been used by lung physiologists for decades and are accepted as gold standards for quantifying emphysema. We validated our MRI-based method in six human lung specimens with different levels of emphysema against direct unbiased stereological measurements. We demonstrate for the first time MRI images of these lung microgeometric parameters in healthy lungs and lungs with different levels of emphysema (mild, moderate, and severe). Our data suggest that decreases in lung surface area per volume at the initial stages of emphysema are due to dramatic decreases in the depth of the alveolar sleeves covering the alveolar ducts and sacs, implying dramatic decreases in the lung's gas exchange capacity. Our novel methods are sufficiently sensitive to allow early detection and diagnosis of emphysema, providing an opportunity to improve patient treatment outcomes, and have the potential to provide safe and noninvasive in vivo biomarkers for monitoring drug efficacy in clinical trials.

Relationship between structural changes and hyperpolarized gas magnetic resonance imaging in chronic obstructive pulmonary disease using computational simulations with realistic alveolar geometry

Both the development of accurate models of lung function and their quantitative validation can be significantly enhanced by the use of functional imaging techniques. The advent of hyperpolarized noble gas magnetic resonance imaging (MRI) technology has increased the amount of local, functional information we can obtain from the lung. In particular, application of (3)He to measure apparent diffusion coefficients has enabled some measure of lung microstructure and airspace size within the lung. Models mimicking image acquisition in hyperpolarized gas MRI can improve understanding of the relationship between image findings and lung structure, and can be used to improve the definition of imaging protocols. In this paper, we review the state of the art in hyperpolarized gas MRI modelling. We also present our own results, obtained using a Monte Carlo approach and a realistic alveolar sac geometry, which has previously been applied in functional lung studies. In this way, we demonstrate the potential for models combining lung function and image acquisition, which could provide valuable tools in both basic studies and clinical practice.

Helium-3 diffusion MR imaging of the human lung over multiple time scales

RATIONALE AND OBJECTIVES

Diffusion magnetic resonance imaging (MRI) with hyperpolarized (3)He gas is a powerful technique for probing the characteristics of the lung microstructure. A key parameter for this technique is the diffusion time, which is the period during which the atoms are allowed to diffuse within the lung for measurement of the signal attenuation. The relationship between diffusion time and the length scales that can be explored is discussed, and representative, preliminary results are presented from ongoing studies of the human lung for diffusion times ranging from milliseconds to several seconds.

MATERIALS AND METHODS

(3)He diffusion MRI of the human lung was performed on a 1.5T Siemens Sonata scanner. Using gradient echo-based and stimulated echo-based techniques for short and medium-to-long diffusion times, respectively, measurements were performed for times ranging from 2 milliseconds to 6.5 seconds in two healthy subjects, a subject with subclinical chronic obstructive pulmonary disease and a subject with bronchopulmonary dysplasia.

RESULTS

In healthy subjects, the apparent diffusion coefficient decreased by about 10-fold, from approximately 0.2 to 0.02 cm(2)/second, as the diffusion time increased from approximately 1 millisecond to 1 second. Results in subjects with disease suggest that measurements made at diffusion times substantially longer than 1 millisecond may provide improved sensitivity for detecting certain pathologic changes in the lung microstructure.

CONCLUSIONS

With appropriately designed pulse sequences it is possible to explore the diffusion of hyperpolarized (3)He in the human lung over more than a 1,000-fold variation of the diffusion time. Such measurements provide a new opportunity for exploring and characterizing the microstructure of the healthy and diseased lung.

Theoretical prediction and experimental measurement of the field dependence of the apparent transverse relaxation of hyperpolarized noble gases in lungs

In this work, computer modeling based on a finite element method is used to simulate the T2* relaxation of hyperpolarized noble gases (HNG) in the lungs. A physical model of lung airways consisting of a phantom constructed from micro-capillary fibers of diameters similar to the size of lung airways with semi-permeable walls is also presented. The fibers are surrounded by a liquid medium (water) of magnetic susceptibility similar to lung tissue. Theoretical predictions of the field strength dependence of T2* for 129Xe in the phantom and in vivo rat lung are presented. These predictions are in good agreement with experimental T2* values obtained from the phantoms and in vivo rat lungs (160, 19 and 8 ms) at three different field strengths (0.074, 1.89 and 3T, respectively) using hyperpolarized 129Xe. The strong dependence of T2* on field strength is consistent with the theoretical prediction that low fields may be optimal for HNG MR imaging of the lungs as the decreased T2* at high fields necessitates an increase in bandwidth for conventional MR imaging.

In vivo lung morphometry with hyperpolarized 3He diffusion MRI: theoretical background

MRI-based study of (3)He gas diffusion in lungs may provide important information on lung microstructure. Lung acinar airways can be described in terms of cylinders covered with alveolar sleeve [Haefeli-Bleuer, Weibel, Anat. Rec. 220 (1988) 401]. For relatively short diffusion times (on the order of a few ms) this geometry allows description of the (3)He diffusion attenuated MR signal in lungs in terms of two diffusion coefficients-longitudinal (D(L)) and transverse (D(T)) with respect to the individual acinar airway axis [Yablonskiy et al., PNAS 99 (2002) 3111]. In this paper, empirical relationships between D(L) and D(T) and the geometrical parameters of airways and alveoli are found by means of computer Monte Carlo simulations. The effects of non-Gaussian signal behavior (dependence of D(L) and D(T) on b-value) are also taken into account. The results obtained are quantitatively valid in the physiologically important range of airway parameters characteristic of healthy lungs and lungs with mild emphysema. In lungs with advanced emphysema, the results provide only "apparent" characteristics but still could potentially be used to evaluate emphysema progression. This creates a basis for in vivo lung morphometry-evaluation of the geometrical parameters of acinar airways from hyperpolarized (3)He diffusion MRI, despite the airways being too small to be resolved by direct imaging. These results also predict a rather substantial dependence of (3)He ADC on the experimentally-controllable diffusion time, Delta. If Delta is decreased from 3 ms to 1 ms, the ADC in normal human lungs may increase by almost 50%. This effect should be taken into account when comparing experimental data obtained with different pulse sequences.

Simulations of short-time diffusivity in lung airspaces and implications for S/V measurements using hyperpolarized-gas MRI

We demonstrate a method for simulating restricted diffusion of hyperpolarized gases in lung airspaces that does not rely on an idealized analytic model of alveolar structure. Instead, the restricting geometry was generated from digital representations of histological sections of actual lung tissue obtained from a rabbit model of emphysema. Monte-Carlo simulations of restricted diffusion were performed in the short-time-scale regime, for which the time-dependent diffusivity is quantitatively related to the surface-to-volume ratio (S/V) of the pore space. In each of the eight samples studied, the S/V extracted from the simulated time-dependent diffusivity curves differed by less than 3% from direct assessment of S/V using image-processing methods. Simulated MRI measurements of apparent diffusion coefficients (ADCs) were performed in three representative lung sections to determine the effect of realistic gradient pulse shapes on the extracted S/V values. It was confirmed that ADCs measured at short diffusion times using either narrow or square gradient pulses yield accurate S/V values based on previously derived theoretical relationships. Simulations of triangular and sinusoidal diffusion-sensitizing gradients were then used to quantify the modifications required to extract accurate S/V values from ADC measurements obtained using more realistic gradient waveforms.

Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results

A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.

Time dependence of 3He diffusion in the human lung: measurement in the long-time regime using stimulated echoes

A stimulated-echo-based technique was developed to measure the long-time-scale apparent diffusion coefficient (ADC) of hyperpolarized 3He during a single breath-hold acquisition. Computer simulations were used to evaluate the performance of the technique and guide the selection of appropriate parameter values for obtaining accurate ADC values. The technique was used in 10 healthy subjects and two subjects with chronic obstructive pulmonary disease (COPD) to measure the global ADC for diffusion times between a few tenths of a second and several seconds, and to acquire spatial maps of the ADC for a diffusion time of 1.5 s. The reproducibility of the technique and its sensitivity to the direction of diffusion sensitization were also investigated. In healthy subjects, global ADC values decreased by severalfold over the range of diffusion times measured (mean values = 0.039 and 0.023 cm2/s at diffusion times of 0.61 and 1.54 s, respectively). ADC maps were generally uniform, with mean values similar to the corresponding global values. For the two COPD subjects, global ADC values were substantially greater than those of every healthy subject at all diffusion times measured. In addition, regional elevations of ADC values were far more conspicuous on long-time-scale ADC maps than on short-time-scale ADC maps.

In vivo lung morphometry with hyperpolarized 3He diffusion MRI in canines with induced emphysema: disease progression and comparison with computed tomography

Despite a long history of development, diagnostic tools for in vivo regional assessment of lungs in patients with pulmonary emphysema are not yet readily available. Recently, a new imaging technique, in vivo lung morphometry, was introduced by our group. This technique is based on MRI measurements of diffusion of hyperpolarized (3)He gas in lung air spaces and provides quantitative in vivo tomographic information on lung microstructure at the level of the acinar airways. Compared with standard diffusivity measurements that strongly depend on pulse sequence parameters (mainly diffusion time), our approach evaluates a "hard number," the average acinar airway radius. For healthy dogs, we find here a mean acinar airway radius of approximately 0.3 mm compared with 0.36 mm in healthy humans. The purpose of the present study is the application of this technique for quantification of emphysema progression in dogs with experimentally induced disease. The diffusivity measurements and resulting acinar airway geometrical characteristics were correlated with the local lung density and local lung-specific air volume calculated from quantitative computed tomography data obtained on the same dogs. The results establish an important association between the two modalities. The observed sensitivity of our method to emphysema progression suggests that this technique has potential for the diagnosis of emphysema and tracking of disease progression or improvement via a pharmaceutical intervention.

3D volume-localized pO2 measurement in the human lung with 3He MRI

A method for 3D volume-localized quantification of pO2 in the lungs is presented that uses repetitive frame 3D gradient-echo imaging of (3)He. The method was demonstrated by experiments on (3)He phantoms containing known concentrations of O(2) and in vivo on a group of three healthy human volunteers. The results were compared with those obtained by equivalent 2D thin-slice and 2D projection methodologies, and were found to be consistent with published results from the 2D projection methodologies (pO(2) = 0.09-0.18 bar). Studies performed on the same subject, on three separate occasions, demonstrated a repeatability of pO(2) measurement to within 14% using the 3D technique. Experimental differences between the 2D and 3D methods were substantiated with theoretical and numerical analyses of the signal decay, which took into account the effects of out-of-slice diffusion as a source of error in the thin-slice 2D experiments. It is shown that the 2D thin-slice technique systematically underestimates pO2 when there is significant gas diffusion (factor of 4 underestimate for D = 0.9 cm(2)s(-1) representative of free (3)He in air).

NMR measurements of hyperpolarized He3 gas diffusion in high porosity silica aerogels

Hyperpolarized 3He is used to non-destructively probe by NMR the structure of custom-made and commercial silica aerogels (97% and 98.5% porous). Large spin-echo signals are obtained at room temperature and very low magnetic field (2 mT) even with small amounts of gas. Attenuation induced by applied field gradients results from the combined effects of gas diffusion and confinement by the porous medium on atomic motion. Nitrogen is used as a buffer gas to reach equivalent 3He pressures ranging from 5 mbars to 3.5 bars. The observed pressure dependence suggests a nonuniform structure of the aerogels on length scales up to tens of micrometers. A description by broad phenomenological distributions of mean free paths is proposed, and quantitatively discussed by comparison to numerical calculations. The investigated aerogel samples exhibit different effective diffusion characteristics despite comparable nominal porosities.

Measurements and modeling of long range 3He diffusion in the lung using a "slice-washout" method

In healthy lung tissue, pulsed-gradient-spin-echo (PGSE) methods reveal apparent diffusion coefficients (ADC) of the order 0.20 cm2 s(-1); for diffusion times of approximately 2 ms. For these short diffusion times the ADC is only sensitive to structures approximately (2Dt)1/2 approximately 0.6mm in size. Recent work, using magnetic tagging of the longitudinal magnetization has revealed much smaller ADC values for longer length scales. In this work, the in vivo ADC from within the air-spaces, was measured using a new technique. The signal from a series of images was analyzed from a slice that was repeatedly imaged. Diffusion tends to "top-up" the non-renewable polarization within the slice, which leads to a non-exponential decay in image signal. Image data were compared to 1D finite-difference simulations of diffusion to calculate a long range ADC value. The results yield values of the order 0.034 cm2 s(-1), which are nearly an order of magnitude smaller than those reported by PGSE measurements at shorter diffusion times.

Finite-difference simulations of 3He diffusion in 3D alveolar ducts: comparison with the "cylinder model"

Time-dependent measurements of 3He diffusion in the lung could provide an accurate method to quantify alveolar length scales and the progression of diseases such as emphysema. However, the apparent diffusion coefficient (ADC) presents a complex problem to model and solve analytically. Here, finite-difference methods were used to simulate diffusion in 3D alveolar ducts. The results were compared to the only available analytical model--the "cylinder model"--from which it is possible to estimate the average radii of the alveolar ducts from in vivo data. The trend in data observed from simulations was found to agree well with the cylinder model. However, the cylinder model always overestimated the average radii of the simulated alveolar ducts. The simulations also demonstrated that the measurement of the longitudinal ADC (along the alveolar ducts) should be sensitive to early emphysematous changes, whereas the measured radii should be far less sensitive.

Restricted diffusion within a single pore

The time-dependent diffusion of 3Heatoms perpendicular to the axis of a single macroscopically large cylindrical pore is studied using a steady (or constant) gradient-recalled echo sequence. Measurements of the effective 3Hediffusion coefficient extending from the free-diffusion regime to the motionally averaged regime are presented, and are well-described by analytic solutions to the Bloch-Torrey equation based on the gaussian phase approximation. Our data yield the value 0.140(6)m2/s for the self diffusion coefficient of 3Heat a temperature of 296 K and a pressure of 1.00 Torr. Adaptations of these methods should enable the study of complex pore geometries as model systems.