Controlling the Diffusion of ³He by Buffer Gases as a Structural Contrast Agent in Lung MRI

 

R. H. Acosta¹, P. Blümler*¹, L. Agulles-Pedrós^1,3, A. E. Morbach², J. Schmiedeskamp³,
A. Herweling⁴, U. Wolf², A. Scholz⁴, W. G. Schreiber², W. Heil³, M. Thelen² and H. W. Spiess¹

 

 

Abstract:

The influence of the pulse sequence and the diffusion coefficient on the appearance of MRI of (hyperpolarized) gases is analysed using basic theoretical concepts. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. Their molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this enables images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

 

 

Introduction:

In physiological applications of imaging techniques the fundamental quest is for improved resolution and contrast. MRI has undergone a tremendous development from this point of view with images from lungs using hyperpolarized gases as one of the recent highlights [1].

This application became possible because hyperpolarization is most successful in gases using optical techniques for spin polarization, which makes ³He and ¹²⁹Xe the primary candidates for MRI-investigations of hollow cavities in materials and the human body. Despite the important fact that now for the first time non-invasive, non-radioactive, high resolution imaging of the respiratory system was possible, the increase in polarization by up to 5 orders of magnitude was also believed to boost the principle resolution in MRI significantly. A drawback of this approach, however, is the fact that only gases can be hyperpolarized which directly costs 3 orders of magnitude in sensitivity due to lower density. In addition, the rapid kinetics of the gas particles increases the diffusion constants by 5 orders of magnitude when compared to that of liquids. The typical strategy to reduce the influence of diffusion by applying a burst of 180°-pulses [2] in a CPMG-type sequence is problematic in the non-equilibrium state of polarization, because imperfections in the rf-homogeneity will cause a very rapid depolarization, if applicable at all due to the very strict limits of rf-irradiation in clinical practice. Therefore, rapid data acquisition is the commonly used approach to minimize the influence of diffusion on the MRI-signal. Of course the timing of sequences is constrained by technical and safety limits for the gradient strength and rise time, which typically causes TE > 0.5 ms corresponding to a mean diffusive path length of about half a millimetre for ³He.

Fortunately, this effect is less dramatic if this mean path length is restricted by the size of the voids, as it is the case in the lung. However, broad distributions of void sizes (e.g. in the lung) will then cause very different image intensities in complex structures. The essential parameters which control the influence of diffusion on the MRI-signal are the sequence timing, the gradient strength and the diffusion coefficient. While the gradient strength and timing is predefined by the field of view and the spatial resolution additional delays in the sequence and the diffusion coefficient can be varied to optimize the contrast for structural elements. As temperature and pressure are no variables in most clinical applications, at first sight, the diffusion coefficient of hyperpolarized ³He doesn’t seem to be a variable that can be controlled. Such control can however be achieved by mixing ³He with was altered by mixing it with inert buffer gases of different molecular mass.

The purpose of this communication is the presentation of the principle idea of contrast optimization by using buffer gases to a medical oriented readership. Although this has relevance for all MRI using gases, the strongest effects will be observed in sequences that employ strong gradients, as it is the typical case in NMR-microscopy. Emphasis is put on the sequence timing and gas mixtures can be used to tailor the image contrast by introducing a structural threshold. All the details of the theory, gas handling, NMR measurements and data analysis will be published elsewhere [3].

 

Theory:

Diffusion Limited Sensitivity and Resolution:

Because of the enormous diffusion coefficients in gases even simple MR-images are strongly diffusion weighted, in particular when the object contains large voids which do not spatially restrict the diffusive motion. Therefore, simple gradient echo sequences without additional diffusion gradients shall be subject to the discussion. In such a simple imaging experiment (i.e. when the switching time of the gradient can be neglected) the signal attenuation, E, due to diffusion is usually related to the experimental b-value [4],

                                                      (1)

with g as the gyromagnetic ratio, G the gradient strength, δ the duration of a gradient pulse and D as a possible delay between the starting points of the bipolar gradient pulses (cf. Fig. 1). Because time enters the equation in the 3^rd power, it is most effective to reduce the influence of diffusion on the signal by reducing d and D as much as technical and safety limits allow. The gradient strength is then determined by the necessary field of view (FOV) to place n points across the sample. From this a spatial resolution, Dr, can also be defined (ignoring influences of the line width and data post-processing)

                                                                       (2)

Hence, this predefines the strength and duration of the read-gradients. For the moment there is no need to include additional diffusion weighting by setting D different from d.

Between excitation and detection (a duration of 2d) the mean path of a diffusing spin is

                                                                                                                             (3)

along the direction of the gradient. The time during which the phase of the spins are influenced by diffusion and the free (unrestricted) diffusion coefficient, D₀, then can be used to define a critical size, r_c

                                           with                                        (4)

This is a very coarse approximation, which will be refined later. For the moment it should just clarify that for a pore with radius smaller than r_c the apparent diffusion coefficient is determined by the pore size and for all voids with bigger diameters the diffusion is essentially free.

However this puts a very stringent limit to the achievable spatial resolution, as it becomes clear when eqns. (2) and (3) are substituted into eq. (1) [5]

                                                                                          (5)

This means that if the spatial resolution, Dr, should be set well below this critical size  the signal in eq. (5) will vanish rapidly, i.e. the pore cannot be resolved.

Assuming that the timing is already minimised, eq. (4) states the only parameter left to manipulate is D₀. A lower D₀ would decrease r_c; hence increase the signal and the spatial resolution. For a given volume the diffusion coefficient is proportional to

                                                                                                                          (6)

with T as the absolute temperature and p the pressure of the system, which are both typically not variables (in biomedical applications). However, D₀ can be lowered by admixture of inert buffer gases of high molecular mass, M, and/or large collision cross-sections, σ, acting as spatial restrictions for the light ³He in the gas phase.

 

Binary Gas Mixtures:

The diffusion coefficient in a gas mixture without spatial restrictions is given by the sum of the individual diffusion rates weighted by their molar fraction [6, 7]. Hence, for a binary mixture of helium (He) and a buffer gas (BG)

                                                                                                              (7)

However, the relevant diffusion coefficient for MRI is not that of the bulk mixture (D_mix), but rather that of the signal carrying isotope (here ³He) in various dilution, so that eq. (7) has to be modified [8]

                                                                                              (8)

where x is the molar fraction of ³He and D the diffusion coefficients with nomenclature: of ³He in the mixture with BG, D_He for pure ³He (x = 1) and  of ³He in infinite dilution  in the buffer gas. Table 1 shows the obtained values [3, 9] for ³He as a spatially unrestricted gas within three binary mixtures. This demonstrates in agreement with eq. (6) how buffer gases with high molecular masses can effectively reduce the diffusion of ³He by a factor 3 – 4, becoming minimal when there is no signal carrier (³He) left in the mixture as , or as the NMR-signal vanishes.

The attenuation of a MRI-signal in binary gas mixtures with variable concentration is a combination of eq. (1) with (8) scaled by a signal proportionality to x

                                                               (9)

This functionality is shown as the curves in Fig. 2 for the gas pair ³He/SF₆ at three different b-values with a maximum at position

                                   (10)

within the physically reasonable range of x depending on b. For larger b-values the signal at this maximum can exceed the one for pure ³He quite significantly (cf. Fig. 2b). Hence, the somewhat paradox situation arises, that less substance results in increased MRI-signal, as illustrated by Fig. 3. It should be mentioned, that such a pronounced maximum is only observable for high b-values and the entire discussion strictly only holds for the relatively uninteresting case of unrestricted diffusion.

 

Restricted diffusion:

Real objects show restrictions of the free diffusive path. Even if their dimension is much larger than the critical size defined in eq. (4) it has to fit into a coil of finite length, causing reduced diffusion close to all internal surfaces (an effect usually described as “edge enhancement” [10, 11]. The analytical solution of the signal attenuation in pores is determined by the shape of the pore, which for lungs will be a fractal object of branching cylinders of decreasing size (the terminal alveoli might be better approximated by spheres, but this geometrical detail is neglected). The exact solution for diffusion perpendicular to the cylinder axis observed by the experiment in Fig. 1 is given by [12]

                                 (11)

and D₀ the coefficient for unrestricted diffusion. The a_m are the roots of the spatial derivative of the first order Bessel function of the first kind

                                                                    (12)

Equation (11) is a refinement of eq. (4) resulting in a power of ca. 4 rather than 2 dependence of the apparent diffusion coefficient for the pore radii, r, below the critical radius, as it can be seen from Fig. 4d.

 

Methods and Materials:

Batches of ³He were polarized in a home built, large scale polarizer located at the department of Physics (University of Mainz), which produces a typical polarization of 60% at 3.3 bar·l/h [13]. The polarization is achieved via metastable spin exchange [14]. Transport cells of iron-free glass (Supremax glass, Schott, Mainz, Germany), were filled with 2.1 bars of 60% hyperpolarized ³He. Subsequently, the cells were placed in a container with a permanent shielded low-field (0.8 mT) magnet [13] and transported to the MRI Laboratory in the Max Planck Institute. Helium is then stored in very homogeneous magnetic field of 2.5 mT, generated by five coaxial coils of 45 cm diameter and of a total length of 70 cm.

For the experiments (Figs. 2 and 3) the ³He was filled at varying pressure into the previously evacuated sample cell. In a second step this volume was equilibrated to 1 bar. In successive steps small amounts of buffer gases (here SF₆) were added. The amount was roughly controlled by pneumatic valves operated by the spectrometer. Subsequently the mixture was expanded to 1 bar and the exact amount of gas was determined by the NMR-signal intensity of ³He in a separate experiment. The details of this procedure will be published elsewhere [3].

The data in Figs. 2 and 3 were acquired in a 4.7 T horizontal, 20 cm bore magnet (Magnex Scientific Ltd., UK) equipped with actively shielded gradients (capable to produce gradients up to 0.3 T/m) from Bruker (Bruker Biospin GmbH, Germany). The gradients were driven by amplifiers from Copley (Copley Controls Corp., USA).  A birdcage-coil with an inner diameter of 21 mm from Bruker was used for rf excitation and detection. The gradients and the RF were controlled from a Maran DRX console (Resonance Instruments Ltd, Witney, UK) which runs under a Matlab12 (MathWorks Inc., USA) home made software environment.

The data in Fig. 2 were measured by a 1D version of the sequence in Fig. 1 (no phase gradient) using an excitation pulse of 2 μs, which corresponds to a tip angle of 3°. A total of n = 32 points were recorded and 4 times accumulated, the echo maximum was then extracted and displayed in the graph. The gradient strengths and duration are given in the figure caption. Small corrections due to finite rise times [15] of the gradients had to be included, which were determined from observations on an oscilloscope. The direction of G_read was set parallel to the sample tube axis (z-direction) to allow unrestricted diffusion. Because the dwell time of the receiver was altered during this procedure, the signals were normalised to that of pure ³He of each run.

For the images in Fig. 3 a sample tube was filled with different concentrations of ³He/SF₆ using the same technique as described above. The sequence of Fig. 1 was used to acquire a 64 ´ 64 matrix with a hard rf pulse of 5 ms length corresponding to a 5° tip angle. The spectral width was set to 50 kHz which results in a field of view of 28 ´ 28 mm² with G_read = G_phase = 53 mT/m. The delay between experiments was 10 ms and 4 scans were accumulated resulting in a total acquisition time of 3 s per image.

After further studies on phantoms with restricted geometries [9] lung images of a porcine model were acquired (cf. in Fig. 5) using a whole body magnet with a field strength of 1.5 T (Siemens Magnetom Vision, Siemens Medical Solutions, Erlangen, Germany). A custom-built chest coil (Fraunhofer Institute, St. Ingbert, Germany) was used for rf transmission and reception. The coil design comprised a dual ring construction with a sensitive volume of 450 ´ 365 ´ 340 mm³ (L ´ W ´ H). It was manually tuned to the ³He Larmor frequency at 48.4 MHz. A slice selective gradient echo sequence (cf. Fig. 1) with additional gradient weighting was used with the b-values given in the figure captions. Five slices of 2 cm thickness were acquired with the following parameters: tip angle ca. 6°, TE = 6 ms, TR = 16.1 ms, FOV = 32 cm, a 64 ´ 128 (phase ´  read) data matrix was acquired in one scan.

With approval of the animal care committee, a domestic pig (mass: 20 kg) was anaesthetized and tracheal tube inserted. The lungs were flushed with pure nitrogen for about 15 min using a servo ventilator 900C (Siemens-Elema) with a tidal volume of 400 ml and a respiratory frequency of 40 min^-1 using volume controlled ventilation. To avoid asphyxia the anesthetised animal was killed by a potassium overdose. 45 min post mortem the first set of images (Fig. 5a) was acquired after applying a ³He-bolus of 178 ml (x = 0.089). The flushing was repeated to replace N₂ with ⁴He and imaged after 2.5 h with a ³He bolus of 210 ml (x = 0.105 shown in Fig. 5b). Finally the helium was replaced by SF₆ and Fig. 5c was acquired with a ³He bolus of only 112 ml (x = 0.056) 5 h after onset of death.

 

 

Results and Discussion:

The possibility to enhance the MRI-signal significantly by diluting the detected gas by inert buffer gases of high molecular weight is clearly demonstrated in Fig. 2. These data also validate a sufficient accuracy in the theoretical description which led to eqs. (9) and (10). Clear maxima in the MRI-signal intensity are revealed at the predicted gas concentrations, where a signal gain of E(x_max) = 18 was measured for ³He in SF₆ and sufficiently high b-values. It must be emphasized that these signal gains are not absolute but by definition only with respect to the pure ³He gas. Of course higher signals (cf. eq. (9)) are observed for lower b-values, which might be sufficient for clinical MRI. However, considerations of the nature and concentration of the gas mixture are of importance when either b or x is predefined. Practical examples are strongly diffusion weighted sequences or “microscopic” MRI. The latter case is illustrated in Fig. 3, where the “paradox” case is illustrated, that less signal-carrier can result in higher signal intensity. One should not forget that this description and observation is only valid for unrestricted diffusion, which might be interesting for imaging larger cavities in the body (trachea, bronchi and sinus).

However, the smaller structures of the respiratory system are usually first affected by pulmonary diseases. As discussed in eq. (4) there is a critical size below which the diffusion coefficient is controlled by the size of the cavity and the only parameters which influence this critical limit are the diffusion time and coefficient. Their influence on the MRI-signal is illustrated in Fig. 4, which is a calculation of eq. (11) for the range of sizes in a human lung (Ranging from a diameter of 3 cm for the trachea down to 200 μm for the alveoli. The steps in between were adopted from [16]). Of course this is a coarse approximation of the real situation, because demagnetization and relaxation effects are neglected as well as the various (non isotropic) orientations of the cylindrical segments of the bronchi tree with respect to the direction of the gradient.

From Fig. 4a it becomes evident, that there is a pronounced step in the contrast between the smaller and the larger structures. The point of inflection is well approximated by  as defined in eq. (4). However, the contrast between the signal originating from smaller and larger structures is determined by a combination of these times with the used gradient strength, i.e. the b-value. This is shown in Fig. 4b, where the gradient strength is varied for a fixed diffusion time resulting in great signal changes for the larger voids and no influence on the structures below r_c. Similar observations are observed for changing the buffer gas with which ³He is mixed, as demonstrated in Fig. 4c. However, in this case both features, r_c and contrast, are influenced. Therefore, knowledge about the approximate size distribution in a sample and the diffusion coefficients of the mixing pair “signal-“ and buffer-gas is required to optimize the contrast in complex samples. Although these principles were validated on phantoms consisting of tubes of various diameters [3], it must be mentioned that eq. (11) neglects effects described “motional narrowing” [11], which will cause additional complication of description. Figure 4d also shows the ADCs for the three gas mixtures. From this it can be seen that the principal behaviour in the restricted and free domain is only scaled by the diffusion coefficients.

To demonstrate the possibility to use such buffer gases as structural contrast agents, the lung of a dead, ventilated pig was imaged using hyperpolarized ³He in mixtures around x = 0.08 (assuming a total lung volume of 2 l) with the gases ⁴He, N₂ and SF₆. Special care was taken to replace all residual gases from previous experiments by extensive ventilation cycles.

Figure 5 shows the resulting images. The experiments in the first row were acquired without an additional diffusion gradient. Therefore, they possess a relatively low b-value when compared to the microscopic MRI of Fig. 3. Due to the different amounts of ³He and continuous spatial changes in the lung over the long experimental time, it is difficult to quantify the signal changes. However, a visual comparison might be sufficient to appreciate the change in contrast in different structural elements (e.g. the trachea and non-dependent parts of the bronchial system when compared to the dependent parts, i.e. the alveoli) by changing the buffer gas. From ⁴He (Fig. 5a) to SF₆ (Fig. 5c) the trachea and main bronchi become more visible. On the other hand, the images with light buffer gases reveal more detail (cf. Fig. 5a1), because only the very small structures contribute to the signal. This observation resembles the calculated contrast curves in Fig. 4c.

In order to quantify to some extend the contrast due to changes in the b-value for the three buffer gases, an additional bipolar gradient in sagittal direction was added to the otherwise unchanged sequence. The second row of Fig. 5 shows a quotient image of the ones in the top row by this strongly diffusion weighted experiments. Of course the signal ratio is highest for the large airspaces (see trachea). However, this ratio decreases going from helium (Fig. 5a2) to SF₆ (Fig. 5c2), because the diffusion is slowed down more effectively by the heavier buffer gas. These quotient images also reveal very clearly that similar processes can be obtained in the next smaller airspaces (e.g. bronchi lob. caud., which become clearly visible in Fig. 5a2). Hence the contrast in the quotient images is biggest in Fig. 5a2 and reaches noise level in Fig. 5c2 as predicted in the previous calculation.

 

Conclusion:

Buffer gases with low molecular mass (e.g. ⁴He) can be used to keep the diffusion coefficient high in the applied gas mixture (or in the case of hyperpolarized ¹²⁹Xe even increase it) while heavy gases (e.g. SF₆) can be used for the opposite. Such differences in the inhaled gas mixture can cause significant changes of the image contrast for suitably chosen b-values. While mixtures with high diffusion coefficients can be used to suppress the larger airways, a complete, unbiased image can be obtained for the mixtures with low diffusivity. Of course the binary mixtures used in this study have to become ternary including sufficient oxygen.

While a change of the breathing gas might be impractical for clinical investigations, these two scenarios might have an assistive influence on the choice of gas-mixtures depending on the type of experiment to follow. For instance, experiments which locally determine the diffusion coefficients [17] can profit from a lower D, because it would make the experiment more reliable and less critical in the timing. However, the opposite approach seems to have more importance, because an increase of the diffusion coefficient will allow to tailoring the image contrast to originate mainly from structures below an adjustable size. If this is a certainty the image resolution can be reduced, because a visual selection of ROIs excluding larger bronchi is no longer necessary. A reduced resolution, however, will increase the signal which can then be used to reduce the measurement time or acquire additional positions.

 

Acknowledgements:

We want to thank Manfred Hehn and Hanspeter Raich (MPI for Polymer Research) for  their help in the design and construction of the gas handling system at the MPI-P.

Financial support by DFG (Forschergruppe “Bildgestützte zeitliche und regionale Analyse der Ventilations - Perfusionsverhältnisse in der Lunge“) and a special grant of the Max Planck society made this work possible.

 

References:

1.             Goodson, B.M., Nuclear Magnetic Resonance of Laser-Polarized Noble Gases in Molecules, Materials, and Organisms. J. Magn. Reson., 2002. 155: p. 157-216.

2.             Durand, E., et al., CPMG measurements and ultrafast imaging in human lungs with hyperpolarized helium-3 at low field (0.1 T). Magnetic Resonance in Medicine, 2002. 47(1): p. 75-81.

3.             Acosta, R.H., L. Agulles-Pedrós, and P. Blümler, unpublished results. 2004.

4.             Stejskal, E.O. and J.E. Tanner, Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient. J. Chem. Phys., 1965. 42: p. 288.

5.             Acosta, R.H., P. Peter Blümler, and H.W. Spiess. Sensitivity and Resolution in Magnetic Resonance Imaging of Diffusive Materials. in Proceedings of NATO, Advanced Study Institute: Fluid Transport in Nanoporous Materials. 2004. La Colle sur Loupe, France 16.-27.6. 03.

6.             Wilke, C.R., Diffusional Properties of Multicomponent Gases. Chemical  Engineering Progress, 1950. 42(2): p. 95-104.

7.             Mathur, B.P. and S.C. Saxena, A New Method for the Calculation of Diffusion Coefficients of Multicomponent Gas Mixtures. Indian J. Pure Appl. Phys., 1966. 4: p. 266-268.

8.             Mair, R.W., et al., The Narrow Pulse Approximation and Long Length Scale Determination in Xenon Gas Diffusion NMR Studies of Model Porous Media. J. Magn. Reson., 2002. 156: p. 202-212.

9.             Agulles-Pedrós, L., Influence of Diffusion on Contrast and Sensitivity in MRI of Gases, in Institute of Physics. 2004, Johannes-Gutenberg University: Mainz.

10.           Callaghan, P.T., et al., Diffusive Relaxation and Edge Enhancement in NMR Microscopy. J. Magn. Reson., 1993. A 101: p. 347-350.

11.           de Swiet, T., Diffusive Edge Enhancement in Imaging. J. Magn. Reson., 1995. B 109: p. 12-18.

12.           Neumann, C.H., Spin echo of spins diffusing in a bounded medium. J. Chem. Phys., 1974. 60: p. 4508.

13.           van Beek, E.J.R., et al., Hyperpolarized 3-helium MR imaging of the lungs: testing the concept of a central production facility. Eur Radiol., 2003. 13: p. 2583-2586.

14.           Becker, J., et al., Study of mechanical compression of spin-polarized 3He gas. Nucl. Instrum. Methods, 1994. A 346: p. 45-51.

15.           Chen, X.J., et al., Spatially Resolved Measurements of Hyperpolarized Gas Properties in the Lung In Vivo. Part I: Diffusion Coefficient. Magn. Reson. Med., 1999. 42: p. 721-728.

16.           Stypa, J., Charakterisierung des menschlichen Bronchialbaums als Fraktal, in Institut für Numerische und Instrumentelle Mathematik. 1997, Westfälische Wilhelms-Universität: Münster, Germany.

17.           Schreiber, W.G., et al. Ultrafast MR-Imaging of 3-Dimensional Distribution of Helium-3 Diffusion Coefficients in the Lung. in International Society for Magnetic Resonance in Medicine, 7th Scientific Meeting. 1999. Philadelphia.

 

 

Figure Captions:

 

Fig. 1:   Schematic representation of a gradient echo sequence showing the used nomenclature. Top row: rf excitation and NMR-signals; central row: read gradient and bottom row: phase gradient.

 

Fig. 2:   Signal dependence of freely diffusing ³He as a function of the molar fraction of buffer gas SF₆. a) For two moderate b-values, W b = 6758 s/m² (realized with G_read = 86.4 mT/m and d = 320 μs), + b = 13525 s/m² (realized with G_read = 43.2 mT/m and d = 640 μs ) and b) a relatively high b = 27057 s/m² (realized with G_read = 21.6 mT/m and d = 1280 μs). The ordinate is the NMR-signal normalised to the value at x = 1. The curves show eq. (9) using the diffusion coefficients from Tab. 1. The dashed lines are the values of x_max calculated from eq. (10).

 

Fig. 3:  Demonstration of the signal increase by dilution of the signal carrier with heavy buffer gases. Therefore, hyperpolarized ³He is filled in a sample of concentric glass tubes.
a) geometry and size of the sample. b) 100% ³He and c) 50% ³He in SF₆. Sequence parameters: d = D = 640 μs and G = 53 mT/m corresponding to a b = 20388 s/m².

 

Fig. 4:  The NMR-signal and ADC for a pore radii range from 100 μm up to 15 mm representing the size distribution of the alveoli up to the trachea. Different scenarios are covered by calculating eq. (11).

a) varying the diffusion time: # D = 1 ms, ! D = 5 ms, W D = 10 ms and + D = 50 ms. The other parameters were D = 1.8·10^-4 m²/s and d = 1 ms. The gradient strength was set so that all curves have the same b = 7000 s/m². The dashed lines indicate the critical radius, .

b) varying b: # b = 100 s/m², ! b = 1000 s/m², W b = 10000 s/m². The other parameters were D = 1.8·10^-4 m²/s and d = D = 1 ms.

c) varying D:  # D = 1.8·10^-4 m²/s, ! D = 8.5·10^-5 m²/s, W D = 5.4·10^-5 m²/s. These diffusion coefficients correspond to that of ³He with a molar fraction of x = 0.1 in # ⁴He, ! N₂ and W SF₆. The other parameters were d = 1 ms, D = 2 ms, G = 10 mT/m resulting in b = 6922 s/m². The critical radii are also indicated for ⁴He (dashed), N₂ (dot-dahed) and SF₆ (dotted).

d) same conditions as in c) but showing the calculated ADC in a double logarithmic plot (same symbols and line styles as in c).

 

Fig. 5: ³He images of a pig lung using ³He in different buffer gases: a) in ⁴He b) in N₂ and c) in SF₆. Row 1 shows the resulting images for a reference measurement without additional diffusion gradients and b = 1525 s/m² along the vertical read-direction. The gray scale stretches from 0 to 90% of the maximal intensity of each image. Row 2 shows the same images of row 1 divided by strongly diffusion weighted, but otherwise identical, images. Therefore a diffusion weighting gradient in sagittal direction (normal to paper plane) was added to the sequence with b = 38897 s/m². The gray scales for this row stretches from ratio 1 to 2. Noise was masked out by applying a suitable threshold filter.

Table 1:

 

The diffusion coefficients of ³He in binary mixtures with three buffer gases (BG) without spatial restrictions according to eq. (2) [3]. The error is in the order of 5 %.

 

	BG = 4He	BG = N2	BG = SF6
[m2/s]	1.8 · 10-4	1.8 · 10-4	1.8 · 10-4
[m2/s]	1.7 · 10-4	8 · 10-5	5 · 10-5

 

 

 

 

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