Search tips
Search criteria 


Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Phys Chem B. Author manuscript; available in PMC 2010 September 17.
Published in final edited form as:
PMCID: PMC2747043

Continuously Infusing Hyperpolarized 129Xe into Flowing Aqueous Solutions Using Hydrophobic Gas Exchange Membranes


Hyperpolarized (HP) 129Xe yields high signal intensities in magnetic resonance (MR) and, through its large chemical shift range of ~300 ppm, provides detailed information about the local chemical environment. To exploit these properties in aqueous solutions and living tissues requires the development of methods for efficiently dissolving HP 129Xe over an extended time period. To this end, we have used commercially available gas exchange modules to continuously infuse concentrated HP 129Xe into flowing liquids, including rat whole blood, for periods as long as one hour, and have demonstrated the feasibility of dissolved-phase MR imaging with sub-millimeter resolution within minutes. These modules, which exchange gases using hydrophobic microporous polymer membranes, are compatible with a variety of liquids and are suitable for infusing HP 129Xe into the bloodstream in vivo. Additionally, we have developed a detailed mathematical model of the infused HP 129Xe signal dynamics that should be useful in designing improved infusion systems that yield even higher dissolved HP 129Xe signal intensities.

Keywords: xenon-129, laser polarized, spin exchange optical pumping, microporous membrane, gas exchange


Gas-phase 129Xe is increasingly used in a variety of disciplines because of this isotope’s unique magnetic resonance (MR) characteristics 1,2. Through its large chemical shift range of ~300 ppm, pronounced chemical shift anisotropy (CSA) 3,4, and variable longitudinal relaxation 5-7, 129Xe provides a wealth of information about its chemical environment. Additionally, the nuclear spin polarization of 129Xe can be enhanced by orders of magnitude using spin exchange optical pumping (SEOP) 8, enabling novel MR applications such as probing single crystal surfaces 9, measuring the permeability and tortuosity of porous materials 10,11, and examining combustion processes 12. Hyperpolarized (HP) 129Xe also permits magnetic resonance imaging (MRI) of structure and gas exchange pathways in both healthy and injured lungs 13-15, which makes this isotope of biomedical interest. However, the greatest promise for 129Xe in biomedicine stems from its reasonably high solubility (~10%) in aqueous solutions and tissues 16.

In solution, 129Xe can be used to probe protein structure 17-19 and physiologically important parameters such as blood oxygenation 20. Dissolved HP 129Xe residing in the pulmonary capillaries rapidly diffuses into the alveolar gas spaces where its resonance frequency is shifted by ~200 ppm. Thus, HP 129Xe can serve as a spatially resolved probe of pulmonary function 21. Dissolved HP 129Xe also allows MR studies to extend beyond the lungs to organs including the brain 22, where multiple 129Xe resonances are observed 23. Additionally, HP 129Xe MR, when used in concert with xenon encapsulating cryptophane biosensors 24, allows the sensitive detection of proteins 25,26 and nucleic acids 27, and shows promise as molecular imaging contrast agent 28. Despite this range of applications, aqueous HP 129Xe studies are relatively infrequent.

This low number of solution studies results in part from the difficulties involved in efficiently dissolving HP 129Xe at high concentrations. Typically, HP 129Xe is dissolved by introducing gaseous xenon into a container above the solution of interest and then manually shaking the container 29,30. This method requires that the solutions be degassed before experiments to prevent longitudinal relaxation through dipole coupling to paramagnetic O2 gas. However, degassing introduces considerable experimental delays and the approach is limited to solutions that are not damaged by evacuation or freeze-thaw cycles. For more fragile systems, such as blood 20,31,32, the HP 129Xe-saturated solution must be prepared separately and then delivered, usually by injection, into the sample of interest. This subsequent injection avoids depolarization by oxygen and degassing-induced mechanical damage but, at least to some degree, alters the chemical composition of the sample.

Alternately, HP 129Xe can be dissolved by flowing gas from the polarizer and bubbling the SEOP mixture directly into the solution of interest 33. Bubbling enables signal averaging by providing continuous HP 129Xe signal and can be applied to flowing solutions. However, bubbling yields low dissolved xenon concentrations due to the low xenon partial pressures typically used in SEOP (~1% xenon) 34 and can lead to susceptibility artifacts unless liquid flow is stopped during data acquisition 35. Further, this method is limited to in vitro studies because, if attempted in vivo, xenon bubbles could produce fatal gas emboli.

Recently, Baumer et al. 36 produced high dissolved HP 129Xe signal intensities by passing HP gas through hollow, microporous polymer membranes fibers. The hydrophobicity of these hollow membrane fibers prevented fluids from wetting the interior of the fibers and membrane pores, allowing HP 129Xe to continuously diffuse through the pores directly into the sample. However, directly infusing into the solution within the detection region allows gas-phase HP 129Xe to be subjected to RF excitation. In experiments where chemical shift selective pulses cannot be used, gas-phase HP 129Xe will inevitably be excited, depolarizing the longitudinal gas-phase magnetization and producing transverse gas-phase magnetization that could diffuse into solution and interfere with phase dependent and T2 dependent experiments.

In this work, we describe the use of commercially available gas exchange modules to infuse HP 129Xe into flowing solutions outside the RF coil. Because infusion occurs remotely, hard RF pulses can be used without exciting and depolarizing the gas-phase magnetization. Further, this method requires no special sample pretreatment and operates at near ambient pressure with fully concentrated HP 129Xe. Compared to dilute SEOP mixtures, it produces higher dissolved HP 129Xe concentrations and thus improved signal intensities. The large signals enable dissolved-phase HP 129Xe imaging with sub-millimeter resolution with acquisition times of a few minutes. Moreover, continuous infusion enables nonequilibrium signal to be detected for up to an hour using only 300 ml of xenon gas at ambient pressure and temperature.

Finally, we describe the infused HP 129Xe signal dynamics with a detailed mathematical model that incorporates the effects of gas and fluid flow, mass transport across the exchange membranes, and 129Xe longitudinal relaxation. This model elucidates a number of important features of the infused HP 129Xe signal dynamics and can, therefore, be used to guide the development of improved HP 129Xe infusion systems.


2.1. Method Overview

Within a gas exchange module (see Fig. 1A), gaseous HP 129Xe does not immediately contact the liquid, but rather diffuses through 0.04-μ m pores within a bundle of hollow polypropylene membrane fibers (Celgard® X50, Membrana, Charlotte, NC). The volume within the module that is accessible to the liquid is known as the ‘empty volume’ and was 2.7 ml for the modules used in this work. Because the membrane fibers are highly hydrophobic, liquids within the module empty volume cannot wet the microscopic membrane pores and are thus prevented from reaching the interior of membrane fibers. In contrast, gases such as HP 129Xe located within the hollow fibers can continuously diffuse through the membrane pores into solution.

Figure 1
Schematic depicting HP 129Xe infusion. (A) Gas exchange module. HP 129Xe enters the module and flows through a bundle of hollow, hydrophobic membrane fibers, having an outer diameter of do. The fibers are perforated with submicron pores, but the hydrophobicity ...

Although these membranes enable rapid gas dissolution, the final dissolved gas concentration cannot exceed the limit set by the Ostwald solubility of the gas. For gases with solubilities that are less than one, such as the xenon, nitrogen, and helium used in this work, the concentration of the gas within the fibers will always be greater than the concentration in solution. Provided that there is a constant supply of gas, the mass transport across the membrane is therefore expected to be essentially independent of gas flow 37. However, slow gas flows would lead to extended HP 129Xe residence times within the gas transfer tubing and the hollow membrane fibers and cause unacceptable levels of gas-phase longitudinal relaxation. To limit polarization losses, all of the experiments involving membranes described in this work were performed by flowing excess HP 129Xe gas through the module. HP 129Xe that was not dissolved by the flowing aqueous solution is referred to throughout the text as “exhaust.”

Unless otherwise stated, the excess xenon mixtures were exhausted to outside the superconducting magnet through an unrestricted polyethylene tube. The exhaust gas could thus freely pass through the exchange module without producing gas bubbles in the liquid as long as the pressure on the liquid side of the membranes exceeded the gas pressure within the fibers. This requirement for bubble-free gas infusion, for pure xenon and the xenon, nitrogen, and helium containing SEOP gas mixture, was met in all of the experiments described in this work.

2.2. 129Xe Polarization

Either natural abundance (26% 129Xe, Airgas National Welders Inc., Durham, NC) or isotopically enriched (83% 129Xe, Spectra Gases Inc., Alpha, NJ) xenon, was hyperpolarized by SEOP 8,38 using a prototype commercial polarizer (model 9800, MITI, Durham, NC). This system employs a continuous flow of dilute xenon (1% xenon, 89% helium, and 10% N2) passing through a rubidium vapor-containing optical cell at 160° C and a pressure of 5 atm. After exiting the cell, HP 129Xe can be cryogenically extracted from the buffer gases using liquid nitrogen 34 with final polarizations of 5-10%. In other experiments, the dilute HP 129Xe mixture was allowed to flow from the polarizer at ~150 ml/min without cryogenic extraction 39. In this method, SEOP was also performed at 5 atm but was passed through a perfluoroalkoxy polymer (PFA) regulator (Partek, Tuscon, AZ) to reduce the total gas pressure to ~1 atm.

2.3. Membrane Infusion of HP 129Xe

Following cryogenic accumulation, xenon ice was removed from liquid nitrogen and thawed into 350-ml Tedlar bags (Jensen Inert Products, Coral Springs, FL) located within a Plexiglas cylinder. The cylinder was immediately placed within the fringe field of the superconducting magnet and aligned with the bore of the magnet to minimize relaxation due to transverse magnetic field gradients 40. The bag was then pressurized to ~1.2 kPa above ambient pressure by flowing N2 gas from a supply tank into the cylinder (see Fig. 1B). The flow of xenon out of the bag was initiated by opening a plastic stopcock and was controlled using a direct reading gas flow meter (Cole-Parmer, Vernon Hills, IL) located inline between the xenon containing cylinder and the N2 supply tank.

Because of the small applied N2 pressure, the gas volume that entered the reservoir and compressed the collapsing Tedlar bag was essentially identical to the HP 129Xe volume that flowed from the bag toward the exchange module. By controlling the N2 flow into the Tedlar bag reservoir, the xenon flow could be controlled without passing the gas through potentially depolarizing flow constrictors. After traversing ~1.2 m of polyethylene tubing [outer diameter (OD) = 3.2 mm, inner diameter (ID) = 1.6 mm], HP 129Xe was infused directly into aqueous solution using a Liqui-Cel MicroModule™ (Membrana, Charlotte, NC) located within the magnet bore.

Unless otherwise stated, the liquid flowed from a 5-L polyethylene reservoir (Nalgene, Thermo Fisher Scientific Inc., Waltham, MA) located 2.4 m above the magnet bore (Fig. 1B). Liquid flow was controlled by a direct-reading water flow meter (Cole-Parmer) located between the liquid reservoir and the exchange module. After passing through the module, liquid was collected in a second polyethylene reservoir (Nalgene) and returned to the supply reservoir using a peristaltic pump (MasterFlex, Cole-Parmer). Return flow was monitored by a direct-reading flow meter (Cole-Parmer) between the pump and the supply reservoir and was maintained at the same flow as the liquid exiting the supply reservoir. Alternatively, a peristaltic pump alone was used to continuously recirculate ~5 ml of liquid in a closed circuit.

2.4. HP 129Xe MR Imaging and Spectroscopy

Images and spectra were acquired using a 2.0-T, 30-cm bore, horizontal superconducting magnet (Oxford Instruments, Oxford, UK) with shielded gradients (400 mT/m), controlled by a GE EXCITE 12.0 console (GE Healthcare, Milwaukee, WI). The scanner was interfaced with 23.66-MHz linear RF coils by an integrated transmit/receive switch with 31-dB gain preamplifier (Nova Medical, Wilmington, MA) and made to operate at 23.66 MHz instead of its intrinsic 63.86-MHz frequency using an up-down converter (Cummings Electronics Labs, North Andover, MA). Dissolved 129Xe images were obtained with isotopically enriched xenon using an 8-cm long, 7-cm diameter birdcage coil. The images were obtained from a phantom comprising a 15-cm long, 1.6-mm ID polyethylene tube coiled around a 4-cm long, 1.5-cm OD cylinder and were acquired using a non-slice-selective gradient-echo sequence with a 30° flip angle, repetition time (TR) = 500 ms, bandwidth = 4 kHz, matrix = 64×64, field of view (FOV) = 4.0 cm, and number of acquisitions = 16. HP 129Xe spectra were obtained from natural abundance xenon using the probe described above or a 6.6-cm long, 3.3-cm diameter solenoid probe.

To obtain flow-dependent relaxation data, concentrated HP 129Xe at a fixed gas flow was infused into distilled water or aqueous 0.02 M CuSO4 at liquid flows of 4-50 ml/min. Prior to RF excitation, the liquid flow was halted using a plastic stopcock located immediately outside the RF coil. To measure relaxation in fully degassed samples, cryogenically accumulated HP 129Xe was dispensed into a 100-mL Pyrex shaker 30 containing 30-40 ml distilled water that had been degassed by evacuation with a rotary vane vacuum pump (Pfeiffer Vacuum, Nashua, NH). The shaker was then moved to the 0.2-T fringe field of the MR imaging magnet, where it was shaken vigorously by hand for 20 s to dissolve the 129Xe gas. HP 129Xe saturated solution was then withdrawn into a 10 ml plastic syringe and immediately placed in the RF coil.

T1 measurements were performed by observing the dissolved HP 129Xe magnetization with a series of small evenly spaced RF pulses. For distilled water 32, 1° pulses were applied. To compensate for the lower 129Xe polarization in the 0.02 M CuSO4 solution, 16, 5° RF pulses were used. The data were fit to monoexpontential decays with corrections applied for magnetization lost to the RF pulses.

Spectra were processed using HiRes Version 1.6 (Hatch Center for MR Research, Columbia University, New York, NY). Data fitting was performed in Igor Pro (Wavemetrics, Inc., Lake Oswego, OR) or routines written in MATLAB (The MathWorks, Inc., Natick, MA). Simulations were also performed using MATLAB.

2.5. Animal Care and Use

Blood was taken from a 645 g Sprague-Dawley rat (Charles River, Raleigh, NC) following a protocol approved by the Duke University Institutional Animal Care and Use Committee. Briefly, the rat was anesthetized with intraperitoneal (IP) injection of 65 mg/kg Nembutal (sodium pentobarbital) and heparinized (420 UI/kg) before withdrawing 15 ml of blood from the carotid artery. The animal was then euthanized by an overdose of pentobarbital.

3. Theoretical Model

3.1. Mass Transfer

To make the fullest use of membrane-based HP 129Xe infusion, it will be necessary to quantitatively understand the factors that govern magnetization transport from the gas-phase into solution. Because these membranes are of considerable practical interest due to their common use in extracorporeal blood oxygenation 41, their mass transport properties have been extensively studied and characterized 37,42. By adapting the results of these earlier studies and including the influence of longitudinal relaxation, we have developed a detailed model describing the observable HP 129Xe magnetization obtained using gas exchange membranes.

The mass transfer of a substance from the gas-phase into a liquid across a bundle of hollow fiber gas-exchange membranes with total surface area, Am, can be described in analogy to Fick’s law by 43


where n and cl are the number of moles and the concentration of the solute gas, respectively; cl,eq is the concentration in the liquid that would be in equilibrium with the gas-phase; t is time; and K is the mass-transfer coefficient (units m/s). Assuming that the liquid flow through the gas-exchange module is along the z-direction and characterized by a flow rate, Ql, Eq. 1 can be rewritten as


where Vl is the module empty volume (liquid volume within the module); Δz is the length of the module in the direction of liquid flow; and u = ΔzQl/Vl is the liquid velocity. Note that cl,eq has now been expressed in terms of the gas-phase concentration, cg, by employing the definition of the Ostwald solubility (i.e., Ll = cl,eq/cg). Integrating Eq. 2 with respect to cl on the interval from the concentration at the module inlet, cin, to the concentration at the module outlet, cout, and solving for cout yields


For hollow-fiber gas-exchange membranes, the mass-transfer coefficient used in Eqs. 1-3 is most conveniently expressed as 37,43


where Sh is the dimensionless Sherwood number; Dl is the diffusion coefficient of the dissolved solute; and de is the equivalent diameter of the flow path, defined by 42,44


In Eq. 5, ε is the void fraction of the gas-exchange module, which is defined as the ratio of the module empty volume, Vl, to the total volume of the module, Vtot; and d0 is the outside diameter of the hollow fibers. The Sherwood number, in turn, can be expressed in terms of the mass-transfer correlation by


where a, b, and c are empirical constants 42. In Eq. 6, Re and Sc are the Reynolds and Schmidt numbers given by


where, ν and ρ are the dynamic viscosity and density of the liquid, respectively. Note that the expression for de given in Eq. 5, and thus the definition of Re in Eq. 7, is strictly valid only for fully developed turbulent flow 42,45. However, both expression are used extensively in modeling hollow fiber membrane blood oxygenators and lead to predicted mass transfer behavior that agrees well with experimental observations 37,42.

Combining Eqs. 4-8 allows the mass transfer coefficient to be expressed as


Together, Eqs. 5 and 9 permit the mass transfer coefficient to be calculated for a given set of experimental conditions using only the physical properties of the fluid, the fiber and module dimensions, and experimentally determined values that can be obtained from the literature. These values, along with the relevant references, are provided in Table 1.

Table 1
Nonstandard Symbols and Literature Values Used in the Theoretical Model

3.2. Polarization Transfer

While the ability to calculate the mass transport of xenon, and thus the xenon concentration in solution, is a necessary step in quantifying the signal dynamics of infused HP 129Xe, additional factors must be taken into account to reflect that in MR, we are not primarily concerned with concentration, but rather magnetization. The dissolved longitudinal magnetization, mz,l, may be expressed as


where NA is Avogadro’s constant; γ is the gyromagnetic ratio of the nucleus; [variant Planck's over 2pi] is Planck’s constant divided by 2π; and Pl is the nuclear polarization of the solute. By differentiating Eq. 10, the rate of the change in magnetization can be expressed as


where the change in solute concentration is given by Eq. 1. Neglecting the small contribution from thermal polarization, the change in dissolved polarization can be approximated by a first-order decay with time constant, T1,l. Thus, Eq. 11 becomes


where mz,i is the gas-phase magnetization at the gas-liquid interface.

For the setup depicted in Fig. 1B, it may be assumed that the liquid enters the module at time t = 0 with no initial magnetization and exits after a residence time, Δt = Vl/Ql. Integrating Eq. 12 according to


leads to a magnetization at the liquid outlet, mz,out, of


Finally, the dissolved 129Xe magnetization at the module outlet will be decreased by longitudinal relaxation during transport to the detection region. The magnetization that will be observed after transport, mz,obs, will thus be given by


where τl = Vl,t/Ql is the liquid transit time through the transfer line with volume, Vl,t. From the above discussion, in particular Eqs. 14 and 15, the signal intensity, S, observed from infused HP 129Xe can be expressed as


where κP is a proportionality constant that accounts for factors such as the coil sensitivity and the polarization of HP 129Xe at the gas-liquid interface within the module.

3.3. Gas-phase HP 129Xe Longitudinal Relaxation

To fully describe how experimental parameters influence the signal intensity obtained from infused HP 129Xe, gas-phase polarization losses prior to dissolution must also be considered. Thus, in addition to the factors listed in Eqs. 14 and 15 magnetization, we will have


where mz,g is the initial gas-phase 129Xe magnetization entering the exchange module; τp is the xenon gas transit time through the membrane pores; τf is the xenon transit time through the hollow-fibers; and T1,p and T1, f are the gas-phase spin-lattice relation times in the membrane pores and the hollow fibers, respectively.

We assume that xenon transport across the membrane is driven simply by one-dimensional diffusion through the pores. This assumption is reasonable because mass transport driven by pressure gradients would produce bubbles on the liquid side of membrane, which were not observed in the experimental work. Hence, transit time through the membrane pores is given by τp = l2/2Dg, where l is the length of the pore and Dg is the gas-phase diffusion coefficient of xenon.

The purely gas-phase longitudinal relaxation time for 129Xe in pure xenon gas will exceed 4 hrs at pressures near 1 atm 46 and can be considered negligible. Therefore, the relaxation in pure xenon is expected to be dominated by dissolution into the polymer, and the relaxation rate will be given by 47,48


where Lp is the Ostwald solubility of xenon in the polymer; Ap is the surface area of the pore; Vp is the volume of the pore; Dd is the diffusion coefficient of xenon dissolved in the polymer; and T1,d is the relaxation time of 129Xe dissolved in the polymer. By assuming that the pores are cylinders of radius, r, Eqs. 17-18 yield


Inserting the values from Table 1 into Eq. 19, with T1,d = 7.6 s, yields exp(-τp/T1,p) ≈ 0.99. This expectation of negligible polarization loss due to relaxation within the membrane pores is in agreement with the empirical results of Baumer et al. 36. Note that even if relaxation caused by the presence of O2 gas is considered (see the discussion that follows), the relaxation within the pores is still negligible because of the short time required for xenon gas to diffuse a distance of l = 40 μ m. Similarly, the relaxation rate due to dissolution into the fibers can be expressed as


where Vf is the gas volume of the fibers. (Note that for simplicity, we ignore the small volume occupied by the membranes themselves.)

While Eq. 20 accounts for relaxation due to dissolution into the hollow fiber membranes, O2 within the gas space of the fibers may contribute to polarization loss. The highest O2 gas concentration, and thus the maximum 129Xe relaxation rate, will occur if water enters the module at equilibrium with the atmosphere and then equilibrates with the initially O2-free gas space within the fibers. Under these conditions, the relaxation rate within the fibers would be given by


where BO2 is the relaxivity of O2 gas 49, LO2 is the Ostwald solubility of O2 in water, and cO2,atm is the atmospheric O2 concentration. Unlike the xenon in membrane pores, mass transport through the hollow fibers will be dominated by gas flow, Qg, rather than diffusion. Because HP 129Xe can diffuse through the membrane at any point along the length of the fiber, it is appropriate to calculate the relaxation using the average residence time of τf = Vf/2Qg .

From the above discussion, it is now possible to express the observable magnetization as a function of both liquid flow and gas flow as


where 1/T1,f will lie between the lower limit set by Eq. 20 and the upper limit set by Eq. 21, and K is defined in Eq. 9. Note that the negligible contribution of relaxation within the membrane pores (Eq. 19) has been omitted for clarity.


4.1. NMR Spectroscopy

Figure 2 depicts typical spectra, obtained using the setup shown in Fig. 1, to infuse HP 129Xe directly into distilled water. The spectra in Fig. 2A and 2B both display high signal-to-noise ratios (SNRs) and demonstrate the effectiveness of membrane based infusion of concentrated HP 129Xe. Note that high SNR was obtained despite the low coil filling factor used in the experiment (i.e., the 0.13 ml sample volume was ~0.2% that of the coil volume). In Fig. 2A, aqueous and gaseous 129Xe peaks are observed because the excess xenon gas from the exchange module was intentionally passed through the RF coil. The spectrum in Fig. 2B was obtained under identical conditions except that excess xenon was exhausted to the outside of the magnet away from the RF coil and, thus, displays no gas-phase 129Xe peak. Further, no gas-phase signal was observed even after averaging 128 scans (data not shown), confirming that membrane-based infusion of HP 129Xe provides high signals without forming xenon gas bubbles.

Figure 2
Spectra from HP 129Xe infused into distilled water. All spectra were acquired with a 5 kHz bandwidth and are referenced to the gas-phase peak at 0 ppm. 10 Hz broadening were applied. (A) Spectrum obtained from a hard 90° RF pulse with liquid and ...

Figure 2C displays an aqueous 129Xe spectrum obtained by flowing the dilute SEOP (1% xenon) mixture at a total pressure of ~1 atm directly from the polarizer into the exchange module. The spectrum was acquired by averaging signal from 32, 90° RF pulses and employed a sufficiently long repetition time (TR = 5 s) to completely replace the 129Xe magnetization in the sample volume. Despite the full recovery of dissolved 129Xe magnetization, the spectrum displays a substantially lower SNR than do the aqueous peaks shown in Fig. 2A and 2B. This lower SNR occurred even though the polarization of the HP 129Xe flowing directly from the polarizer can be as much as three-times higher than the cryogenically accumulated HP 129Xe 39. This lower SNR results because the dissolved HP 129Xe concentration is limited by the Ostwald solubility to be at most 10% of the gas-phase xenon concentration 16, producing a dissolved xenon concentration that is ~100 times lower than can be obtained for concentrated HP 129Xe. Thus, despite the higher polarization of the SEOP mixture, up to a 30-fold lower signal intensity relative to dissolved, cryogenically accumulated 129Xe is expected depending on the duration of the experiment (see Section 4.3).

4.2. MR Imaging of Infused HP 129Xe

The high signal intensities shown in Fig. 2A and 2B suggest that it should be possible to perform rapid MR imaging of dissolved HP 129Xe. Indeed, Fig. 3 displays an MR image of HP 129Xe dissolved in water, flowing through a coil of 1.6 mm ID polyethylene tubing that was acquired with an in-plane resolution of 625×625 μm2. The image, which as acquired in less than 9 min, displays an SNR ≈ 10 throughout most of the dissolved 129Xe containing region but also exhibits six brighter regions having SNR ≈ 30. These higher SNR areas correspond to the regions of the phantom where the coiled tubing was perpendicular to the image plane and, thus, contributed a greater volume of xenon-infused water.

Figure 3
MRI of HP 129Xe dissolved in a flowing aqueous solution (FOV = 4 cm). The HP 129Xe was delivered by the membrane infusion setup shown in Fig. 1. The phantom comprised a 1.6-mm ID tube coiled around a 1.5-cm OD cylinder. The image was acquired in less ...

4.3. Signal Dynamics from Concentrated HP 129Xe

In some systems, especially biological systems, long-term behavior may be of interest. To assess the ability of infused HP 129Xe to probe these systems, we investigated the HP 129Xe signal intensity as a function of time. As is seen in Fig. 4A, the highest signals were observed for about 15 min, but signal then decayed over the next 35 min. Similar behavior was also observed for initial gas volumes of 100 to 300 ml and gas flows ranging from 2 to 15 ml/min. This signal decay pattern has been reported previously 50 and was attributed to HP 129Xe relaxation within the supply reservoir.

Figure 4
Integrated HP 129Xe signal intensity as a function of time. (A) Dissolved 129Xe signal intensity in water. 300 ml of HP 129Xe was infused into distilled water using the setup depicted in Fig. 1B with gas and liquid flows set to 5 ml/min and 20 ml/min ...

Relaxation in the reservoir should depend on the surface-to-volume ratio within the Tedlar bag and thus be influenced by the initial inflation volume, xenon gas flow, and the duration of the experiment. Gas-phase depolarization within the reservoir is demonstrated in Fig. 4B, which shows the gas-phase signal intensity observed by removing the exchange module and passing the HP 129Xe gas at 5 ml/min directly through the RF coil. Other than displaying higher intensity, which is expected from the higher gas-phase xenon concentration, the gas-phase 129Xe signals in Fig. 4B exhibit the same general features as the dissolved-phase 129Xe signals shown in Fig. 4A.

4.4. Influence of Flow on HP 129Xe Longitudinal Relaxation

The use of exchange membranes limits the time during which HP 129Xe gas contacts the solution of interest. Thus, even though the solutions have not been degassed prior to infusion, the short contact time greatly reduces O2 induced gas-phase relaxation within the exchange module (see Section 4.6). However, dissolved oxygen may still be a concern, as it has been shown to substantially accelerate the longitudinal relaxation of aqueous 129Xe 51. To investigate the influence of dissolved O2, the longitudinal relaxation rate of thoroughly degassed, dissolved 129Xe was compared with the relaxation rate of HP 129Xe that was infused into solution at liquid flows ranging from 4 to 50 ml/min. As seen in Fig. 5, the degassed, distilled water yielded an average 129Xe T1 of 125 s, whereas the average T1 for the infused HP 129Xe was 92 s. Further the T1 values for the infused 129Xe varied from ~80 s at the highest liquid flow to ~100 s at the lowest flow. Fig. 5 also shows relaxation data from HP 129Xe infused into distilled water at two different xenon gas flows (5 ml/min and 15 ml/min). Although substantial scatter is present, the data suggest that the dissolved 129Xe relaxation rate is relatively insensitive to gas flow.

Figure 5
Infused HP 129Xe longitudinal relaxation rate as a function of distilled water flow. The fully degassed data (squares at liquid flow = 0 ml/min) were obtained from dissolved HP 129Xe in a 10 ml plastic syringe. All other data were acquired by temporarily ...

The sensitivity to liquid flow resulted from the more efficient removal of O2 from the fluid by the exchange membranes at low liquid flows, which increased the time that the liquid spent within the module. However, the longer T1 of 100 s suggests that some O2 must remain in solution after passing through the module. For solutions with stronger relaxation mechanisms than coupling to O2, the signal intensity dependence on dissolved oxygen removal is expected to be less pronounced. For instance, in 0.02 M CuSO4, where the 129Xe relaxation should be dominated by paramagnetic Cu2+ ions, the average T1 was only 18 s and ranged from 16.9 s to 18.6 s as the liquid flow was varied from 45 to 5 ml/min.

4.5. Liquid Flow Dependent Magnetization Transfer

To validate the model presented in Section 3, the signal from infused HP 129Xe was studied as a function of liquid flow. These experiments were performed using HP gas delivered directly from the polarizer to avoid the complex relaxation behavior exhibited by the concentrated HP 129Xe seen in Fig. 4. Although this approach produced a lower dissolved xenon concentration, it simplified data interpretation by providing constant polarization at the gas-liquid interface within the module. The results of these experiments are shown in Fig. 6. For distilled water, the signal increased rapidly before reaching a maximum at a liquid flow of ~5 ml/min and then steadily decreased at higher flows. The increasing portion of the curve resulted from higher liquid flows lowering the residence time within the exchange module and the transfer tubing, and, therefore, reducing the polarization lost to relaxation. At higher liquid flows, the signal was reduced because xenon mass transport across the membranes became less efficient.

Figure 6
Dissolved HP 129Xe signal as a function of liquid flow. The lines are fits of the data to Eq. 16, assuming average relaxation times of T1 = 92 s in distilled water and T1 = 18 s in 0.02 M CuSO4. The error bars are the standard deviations from replicate ...

In a faster relaxing liquid, the signal maximum would be expected to appear at a higher liquid flow and display a lower value. This trend is observed in the signal intensity from the Cu2+ doped water, which reaches a maximum value of only about 40% percent of that observed from distilled water. At high enough flows, one would expect the HP 129Xe signal from the Cu2+-containing solution to decrease due to reduced mass transport, but this point lies beyond the operating range of the infusion system used in this work.

Fig. 6 also demonstrates the strong quantitative agreement between our empirical results and the theory presented in Sections 3.1 and 3.2. For both aqueous solutions, the data were fit to Eq. 16 by holding all parameters constant except κP, which was used as the sole fitting parameter. The average relaxation times discussed in Section 4.4 were used for T1,l values required for the fittings. All other parameters were held constant at the values provided in Table 1. Despite using literature values from a variety of sources (see Table 1) and average dissolved relaxation times, the κP values for the two solutions differed by only 12%, which is within the typical day-to-day variations in polarization.

4.6. Simulating HP 129Xe Infusion

With a detailed understanding of the factors that influence HP 129Xe mass transport and polarization within the membranes, it is possible to evaluate the influence of various experimental parameters on the expected HP 129Xe signal dynamics. Fig. 7 shows the results from a series of simulations based on the model presented Section 3 and summarized in Eq. 22. Throughout the figure, the observable magnetization, mz,obs, is plotted as a fraction of the gas-phase magnetization entering the system, mz,gas. Thus the highest possible value would occur at mz,obs/mz,gas = 0.1068, which is the Ostwald solubility of xenon water 16.

Figure 7
Infusion HP 129Xe magnetization transfer. (A) Observable magnetization relative to the gas-phase magnetization entering the module as a function of liquid flow. The upper curve was produced assuming relaxation was negligible. The two lower curves were ...

Fig. 7A displays mz,obs/mz,gas as a function of liquid flow. (Note, gas-phase relaxation has been neglected.) The dotted line depicts mz,obs/mz,gas if longitudinal relaxation is neglected (i.e. only mass transport is considered), and the other two lines represent mz,obs/mz,gas in the presence of two different dissolved 129Xe relaxation times. T1,l = 125 s was selected to demonstrate the conditions under which HP 129Xe infusion would be most favorable, and T1,l = 6 s was selected as a typical T1 expected for HP 129Xe in blood 32. For the mass transport curve, the value of mz,obs/mz,gas approaches the Ostwald solubility limit at the lowest flows but monotonically decreases with increasing liquid flow due to reduced xenon mass transport. The behavior changes dramatically if the longest dissolved longitudinal relaxation time is considered (solid line) and becomes quite similar to the empirical data for distilled water shown in Fig. 6. Similar behavior was also observed for the faster relaxing solution (dashed line). This simulation suggests that little signal intensity would be observed in a fluid with T1 = 6 s under the exact experimental conditions used to produce Fig. 6.

Although mass transport into solution depends only weakly upon the gas flow 37, it is experimentally difficult to quantify the role of gas flow in determining the infused HP 129Xe signal intensity because gas-phase T1 measurements are complicated by xenon exchange between the gas-phase and the dissolved-phase. Fortunately, as discussed Section 3.3, it is possible to place lower (Eq. 20) and upper (Eq. 21) limits on the gas-phase 129Xe longitudinal relaxation rate within the membrane fibers. Fig. 7B displays mz,obs/mz,gas as a function of gas flow using both the upper (solid line) and lower (dotted line) gas-phase limits on 1/T1, f. In both limits, mz,obs/mz,gas increases with increasing gas flow but quickly saturates, indicating that only small signal gains are expected at high gas flows. Gas-phase relaxation between the HP 129Xe source and the exchange module is expected to further increase the signal intensity dependence on gas flow. However, we observed no advantage in using gas flows that exceeded 5 ml/min.

Because of relaxation, the optimum HP 129Xe infusion conditions may not be achieved from commercially available exchange models. To evaluate this possibility, we performed a series of simulations in which we assumed the maximum possible gas-phase relaxation (Eq. 21) while varying the exchange module surface area and empty volume (liquid volume within the exchange module). Fig. 7C, which was simulated using a dissolved T1 of 125 s, indicates that the highest observable magnetization is expected at the lowest empty volumes because dissolved HP 129Xe relaxation within the exchange module is reduced. However, increasing the membrane surface area partially compensates for polarization losses by improving mass transport. For instance, halving the empty volume and doubling the membrane surface area may increase the signal intensity by up to 50%.

The need to optimize magnetization transfer is even more pronounced in quickly relaxing solutions. Fig. 7D, which shows the simulated magnetization transfer dynamics at T1,l = 6 s, was produced using identical parameters to those used for Fig. 7C except that the transfer line volume was reduced from 2.26 to 1.0 ml and the liquid flow was increased from 5 to 15 ml/min. These changes were made to anticipate the experimental necessities required to work with rapidly relaxing solutions such as blood. These results indicate that the current membrane design is far from optimum for liquids that produce short 129Xe relation times. Fortunately, the advantage expected from reducing the empty volume and increasing the membrane surface area is significantly more pronounced than it is for slowly relaxing liquids. Thus, high dissolved signal intensities should be achievable even in short 129Xe T1 liquids such as blood.

4.7. Infusing HP 129Xe into Whole Blood

To infuse HP 129Xe into biological fluids, it will be necessary to work with less liquid than is required for the setup shown in Fig. 1B. Furthermore, it will be necessary for the membranes to operate for long periods while in contact with complex fluids without fouling or restricting liquid flow. To demonstrate this potential, we replaced the gravity-driven flow setup shown in Fig. 1B with a single peristaltic pump. This modification, coupled with reducing the transfer tubing volume to 1.0 ml, allowed us to infuse HP 129Xe into only ~5 ml of whole, heparinized rat blood. A typical spectrum from these experiments is shown in Fig. 8 and displays two peaks at 211.6 and 196.9 ppm, which correspond to 129Xe residing in the red blood cells and plasma, respectively. These peak positions are consistent with those observed from in vivo spectroscopy of rats 15 and indicate that interactions with the exchange membranes do not significantly affect the blood.

Figure 8
Spectrum of HP 129Xe infused into whole rat blood. The spectrum was acquired by averaging 128 scans (bandwidth =1.25 kHz, TR = 3 s), and was referenced to gas-phase 129Xe at zero ppm. The peaks at 211.6 and 196.9 ppm correspond to 129Xe in the red blood ...

The spectrum in Fig. 8 shows a substantially lower SNR than the spectra in Fig. 2A or 2B, consistent with magnetization losses due to the 4-6 s 129Xe T1 in blood32. While it is difficult to accurately determine the polarization of the 129Xe dissolved in blood, it is possible (using the module empty volume, the liquid transfer volume, T1 ~ 6 s, and a flow of 15 ml/min) to crudely estimate the value at P ~ 0.5%. Fortunately, it is possible to partially compensate for this lower polarization by signal averaging, which could be continued for more than an hour without noticeable membrane module clogging or diminished flow. As a final point, the membranes used with whole blood could be cleaned in accordance with the manufacturer’s instructions without noticeably reducing the module performance.


The experimental setup shown in Fig. 1B provides a simple method for producing high aqueous HP 129Xe signal intensities in situation where the volume of the flowing liquid is effectively unlimited, for instance when biomolecules are bound to a matrix such as agarose. For studying samples such as unbound biomolecules or blood, the setup can easily be modified to accommodate much smaller volumes by recirculating the liquid using only a peristaltic pump. Additionally, this second approach is similar to the extracorporeal gas exchange systems currently used in rodent models of cardiopulmonary bypass 52. This similarity suggests that continuous infusion of HP 129Xe should be suitable for a number of in vivo applications.

By supplying signal continuity, infused HP 129Xe will permit substantial signal averaging and may enable novel studies of fundamental physiological processes in vivo. For instance, when xenon-saturated saline is injected intravenously, the HP 129Xe emerging into the alveolar airspaces provides spatially resolved information about pulmonary perfusion and gas exchange pathways in the lungs 21. The in vivo availability of injected HP 129Xe, however, is constrained by the tolerable injection volumes. This volume constraint could be eliminated by infusing HP 129Xe directly into the blood using an extracorporeal circuit to enable continuous in vivo delivery of HP 129Xe 53. Additionally, extracorporeal xenon infusion should also be useful in supplying HP 129Xe to organs other than the lungs.

For these longer duration studies, the influence of the gas-phase relaxation within the HP 129Xe reservoir is a concern. Although the final signal intensity shown in Fig 4A from concentrated xenon is substantially lower than the initial intensity, the SNR observed after 50 min was still as high as that observed in Fig. 2C, which was obtained using the dilute (1% xenon) SEOP gas mixture flowing directly from the polarizer. Thus, the higher polarization of the dilute mixture does not offset the higher signal intensity obtained from concentrated HP 129Xe until nearly an hour has elapsed. Because 300 ml batches of concentrated HP 129Xe gas can be readily produced in less than 30 minutes, cryogenic accumulation is preferable to delivering dilute SEOP mixtures unless the experiment requires constant signal intensity.

Regardless of the gas-phase polarization, it will be advantageous to improve the magnetization transfer into solution. A number of approaches for improving magnetization transfer are suggested by the simulation results. The simplest of these will be to reduce the liquid transfer volumes. Additional gains are expected by optimizing the empty volume and membrane surface area within the exchange module.


In this work, we have introduced a method of infusing concentrated HP 129Xe at near ambient pressure directly into flowing solutions using commercially available gas exchange modules. This approach allows the use of hard RF pulses, requires no special sample pretreatment, and avoids potentially problematic bubble formation. By providing large dissolved xenon concentrations, this method yields high HP 129Xe signal intensities and allows dissolved-phase HP 129Xe MR imaging with sub-millimeter resolution within minutes. Moreover, the infusion of HP 129Xe can be continued, albeit with reductions in signal intensity, for up to an hour using only 300 ml of xenon gas.

We also developed a detailed mathematical model describing the infused HP 129Xe signal dynamics that incorporates gas and fluid flow, mass transport, and longitudinal relaxation. This model suggests that the commercially available modules used in this work do not provide the highest possible 129Xe signal intensities. However, optimized exchange modules should substantially improve aqueous signal intensities.

These modules can also infuse HP 129Xe into complex biological fluids such as blood. More recently, we have successfully used this approach to infuse HP 129Xe into the bloodstream of living rats 53. This ability to efficiently deliver HP 129Xe to the blood in vivo promises to enable novel studies of the pulmonary system and, potentially other organs such as the brain. As a final note, HP 129Xe MR imaging could also be used to visualize and quantify mass transport from the gas-phase into solution and, thus, provide novel methods for characterizing the gas exchange membranes themselves.


The authors wish to thank Bodo von Harten, Horst-Dieter Lemke, and Detlef Krieter from Membrana GmbH for stimulating discussions and supplying some of the gas-exchange modules; Gary P. Cofer for building the 129Xe solenoid probe used in this work; Boma Fubara for assisting with animal preparation; and Sally Zimney for carefully proofreading the manuscript. This work was performed at the Duke Center for In Vivo Microscopy, an NIH/NCRR National Biomedical Technology Research Center (P41 RR005959) and NCI Small Animal Imaging Resource Program (U24 CA092656), with additional support from NHLBI R21HL087094.


(1) Ratcliffe CI. Ann. Rep. NMR Spectrosc. 1998;36:123.
(2) Raftery D. Ann. Rep. NMR Spectrosc. 2006;57:205.
(3) Ripmeester JA, Ratcliffe CI. J. Chem. Phys. 1995;99:619.
(4) Meersmann T, Logan JW, Simonutti R, Caldarelli S, Comotti A, Sozzani P, Kaiser LG, Pines A. J. Phys. Chem. A. 2000;104:11665.
(5) Smith ML, Dybowski C. J. Phys. Chem. 1991;95:4942.
(6) Cain EJ, Wen WY, Jost RD, Liu X, Dong ZP, Jones AA, Inglefield PT. J. Phys. Chem. 1990;94:2128.
(7) Cleveland ZI, Stupic KF, Pavlovskaya GE, Repine JE, Wooten JB, Meersmann T. J. Am. Chem. Soc. 2007;129:1784. [PubMed]
(8) Goodson BM. J. Magn. Reson. 2002;155:157. [PubMed]
(9) Jansch HJ, Gerhard P, Koch M. Proc. Natl. Acad. Sci. USA. 2004;101:13715. [PubMed]
(10) Mair RW, Wong GP, Hoffmann D, Hürlimann MD, Patz S, Schwartz LM, Walsworth RL. Phys. Rev. Lett. 1999;83:3324. [PubMed]
(11) Wang RP, Pavlin T, Rosen MS, Mair RW, Cory DG, Walsworth RL. Magn. Reson. Imaging. 2005;23:329. [PubMed]
(12) Anala S, Pavlovskaya GE, Pichumani P, Dieken TJ, Olsen MD, Meersmann T. J. Am. Chem. Soc. 2003;125:13298. [PubMed]
(13) Ruppert K, Brookeman JR, Hagspiel KD, Mugler JP. Magn. Reson. Med. 2000;44:349. [PubMed]
(14) Ruppert K, Mata JF, Brookeman JR, Hagspiel KD, Mugler JP. Magn. Reson. Med. 2004;51:676. [PubMed]
(15) Driehuys B, Cofer GP, Pollaro J, Mackel JB, Hedlund LW, Johnson GA. Proc. Natl. Acad. Sci. USA. 2006;103:18278. [PubMed]
(16) Weathersby PK, Homer LD. Undersea Biomed. Res. 1980;7:277. [PubMed]
(17) Lowery TJ, Doucleff M, Ruiz EJ, Rubin SM, Pines A, Wemmer DE. Protein Sci. 2005;14:848. [PubMed]
(18) Locci E, Casu M, Saba G, Lai A, Reisse J, Bartik K. ChemPhysChem. 2002;3:812. [PubMed]
(19) Dubois L, Da Silva P, Landon C, Huber JG, Ponchet M, Vovelle F, Berthault P, Desvaux H. J. Am. Chem. Soc. 2004;126:15738. [PubMed]
(20) Wolber J, Cherubini A, Leach MO, Bifone A. NMR Biomed. 2000;13:234. [PubMed]
(21) Driehuys B, Möller HE, Cleveland ZI, Pollaro J, Hedlund LW. Radiology. in press.
(22) Swanson SD, Rosen MS, Agranoff BW, Coulter KP, Welsh RC, Chupp TE. Magn. Reson. Med. 1997;38:695. [PubMed]
(23) Nakamura K, Kondoh Y, Wakai A, Kershaw J, Wright D, Kanno I. Magn. Reson. Med. 2005;53:528. [PubMed]
(24) Spence MM, Rubin SM, Dimitrov IE, Ruiz EJ, Wemmer DE, Pines A, Yao SQ, Tian F, Schultz PG. Proc. Natl. Acad. Sci. USA. 2001;98:10654. [PubMed]
(25) Wei Q, Seward GK, Hill PA, Patton B, Dimitrov IE, Kuzma NN, Dmochowski IJ. J. Am. Chem. Soc. 2006;128:13274. [PubMed]
(26) Chambers JM, Hill PA, Aaron JA, Han Z, Christianson DW, Kuzma NN, Dmochowski IJ. J. Am. Chem. Soc. 2009;131:563. [PMC free article] [PubMed]
(27) Roy V, Brotin T, Dutasta JP, Charles MH, Delair T, Mallet F, Huber G, Desvaux H, Boulard Y, Berthault P. ChemPhysChem. 2007;8:2082. [PubMed]
(28) Schroder L, Lowery TJ, Hilty C, Wemmer DE, Pines A. Science. 2006;314:446. [PubMed]
(29) Bifone A, Song YQ, Seydoux R, Taylor RE, Goodson BM, Pietrass T, Budinger TF, Navon G, Pines A. Proc. Natl. Acad. Sci. USA. 1996;93:12932. [PubMed]
(30) Moller HE, Chawla MS, Chen XJ, Driehuys B, Hedlund LW, Wheeler CT, Johnson GA. Magn. Reson. Med. 1999;41:1058. [PubMed]
(31) Wolber J, Cherubini A, Leach MO, Bifone A. Magn. Reson. Med. 2000;43:491. [PubMed]
(32) Wolber J, Cherubini A, Dzik-Jurasz ASK, Leach MO, Bifone A. Proc. Natl. Acad. Sci. USA. 1999;96:3664. [PubMed]
(33) Han SI, Garcia S, Lowery TJ, Ruiz EJ, Seeley JA, Chavez L, King DS, Wemmer DE, Pines A. Anal. Chem. 2005;77:4008. [PubMed]
(34) Driehuys B, Cates GD, Miron E, Sauer K, Walter DK, Happer W. Appl. Phys. Lett. 1996;69:1668.
(35) Hilty C, Lowery TJ, Wemmer DE, Pines A. Angew. Chem. Int. Ed. 2006;45:70. [PubMed]
(36) Baumer D, Brunner E, Blumler P, Zanker PP, Spiess HW. Angew. Chem. Int. Ed. 2006;45:7282. [PubMed]
(37) Wickramasinghe SR, Han B, Garcia JD, Specht R. AIChe J. 2005;51:656.
(38) Moller HE, Chen XJ, Saam B, Hagspiel KD, Johnson GA, Altes TA, de Lange EE, Kauczor HU. Magn. Reson. Med. 2002;47:1029. [PubMed]
(39) Driehuys B, Pollaro J, Cofer GP. Magn. Reson. Med. 2008;60:14. [PMC free article] [PubMed]
(40) Cates GD, Schaefer SR, Happer W. Phy. Rev. A. 1988;37:2877. [PubMed]
(41) Voorhees ME, Brian BF. Int. Anesthesiol. Clin. 1996;34:29. [PubMed]
(42) Wickramasinghe SR, Garcia JD, Han BB. J. Membrane Sci. 2002;208:247.
(43) Cussler EL. Mass Transfer in Fluid Systems. 2nd ed. Cambridge University Press; New York: 1997.
(44) Matsuda N, Sakai K. J. Membrane Sci. 2000;170:153.
(45) Brodkey RS, Hershey HC. Transport Phenomena: A Unified Approach. Brodkey Publishing; Columbus, OH: 2003.
(46) Anger BC, Schrank G, Schoeck A, Butler KA, Solum MS, Pugmire RJ, Saam B. Phys. Rev. A. 2008;78:043406.
(47) Deaton DM. M.S. Thesis. North Carolina State University; 1998.
(48) Jacob RE, Driehuys B, Saam B. Chem. Phys. Lett. 2003;370:261.
(49) Jameson CJ, Jameson AK, Hwang JK. J. Chem. Phys. 1988;89:4074.
(50) Moller HE, Chen XJ, Chawla MS, Driehuys B, Hedlund LW, Johnson GA. J. Magn. Reson. 1998;135:133. [PubMed]
(51) Dimitrov IE, Reddy R, Leigh JS. J. Magn. Reson. 2000;145:302. [PubMed]
(52) Grocott HP, Mackensen GB, Newman MF, Warner DS. Perfusion-UK. 2001;16:75. [PubMed]
(53) Moller HE, Cleveland ZI, Hedlund LW, Fubara B, Cofer GP, Driehuys B. Proceedings ISMRM 17th Annual Meeting; Honolulu, HI. 2009.
(54) Junker F, Veeman WS. Macromolecules. 1998;31:7010.
(55) Mair RW, Cory DG, Peled S, Tseng CH, Patz S, Walsworth RL. J. Magn. Reson. 1998;135:478. [PubMed]
(56) Wolber J, Doran SJ, Leach MO, Bifone A. Chem. Phys. Lett. 1998;296:391.
(57) Yeh S, Peterson RE. J. Pharm. Sci. 1964;53:822. [PubMed]
(58) Lide DR, editor. CRC Handbook of Chemistry and Physics. Vol. 89. CRC Press, LLC; Boca Raton, FL: 2009.
(59) Butler JP, Mair RW, Hoffmann D, Hrovat MI, Rogers RA, Topulos GP, Walsworth RL, Patz S. J. Phys.: Condens. Matter. 2002;14:L297. [PMC free article] [PubMed]