2. Theory

1. Introduction

248 Raman Spectroscopy and Applications

to compound this issue.

10−<sup>6</sup>

Magnetic resonance imaging (MRI) is a powerful tool for diagnostic imaging of soft tissue, combining superior contrast, dynamic capability, and no risk of damage caused by ionizing radiation compared to computerized tomography (CT) [1]. Most MRI techniques conveniently detect the nuclear spin of protons in water, which makes up a significant portion of the human body. This detection modality poses a problem within the lungs, however, as the low proton density translates to greatly reduced signal-to-noise ratios for conventional MRI techniques. Even at high magnetic field strengths, the equilibrium nuclear spin polarization is very low (~10−<sup>4</sup> to

). To facilitate MRI inside the lungs, far greater signal-to-noise ratios are needed, requiring nuclear spin polarizations to be increased far above equilibrium levels—a process known as hyperpolarization. Indeed, inhalation of hyperpolarized gases provides greatly improved sensitivity and bright images, outweighing the low spin densities of the gas phase. Gas hyperpolarization can now be readily achieved using established techniques; however in these approaches, maximizing the available spin polarization is hampered by complex system dynamics and

In most studies relevant to lung imaging, this hyperpolarized state is achieved by utilizing circularly polarized photons to shift particles with a nonzero magnetic moment between discrete spin states. During gas-phase collisions, spin angular momentum is transferred from alkali metal electrons to noble gas nuclei, a technique known as spin-exchange optical pumping (SEOP) [2]. Noble gases are used in SEOP because of their lack of reactivity with alkali metal vapors and their ultra-long hyperpolarization lifetimes. Nitrogen is present as a buffer gas to prevent radiation trapping, helping to maximize the alkali metal electron spin polarization—and hence, the noble gas nuclear spin polarization. Thus, inhalation of a hyperpolarized noble gas sample such as 129Xe while inside the MRI scanner enables both structural and functional high-resolution imaging of the lungs in real time. Despite significant advances in polarizer technology in recent years, many underlying aspects of the SEOP process, such as energy- and mass transport mechanisms within the OP cell and the temperature dependences of many parameters, remain poorly understood. Ironically, the desire to maximize the available nuclear spin magnetization leads to a demand for higher pump laser powers and richer noble gas mixtures, which only serve

In an attempt to overcome these challenges, Raman spectroscopy may be used to complement more commonly used techniques such as optical absorption spectroscopy and low-field NMR in order to optimize the multidimensional SEOP parameter space, thereby improving the 129Xe hyperpolarization process for MR applications. Conventional temperature measurement (e.g., using a thermocouple) would be challenging to implement, given that the SEOP process takes place inside a sealed vessel, within a magnetic field, and under constant uniform illumination by high-power laser light; moreover, temperature measurement of the exterior cell walls may often provide only a poor reflection of the true gas behavior within the cell. However, if optical access is available, Raman spectroscopy can be used to acquire in situ rotational and vibrational temperature measurements of the nitrogen buffer gas—and hence, an accurate picture of the true gas temperature at a given location within the cell. This capability should provide a more complete

codependence of many variables that are heavily temperature-dependent.

#### 2.1. Spin-exchange optical pumping

The SEOP process consists of two major steps. Firstly, circularly polarized photons (necessary to satisfy the selection rules for optical absorption) are used to transfer angular momentum to a gaseous target with nonzero spin, such as spin-½ electrons. A vaporized alkali metal such as rubidium is typically used, since its single outer shell electron is easier to manipulate and existing laser technology at the required transition wavelengths is well developed. The net polarization, P, of the alkali metal can then be given by [3]

$$P = S\_z \frac{R}{\Gamma\_{SD} + R} \tag{1}$$

where Sz is the photon spin of the circularly polarized laser light, R is the optical pumping rate, and ΓSD is the rate of spin destruction or spin relaxation due to collisions with the walls of the system or other gas-phase species (particularly xenon atoms). Assuming the optical pumping rate exceeds the rate of relaxation, a large population excess will accumulate in one of the two electronic spin states, leading to the alkali metal as a whole becoming highly polarized. The particular favored state depends on the directional helicity of the light.

The second stage in the SEOP process is that of spin-exchange. Bringing an unpolarized gaseous system into contact with the polarized alkali metal vapor results in spin-coupling via a hyperfine interaction. Gas phase collisions then lead to transfer of polarization from alkali metal electrons to noble gas nuclei on short timescales. The net spin polarization of the noble gas during the spin-exchange process is calculated using [3]

$$P\_G = P\_A \frac{\Gamma\_{SE}}{\Gamma\_{SE} + \Gamma\_{SD}} \left[ 1 - e^{-t(\Gamma\_{SE} + \Gamma\_{SD})} \right] \tag{2}$$

where PG and PA represent the net spin polarizations of the gas and alkali metal, respectively, ΓSE is the rate of spin exchange between alkali metal electrons and gas nuclei, ΓSD is the rate of alkali metal electron spin destruction, and t is the time elapsed after the commencement of laser polarization in seconds. The SEOP process requires temperatures on the order of 100°C to ensure sufficient alkali metal vapor density. Buffer gases such as nitrogen is commonly used to quench radiation trapping and slow the rate of electron spin relaxation to help maintain high net spin polarizations by preventing unwanted fluorescence and reabsorption of unpolarized light [4] by alkali metal electrons. An overview of the SEOP process is illustrated in Figure 1.

Figure 1. The spin-exchange optical pumping (SEOP) process. (a) Optical pumping and collisional mixing of the alkali metal electron spin states using circularly polarized light. (b) Polarization of noble gas nuclei via collision and spin-exchange process in the formation and breakup of an alkali-metal/noble-gas van der Waals molecule. Figures adapted from [7].

As previously mentioned, temperature is one of the most important variables governing the SEOP process. Elevated temperatures raise the alkali metal vapor density within the cell, increasing the probability of collisions between pump laser photons and alkali metal electrons and more importantly resulting in increased spin-exchange rates. As evidenced by Eq. (2), the latter effect should lead to a greater net spin polarization of the noble gas, provided there is sufficient pump light intensity to maintain good illumination of the optical cell (and hence, good alkali metal polarization). This prediction holds to a certain extent—as temperature continues to rise however, the alkali metal number density can increase rapidly in a selfpropagating fashion; the alkali metal vapor absorbs more light, whose energy is rapidly converted to heat, which can in turn lead to even more alkali metal vaporization. This results in the form of optical opacity, whereby pump laser light is unable to penetrate the length of the optical cell. This actually reduces the efficiency of optical pumping in the areas of the cell furthest from the pump laser, because although the spin-exchange rate may be quite high, the alkali metal polarization in much of the cell is low, greatly reducing noble gas polarization. This is known as a "runaway" process [5, 6], and is clearly detrimental to a stable, efficient SEOP process. In the interest of obtaining the highest possible NMR signal, it is desirable to conduct experiments at an optimal temperature where net spin polarization and build-up rates are maximized, while avoiding the unstable runaway regime.

#### 2.2. Temperature measurement using Raman spectroscopy

As mentioned above, the presence of nitrogen gas inside the optical cell is primarily meant to quench the rate of radiative spin-destruction, achieved by collisions with electronically excited alkali metal atoms. The energy transferred as a result of these collisions is pooled in the rotational and vibrational modes of the N2 molecules; these modes quickly relax to the translational degrees of freedom, thereby increasing the local gas temperature inside of the cell. Since SEOP must take place inside a closed system due to the high reactivity of alkali metals in air, physical insertion of a thermocouple is impractical for the reasons listed above, and merely measuring the cell surface temperature does not provide a true account of the internal temperature, nor the corresponding energy transport processes occurring within the cell. Additionally, progressively stronger light sources have been utilized for SEOP over the years, and lasers emitting tens or hundreds of watts of energy are now standard [6]. Virtually all of the laser energy absorbed by Rb is transferred to the rotational and vibrational degrees of freedom in the N2 buffer gas, which then rapidly equilibrates with the translational temperature (corresponding to the local temperature of the gas mixture). These changes in temperature are capable of significantly affecting SEOP (hence, xenon polarization) through changes to the alkali metal density and absorption profile [8], degradation of organic coatings on the OP cell surface [9], and convective gas transport that may bring xenon in closer proximity to paramagnetic relaxation centers in the cell wall surface [4, 10, 11]; changes to temperature-dependent cross-sections that govern polarization and depolarization rates in SEOP may also occur. Remote sensing of the N2 rotational (and vibrational) temperatures inside the pump cell during SEOP can be achieved using in situ Raman spectroscopy.

Hickman et al. [12] demonstrated that the intensity of each peak, numbered J, in the N2 Raman spectrum follows the relation

$$I(J)\infty\nu^4 g(J)(2J+1)P\_{J\to f}e^{-\frac{\delta l(l+1)}{k\_BT}}\tag{3}$$

where ν is the frequency of the rotational line in Hertz, g(J) is the ground state degeneracy due to the nuclear spin, B is the rotational constant for nitrogen (taken to be ~2), kB is Boltzmann's constant, J is the peak number, and

$$P\_{f \to f} = \frac{3(f+1)(f+2)}{2(2f-1)(2f+1)}\tag{4}$$

Combining Eqns. (3) and (4) produces the relation

As previously mentioned, temperature is one of the most important variables governing the SEOP process. Elevated temperatures raise the alkali metal vapor density within the cell, increasing the probability of collisions between pump laser photons and alkali metal electrons and more importantly resulting in increased spin-exchange rates. As evidenced by Eq. (2), the latter effect should lead to a greater net spin polarization of the noble gas, provided there is sufficient pump light intensity to maintain good illumination of the optical cell (and hence, good alkali metal polarization). This prediction holds to a certain extent—as temperature continues to rise however, the alkali metal number density can increase rapidly in a selfpropagating fashion; the alkali metal vapor absorbs more light, whose energy is rapidly converted to heat, which can in turn lead to even more alkali metal vaporization. This results in the form of optical opacity, whereby pump laser light is unable to penetrate the length of the optical cell. This actually reduces the efficiency of optical pumping in the areas of the cell furthest from the pump laser, because although the spin-exchange rate may be quite high, the alkali metal polarization in much of the cell is low, greatly reducing noble gas polarization. This is known as a "runaway" process [5, 6], and is clearly detrimental to a stable, efficient SEOP process. In the interest of obtaining the highest possible NMR signal, it is desirable to conduct experiments at an optimal temperature where net spin polarization and build-up rates

Figure 1. The spin-exchange optical pumping (SEOP) process. (a) Optical pumping and collisional mixing of the alkali metal electron spin states using circularly polarized light. (b) Polarization of noble gas nuclei via collision and spin-exchange process in the formation and breakup of an alkali-metal/noble-gas van der Waals molecule. Figures adapted from [7].

As mentioned above, the presence of nitrogen gas inside the optical cell is primarily meant to quench the rate of radiative spin-destruction, achieved by collisions with electronically excited

are maximized, while avoiding the unstable runaway regime.

250 Raman Spectroscopy and Applications

2.2. Temperature measurement using Raman spectroscopy

$$-Bf(f+1)\frac{hc}{k\_B T} = \ln \frac{S(f)}{g(f)f(f)} + 4\ln \frac{1}{\nu} \tag{5}$$

where S(J) is the measured intensity of the Raman peak, h is the Planck constant, c is the speed of light in m s−<sup>1</sup> , and

$$f(f) = \frac{3(f+1)(f+2)}{2(2f+3)}\tag{6}$$

A plot of F JðÞ¼ ln S Jð Þ g Jð Þf Jð Þ h i against <sup>J</sup>(<sup>J</sup> <sup>+</sup> <sup>1</sup>) then yields a straight line with gradient <sup>m</sup> <sup>¼</sup> Bhc kBT. Rearranging this equation for T thus allows calculation of the rotational temperature of N2.

#### 2.3. Hyperpolarized lung imaging

Any noble gas isotope with nonzero spin can theoretically be used as a hyperpolarized contrast agent with a view for clinical lung MRI. Traditionally, helium-3 was most commonly used due to its high gyromagnetic ratio—resulting in stronger MRI signals. However, due to its insolubility in blood and water, perfusion across the alveolar wall cannot occur, primarily limiting the use of 3 He to gas-phase ventilation and diffusion imaging. The difficulty in wide-spread clinical <sup>3</sup> He adoption is further compounded by the difficulty and expense of acquisition, since <sup>3</sup> He is a nonrenewable by-product of tritium decay in nuclear reactors. As such, most current clinical studies on hyperpolarized noble gases use 129Xe for its solubility in tissue and blood, significant chemical shift range, low cost of acquisition, and high natural abundance.

As discussed previously, higher net spin polarizations directly result in stronger MR signal generation and hence, improved image contrast between areas of interest and background noise. Recent hyperpolarization methods can create near-unity net spin polarizations [13], resulting in spectroscopic signals four to five orders of magnitude greater than nonhyperpolarized samples. Such improvements in image quality facilitate the use of HP noble gas MRI within the lungs as a diagnostic imaging tool for characterizing lung structure and function [14], and consequently may potentially enable earlier and more reliable diagnosis of various respiratory disorders, such as idiopathic pulmonary fibrosis (IPF) and chronic obstructive pulmonary disease (COPD) 7]. An example of a HP 129Xe lung ventilation image can be seen in Figure 2.

Figure 2. (a) Coronal plane 25 mm slice 129Xe-MR ventilation image of a healthy adult male, with 129Xe appearing bright, upper airways are clearly delineated. (b) Second coronal plane 25 mm slice fused 129Xe-MR ventilation and proton coregistration image, with 129Xe appearing green blue-green. On the fused image, it can be seen that ventilation defects on the ventilation image (yellow arrows) correspond to a diaphragmatic eventration and pulmonary vasculature on the fused image (blue arrows) [15].
