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Microengineering Improves MR Sensitivity

Neil MacKinnon, Jan G. Korvink, and Mazin Jouda

Institute of Microstructure Technology, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany

1.1 Introduction

Thirty years have passed since 1991 when Paul Callaghan published his book on magnetic resonance microscopy [1], and many works have subsequently appeared that have made numerous advances in this exciting field possible. Our goal for this chapter is to (informally) revisit some of Callaghan's analysis, to reflect on it, and then take account of some of the advances and insights that have been reported since then.

1.1.1 Comparative Electromagnetic Radiation Imaging

Paul Callaghan's book [1] is perhaps the first publication to consider magnetic resonance imaging (MRI) in the same light as optical microscopy. This will also be our starting point.

Until the advent of super-resolution microscopy, refractive optical microscopy was essentially a radiation scattering method, in which a beam of photons from an independent light source was sent on its way to scatter off objects, followed by traversal of the beam through a focusing objective on its way back to a detector, to thereby reveal the structure and composition of the scattering object. The limitations of this approach, in terms of resolution, is known as the Abbe limit d = ?/(2 n sin ?), where n is the refractive index, ? the half-angle of the spot subtended by the lens, and ? the radiation wavelength.

Using radio waves taken for convenience at 300 MHz, a thus interpreted refractive MRI system would have a resolution of ~500 mm, which is a dire prospect for applications of MRI. In a seminal paper, Mansfield et al. [2] reported on a form of nuclear magnetic resonance (NMR) diffraction, in which they considered a solid-state periodic lattice of spins in a macroscopically sized lattice, revealing diffraction patterns on the order of the lattice. As a follow-up to this idea, Blümler et al. [3] and Bernhard Blümich [4] reported (the latter in a paper dedicated to Paul Callaghan) on an interesting intertwining of concepts of the k -space vector of refractive MRI and the spatial periodicity of a lattice-like diffractive structure, further exploring diffractive imaging. Blümich's paper contains a few more gems worth discussing, but would distract us too far from the optical viewpoint we are considering here.

Near-field effects can be further exploited to increase the resolution of an imaging system. At optical wavelengths, one is hardly able to extend beyond 200 nm of resolution with currently available light sources. "The diffraction limit of light is 100 times the size of structures that cell biologists study as they characterise events in organelles or membranes," Hari Schroff (NIH/NIBIB) is quoted to say in [5], yet below 200 nm "is where most cellular action is," the author notes. The alternative is to avoid scattering as an imaging paradigm, instead, to image photon sources (also known as quantum emitters).

Interestingly, deep space astronomy always worked this way around by observing photon emitters, so that astronomers only consider objects that were once themselves sources of radiation, such as stars and their predecessors and descendants. In astronomy, the limit of resolution is therefore not dominated by the wavelength of the radiation, which can be very small when compared to the size and distance of the astronomical objects, but rather by the measuring instrument's principle of operation, its detection sensitivity, and in particular, its effective aperture.

When imaging radiation sources, such as single photon emitters in molecules, we now know that we can greatly improve on the Abbe limit, by about a factor of 10, especially when combined with techniques of stimulated emission and depletion, and one of the numerous variations based on fluorophore emission dynamics. These techniques, which have revolutionized cellular biology and won its inventor Stefan Hell the Nobel Prize in 2014, are of course not accessible to astronomers, who would have to wait too long for excitation signals to pass from observer to object and back again. But for cell biology this is not problematic. Although at currently ~30 nm, the resolution is still far from the desired 1 nm limit, advances in image processing present a feasible route to achieve further improvements. But the technique also raises some questions. Sample preparation is very difficult, and imaging is indirect as fluorophores have to be invasively attached to interesting molecules, almost certainly modifying their behavior.

Magnetic resonance microimaging is a noninvasive technique that is clearly more closely related to stimulated emission depletion (STED) microscopy than to conventional scattering light microscopy. A localized atomic nucleus' spin is a quantum absorber/emitter. By localizing the excitation field spatially or by frequency, a sub-selection of the spins in a sample can be prepared to absorb radiation. Further localization can ensure that emission of radiation energy is again sub-selected, for example along the geometrical intersection of two orthogonal manifold slices, the one for excitation, the other for emission. A range of further techniques, such as available through relaxation contrast, or phase accumulation, can again further sub-select spins before readout, thereby improving resolution in direct analogy to the techniques of fluorophore emission dynamics. Noninvasive Faraday-detected MRI has been reported down to ~3 µm resolution [6], which is already five orders of magnitude below the radiation wavelength. Nevertheless, even though MRI records radio frequency emissions, this is done almost exclusively through near-field interactions, i.e. by Faraday induction, and not from a beam or ray that requires a lens for focusing.

One of the limitations in NMR is certainly that a single quantum emission event is not yet readily observable as it would be in photonics, even though Dan Rugar showed that a single spin can be observed [7]. Thus all Faraday induction-acquired MRI images have to resort to averaging of a vast number of emission events, and over extended time, to yield useful information. If detection sensitivity were to be increased, fewer emitters could be used, and could perhaps be averaged over shorter times.

1.1.2 Limit of Detection

The statistical polarization level, i.e. that proportion of the total spin population that is available for quantum emission, is an additional cause of lack of signal. Proton spins for example are indistinguishable fermions, with a level occupation that follows

and which collapses to Maxwell-Boltzmann statistics when e(ei-µ)/kT » 1, because the energy of a proton flip ?hB0 = 3.3 × 10-25 J is tiny compared with the thermal energy kT = 4.11 × 10-21 J. Thus at typical equilibrium polarization levels at 11.7 T, a factor of only 10-4 in excess in population difference with respect to the Fermi level µ can contribute to the signal. An imaging voxel size is therefore principally limited by polarization, because we find - for microcoils at their limit of detection - a sample containing around 1013 spins is needed to form an observable signal. Clearly, this sets a lower concentration limit once the voxel size is specified. For example, at the average size of a single eukaryotic cell of (10 µm)3, containing the required nuclei, implies a concentration of at least 1.66 µM. By increasing polarization, the voxel size is thus principally reduced, or the lower concentration limit is reduced, which could be achieved by resorting to out-of-equilibrium polarization techniques such as parahydrogen-induced polarization (PHiP), signal amplification by reversible exchange (SABRE), or dynamic nuclear polarization (DNP), all of which are rather hard to perform noninvasively, and hard to selectively localize too. We will return to this point shortly. One of the key advantages of MR-based microscopy is the ability to noninvasively reveal molecular composition, correlated with morphology. From the perspective of biological systems, this can be leveraged to monitor, for example, spatially resolved metabolism. To estimate the best achievable spatial resolution (voxel size), signal-to-noise ratio (SNR) should be considered in the context of the metabolically active system. Key parameters are the molecule abundances (concentrations) and timescale that are targeted. Consider a spatially resolved fluxomic investigation: can one estimate a realistic MRI spatial resolution taking into consideration the expected biological dynamics? Alternatively, what is the smallest biological structure with which metabolic flux can be measured - thus, is it possible to monitor flux at the level of an organelle, single cell, cell cluster, or tissue?

Water is the most abundant molecule in biosystems and can be used as a useful reference from which scaling based on metabolite concentrations can be made. Using only the physical volume of a water molecule (0.03 nm3), and an optimistic limit of detection (LOD) of 1013 spins, then an order of magnitude estimate of the smallest voxel is 0.1 pl (approximately 4.5 µm isotropic resolution). This is approximately the volume of a single red blood cell. Intracellular metabolite concentrations vary over several orders of magnitude, with the...