Magnetic resonance imaging (MRI) of solids is rarely attempted. One of the main reasons is that the broader MR linewidths, compared to the narrow resonance of the hydrogen ( 1 H) in free water, limit both the attainable spatial resolution and the signal-to-noise ratio. Basic physics research, stimulated by the quest to build a quantum computer, gave rise to a unique MR pulse sequence that offers a solution to this long-standing problem. The "quadratic echo" significantly narrows the broad MR spectrum of solids. Applying field gradients in sync with this line-narrowing sequence offers a fresh approach to carry out MRI of hard and soft solids with high spatial resolution and with a wide range of potential uses. Here we demonstrate that this method can be used to carry out three-dimensional MRI of the phosphorus ( 31 P) in ex vivo bone and soft tissue samples.bone mineral | cell membranes M agnetic resonance imaging (MRI) has become an invaluable tool for clinical medicine, fundamental biomedical research, the physical sciences, and engineering (1). Typically, MRI detects only the signal from free water, using just a single nuclear isotope ( 1 H). Extending the reach of MRI to the study of other elements, and to hard or soft solids, opens new frontiers of discovery. One example is phosphorus ( 31 P), which is abundant in both bone mineral and cell membranes, so 31 P MRI of tissues is, in principle, possible. In practice, however, the slower motion of 31 P in those environments (compared to 1 H in water) results in much broader MR spectra (Fig. S1), limiting both the attainable spatial resolution and the signal-to-noise ratio (2). In this paper, we describe the use of a pulse sequence to narrow the 31 P MR spectrum of solids to that of a liquid (3), making high-resolution imaging possible. This line-narrowing MR sequence was discovered in the course of basic research (3-6) initiated by Kane's proposal (7) to build a quantum computer using phosphorus spins in silicon. Applying field gradients in synch with this sequence, we have obtained high-resolution 3D MR images of the 31 P in a variety of ex vivo animal bone samples. This is a unique probe of a key element in bone mineral, which complements existing assessments of bone quality. Using the same approach, we have obtained 3D MR images of 31 P in several ex vivo soft tissues.Bone is a composite material (8), containing approximately 45% bone mineral by volume (9). Bone mineral is similar to calcium hydroxyapatite (i.e., Ca 10 ðOHÞ 2 ðPO 4 Þ 6 Þ, but it is less crystalline, and it has a unique stoichiometry (10). The spatial distribution, composition, and quantity of bone mineral are primarily responsible for the compressive strength and stiffness of bone (8-10). While a few 31 P MRI studies have successfully targeted in vivo (10-12) and ex vivo (10, 13, 14, 15) bone, the broad MR spectra have limited the achievable spatial resolution to no better than 0.5 mm (15) and more typically in the range of 2 mm. There is currently a great need to probe the internal compositi...

Techniques that accelerate data acquisition without sacrificing the advantages of fast Fourier transform (FFT) reconstruction could benefit a wide variety of magnetic resonance experiments. Here we discuss an approach for reconstructing multidimensional nuclear magnetic resonance (NMR) spectra and MR images from sparsely-sampled time domain data, by way of iterated maps. This method exploits the computational speed of the FFT algorithm and is done in a deterministic way, by reformulating any a priori knowledge or constraints into projections, and then iterating. In this paper we explain the motivation behind this approach, the formulation of the specific projections, the benefits of using a ‘QUasi-Even Sampling, plus jiTter’ (QUEST) sampling schedule, and various methods for handling noise. Applying the iterated maps method to real 2D NMR and 3D MRI of solids data, we show that it is flexible and robust enough to handle large data sets with significant noise and artifacts.

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