Distortion-free magnetic resonance imaging in the zero-field limit

Abstract

In MRI, the Larmor precession frequency ω(x, y, z) = γB(x, y, z) of the proton spins in the position-dependent magnetic field B(x, y, z) frequency-and phase-encodes the proton density distribution into a magnetic signal that is subsequently decoded to form an image 4 (γ is the magnetogyric ratio). In clinical MRI machines 4 the strength of the applied homogeneous static magnetic field B 0 = B 0 ẑ is typically 1.5 T. There has been recent interest, however, in systems operating in magnetic fields of the order of 10 -4 T (for example [13][14][15][16][17][18] ), where T 1 -weighted contrast is significantly enhanced 16 (T 1 is the longitudinal relaxation time). The loss of polarization is compensated-at least in part-by 3 prepolarizing 19 the spins at a much higher field, or by hyperpolarization techniques using lasers 20 , dynamic nuclear polarization 21,22 or parahydrogen-induced polarization 23 . The loss of signal amplitude inherent in Faraday-Law detection is mitigated by detecting the nuclear magnetization with either a Superconducting QUantum Interference Device (SQUID) 9 or an atomic magnetometer 24 , both of which respond to the magnetic flux itself, rather than its time rate of change. Regardless of the magnitude of B 0 , all currently used imaging processes involve the superposition of magnetic field gradients on a static field to impose spatial variations of the total field across the subject or sample. In the zero static field regime reported here, conventional MRI gradients are unable to encode the spins along a given direction and Fourier encoding breaks down.In conventional MRI techniques, the applied magnetic field gradients are assumed to be linear and unidirectional so that the field due to gradients is given by B(x, y, z) = (G x x + G y y + G z z) ẑ , where G x = ∂B z /∂x, G y = ∂B z /∂y, and G z = ∂B z /∂z are constants 4 . As an example, B(x, y, z) = G z z ẑ is shown in Fig. 1a. In reality, however, such idealized gradients are forbidden by the Maxwell equations divB = curlB = 0 for any magnetic field B in free space. In fact, any gradient must be accompanied by concomitant gradients in at least one additional direction, as illustrated in Fig The gradient field B(y, z) = (∂B y /∂y)y ŷ + (∂B z /∂z)z ẑ is turned on, and subsequently turned off nonadiabatically at time τ (point B). During this time interval, the spin precesses about B(y′, z′). The time τ is chosen to satisfy the requirement τ << 1/γG z L.Consequently, the precession during the interval τ is small, and we can treat it as the sum of precessions around ẑ and ŷ : δ z = γ(∂B z /∂z)z'τ around ẑ (Fig. 2b) and δ y = γ(∂B y /∂y)y'τ around ŷ (Fig. 2c). After the gradient pulse, a π pulse of uniform field Β π is applied along the z-axis with amplitude and duration adjusted to produce a precession angle of π around ẑ . This pulse flips the spin to the point C in Figs. 2b and 2c. 5Subsequently, a second gradient pulse brings the spin to D, and a second π pulse to E. This sequence of pulses produces a net precession of the spin about B z , ...

Solving the problem of concomitant gradients in ultra-low-field MRI

“…However, when e > 1, Fourier reconstruction needs support from special sequences [10][11][12][13] to avoid artifacts in the final image.…”

“…Rotating frame gradients, generated by driving oscillating currents at the Larmor frequency simultaneously in two gradient coils, can be used to substantially reduce distortions in the Fourier encoding at ULF MRI [12]. Also tailored pulse sequences can be used to average out the effects of the concomitant gradients [10,11,13]. These methods allow one to perform MRI at arbitrary values of e; however, they need modified pulse sequences, which limits their usability.…”

Increased risk of high‐grade dermatologic toxicities with radiation plus epidermal growth factor receptor inhibitor therapy

“…While the applied gradient fields are typically assumed to be linear and along the principle magnetic field direction, Maxwell's equations dictate that small nonlinear components are also present in the transverse direction. The magnetic field amplitude offset caused by these concomitant gradient fields scales inversely with the static magnetic field strength and have historically been a concern in low‐field applications (1–3). While concomitant gradient fields can usually be ignored for common pulse sequences at most field strengths, there are some pulse sequences that are susceptible to their effects, such as echo‐planar imaging (EPI) (4–6), fast spin‐echo (7), spiral trajectories (8, 9), phase contrast MRI (10), balanced steady‐state free precession (11), and combined gradient and spin‐echo acquisition (12).…”

Fast field-cycling magnetic resonance imaging

“…More recently, the same group has published details of an improved Earth's field imaging system, this time using pre-polarisation at 60 mT [12]. Other workers have taken a similar approach, using pre-polarisation prior to signal detection in the Earth's field [13] or even at zero field [14].…”