Magnetic Resonance Imaging

Abstract

Magnetic Resonance Imaging (MRI) has witnessed a huge amount of growth in its application to cardiac disease in the last ten years due, in part, to developments in signal acquisition and processing. MRI provides clinicians with important information regarding anatomy, function, perfusion, and viability of the myocardium.

Appendix: MRI Image Formation

The basis of the signal in MRI is the excitation of nuclear spins which emit a RF signal. When returning to their unperturbed state, water molecules emit an electromagnetic signal that is slightly different, depending on the local environment. This process is known as relaxation. The process by which the perturbed spins return to their unperturbed state is complex, but is well described by a differential equation known as the Bloch equation,

$$ \frac{d\overrightarrow{M}}{dt}=\overrightarrow{M}\times \gamma \overrightarrow{B}{­}\frac{{M}_{x}\widehat{i}+{M}_{y}\widehat{j}}{{T}_{2}}{­}\frac{({M}_{z}{­}{M}_{0})\widehat{k}}{{T}_{1}}. $$

In the Bloch equation, M is the magnetization vector of a small macroscopic volume of tissue (or “Voxel”). Magnetization is a vector quantity, and changes in this vector are accompanied by the emission of electromagnetic waves that are detected in the MRI receiver coils. The Bloch equation consists of three terms. The first term:

$$ \overrightarrow{M}\times \gamma \overrightarrow{B} $$

is a mathematical representation of the RF excitation pulse which tips the magnetization from its unperturbed state. The second and third terms describe the transverse and longitudinal relaxation of the magnetization. The rate of the transverse relaxation or “dephasing” depends on the T2 rate constant. In other words, the second term describes the rate at which spins lose phase coherence. T2 will vary from tissue to tissue and this term describes T2 image contrast. The last term describes the rate at which the magnetization realigns itself with the main magnetic field. It is referred to as the longitudinal relaxation rate (T1).

The MRI signal that is acquired, S(t), by the scanner is the frequency space representation of the image, I(x,y). Spatial localization of the MRI signal is achieved by shifting the frequency and phase of the local magnetic field. These slight differences in frequency are sufficient to localize the signal to better than 1 mm. The amount of phase and frequency shift is controlled by the MRI pulse sequence through the application of local field gradients, Gx and Gy. The MRI signal is recorded as segments of an electromagnetic signal S(t, ty). This signal is related to the true MRI image by:

$$ S(t;{t}_{y})=\underset{x}{\int }\underset{y}{\int }I(x,y){e}^{-i\gamma {G}_{y}y{t}_{y}}{e}^{-i\gamma {G}_{x}xt}dydx. $$

The expression shown above is well known in the engineering literature as the Fourier Transformation of the Image. Fast Fourier transform algorithms for the calculation of the image, I(x, y), have existed since the early 1960s. After a signal is acquired, a Fast Fourier Transform must be performed by the scanners image reconstruction computer prior to review.