Our very hypothetical water and oil resonances have T2 relaxation times of 67 and 25 ms, respectively, yielding line widths of 4.75 and 12.7 Hz. Line widths this narrow would occur only in a very uniform magnetic field. The large bore (>12 cm) magnets suitable for imaging of food samples have spatially varying fields ; that and the relatively large sample size (several centimeters) usually produce line widths sufficient to partially overlap resonances from oil and water. In recognition of the actual situation, T2* (T2 star) denotes the combined effect of T2 and field irregularities:

Nonuniformities in the magnetic field cause spatial variations in the resonant frequency as gradients do, but in an undesirable, non-linear fashion. Resolution decreases as T2* increases.

1.2. Gradients

The foundation of magnetic resonance imaging lies in the response of resonance frequency to changes in the magnetic field; difference in frequency or phase due to application of magnetic field gradients provides information on position, diffusion rates and flow velocity. In general, imposition of a linear field gradient upon a uniform magnetic field (Bo) influences resonance frequency by a modification of equation 2,

where Gx and x denote a linear gradient in the x dimension and position on the x axis, respectively. Equation 9 describes the phenomenon which permits slice selection, frequency encoding and phase encoding.

Slice selection in a spin-echo experiment (Figure 2) allows excitation of a relatively narrow band of frequencies, which, in the presence of the magnetic field gradient described above, corresponds to a limited volume of resonating nuclei. Excitation of nuclei from a designated volume necessarily restricts the origin of the acquired signal to nuclei from that volume, and facilitates non-invasive observation of the interior of objects.

The phenomenon described by equation 9 also allows encoding of position according to frequency, aptly named frequency encoding (Figure 2). After Fourier transformation (a mathematical method for converting a mixture of frequencies, varying with respect to time, to a frequency map, or spectrum, with variation with respect to frequency; Figure 1) of a signal received from an object within a field gradient, the resulting profile or projection portrays spatial information versus intensity. The resonances of Figure 1 at 25 and 100 Hz could also originate from two objects 1 cm apart in a 75 Hz/cm gradient. Acquisition of the signal proceeds during imposition of the gradient, in contrast to phase encoding. Phase encoding involves application of the linear gradient for a short time, imposing a temporary frequency change (Figure 2); upon removal of the gradient, the resonance frequency returns to its previous value, but its accumulated phase <j> will depend on the strength of the gradient Gx at position x and the duration of application, t:

If no reversal of this gradient effect occurs during the experiment, the acquired signal contains phase encoded positional information; all gradients used in a spinecho imaging sequence must be reversed to avoid imparting undesired phase shifts to stationary nuclei (Figure 2).

MRI technology can quantify any condition which confers a coherent phase shift to the MR signal from an ensemble of nuclei. Application of two gradients, the first inducing phase, the second, opposite in sign, reversing phase, encode motion. Setting the phase accumulation to zero in this way erases any positional information from stationary nuclei; any nucleus moving to another position in the gradient field, different in magnetic field strength, will accumulate phase, and its phase difference depends upon the distance moved during time t. The time frame of the motion determines the design of the experiment. Slow motions such as diffusion or perfusion, involving translations at 10"5 cm2/s, require relatively long (e. g., 40 ms), high amplitude gradient pulses, separated by durations of sufficient length to allow motion and accumulation of phase (Figure 2). Velocity measurements, though similar in general structure, demand particular gradient durations and separation times for investigation of each velocity distribution (Figure 2). Mobility of nuclei determines the behavior of the NMR signal, and analysis of the NMR signal can in turn define the mobility of the nuclei, ranging from slow to fast, from the slow molecular movements of crystallisation to flow rates of meters per second.

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