The Bloch equations describe the evolution over time of the magnetization in x, y, and z (Mx, My, and Mz) as a function of the strength of the homogeneous magnetic field (B0), any applied gradients in the magnetic field (G), transverse relaxation (T2), and longitudinal relaxation (T1). equation(1) dMxdt=γMy(B0+G·r)-MxT2 equation(2) dMydt=-γMx(B0+G·r)-MyT2 Ku-0059436 supplier equation(3) dMzdt=-(Mz-M0)T1 The Bloch equations were
solved in Matlab using numerical integration [31]. A homogeneous sample of length 5 mm was used and resolved with a spatial resolution of 0.1 mm. The temporal resolution of the r.f. and gradient shape was 1 μs. The Bloch equations were used to compare three different slice selection profiles for a 1024 μs full Gaussian pulse, a 512 μs half Gaussian pulse with positive and negative slice selection and a 537 μs VERSE pulse with positive and negative slice selection. The 537 μs VERSE pulse was then used for artifact simulation. The potential artifacts arising from errors in timing during UTE slice selection were simulated, with the gradient pulse switching off 10 μs before or after the VERSE r.f. pulse. The latter shows a similar artifact as would be obtained if VERSE were not used, as in that case the ramp down of the gradient will be longer than the ramp down of the r.f.
pulse. The implemented pulse sequence for UTE is shown in Fig. 1. The sequence can be split into two almost identical parts, each consisting selleck products of an excitation pulse and slice select gradient, a set delay or TE, then the acquisition. The acquisition is displayed Myosin as a free induction decay (FID) during which gradients in both the x and y direction are ramped up to acquire radially sampled data as shown in Fig. 1b. The spokes are sampled from the center out which means that the maximum signal of the FID is sampled in the center of k-space. The only difference between the first and second half of the sequence is the sign
of the slice select gradient. The acquired data from both the positive and negative slice select experiments are added prior to using a re-gridding approach to obtain the image. Here, the re-gridding algorithm of Fessler and Sutton is used [29]. The sensitivity of an MRI sequence to T2 relaxation is characterized by the TE which is a measure of the T2 or T2* weighting of a sequence and, in this study, refers to the time after excitation at which the center of k-space is acquired. If the signal lifetime is shorter than the TE, there will be little signal left during acquisition and hence the signal to noise ratio (SNR) of the image will be low and in the limit approximately zero. In a spin echo, TE is defined as twice the time between the 90° and 180° pulses, or the time from the zero phase point of the excitation to the peak of the spin echo; the gradient echo and spin echo coincide. The minimum TE for a spin echo is on the order of 1 ms.
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