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(19) to estimate the time ��r required to reach a particular point in k-space that corresponds to 1/(2r) for any resolution. This in turn gives an analytical estimate of the accrued spin phase http://www.selleck.cn/products/azd6738.html �� in k-space due to off-resonance ��B in the main field B0, which creates blurring in a spiral image. (20) To calculate the heat load, first integrate over the scan time using Eqs. (15), (16), and (18), i.e., (21) The energy expressed in Eq. (21) is split between coils, so to calculate the rms gradient per coil, we divide this by 2, divide by ��SC, and take the square root, i.e., (22) This shows that for a slew-constrained Archimedean spiral, the rms gradient amplitude is roughly 54.8% of the maximum (final) gradient amplitude, independent of slew rate, resolution, field of view, number of interleaves etc. From Eq. (12), gm (��GC) is less than gmax when (24) When imaging at higher resolutions (r? http://www.selleckchem.com/products/VX-765.html is given by solving Eq. (17) replacing ?max with ?P1, the phase when the maximum gradient is reached. This is given by reworking Eq. (18) to (25) The duration ��P2 of the second phase is given by (27) As with ��GC, the heat load for can be http://www.selleckchem.com/products/pf-562271.html calculated separately in the two phases, before and after the transition to a gradient-constrained spiral. The first phase is calculated similarly to Eq. (21), using ?P1 instead of ?max. (29) The second phase is calculated as (30) The total rms heat load is then calculated (32) Note for the transition state, where gm (��SC)?=?gmax (from Eq. (24)), Eqs. (22) and (32) are equivalent. The numerical algorithm was used to generate a variety of spirals by changing the value of R through different functions kr, which are listed in Table 1. The first four spiral trajectories (A�CD) were based on a base Archimedean spiral (R?=?1) with added oversampling. In each case, the radial spacing was increased either linearly, quadratically, or through a Hanning-shaped function of kr during a transition zone of (33) For Spiral D, a perturbed spiral [19] was created by adding a sinusoidal variation to R, i.e., (34) Spiral E was created as a base spiral waveform for a spherical distributed spiral trajectory [9], i.e., (35) An additional linear radial undersampling (as defined in Table 1) was added to this undersampling (the two equations for R are multiplied). Spiral F was created to be a Fermat spiral for a FLORET waveform [10], i.e., (36) Note each of these waveforms require only a single additional line of code to redefine R. For all of these examples, S?=?150 mT/m/ms, gmax?=?40 mT/m, f?=?24 cm, r?=?1 mm, and N?=?8.