2D balanced SSFP (steady state free precession). TR = 10 ms, TE = 5 ms. The image matrix is 256×256. The number of subvoxels is 1×1×4. The total number of subvoxels is 13,572,096. The calculation time was 8.8 s.
FA = 15º FA = 30º
FA = 45º FA = 60º
Signal intensity vs Flip angle: S ∝ sinα/(1+cosα+(1-cosα)*(T1/T2))
Pulse sequence visualized by the SequenceViewer:
Two data-acquisition sequence. TR = 10 ms, TE = 5 ms. The phase of the RF pulse alternates between + and –.
Entire sequence. The half flip angle pulse is applied initially to shorten the time to establish the steady state.
Python sequence code:
from psdk import * import numpy as np gamma = 42.57747892 # [MHz/T] TR = 10.0e+3 # [us] TE = 5.0e+3 # [us] NR = 256 # Number of readout points NPE1 = 128 # Number of 1st phase encoding fov = [220.0, 220.0, 256.0] # [mm] dwell_time = 10.0 # [us] slice_width = 5.0 # [mm] gx_value = 1e+6 / (dwell_time * gamma * fov[0]) # [mT/m] gy_value = 2e+6 / (dwell_time * gamma * fov[1]) * NPE1 / NR # [mT/m] gz_value = 2.5 / (slice_width * 1.0e-3) / gamma # [mT/m] gx_rt = 300.0 # [us] gx rise time gy_rt = 300.0 # [us] gy rise time gz_rt = 300.0 # [us] gz rise time ex_pulse_width = 1600.0 # [us] ex_pulse_flip_angle = 60.0 # [degree] delta = -80.0 def sinc_with_hamming(flip_angle, pulse_width, points, *, min = -2.0 * np.pi, max = 2.0 * np.pi): x0 = np.arange(min, max, (max - min) / points) x1 = x0 + (max - min) / points y = (np.sinc(x0 / np.pi) + np.sinc(x1 / np.pi)) * 0.5 * np.hamming(points) return flip_angle * y * points / (y.sum() * pulse_width * 360.0e-6 * gamma) with Sequence('2D Balanced_SSFP'): with Block('Excitation_half-', ex_pulse_width * 1.5 + 3.5 * gz_rt): GZ(0.0, gz_value, gz_rt) RF(gz_rt, sinc_with_hamming(ex_pulse_flip_angle * 0.5, ex_pulse_width, 160), ex_pulse_width / 160, phase = np.pi) GZ(ex_pulse_width + gz_rt, -gz_value, gz_rt * 2.0) GZ(ex_pulse_width * 1.5 + gz_rt * 2.0 - delta, 0.0, gz_rt ) with Block('Excitation+', ex_pulse_width + 1.0 * gz_rt): GZ(0.0, gz_value, gz_rt) RF(gz_rt, sinc_with_hamming(ex_pulse_flip_angle, ex_pulse_width, 160), ex_pulse_width / 160, phase = 0.0) with Block('Excitation-', ex_pulse_width + 1.0 * gz_rt): GZ(0.0, gz_value, gz_rt) RF(gz_rt, sinc_with_hamming(ex_pulse_flip_angle, ex_pulse_width, 160), ex_pulse_width / 160, phase = np.pi) with Block('PhaseEncoding+', 1650 + gx_rt * 2.5): GX(0.0, -gx_value, gx_rt) GY(gz_rt, ([gy_value * (2 * i - NPE1) / NPE1 for i in range(NPE1)], ['PE1']), gy_rt) GY(NR // 2 * dwell_time + gz_rt, 0.0, gy_rt) GX(1650 + gx_rt * 0.5, gx_value, gx_rt * 2.0) GZ(0.0, -gz_value, gz_rt * 2.0) GZ(ex_pulse_width * 0.5 + gz_rt * 2.0 - delta, 0.0, gz_rt) with Block('PhaseEncoding-', 1650 + gx_rt * 2.5): GX(0.0, -gx_value, gx_rt) GY(gz_rt, ([gy_value * (2 * i + 1 - NPE1) / NPE1 for i in range(NPE1)], ['PE1']), gy_rt) GY(NR // 2 * dwell_time + gz_rt, 0.0, gy_rt) GX(1650 + gx_rt * 0.5, gx_value, gx_rt * 2.0) GZ(0.0, -gz_value, gz_rt * 2.0) GZ(ex_pulse_width * 0.5 + gz_rt * 2.0 - delta, 0.0, gz_rt) with Block('Readout+', 1650 * 2.0): AD(370, NR, dwell_time, phase = 0.0) with Block('Readout-', 1650 * 2.0): AD(370, NR, dwell_time, phase = np.pi) with Block('Rewinding+', 1650 + gx_rt * 2.5): GX(0.0, -gx_value, gx_rt * 2.0) GX(1650 + gx_rt * 1.5, 0.0, gx_rt) GY(1650 + gx_rt * 1.5 - NR // 2 * dwell_time, ([gy_value * (NPE1 - 2 * i) / NPE1 for i in range(NPE1)], ['PE1']), gy_rt) GY(1650 + gx_rt * 1.5, 0.0, gy_rt) GZ(1650 + gx_rt * 0.5 - ex_pulse_width * 0.5 + delta, -gz_value, gz_rt) GZ(1650 + gx_rt * 1.5, 0.0, gz_rt) with Block('Rewinding-', 1650 + gx_rt * 2.5): GX(0.0, -gx_value, gx_rt * 2.0) GX(1650 + gx_rt * 1.5, 0.0, gx_rt) GY(1650 + gx_rt * 1.5 - NR // 2 * dwell_time, ([gy_value * (NPE1 - (i * 2 + 1)) / NPE1 for i in range(NPE1)], ['PE1']), gy_rt) GY(1650 + gx_rt * 1.5, 0.0, gy_rt) GZ(1650 + gx_rt * 0.5 - ex_pulse_width * 0.5 + delta, -gz_value, gz_rt) GZ(1650 + gx_rt * 1.5, 0.0, gz_rt) with Main(): BlockRef('Excitation_half-') WaitFor(TR * 0.5 - ex_pulse_width * 1.5 - gz_rt * 3.5) with Loop('PE1', NPE1): BlockRef('Excitation+') BlockRef('PhaseEncoding+') BlockRef('Readout+') BlockRef('Rewinding+') BlockRef('Excitation-') BlockRef('PhaseEncoding-') BlockRef('Readout-') BlockRef('Rewinding-')