Paramagnetic effects of gradient magnetic fields on the pulmonary circulation during human brain mapping. (A) Magnetic field strength (Bz), and calculated field gradient (-dBz/dz) and force product (-Bz·dBz/dz) along the centerline of the magnet (see 'Supplementary Method 2' in Additional file 1). Maximal values of -dBz/dz at Bz = 1.5, 3.0, 4.0, 7.0 and 10 T were 1.03, 2.06, 2.75, 4.81 and 6.87 T/m, respectively (at z = 1.47 m). Maximal values of -Bz·dBz/dz at Bz = 1.5, 3.0, 4.0, 7.0 and 10 T were 1.21, 4.84, 8.60, 26.40 and 53.75 T2/m, respectively (at z = 1.14 m), which are well covered by the range of our experiment shown in Fig. 1B. The head and lung of a healthy volunteer, whose height is 1.75 m, head length is 0.25 m, length of epigastric fossa from top of head is 0.5 m, were positioned at the magnet's center (A: z = 0 m) and at maximal of -Bz·dBz/dz (B: z = 1.14 m), respectively. (B) Maximally estimated redistribution of erythrocytes estimated in the pulmonary circulation at position B (see 'Supplementary Method 3' in Additional file).