Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

Net gradient = ~G 2 + G 2 + G 2x Y zFIGURE 15-2. Within a large stationary magnetic field, field gradients are produced by three separatesaddle coils placed within the central core of the magnet, along the x, y, or z direction. Magneticfield gradients of arbitrary direction are produced by the vector addition of the individual gradientsturned on simultaneously. Any gradient direction is possible by superimposition of thethree-axis gradient system.The Larmor equation (m = yB) allows the gradient amplitude (for protons) tobe expressed in the units of Hz/em. For instance, a 10-mT/m gradient can beexpressed as 10 mT/m X 42.58 MHz/T X IT/l,OOO mT = 0.4258 MHz/m, whichis equivalent to 425.8 kHz/m or 4258 Hz/em. This straightforward description ofthe gradient strength facilitates determining the frequency BW across the FOY,independent of the main magnet field strength.Slightly lowermagnetic fieldSlightly highermagnetic fieldSlightly lower .••• ----precessional frequencyNullLarmor frequency ---_. Slightly higherprecessional frequencyFIGURE 15-3. The gradient field creates a net positive and negative magnetic environment thatadds to and subtracts from the main magnetic field. Associated with the local change in magneticfield is a local change in precessional frequencies, per the Larmor equation. The frequencies thusdirectly vary across the field in proportion to the applied gradient strength.